due to magnetic pinning [10-11,31,32]. It also yields direct information about the uniform precession mode of the nanowires which can be related to the average anisotropy magnitude [12-15]. Several measurement techniques which have been used to characterise magnetization dynamics such as femtosecond spectroscopy [16-18], pulse inductive microwave magnetometer [19], FMR force microscopy [20], network analyzer FMR [21,31,32] and high-frequency electrical measurements of magnetodynamics [22]. All these techniques can be used for modern application for example in telecommunications and data storage systems.

FMR Measurements of Magnetic Nanostructures 95

*M M H,* (2)

Nx, Ny, Nz are the demagnetization factors in the x, y, z directions, and so on, and where *g* is the spectroscopic splitting factor (Lande factor) and *µB* = *eħ/*2me is the Bohr magneton. The demagnetizing factors affect the shape anisotropy of the magnetic material depending upon

Part of the classical approach to ferromagnetism is to replace the spins by a classical microspin vector *M* magnetization. The time-dependence of the magnetization can be obtained

> *dt*

where = *gµb*/*ħ* is a gyromagnetic ratio. This equation represents an undamped precession of the magnetization. From experiments actual changes of the magnetization are known to decay in a finite time. The occurrence of a damping mechanism leads to reversal of the magnetization towards the direction of *H* within several nanoseconds. The damping is just

*eff eff*

films. Eq. 3 is known as Landau-Lifshitz-Gilbert equation after Gilbert introduces the damping term. *Heff* is the total effective magnetic field which is a sum of static applied magnetic field (*H*), dynamic magnetic field (*hrf*) and internal magnetic field (*Hin*). Internal field constitutes various magnetic anisotropies such as magnetocrystalline anisotropy, shape anisotropy, and magnetoelastic anisotropy etc. This equation therefore describes torque acting on *M*. This torque leads to a rotation of the magnetization towards the direction of the external magnetic field. The damping causes decay in precessional motion which by

**Figure 1.** (a) Torque components exerted on the magnetization *M* by rotational field *H* (b) Motion of *M*

*dd d dt M dt M dt*

applying a dynamic magnetic field becomes continuous as shown in Fig. 1.

*s S*

*MM M M H MH M* (3)

is the dimensionless Gilbert damping constant, of order 10-2 in ferromagnetic thin

directly by calculating the torque acting on *M* by an effective field *Heff*,

*d*

its geometry to be ellipsoid, sphere, thin film etc.

added as a phenomenological term to Eq. 2.

where

for constant *H*.

In the present chapter, we deal with magnetic nanostructures such as nanowires and multilayered nanodiscs and rings which exhibit unique FMR responses since their various anisotropy energies are strongly influenced by size and shape [33]. In addition, interactions between multilayered segments can be tailored such that the FMR response is not only angle-dependent but also influenced strongly at certain frequencies [32]. In this chapter, we shall be describing three different aspects of this topic:

### **2. Fundamental theory of ferromagnetic resonance**

Ferromagnetic resonance (FMR) is a very powerful experimental technique in the study of ferromagnetic nanomaterials. The precessional motion of a magnetization *M* of ferromagnetic material about the applied external magnetic field *H* is known as the Ferromagnetic resonance (FMR). In the physical process of resonance, the energy is absorbed from rf transverse magnetic field *hrf*, which occurred when frequency matched with precessional frequency (). The precession frequency depends on the orientation of the material and the strength of the magnetic field. It allows us to measure all the most important parameters of the material: Curie temperature, total magnetic moment, relaxation mechanism, elementary excitations and others.

A single domain magnetic particle with ellipsoid shape was considered as in [Kittel] to drive the resonance condition for the phenomenon of ferromagnetic resonance. A uniform, static magnetic field H is applied along the z-axis and set the sample in a microwave cavity. A resonance is observed at a frequency given by

$$
\hbar \rho = \g \,\mu\_B \sqrt{[H + (N\_x - N\_z)M][H + (N\_y - N\_z)M]}.\tag{1}
$$

Nx, Ny, Nz are the demagnetization factors in the x, y, z directions, and so on, and where *g* is the spectroscopic splitting factor (Lande factor) and *µB* = *eħ/*2me is the Bohr magneton. The demagnetizing factors affect the shape anisotropy of the magnetic material depending upon its geometry to be ellipsoid, sphere, thin film etc.

94 Ferromagnetic Resonance – Theory and Applications

shall be describing three different aspects of this topic:

storage systems.

discussed.

due to magnetic pinning [10-11,31,32]. It also yields direct information about the uniform precession mode of the nanowires which can be related to the average anisotropy magnitude [12-15]. Several measurement techniques which have been used to characterise magnetization dynamics such as femtosecond spectroscopy [16-18], pulse inductive microwave magnetometer [19], FMR force microscopy [20], network analyzer FMR [21,31,32] and high-frequency electrical measurements of magnetodynamics [22]. All these techniques can be used for modern application for example in telecommunications and data

In the present chapter, we deal with magnetic nanostructures such as nanowires and multilayered nanodiscs and rings which exhibit unique FMR responses since their various anisotropy energies are strongly influenced by size and shape [33]. In addition, interactions between multilayered segments can be tailored such that the FMR response is not only angle-dependent but also influenced strongly at certain frequencies [32]. In this chapter, we

1. We first develop the theory of FMR response of densely packed nanowire arrays that can be treated as two-dimensional periodic nanostructures. We then extend the theory to three-dimensional structures, which can be made using multilayered nanowires. 2. We then describe how to synthesize such nanowire arrays and also direct measurements of such structures. Several different experimental techniques are

3. We then continue the treatment to describe the use of such periodic nanowire arrays in microwave devices to exhibit nonlinear responses and also for circulators and isolators.

Ferromagnetic resonance (FMR) is a very powerful experimental technique in the study of ferromagnetic nanomaterials. The precessional motion of a magnetization *M* of ferromagnetic material about the applied external magnetic field *H* is known as the Ferromagnetic resonance (FMR). In the physical process of resonance, the energy is absorbed from rf transverse magnetic field *hrf*, which occurred when frequency matched with precessional frequency (). The precession frequency depends on the orientation of the material and the strength of the magnetic field. It allows us to measure all the most important parameters of the material: Curie temperature, total magnetic moment, relaxation

A single domain magnetic particle with ellipsoid shape was considered as in [Kittel] to drive the resonance condition for the phenomenon of ferromagnetic resonance. A uniform, static magnetic field H is applied along the z-axis and set the sample in a microwave cavity. A

[ ( ) ][ ( ) ]. *B xz yz*

*g H N NMH N NM* (1)

Although the effects seen till now are weak, these are still quite promising.

**2. Fundamental theory of ferromagnetic resonance**

mechanism, elementary excitations and others.

resonance is observed at a frequency given by

  Part of the classical approach to ferromagnetism is to replace the spins by a classical microspin vector *M* magnetization. The time-dependence of the magnetization can be obtained directly by calculating the torque acting on *M* by an effective field *Heff*,

$$\frac{d\mathbf{M}}{dt} = -\gamma \mathbf{M} \times \mathbf{H}\_r \tag{2}$$

where = *gµb*/*ħ* is a gyromagnetic ratio. This equation represents an undamped precession of the magnetization. From experiments actual changes of the magnetization are known to decay in a finite time. The occurrence of a damping mechanism leads to reversal of the magnetization towards the direction of *H* within several nanoseconds. The damping is just added as a phenomenological term to Eq. 2.

$$\frac{d\mathbf{M}}{dt} = -\gamma \mathbf{M} \times \left(\mathbf{H}\_{e\sharp} - \frac{\alpha}{\gamma M\_s} \frac{d\mathbf{M}}{dt}\right) = -\gamma \mathbf{M} \times \mathbf{H}\_{e\sharp} + \frac{\alpha}{M\_S} \mathbf{M} \times \frac{d\mathbf{M}}{dt} \tag{3}$$

where is the dimensionless Gilbert damping constant, of order 10-2 in ferromagnetic thin films. Eq. 3 is known as Landau-Lifshitz-Gilbert equation after Gilbert introduces the damping term. *Heff* is the total effective magnetic field which is a sum of static applied magnetic field (*H*), dynamic magnetic field (*hrf*) and internal magnetic field (*Hin*). Internal field constitutes various magnetic anisotropies such as magnetocrystalline anisotropy, shape anisotropy, and magnetoelastic anisotropy etc. This equation therefore describes torque acting on *M*. This torque leads to a rotation of the magnetization towards the direction of the external magnetic field. The damping causes decay in precessional motion which by applying a dynamic magnetic field becomes continuous as shown in Fig. 1.

**Figure 1.** (a) Torque components exerted on the magnetization *M* by rotational field *H* (b) Motion of *M* for constant *H*.

### **3. FMR dispersion relation for nanostructures**

Due to miniaturization from bulk to the nanoscale, material properties shows a drastic change like surface-to-volume ratio, electron transport, thermodynamic fluctuations, defects etc. The nanomagnetic material demonstrates distinct magnetic response due to various anisotropies. The one-dimensional nanostructures such as nanowires, nanotubes, nanorods and nanorings are the area of recent research for data storage applications, sensors, biomedical drugs, microwave devices. To perturb the dynamic magnetization in these structures, ferromagnetic resonance is an effective tool.

FMR Measurements of Magnetic Nanostructures 97

(6)

(7)

*H H H eff K* (8)

>

(10)

(10a)

(9)

2

2 2 3 *d r*

where d is the diameter of the pore and r is the centre-to-centre inter-wire distance between the pores. The equilibrium values for polar angles are obtained by minimizing the energy term

> 0 *E E*

2

γ

eq (5)

where, *m*

cases:

*nm m*

*Case 1*: H|| to the wire and Heff>0

*Case 2*: H|| to the wire and Heff<0

*Case 3*: H easy axis and H<Heff

>

From eq (8) we retrieve the dispersion relation which can be written as

cos sin cos sin cos sin 2 0

Here, 2 *eff eff S* is the effective anisotropy field that comes from a combination of effects including shape, magnetocrystalline and magnetoelastic anisotropy. Therefore from

2 13 2 *U*

2 1 3{1 (1 )} 2 *U*

multilayer section. If *hnm* = 0 (i.e. no non-magnetic spacer layer), the above equation represents the case of a single-element nanowire. Depending upon the direction of the external magnetic field along the easy axis of the nanowires, we can determine the various

*H Heff*

*H H eff*

*K M fP M*

*h f h h* , *hm* and *hnm* represents magnetic and non-magnetic thicknesses in

*K M P*

2

ω Hcos H cos Hcos H cos2

H eff H eff

*S*

*S*

(11)

(12)

*M*

*eff S*

For the case of multilayer nanowires, the effective anisotropy field *Heff* is given by

*eff S*

In case of a system which incorporates an array of nanowires dipole-dipole interaction, shape anisotropy, crystalline anisotropy and Zeeman energy interaction plays a complex role. Therefore the total energy will be the sum of all internal energies.

**Figure 2.** Coordinate system for an array of nanowires

Fig. 2 shows the schematic of an array of nanowires with relative orientation of the magnetization *M* and the applied magnetic field *H w.r.t* nanowire axis in spherical coordinate systems. The free energy density equation for an array of magnetic nanowires in the presence of external magnetic field at angles ( *H*) from nanowires axis can be written as

$$\mathbf{E} \approx -\mathbf{M} \mathbf{H} \left( \sin \theta \sin \theta\_H \cos \left( \phi - \phi\_H \right) + \cos \theta \cos \theta\_H \right) + K\_{e\sharp} \sin^2 \theta \tag{4}$$

where *Keff* is the effective uniaxial anisotropy which can be written as

$$\mathbf{K}\_{eff} = \pi \mathbf{M}^2 \left( \mathbf{I} - \Im \mathbf{P} \right) + \mathbf{K}\_{\mathrm{ul}} \tag{5}$$

The first term includes the dipole-dipole interaction between the nanowires and second term represents second-order uniaxial anisotropy along the wire axis. P is the porosity which can be obtained from

FMR Measurements of Magnetic Nanostructures 97

$$\mathbf{P} = \frac{\pi}{2\sqrt{3}} \frac{d^2}{r^2} \tag{6}$$

where d is the diameter of the pore and r is the centre-to-centre inter-wire distance between the pores. The equilibrium values for polar angles are obtained by minimizing the energy term

$$E\_{\theta} = \frac{\partial E}{\partial \theta} = 0 \tag{7}$$

$$\mathbf{E}\_{\theta} = -\mathbf{M} \mathbf{H} \left( \cos \theta \sin \theta\_{H} \cos \left( \phi - \phi\_{H} \right) - \sin \theta \cos \theta\_{H} \right) + K\_{\text{eff}} \sin 2\theta = 0 \tag{8}$$

From eq (8) we retrieve the dispersion relation which can be written as

$$\left(\frac{\omega}{\gamma}\right)^2 = \left[\text{H}\cos\left(\theta - \theta\_{\text{H}}\right) + \text{H}\_{\text{eff}}\cos^2\theta\right] \left[\text{H}\cos\left(\theta - \theta\_{\text{H}}\right) + \text{H}\_{\text{eff}}\cos2\theta\right] \tag{9}$$

Here, 2 *eff eff S* is the effective anisotropy field that comes from a combination of effects including shape, magnetocrystalline and magnetoelastic anisotropy. Therefore from eq (5)

$$\mathcal{H}\_{\rm eff} = 2\pi M\_S \left( 1 - 3P \right) + 2 \frac{K\_U}{M\_S} \tag{10}$$

For the case of multilayer nanowires, the effective anisotropy field *Heff* is given by

$$\mathcal{H}\_{\rm eff} = 2\pi M\_S \left( 1 - 3\{1 - f(1 - P)\} \right) + 2\frac{K\_{\underline{U}}}{M\_S} \tag{10a}$$

where, *m nm m h f h h* , *hm* and *hnm* represents magnetic and non-magnetic thicknesses in

multilayer section. If *hnm* = 0 (i.e. no non-magnetic spacer layer), the above equation represents the case of a single-element nanowire. Depending upon the direction of the external magnetic field along the easy axis of the nanowires, we can determine the various cases:

*Case 1*: H|| to the wire and Heff>0

96 Ferromagnetic Resonance – Theory and Applications

**3. FMR dispersion relation for nanostructures**

structures, ferromagnetic resonance is an effective tool.

**Figure 2.** Coordinate system for an array of nanowires

the presence of external magnetic field at angles ( *H*

which can be obtained from

where *Keff* is the effective uniaxial anisotropy which can be written as

role. Therefore the total energy will be the sum of all internal energies.

Due to miniaturization from bulk to the nanoscale, material properties shows a drastic change like surface-to-volume ratio, electron transport, thermodynamic fluctuations, defects etc. The nanomagnetic material demonstrates distinct magnetic response due to various anisotropies. The one-dimensional nanostructures such as nanowires, nanotubes, nanorods and nanorings are the area of recent research for data storage applications, sensors, biomedical drugs, microwave devices. To perturb the dynamic magnetization in these

In case of a system which incorporates an array of nanowires dipole-dipole interaction, shape anisotropy, crystalline anisotropy and Zeeman energy interaction plays a complex

Fig. 2 shows the schematic of an array of nanowires with relative orientation of the magnetization *M* and the applied magnetic field *H w.r.t* nanowire axis in spherical coordinate systems. The free energy density equation for an array of magnetic nanowires in

2 sin sin cos cos cos sin

 2 1 3 *eff U*

The first term includes the dipole-dipole interaction between the nanowires and second term represents second-order uniaxial anisotropy along the wire axis. P is the porosity

) from nanowires axis can be written as

*H H H eff K* (4)

(5)

$$\frac{d\phi}{d\gamma} = H + H\_{\text{eff}} \tag{11}$$

*Case 2*: H|| to the wire and Heff<0

$$\frac{d\theta}{d\gamma} = H\_{\text{eff}} - H$$

*Case 3*: H easy axis and H<Heff

$$
\left(\frac{\alpha}{\mathcal{I}}\right)^2 = \left(H^2{}\_{eff} - H^2\right) \tag{13}
$$

FMR Measurements of Magnetic Nanostructures 99

**5. Growth of nanostructures**

**Polycarbonate track etched (PCTE)**

to 1012 per cm2) in case of PCTE. **Anodic aluminum oxide (AAO)**

SEM micrograph of AAO templates.

anodic alumina (cross-section view).

Nanowires were grown by using two different types of templates (commercially available) polycarbonate track etched (PCTE) and aluminum oxide (AAO) from Whatman. These templates are completely different from each other due to their qualities as well as the preparation methods. The methods used for fabrication and properties of templates are

In PCTE template, the pore size varies from 20nm to 200nm and the thickness of ~6µm. To fabricate the PCTE template, initially high energy particle are used to bombard it to produce the path. Later these paths are etched in different chemical bath. The size of the pores is determined by the etching process. Fig.4(a) shows a SEM picture of a commercial PCTE membrane, with a reported pore size of 100 nm. Although the pores seem to have similar diameters, the pore placement is random. The pores density is quite low (in the range of 1010

In 1995, Masuda and Fukuda reported the method to fabricate highly ordered nanohole arrays on aluminum foil. Double anodization of aluminium in acidic solution is adopted to fabricate porous alumina template. The beauty of these templates is their cylindrical pores of uniform diameter, arranged in hexagonal arrays with a thin oxide layer exist at the bottom. Anodic Aluminum Oxide (AAO) templates have been successfully used as templates for the growth of nanowires by electrodeposition. In order to fabricate the AAO template the aluminum is cleaned in the acidic medium to remove the surface impurities. Further the cleaned aluminium processed by two step anodization described by Masuda. The pore size and spacing between pore in the alumina templates are controlled by the anodization voltage.

Temperature of electrolyte also plays a important role in pore parameters. The pores in AAO template cylindrical and highly dense which makes it a good candidate to study the interaction effect between the nanowires on magnetic properties. Fig. 4(b)-(c) shows the

**Figure 4.** SEM micrograph of membranes (a) Polycarbonate (b) Anodic alumina (Top view) and (c)

**Templates**

given below;

*Case 4*: H easy axis, H>Heff>0

$$\left(\frac{\alpha}{\mathcal{Y}}\right)^2 = H(H - H\_{\text{eff}}) \tag{14}$$

The frequency-field characteristics can be studied from these relations for various cases of the direction of the applied field and corresponding angular variation with resonance field of the nanowires as shown in Fig. 3. The horizontal line shows the intersection of the dispersion relation and indicates where in an FMR spectrum the resonance lines would be found for a fixed frequency in Fig. 3(a).

**Figure 3.** Simulated plots (a) dispersion relation for Ni nanowires for various angles in which the external magnetic field is applied (b) resonance field as a function of the externally applied field angle *θH*.

### **4. Sample preparation and characterization**

During last decade magnetic nanowires have attracted enormous research attention in many areas of advanced nanotechnology, including patterned magnetic recording media, materials for optical and microwave applications. Template assisted growth of nanostructures under constant potential in several electrolytes has been carried out by researchers for over 30 years. In comparison to other deposition techniques (sputtering and MBE) electrodeposition is a low cost and simple technique to fabricate magnetic nanowires and multilayers. Arrays of Co nanowires were fabricated by template assisted electrochemical deposition into the nanometer-sized pores.

### **5. Growth of nanostructures**

### **Templates**

98 Ferromagnetic Resonance – Theory and Applications

found for a fixed frequency in Fig. 3(a).

*θH*.

*Case 4*: H easy axis, H>Heff>0

( ) *HH Heff*

The frequency-field characteristics can be studied from these relations for various cases of the direction of the applied field and corresponding angular variation with resonance field of the nanowires as shown in Fig. 3. The horizontal line shows the intersection of the dispersion relation and indicates where in an FMR spectrum the resonance lines would be

a b

**4. Sample preparation and characterization**

electrochemical deposition into the nanometer-sized pores.

**Figure 3.** Simulated plots (a) dispersion relation for Ni nanowires for various angles in which the external magnetic field is applied (b) resonance field as a function of the externally applied field angle

During last decade magnetic nanowires have attracted enormous research attention in many areas of advanced nanotechnology, including patterned magnetic recording media, materials for optical and microwave applications. Template assisted growth of nanostructures under constant potential in several electrolytes has been carried out by researchers for over 30 years. In comparison to other deposition techniques (sputtering and MBE) electrodeposition is a low cost and simple technique to fabricate magnetic nanowires and multilayers. Arrays of Co nanowires were fabricated by template assisted

(13)

(14)

2 2 *H H eff*

2

2

Nanowires were grown by using two different types of templates (commercially available) polycarbonate track etched (PCTE) and aluminum oxide (AAO) from Whatman. These templates are completely different from each other due to their qualities as well as the preparation methods. The methods used for fabrication and properties of templates are given below;

### **Polycarbonate track etched (PCTE)**

In PCTE template, the pore size varies from 20nm to 200nm and the thickness of ~6µm. To fabricate the PCTE template, initially high energy particle are used to bombard it to produce the path. Later these paths are etched in different chemical bath. The size of the pores is determined by the etching process. Fig.4(a) shows a SEM picture of a commercial PCTE membrane, with a reported pore size of 100 nm. Although the pores seem to have similar diameters, the pore placement is random. The pores density is quite low (in the range of 1010 to 1012 per cm2) in case of PCTE.

### **Anodic aluminum oxide (AAO)**

In 1995, Masuda and Fukuda reported the method to fabricate highly ordered nanohole arrays on aluminum foil. Double anodization of aluminium in acidic solution is adopted to fabricate porous alumina template. The beauty of these templates is their cylindrical pores of uniform diameter, arranged in hexagonal arrays with a thin oxide layer exist at the bottom. Anodic Aluminum Oxide (AAO) templates have been successfully used as templates for the growth of nanowires by electrodeposition. In order to fabricate the AAO template the aluminum is cleaned in the acidic medium to remove the surface impurities. Further the cleaned aluminium processed by two step anodization described by Masuda. The pore size and spacing between pore in the alumina templates are controlled by the anodization voltage.

Temperature of electrolyte also plays a important role in pore parameters. The pores in AAO template cylindrical and highly dense which makes it a good candidate to study the interaction effect between the nanowires on magnetic properties. Fig. 4(b)-(c) shows the SEM micrograph of AAO templates.

**Figure 4.** SEM micrograph of membranes (a) Polycarbonate (b) Anodic alumina (Top view) and (c) anodic alumina (cross-section view).

### **Template assisted electrodeposition technique**

Electrodeposition process involves the electric current to reduce cations from electrolyte and deposited that material as a thin film onto a conducting substrate. At the cathode the metal reduction takes place and metal deposits according to:

FMR Measurements of Magnetic Nanostructures 101

**Steps involved in the template assisted synthesis of nanowires**

**Step 4:** The growth of nanowires is carried at the optimized potential.

electrode in a three-electrode electrochemical cell.

pores.

condition for deposition.

electrodeposition process.

oxide and dichloromethane respectively.

**Step 1:** The porous anodic alumina (AAO) /polycarbonate templates were taken and one side of the AAO were sputtered with Au by RF sputtering, which acted as the working

**Step 2:** The electrodeposition solution was restrained to the other side of the membrane so that deposition was initiated onto the Au layer within the pores. The array of Co nanowires was deposited from a solution of 25 gm/L CoSO4.7H2O, 5 gm/L H3BO3 and sodium Lauryl Sulphate (SLS), which is used to reduce the surface tension of water for proper wetting of

**Step 3:** The cyclic voltammetry is used to figure out the constant deposition potential of the working electrode with respect to a standard reference electrode **RE** to get the favourable

**Step 5:** For further investigation of freely standing nanowires, the templates is used to dissolve in an appropriate solution. Etching solution for AAO and PCTE are sodium hydro-

**Figure 6.** Schematic illustration of the growth of magnetic nanowire in alumina template by

$$\mathbf{M} \mathbf{n}^+ + \mathbf{n} \text{ e }^- = \mathbf{M}(\mathbf{s})$$

In order to form the nanowires, the cations from electrolyte move through the nonconducting template (AAO/ PCTE) having nanosized pores and deposited on the conducting substrate.

The desired material properties depends upon the various process parameters like electrolyte composition, bath pH, mode of deposition (DC, pulse and AC) and deposition temperature.

**Figure 5.** Schematic representation of three-electrode electrochemical cell setup employed. AAO template mounted electrodes act as a working electrodes (WE), platinum foil counter electrode (CE) and Saturated calomel electrode (SCE), reference electrode (RE).

Fig.5 illustrates the three-electrode cell set-up used in this study. A platinum foil and a saturated calomel electrode (SCE) were used as the anode (or counter electrode) and as a reference electrode respectively. The steps of preparation of nanostructure are as followed;

### **Steps involved in the template assisted synthesis of nanowires**

100 Ferromagnetic Resonance – Theory and Applications

conducting substrate.

temperature.

**Template assisted electrodeposition technique**

reduction takes place and metal deposits according to:

Electrodeposition process involves the electric current to reduce cations from electrolyte and deposited that material as a thin film onto a conducting substrate. At the cathode the metal

**Mn n e M s**

In order to form the nanowires, the cations from electrolyte move through the nonconducting template (AAO/ PCTE) having nanosized pores and deposited on the

The desired material properties depends upon the various process parameters like electrolyte composition, bath pH, mode of deposition (DC, pulse and AC) and deposition

**Figure 5.** Schematic representation of three-electrode electrochemical cell setup employed. AAO template mounted electrodes act as a working electrodes (WE), platinum foil counter electrode (CE) and

Fig.5 illustrates the three-electrode cell set-up used in this study. A platinum foil and a saturated calomel electrode (SCE) were used as the anode (or counter electrode) and as a reference electrode respectively. The steps of preparation of nanostructure are as followed;

Saturated calomel electrode (SCE), reference electrode (RE).

**Step 1:** The porous anodic alumina (AAO) /polycarbonate templates were taken and one side of the AAO were sputtered with Au by RF sputtering, which acted as the working electrode in a three-electrode electrochemical cell.

**Step 2:** The electrodeposition solution was restrained to the other side of the membrane so that deposition was initiated onto the Au layer within the pores. The array of Co nanowires was deposited from a solution of 25 gm/L CoSO4.7H2O, 5 gm/L H3BO3 and sodium Lauryl Sulphate (SLS), which is used to reduce the surface tension of water for proper wetting of pores.

**Step 3:** The cyclic voltammetry is used to figure out the constant deposition potential of the working electrode with respect to a standard reference electrode **RE** to get the favourable condition for deposition.

**Step 4:** The growth of nanowires is carried at the optimized potential.

**Step 5:** For further investigation of freely standing nanowires, the templates is used to dissolve in an appropriate solution. Etching solution for AAO and PCTE are sodium hydrooxide and dichloromethane respectively.

**Figure 6.** Schematic illustration of the growth of magnetic nanowire in alumina template by electrodeposition process.

FMR Measurements of Magnetic Nanostructures 103

**Figure 9.** Scanning electron micrograph (SEM) of electrodeposited nanostructure in (a) Polycarbonate

Transmission Electron Microscope (TEM) is a widely used instrument for characterizing the interior structure of materials. For TEM, the template was completely etched and rinsed several times with deionised water to clean the residual template part. Template etching is an important step of sample preparation of nanowires for TEM characterization. Cobalt nanowires were scratched from the substrate and ultrasonicated in acetone for 15 min so that the nanowires could disperse properly. Few drops of the suspension were then transferred on to a carbon coated copper grid and the microstructures were analyzed by high resolution TEM (HRTEM: Technai G20 S-Twin model) operating at 200 kV. To get the actual diameter of the nanowire, the complete dissolving of residual template from surrounding the nanowires is very important. Typical TEM results obtained are shown in Figure 10. While nanowires grown in PCTE templates typically have a tapered cross-section due to the non-uniform diameters of the pores, the AAO template-based nanowires grow in

**Figure 10.** Transmission electron micrograph (TEM) of electrodeposited nanostructure in (a)

and (b) & (c) Anodic alumina.

a more uniform manner.

Polycarbonate and (b) Anodic alumina.

**Transmission electron microscopy**

**Figure 7.** Typical choronoamperometery plot during potentiostatic electrodeposition taken during the fabrication of Co nanowires. The various stage of pore filling during deposition is shown as insets at the respective current-time positions.

**Figure 8.** Scanning electron micrograph (SEM) of empty and filled surface morphology of the template.

### **6. Characterization of nanostructures**

#### **Scanning electron microscopy**

For scanning electron microscopy (SEM), the template containing nanowires is partially released from their template by appropriate solution. To remove the residual part of template the etched sample is cleaned by deionised water. To carry out the surface analysis secondary electron imaging in scanning electron microscope has been utilized. Surface morphology of Co nanowire was investigated by scanning electron microscope (SEM: ZEISS EVO 50) operating at 20 kV accelerating voltage by secondary electron imaging. Fig. 8 shows the SEM micrograph of empty AAO and filled with nanowires. The morphology of grown nanowires in PCTE template can be clearly seen in Fig. 9(a). Side and top view of AAO assisted nanowires are presented in Fig. 9(b & c). The growth density of nanowires in AAO template is more as compared to PCTE template.

**Figure 9.** Scanning electron micrograph (SEM) of electrodeposited nanostructure in (a) Polycarbonate and (b) & (c) Anodic alumina.

#### **Transmission electron microscopy**

102 Ferromagnetic Resonance – Theory and Applications

respective current-time positions.

**6. Characterization of nanostructures**

template is more as compared to PCTE template.

**Scanning electron microscopy**

**Figure 7.** Typical choronoamperometery plot during potentiostatic electrodeposition taken during the fabrication of Co nanowires. The various stage of pore filling during deposition is shown as insets at the

**Figure 8.** Scanning electron micrograph (SEM) of empty and filled surface morphology of the template.

For scanning electron microscopy (SEM), the template containing nanowires is partially released from their template by appropriate solution. To remove the residual part of template the etched sample is cleaned by deionised water. To carry out the surface analysis secondary electron imaging in scanning electron microscope has been utilized. Surface morphology of Co nanowire was investigated by scanning electron microscope (SEM: ZEISS EVO 50) operating at 20 kV accelerating voltage by secondary electron imaging. Fig. 8 shows the SEM micrograph of empty AAO and filled with nanowires. The morphology of grown nanowires in PCTE template can be clearly seen in Fig. 9(a). Side and top view of AAO assisted nanowires are presented in Fig. 9(b & c). The growth density of nanowires in AAO Transmission Electron Microscope (TEM) is a widely used instrument for characterizing the interior structure of materials. For TEM, the template was completely etched and rinsed several times with deionised water to clean the residual template part. Template etching is an important step of sample preparation of nanowires for TEM characterization. Cobalt nanowires were scratched from the substrate and ultrasonicated in acetone for 15 min so that the nanowires could disperse properly. Few drops of the suspension were then transferred on to a carbon coated copper grid and the microstructures were analyzed by high resolution TEM (HRTEM: Technai G20 S-Twin model) operating at 200 kV. To get the actual diameter of the nanowire, the complete dissolving of residual template from surrounding the nanowires is very important. Typical TEM results obtained are shown in Figure 10. While nanowires grown in PCTE templates typically have a tapered cross-section due to the non-uniform diameters of the pores, the AAO template-based nanowires grow in a more uniform manner.

**Figure 10.** Transmission electron micrograph (TEM) of electrodeposited nanostructure in (a) Polycarbonate and (b) Anodic alumina.

### **7. Electron paramagnetic resonance**

EPR/FMR measurements obtained from ferromagnetic nanowire arrays give detailed information on the size of the nanowires. The spectra can be used to calculate the interwire magnetic interactions quite accurately [31]. In Fig. 11 are shown typical spectra obtained from Co nanowire arrays. Here, both single-Co nanowire arrays and multilayered Co/Pd nanowire arrays are compared. There is clearly an angular dependence of the applied microwave field with respect to the easy axis of the nanowires, as has been studied previously [32].

FMR Measurements of Magnetic Nanostructures 105

**Figure 12.** Electron Spin resonance (ESR/FMR) spectra of multilayered Co/Pd nanowire arrays in parallel orientation with temperature range (90K-290K). (Inset) Peak height change with temperature.

The increasing demand for higher frequency magnetic microwave structures triggered a tremendous development in the field of magnetization dynamics over the past decade. In order to develop smaller and faster devices, a better understanding of the complex magnetization precessional dynamics, the magnetization anisotropy, and the sources of spin scattering at the nanoscale is necessary [23-25]. Magnetic data storage with its promise of non-volatility, robustness, high speed and low energy dissipation attracted long back. It has been encountered in a number of applications such as smart cards, hard drives, thin film read heads or video tapes [26-28]. Industry activities are also directed to replace semiconductor random access memories by magnet based memory devices. Logical 0 and 1 are encoded by the direction of the magnetization of a small magnetic element, such as a giant magnetoresistance (GMR) or tunneling magnetoresistance (TMR) element. For data manipulation *i.e.* reading and writing, the magnetization has to be switched between the two equilibrium positions. In order to push forward data transfer rates which are already in the GHz range, spin waves transportation mechanism has to be employed in place of current semiconductor based devices [29-32]. To this end an understanding of the dynamic

On the road towards the size reduction of microwave devices, ferromagnetic nanowires embedded into porous templates have proven to be an interesting route to ferrite based materials. The main advantages of what we call ferromagnetic nanowired (FMNW) substrates are that they present a zero-field microwave absorption frequency that can be easily tuned over a large range of frequencies, as well as being low cost and fast to produce

**8. Microwave devices**

motion and the mode spectrum is necessary.

**Figure 11.** Electron paramagnetic resonance (EPR/FMR) spectra of single element Co nanowire arrays in parallel and perpendicular orientation at room temperature.

Fig.12 shows the FMR spectra of Co/Pd MLNW arrays for the temperature range from 90K to 290K. It is clear from the data that two different peaks in the FMR spectrum have been observed. The peak present at the ~ 3310 G is corresponding to the main peak of FMR and it is due to the quantum confinement in the nanostructures which is more in case of Co/Pd multilayered nanowires. The spin waves are confined in the magnetic nanostructure and it is found to be dominant when we reduce the third dimension (in z-direction) of the nanostructure. This main FMR peak present at all the temperature and the variation of resonance field at different temperature is very slow. As we go down to the 90K with decrease of 20K from room temperature the resonance field increases slowly. This slow variation can be explain as temperature decreases the Ms (T) increase and resultant head-totail alignment between FM segments increases, which further reduces the effective field as a result slow increase in the resonance field. Inset in Fig.12 shows the variation of resonance field with temperature.

**Figure 12.** Electron Spin resonance (ESR/FMR) spectra of multilayered Co/Pd nanowire arrays in parallel orientation with temperature range (90K-290K). (Inset) Peak height change with temperature.

### **8. Microwave devices**

104 Ferromagnetic Resonance – Theory and Applications

previously [32].

**7. Electron paramagnetic resonance**

EPR/FMR measurements obtained from ferromagnetic nanowire arrays give detailed information on the size of the nanowires. The spectra can be used to calculate the interwire magnetic interactions quite accurately [31]. In Fig. 11 are shown typical spectra obtained from Co nanowire arrays. Here, both single-Co nanowire arrays and multilayered Co/Pd nanowire arrays are compared. There is clearly an angular dependence of the applied microwave field with respect to the easy axis of the nanowires, as has been studied

**Figure 11.** Electron paramagnetic resonance (EPR/FMR) spectra of single element Co nanowire arrays

Fig.12 shows the FMR spectra of Co/Pd MLNW arrays for the temperature range from 90K to 290K. It is clear from the data that two different peaks in the FMR spectrum have been observed. The peak present at the ~ 3310 G is corresponding to the main peak of FMR and it is due to the quantum confinement in the nanostructures which is more in case of Co/Pd multilayered nanowires. The spin waves are confined in the magnetic nanostructure and it is found to be dominant when we reduce the third dimension (in z-direction) of the nanostructure. This main FMR peak present at all the temperature and the variation of resonance field at different temperature is very slow. As we go down to the 90K with decrease of 20K from room temperature the resonance field increases slowly. This slow variation can be explain as temperature decreases the Ms (T) increase and resultant head-totail alignment between FM segments increases, which further reduces the effective field as a result slow increase in the resonance field. Inset in Fig.12 shows the variation of resonance

in parallel and perpendicular orientation at room temperature.

field with temperature.

The increasing demand for higher frequency magnetic microwave structures triggered a tremendous development in the field of magnetization dynamics over the past decade. In order to develop smaller and faster devices, a better understanding of the complex magnetization precessional dynamics, the magnetization anisotropy, and the sources of spin scattering at the nanoscale is necessary [23-25]. Magnetic data storage with its promise of non-volatility, robustness, high speed and low energy dissipation attracted long back. It has been encountered in a number of applications such as smart cards, hard drives, thin film read heads or video tapes [26-28]. Industry activities are also directed to replace semiconductor random access memories by magnet based memory devices. Logical 0 and 1 are encoded by the direction of the magnetization of a small magnetic element, such as a giant magnetoresistance (GMR) or tunneling magnetoresistance (TMR) element. For data manipulation *i.e.* reading and writing, the magnetization has to be switched between the two equilibrium positions. In order to push forward data transfer rates which are already in the GHz range, spin waves transportation mechanism has to be employed in place of current semiconductor based devices [29-32]. To this end an understanding of the dynamic motion and the mode spectrum is necessary.

On the road towards the size reduction of microwave devices, ferromagnetic nanowires embedded into porous templates have proven to be an interesting route to ferrite based materials. The main advantages of what we call ferromagnetic nanowired (FMNW) substrates are that they present a zero-field microwave absorption frequency that can be easily tuned over a large range of frequencies, as well as being low cost and fast to produce over a large area as compared to standard ferrite devices. Conventional ferrite circulators need to be biased by a magnetic field to operate. This biasing field is generally provided by permanent magnet and in view of the volume reduction, we need to think of FMNW substrates which work at zero fields. A rigorous theory of microwave devices is very cumbersome due to ferromagnetic resonance (FMR) and spin-wave phenomena.

FMR Measurements of Magnetic Nanostructures 107

The transmission response of Ni NWs placed on a co-planar waveguide transmission line (Fig. 14(a)) for different static magnetic field is shown in Fig. 14(b). A small but perceptible and repeatable change was observed when the applied magnetic field was turned on/off. The change is however too small to show up in the plot of Fig. 14(b). This is partly due to masking of the shifts due to reflections from soldering and other undesirable metal deposits near the patterned transmission line and partly due to the relatively small interaction between the RF fields (largely confined to the substrate holding the CPW line) and the nanowires. It is thus expected that clearer shifts can be seen with more careful preparation and patterning of the substrate and ultimately by printing the CPW line on the nanowire

**Figure 14.** (a) CPW geometery for magnetic field applied along perpendicular direction (b)

(a) (b)

**10. Substrate integrated magnetic microwave devices**

transmission response as a function of frequency of Ni nanowires for various applied magnetic field

Newly developed techniques enable to characterize and re-arrange matter at nanometer scale. Now a day, automotive and wireless communication requires reduction in dimensions of nanodevices for yielding higher cut-off frequencies. Here, we propose integrated

**Figure 15.** schematic of band stop filter (b) S-parameter of the DUT for three different samples

template itself.

VNA-FMR is an important technique for the investigation of magnetization dynamics of lowdimensional magnetic structures and patterned microwave devices. Also, broadband flip-chip technique can be used to measure the material intrinsic and extrinsic properties by applying external magnetic field. In this chapter, we will demonstrate both techniques to have better understanding of ferromagnetic resonance. We propose fabrication and measurements of various non reciprocal microwave devices like band-stop filter, isolator and electromagnetic band-gap (EBG) structures using FMNW substrates using Ni and Co nanowires.

## **9. Conventional Ferromagnetic Resonance – Flip-chip based technique (FMR)**

In the frequency domain measurements, the magnetic excitation is sinusoidal magnetic field *hrf* and the response of the sample is detected by vector network analyzer. The magnetic field can be applied along parallel and perpendicular direction of the nanowires satisfying the FMR condition. The main components of the experimental setup are shown in Fig. 13. The VNA is connected to a coplanar waveguide (CPW) having a characteristic impedance of 50 Ω using coaxial cables and microwave connectors. For such radio frequency connections often coaxial cables with Teflon insulation and SMA connectors are employed. They are comparably low priced and offer a bandwidth of typically 18 GHz. The used cables should not have a metallic reinforcement.

Flip-chip based measurements are done to extract the material parameters, which are technologically important for data storage applications [31]. Fig. 13 shows the schematic of the set-up used for flip-chip measurements. Magnetic field is applied parallel to the nanowires and perpendicular to RF magnetic field, so that resonance condition must be satisfied.

**Figure 13.** Schematic representation of VNA-FMR system

The transmission response of Ni NWs placed on a co-planar waveguide transmission line (Fig. 14(a)) for different static magnetic field is shown in Fig. 14(b). A small but perceptible and repeatable change was observed when the applied magnetic field was turned on/off. The change is however too small to show up in the plot of Fig. 14(b). This is partly due to masking of the shifts due to reflections from soldering and other undesirable metal deposits near the patterned transmission line and partly due to the relatively small interaction between the RF fields (largely confined to the substrate holding the CPW line) and the nanowires. It is thus expected that clearer shifts can be seen with more careful preparation and patterning of the substrate and ultimately by printing the CPW line on the nanowire template itself.

**Figure 14.** (a) CPW geometery for magnetic field applied along perpendicular direction (b) transmission response as a function of frequency of Ni nanowires for various applied magnetic field

### **10. Substrate integrated magnetic microwave devices**

106 Ferromagnetic Resonance – Theory and Applications

**(FMR)**

not have a metallic reinforcement.

**Figure 13.** Schematic representation of VNA-FMR system

over a large area as compared to standard ferrite devices. Conventional ferrite circulators need to be biased by a magnetic field to operate. This biasing field is generally provided by permanent magnet and in view of the volume reduction, we need to think of FMNW substrates which work at zero fields. A rigorous theory of microwave devices is very

VNA-FMR is an important technique for the investigation of magnetization dynamics of lowdimensional magnetic structures and patterned microwave devices. Also, broadband flip-chip technique can be used to measure the material intrinsic and extrinsic properties by applying external magnetic field. In this chapter, we will demonstrate both techniques to have better understanding of ferromagnetic resonance. We propose fabrication and measurements of various non reciprocal microwave devices like band-stop filter, isolator and electromagnetic

cumbersome due to ferromagnetic resonance (FMR) and spin-wave phenomena.

band-gap (EBG) structures using FMNW substrates using Ni and Co nanowires.

**9. Conventional Ferromagnetic Resonance – Flip-chip based technique**

In the frequency domain measurements, the magnetic excitation is sinusoidal magnetic field *hrf* and the response of the sample is detected by vector network analyzer. The magnetic field can be applied along parallel and perpendicular direction of the nanowires satisfying the FMR condition. The main components of the experimental setup are shown in Fig. 13. The VNA is connected to a coplanar waveguide (CPW) having a characteristic impedance of 50 Ω using coaxial cables and microwave connectors. For such radio frequency connections often coaxial cables with Teflon insulation and SMA connectors are employed. They are comparably low priced and offer a bandwidth of typically 18 GHz. The used cables should

Flip-chip based measurements are done to extract the material parameters, which are technologically important for data storage applications [31]. Fig. 13 shows the schematic of the set-up used for flip-chip measurements. Magnetic field is applied parallel to the nanowires

and perpendicular to RF magnetic field, so that resonance condition must be satisfied.

Newly developed techniques enable to characterize and re-arrange matter at nanometer scale. Now a day, automotive and wireless communication requires reduction in dimensions of nanodevices for yielding higher cut-off frequencies. Here, we propose integrated

**Figure 15.** schematic of band stop filter (b) S-parameter of the DUT for three different samples

magnetic band-stop filter fabricated on FMNWS and studying their microwave properties like permittivity and permeability using CPW. Fig. 15(a) shows the schematic of the device under test which is a coplanar waveguide on NW substrate. The transmission coefficient of the device for three samples having bare AAO, Ni and Co NWs are shown in Fig. 15(b) at zero biasing. It is observed that by applying the magnetic field the resonance frequency shift towards higher range, so that we can tune our operating frequency of the device. We also observe that material properties also influence the Device-Under-Test (DUT).

FMR Measurements of Magnetic Nanostructures 109

[2] S. Shamaila, R. Sharif, S. Riaz, M. Khaleeq-ur-Rahman and X. F. Han, "Fabrication and magnetic characterization of CoxPt1-x nanowire arrays", Appl. Phys. A, 92 (2008) 687-

[3] Z. Z. Sun and J. Schliemann, "Fast domain wall propagation under an optimal field

[4] M. Yan, A. Kakay, S. Gliga and R. Hertel, "Beating the walker limit with massless

[5] C. T. Boone, J. A. Katine, M. Carey, J. R. Childress, X. Cheng and I. N. Krivorotov, "Rapid domain wall motion in permalloy nanowires excited by a spin-polarized current

[6] B. K. Kuanr, V. Veerakumar, R. Marson, S. Mishra, R. E. Camley and Z. Celinski, "Nonreciprocal microwave devices based on magnetic nanowires", Appl. Phys. Lett. 94

[7] M. Darques, J. De La T. Medina, L. Piraux, L. Cagnon and I. Huynen, "Microwave circulator based on ferromagnetic nanowires in alumina template", Nanotechnology 21

[8] J. De La T. Medina, J. Spiegel, M. Darques, L. Piraux and I. Huynen, "Differential phase shift in nonreciprocal microstrip lines on magnetic nanowired substrates", Appl. Phys.

[9] C. Kittel, "On the theory of ferromagnetic resonance absorption", Phys. Rev. 73 (1948)

[10] C. Kittel, "Excitation of spin waves in a ferromagnet by a uniform rf field", Phys. Rev.

[11] L. Kraus, G. Infante, Z. Frait and M. Vazquez, "Ferromagnetic resonance in microwires

[12] J. De La T. Medina, L. Piraux, J. M. Olais Govea and A. Encinas, "Double ferromagnetic resonanace and configuration-dependent dipolar coupling in unsaturated arrays of

[13] A. Encinas-Oropesa, M. Demand, L. Piraux, I. Huynen and U. Ebels, "Dipolar interactions in arrays of nickel nanowires studied by ferromagnetic resonance", Phys.

[14] C. A. Ramos, M. Vazquez, K. Nielsch, K. Pirota, R. B. Rivas, R. B. Wherspohn, M. Tovar, R. D. Sanchez and U. Gosele, "FMR characterization of hexagonal arrays of Ni

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### **11. Non-reciprocal devices**

It is important to note that it is possible to obtain non-reciprocal structures also using nanowire-based devices. Essentially, the microwave properties like permittivity and permeability can be made to be asymmetric. This is useful to obtain non reciprocal devices such as isolators and circulators. Prototypes of such devices are presently under fabrication. Some of the proposed devices are shown in Fig. 16 below. The detailed studies of these devices are out of scope of this chapter.

**Figure 16.** Possible non-reciprocal structures using nanowires.

### **Author details**

Manish Sharma, Sachin Pathak and Monika Sharma *Indian Institute of Technology Delhi, India*

### **12. References**

[1] A. Fert and L. Piraux, "Magnetic nanowires", J. Magn. Magn. Mater. 200 (1999) 338-358.

[2] S. Shamaila, R. Sharif, S. Riaz, M. Khaleeq-ur-Rahman and X. F. Han, "Fabrication and magnetic characterization of CoxPt1-x nanowire arrays", Appl. Phys. A, 92 (2008) 687- 691.

108 Ferromagnetic Resonance – Theory and Applications

**11. Non-reciprocal devices**

devices are out of scope of this chapter.

**Figure 16.** Possible non-reciprocal structures using nanowires.

Manish Sharma, Sachin Pathak and Monika Sharma

*Indian Institute of Technology Delhi, India*

**Author details**

**12. References**

magnetic band-stop filter fabricated on FMNWS and studying their microwave properties like permittivity and permeability using CPW. Fig. 15(a) shows the schematic of the device under test which is a coplanar waveguide on NW substrate. The transmission coefficient of the device for three samples having bare AAO, Ni and Co NWs are shown in Fig. 15(b) at zero biasing. It is observed that by applying the magnetic field the resonance frequency shift towards higher range, so that we can tune our operating frequency of the device. We also

It is important to note that it is possible to obtain non-reciprocal structures also using nanowire-based devices. Essentially, the microwave properties like permittivity and permeability can be made to be asymmetric. This is useful to obtain non reciprocal devices such as isolators and circulators. Prototypes of such devices are presently under fabrication. Some of the proposed devices are shown in Fig. 16 below. The detailed studies of these

[1] A. Fert and L. Piraux, "Magnetic nanowires", J. Magn. Magn. Mater. 200 (1999) 338-358.

observe that material properties also influence the Device-Under-Test (DUT).

	- [18] W. K. Hiebert, A. Stankiewicz, and M. R. Freeman, "Direct observation of magnetic relaxation in a small permalloy disk by time-resolved scanning Kerr microscopy", Phys. Rev. Lett. 79 (1997) 1134-1137.

**Chapter 5**

© 2013 Singh and Saipriya, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2013 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

**FMR Studies of [SnO2/Cu-Zn Ferrite] Multilayers**

The artificially structured multilayers (ML) have opened a new field of interface magnetism. It is possible to fabricate a multilayer sample with a specific design according to the requirement consisting of magnetic, non-magnetic, metallic or non-metallic components. Various types of interfaces may be synthesized in ML by combining a magnetic component with a non-magnetic one or from two different magnetic components. The interface between two non-magnetic components is particularly interesting if a magnetic anomaly happens to

The oscillations of magnetic parameters as a function of the number of interfaces, spacer layer or magnetic layer thickness in the ML have been gaining attention in the recent years. Bruno et al [1] employed RKKY model and Edwards et al [2] used spin dependent confinement of electrons in the quantum well provided by the spacer layer (quantum interference) to explain the oscillations initially observed in metallic ML. Exchange coupling in ML is also affected by direct dipolar coupling like the correlation of spins at rough interfaces (orange peel coupling), which is magnetostatic in origin and occurs due to the interaction of the dipoles which appear due to the roughness of the material [3]. This coupling favors parallel or anti-parallel alignment of spins depending upon the interplay

The oscillations in exchange coupling are also observed in oxide ML apart from the metallic ML [4]. Oxide materials are more stable and their ML can form magnetic structures which do not exist in bulk form. There are reports on ML of ferrites used along with NiO [5,6],

The mixed spinel structure of Cu-Zn ferrites with composition Cu0.6Zn0.4Fe3O4 (CZF) gives high magnetization when deposited in Ar environment [13]. The properties of non-magnetic (NM) SnO2 are sensitive to oxygen vacancies [14]. The interfacial region between these two materials may give rise to interesting magnetic phenomena. The objective of the present

and reproduction in any medium, provided the original work is properly cited.

R. Singh and S. Saipriya

http://dx.doi.org/10.5772/56330

**1. Introduction**

Additional information is available at the end of the chapter

be induced at the interface atom layer due to some interface effect.

between the magnetostatic exchange and anisotropy energy.

MgO [7] , CoO [8] and SnO2 [ 9-12].

## **FMR Studies of [SnO2/Cu-Zn Ferrite] Multilayers**

R. Singh and S. Saipriya

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[19] T. J. Silva, C. S. Lee, T. M. Crawford, and C. T. Rogers, "Inductive measurement of ultrafast magnetization dynamics in thin-film permalloy", J. Appl. Phys. 85 (1999) 7849-

[20] M. M. Midzor, P. E. Wigen, D. Pelekhov, W. Chen, P. C. Hammel, and M. L. Roukes, "Imaging mechanisms of force detected FMR microscopy", J. App. Phys. 87 (2000) 6493-

[21] O. Mosendz, B. Kardasz, D. S. Schmool, and B. Heinrich, "Spin dynamics at low microwave frequencies in crystalline Fe ultrathin film double layers using co-planar

[22] N. Mecking, Y. S. Gui, and C. M. Hu, "Microwave photovoltage and photoresistance

[23] B. K. Kuanr, M. Buchmeier, D. E. Buergler, P. Gruenberg, R. E. Camley, and Z, Celinski, "Dynamic and static measurements on epitaxial Fe-Si-Fe", J. Vac. Sci. Technol. A 24

[24] J. Curiale, R. D. Sanchez, C. A. Ramos, A. G. Leyva, A. Butera, "Dynamic response of magnetic nanoparticles arranged in a tubular shape", J. Magn. Magn. Mater. 320 (2008)

[25] Can-Ming Hu, "Recent progress in spin dynamics research in Canada", La Physique Au

[26] X. Kou, X. Fan, R. K. Dumas, Q. Lu, Y. Zhang, H. Zhu, X. Zhang, K. Liu and J. Q. Xiao, "Magnetic effects in magnetic nanowire arrays", Adv. Mater. 23 (2011) 1393-1397. [27] T. Schrefl, J. Fidler, D. Suss, and W. Scholz, "Hysteresis and switching dynamics of

[28] X. Kou, X. Fan, H. Zhu and J. Q. Xiao, "Ferromagnetic resonance and memory effects in

[29] K. Nagai, Y. Cao, T. Tanaka and K. Matsuyama, "Binary data coding with domain wall for spin wave based logic devices", J. Appl. Phys. 111 (2012) 07D1301-07D1304. [30] M. Sharma, S. Pathak, S. Singh, M. Sharma and A. Basu, "Highly ordered magnetic nickel nanowires: structural properties and ferromagnetic resonance measurements",

[31] O. Yalçn, et al, Ferromagnetic resonance studies of Co nanowire arrays, Journal of

[32] G. Kartopu, O. Yalçn, et al. Size effects and origin of easy-axis in nickel nanowire

[33] G. Kartopu, O. Yalçn, M. Es-Souni, and A. C. Başaran, Magnetization behavior of ordered and high density Co nanowire arrays with varying aspect ratio, Journal of

transmission lines", J. Magn. Magn. Mater. 300 (2006) 174-178.

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arrays, Journal of Applied Physics 109, 033909 (2011).

effects in ferromagnetic microstrips", Phys. Rev. B 76 (2007) 224430.

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/56330

### **1. Introduction**

The artificially structured multilayers (ML) have opened a new field of interface magnetism. It is possible to fabricate a multilayer sample with a specific design according to the requirement consisting of magnetic, non-magnetic, metallic or non-metallic components. Various types of interfaces may be synthesized in ML by combining a magnetic component with a non-magnetic one or from two different magnetic components. The interface between two non-magnetic components is particularly interesting if a magnetic anomaly happens to be induced at the interface atom layer due to some interface effect.

The oscillations of magnetic parameters as a function of the number of interfaces, spacer layer or magnetic layer thickness in the ML have been gaining attention in the recent years. Bruno et al [1] employed RKKY model and Edwards et al [2] used spin dependent confinement of electrons in the quantum well provided by the spacer layer (quantum interference) to explain the oscillations initially observed in metallic ML. Exchange coupling in ML is also affected by direct dipolar coupling like the correlation of spins at rough interfaces (orange peel coupling), which is magnetostatic in origin and occurs due to the interaction of the dipoles which appear due to the roughness of the material [3]. This coupling favors parallel or anti-parallel alignment of spins depending upon the interplay between the magnetostatic exchange and anisotropy energy.

The oscillations in exchange coupling are also observed in oxide ML apart from the metallic ML [4]. Oxide materials are more stable and their ML can form magnetic structures which do not exist in bulk form. There are reports on ML of ferrites used along with NiO [5,6], MgO [7] , CoO [8] and SnO2 [ 9-12].

The mixed spinel structure of Cu-Zn ferrites with composition Cu0.6Zn0.4Fe3O4 (CZF) gives high magnetization when deposited in Ar environment [13]. The properties of non-magnetic (NM) SnO2 are sensitive to oxygen vacancies [14]. The interfacial region between these two materials may give rise to interesting magnetic phenomena. The objective of the present

© 2013 Singh and Saipriya, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2013 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

work is to study the magnetic properties of SnO2 and Cu-Zn Ferrite multilayers and interpret them in terms of suitable magnetization mechanism.

FMR Studies of [SnO2/Cu-Zn Ferrite] Multilayers 113

**Figure 1.** FESEM images of [SnO2 (46nm) CZF (x nm)]5 for x = 249 (a), 83(b) and 42 nm (c).

This chapter is about the Ferromagnetic Resonance (FMR) studies of (SnO2/Cu-Zn Ferrrite) ML as a function of CZF layer thickness and SnO2 layer thickness.

## **2. Experimental**

Alternate layers of SnO2 and Cu0.6Zn0.4Fe3O4 (CZF) were deposited on quartz substrates at room temperature (RT) using rf-magnetron sputtering in Ar environment from SnO2 and CZF targets at a power of 50W and 70W respectively. The rate of deposition was estimated by depositing thin films of SnO2 and CZF separately. The synthesis method of targets and the rf sputtering system are described in our earlier work [15]. The field emission scanning electron microscopy (FESEM) studies were carried out to observe the multilayer structure. The FMR studies were carried out in the temperature range 100 - 450 K using JEOL x-band spectrometer. FMR studies were carried out at different temperatures and by varying the angle θH between the thin film normal and the direction of the applied field. The peak-to-peak FMR signal intensity (Ipp) which is proportional to the power absorbed was measured between the positive and negative peak points along the y-axis. The peak-to-peak linewidth (∆H) was measured as a function of temperature.

### **3. Ferromagnetic Resonance (FMR) studies**

### **3.1. Effect of CZF layer thickness**

The ML samples [SnO2 (46 nm)/CFZ(x nm)]5 where x = 42 nm, 83 nm and 249 nm were synthesized. A final capping layer of 46 nm of SnO2 was deposited on all the ML samples. The error in the thickness is ± 5 nm. The FESEM images (figure 1) portray a stack of alternate dark and light layers corresponding to CZF and SnO2 respectively as confirmed by the EDAX data. The CZF layer exhibits a columnar growth as observed in many of the sputtered films [16]. The protrusions of CZF column into SnO2 layers visible from the FESEM images indicate that the interfaces are diffused.

FMR studies were carried out at different temperatures and by varying the angle θH between the thin film normal and the direction of the applied field. Figure 2 shows the room temperature FMR spectra of the ML in θH = 90° (parallel) and 0° (perpendicular) configuration. In the parallel geometry, the FMR signal for the ML with x = 249 nm is highly asymmetric. The steep increase in the low field side and a slow increase in the high field side indicate negative anisotropy in the ML [17].

The line shape of FMR signal is sensitive to magnetic interactions in the material and hence a change in line shape is an indication of change in the magnetic interactions in the ML. Many a times the observed single FMR signal may arise from overlapping of 2 or more FMR signals.

**2. Experimental**

temperature.

signals.

interpret them in terms of suitable magnetization mechanism.

**3. Ferromagnetic Resonance (FMR) studies**

**3.1. Effect of CZF layer thickness**

indicate that the interfaces are diffused.

side indicate negative anisotropy in the ML [17].

ML as a function of CZF layer thickness and SnO2 layer thickness.

work is to study the magnetic properties of SnO2 and Cu-Zn Ferrite multilayers and

This chapter is about the Ferromagnetic Resonance (FMR) studies of (SnO2/Cu-Zn Ferrrite)

Alternate layers of SnO2 and Cu0.6Zn0.4Fe3O4 (CZF) were deposited on quartz substrates at room temperature (RT) using rf-magnetron sputtering in Ar environment from SnO2 and CZF targets at a power of 50W and 70W respectively. The rate of deposition was estimated by depositing thin films of SnO2 and CZF separately. The synthesis method of targets and the rf sputtering system are described in our earlier work [15]. The field emission scanning electron microscopy (FESEM) studies were carried out to observe the multilayer structure. The FMR studies were carried out in the temperature range 100 - 450 K using JEOL x-band spectrometer. FMR studies were carried out at different temperatures and by varying the angle θH between the thin film normal and the direction of the applied field. The peak-to-peak FMR signal intensity (Ipp) which is proportional to the power absorbed was measured between the positive and negative peak points along the y-axis. The peak-to-peak linewidth (∆H) was measured as a function of

The ML samples [SnO2 (46 nm)/CFZ(x nm)]5 where x = 42 nm, 83 nm and 249 nm were synthesized. A final capping layer of 46 nm of SnO2 was deposited on all the ML samples. The error in the thickness is ± 5 nm. The FESEM images (figure 1) portray a stack of alternate dark and light layers corresponding to CZF and SnO2 respectively as confirmed by the EDAX data. The CZF layer exhibits a columnar growth as observed in many of the sputtered films [16]. The protrusions of CZF column into SnO2 layers visible from the FESEM images

FMR studies were carried out at different temperatures and by varying the angle θH between the thin film normal and the direction of the applied field. Figure 2 shows the room temperature FMR spectra of the ML in θH = 90° (parallel) and 0° (perpendicular) configuration. In the parallel geometry, the FMR signal for the ML with x = 249 nm is highly asymmetric. The steep increase in the low field side and a slow increase in the high field

The line shape of FMR signal is sensitive to magnetic interactions in the material and hence a change in line shape is an indication of change in the magnetic interactions in the ML. Many a times the observed single FMR signal may arise from overlapping of 2 or more FMR

**Figure 1.** FESEM images of [SnO2 (46nm) CZF (x nm)]5 for x = 249 (a), 83(b) and 42 nm (c).

FMR Studies of [SnO2/Cu-Zn Ferrite] Multilayers 115

The asymmetry parameter, A/B ratio, was estimated by dividing the intensity of the upper part of the FMR signal by that of the lower part (figure 3). A/B > 1 indicates that the intensity of the upper half of the FMR signal is higher than the lower one and vice versa. A/B = 1

The A/B ratio at room temperature in the parallel configuration is 1.27, 1.12 and 0.69 for x = 249, 83 and 42 nm respectively. A/B > 1 gives Dysonian line shape to the spectrum which results from lower skin depth and higher conductivity of the sample [18]. Hence the possibility of occurrence of dispersive component due to diffusion of electrons into and out

The asymmetric nature of the FMR spectra of x = 249 nm may also be attributed to the interlayer coupling in the ML. The asymmetry decreases with decrease in CFZ layer thickness presumably due to the decrease in the interlayer coupling strength between the layers. As a consequence of interlayer coupling, the coupled spins precess out of phase with the uncoupled ones. Hence the FMR spectra of spins which precess at different frequencies overlap to give an asymmetric signal [19]. The peak to peak FMR signal intensity (Ipp) is measured between the positive and negative peak points along the y-axis and is proportional to the power absorbed. In the parallel configuration Ipp values, normalized to the volume of the CZF layers, increases as the magnetic layer (CZF) thickness increases from x = 42 to 83 nm followed by a decrease for x = 249 nm. The resonance field (Hres) decreases with increase in the CFZ layer thickness in this geometry. This is attributed to the increase in internal field with increasing CZF layer (magnetic layer) thickness because of which the magnetization also increases. The FMR parameters for both parallel and perpendicular

The intrinsic line shape and linewidth of an FMR signal is sensitive to variation of magnetization at the interfaces, surface pits, grain boundaries etc. The peak to peak linewidth (∆H) is sensitive to inhomogeneity, surface roughness, internal field etc. ΔH values for the ML reported in this study initially decreases from 631 to 541 Oe as x changes from 42 to 83 nm followed by an increase to 704 Oe for x = 249 nm. The ratio of the active layer thickness to dead layer thickness is low for ML with x = 42 nm. As x changes from 42 to 83 nm, the contribution from the dead layer becomes relatively negligible due to large active layer thickness. The increase in ΔH for x = 249 nm may be due to the presence of

The ML with x = 249 nm exhibits multiple resonances in θH = 0° configuration at RT (figure 2). The resonances occur at 363 and 418 mT for this ML. The occurrence of multiple resonances may be attributed to the excitation of spin waves due to the inter layer coupling of CZF layers mediated by the non-magnetic SnO2 layers [21]. This implies that the entire ML is coupled by the interlayer exchange coupling as a single magnetic entity. The spin waves propagate through the SnO2 layers and are sustained by the entire multilayer film. This confirms that for x = 249 nm the CZF layer thickness is ample enough to polarize SnO2 layer. With decreasing x it loses its capacity to polarize SnO2 layer. The occurrence of

indicates a signal with both its upper and lower half with equal intensity.

of the skin region cannot be ruled out for the ML with x = 249 and 83 nm.

configuration are listed in table 1.

interlayer coupling [20].

**Figure 2.** RT FMR spectra of [SnO2 (46 nm) CZF(x nm)]5 in the parallel and perpendicular configuration for x = 249 (a), 83(b) and 42 nm (c).

**Figure 3.** A representative FMR plot depicting the A/B ratio.

The asymmetry parameter, A/B ratio, was estimated by dividing the intensity of the upper part of the FMR signal by that of the lower part (figure 3). A/B > 1 indicates that the intensity of the upper half of the FMR signal is higher than the lower one and vice versa. A/B = 1 indicates a signal with both its upper and lower half with equal intensity.

114 Ferromagnetic Resonance – Theory and Applications

for x = 249 (a), 83(b) and 42 nm (c).

**Figure 3.** A representative FMR plot depicting the A/B ratio.

**Figure 2.** RT FMR spectra of [SnO2 (46 nm) CZF(x nm)]5 in the parallel and perpendicular configuration

The A/B ratio at room temperature in the parallel configuration is 1.27, 1.12 and 0.69 for x = 249, 83 and 42 nm respectively. A/B > 1 gives Dysonian line shape to the spectrum which results from lower skin depth and higher conductivity of the sample [18]. Hence the possibility of occurrence of dispersive component due to diffusion of electrons into and out of the skin region cannot be ruled out for the ML with x = 249 and 83 nm.

The asymmetric nature of the FMR spectra of x = 249 nm may also be attributed to the interlayer coupling in the ML. The asymmetry decreases with decrease in CFZ layer thickness presumably due to the decrease in the interlayer coupling strength between the layers. As a consequence of interlayer coupling, the coupled spins precess out of phase with the uncoupled ones. Hence the FMR spectra of spins which precess at different frequencies overlap to give an asymmetric signal [19]. The peak to peak FMR signal intensity (Ipp) is measured between the positive and negative peak points along the y-axis and is proportional to the power absorbed. In the parallel configuration Ipp values, normalized to the volume of the CZF layers, increases as the magnetic layer (CZF) thickness increases from x = 42 to 83 nm followed by a decrease for x = 249 nm. The resonance field (Hres) decreases with increase in the CFZ layer thickness in this geometry. This is attributed to the increase in internal field with increasing CZF layer (magnetic layer) thickness because of which the magnetization also increases. The FMR parameters for both parallel and perpendicular configuration are listed in table 1.

The intrinsic line shape and linewidth of an FMR signal is sensitive to variation of magnetization at the interfaces, surface pits, grain boundaries etc. The peak to peak linewidth (∆H) is sensitive to inhomogeneity, surface roughness, internal field etc. ΔH values for the ML reported in this study initially decreases from 631 to 541 Oe as x changes from 42 to 83 nm followed by an increase to 704 Oe for x = 249 nm. The ratio of the active layer thickness to dead layer thickness is low for ML with x = 42 nm. As x changes from 42 to 83 nm, the contribution from the dead layer becomes relatively negligible due to large active layer thickness. The increase in ΔH for x = 249 nm may be due to the presence of interlayer coupling [20].

The ML with x = 249 nm exhibits multiple resonances in θH = 0° configuration at RT (figure 2). The resonances occur at 363 and 418 mT for this ML. The occurrence of multiple resonances may be attributed to the excitation of spin waves due to the inter layer coupling of CZF layers mediated by the non-magnetic SnO2 layers [21]. This implies that the entire ML is coupled by the interlayer exchange coupling as a single magnetic entity. The spin waves propagate through the SnO2 layers and are sustained by the entire multilayer film. This confirms that for x = 249 nm the CZF layer thickness is ample enough to polarize SnO2 layer. With decreasing x it loses its capacity to polarize SnO2 layer. The occurrence of

multiple resonances may also be attributed to the existence of two different magnetic phases pertaining to the interfacial region and the bulk of the magnetic layer.

FMR Studies of [SnO2/Cu-Zn Ferrite] Multilayers 117

**Figure 5.** A representative plot of **a**ngular dependence of A/B ratio of [SnO2(46 nm)CFZ(249 nm)]5 ML.

Figure 6 depicts the angular variation of Hres, ΔH and Ipp. For all the ML there is no significant change in Hres and ΔH the FMR spectra for θH ≥ 60°. Below 60°, Hres and ΔH increase continuously. This shows that the ML is anisotropic in nature. The Ipp value initially increases from 0° till 40° followed by a decrease with further increase in θH. Thus the ML is

When an applied field is oriented along the film plane, Hres increases with decreasing thickness of the CZF layers. But Hres decreases with decreasing thickness of the CZF layers when the external magnetic field is oriented perpendicular to the film plane. This behavior is attributed to the decrease of the perpendicular anisotropy energy with decreasing CZF thickness [22]. The difference between the resonance fields in the parallel and perpendicular configuration decreases with decreasing CZF thickness evidencing the fact that the ML with

In the perpendicular configuration, the ML with x = 249 nm exhibits multiple resonances presumably due to the presence of spin waves. The spin wave resonance spectrum at RT and HT for ML with x = 249 nm were initially analyzed using the dispersion relation

> గ ቁ ଶ

݊ଶ (1)

x = 42 nm is relatively less anisotropic compared to the ML with x = 249 and 83 nm.

ቀ ܯ߉ െ ܪ ൌ ܪ

homogeneous when placed at an orientation of 40°.

developed by Kittel as follows [23]

where ߉ ൌ ଶ

ெబ మ

The number of resonances decreases with decreasing CZF thickness in the perpendicular geometry. As the thickness of CZF layer increases, the ML provides sufficient length for the spin wave modes to be formed.

**Figure 4.** Room temperature FMR spectra of [SnO2(46 nm)CFZ(249 nm)]5 at different orientations.

The FMR spectra of [SnO2(46 nm)/CZF(249 nm)]5 recorded at different orientations is shown in figure 4. For θH > 20° there is only single resonance in the FMR spectra. Small shoulder appears at θH = 20°. The multiple resonances appear at θH < 20°. The relative intensity of the FMR signals is also angle dependent. As θH approaches 0°, the amplitude of the shoulder peaks increases at the cost of that of the main peak. The separation between the resonances also increases and the intensity of the FMR signal decreases as θH approaches 0°. This may be due to the prominent demagnetization effects in the perpendicular configuration. A similar behavior is exhibited by the ML with x = 86 nm. There are no multiple resonances for the ML with x = 42 nm.

Figure 5 is a representative plot of the angular dependence of A/B ratio. A/B is close to 2.1 for the perpendicular configuration and decreases as the ML approaches parallel configuration. A/B = 1 for θH ~ 30° showing that the spectra is symmetric at an orientation of 30° of the sample normal with the applied field. Below 30° A/B is < 1 and above 30° A/B is > 1 evidencing the variation in the intensity of the lower and upper part of the FMR spectra with θH.

**Figure 5.** A representative plot of **a**ngular dependence of A/B ratio of [SnO2(46 nm)CFZ(249 nm)]5 ML.

Figure 6 depicts the angular variation of Hres, ΔH and Ipp. For all the ML there is no significant change in Hres and ΔH the FMR spectra for θH ≥ 60°. Below 60°, Hres and ΔH increase continuously. This shows that the ML is anisotropic in nature. The Ipp value initially increases from 0° till 40° followed by a decrease with further increase in θH. Thus the ML is homogeneous when placed at an orientation of 40°.

When an applied field is oriented along the film plane, Hres increases with decreasing thickness of the CZF layers. But Hres decreases with decreasing thickness of the CZF layers when the external magnetic field is oriented perpendicular to the film plane. This behavior is attributed to the decrease of the perpendicular anisotropy energy with decreasing CZF thickness [22]. The difference between the resonance fields in the parallel and perpendicular configuration decreases with decreasing CZF thickness evidencing the fact that the ML with x = 42 nm is relatively less anisotropic compared to the ML with x = 249 and 83 nm.

In the perpendicular configuration, the ML with x = 249 nm exhibits multiple resonances presumably due to the presence of spin waves. The spin wave resonance spectrum at RT and HT for ML with x = 249 nm were initially analyzed using the dispersion relation developed by Kittel as follows [23]

$$H\_n = H\_0 - \Lambda M\_0 \left(\frac{\pi}{L}\right)^2 n^2 \tag{1}$$

where ߉ ൌ ଶ ெబ మ

116 Ferromagnetic Resonance – Theory and Applications

spin wave modes to be formed.

the ML with x = 42 nm.

with θH.

multiple resonances may also be attributed to the existence of two different magnetic phases

The number of resonances decreases with decreasing CZF thickness in the perpendicular geometry. As the thickness of CZF layer increases, the ML provides sufficient length for the

**Figure 4.** Room temperature FMR spectra of [SnO2(46 nm)CFZ(249 nm)]5 at different orientations.

The FMR spectra of [SnO2(46 nm)/CZF(249 nm)]5 recorded at different orientations is shown in figure 4. For θH > 20° there is only single resonance in the FMR spectra. Small shoulder appears at θH = 20°. The multiple resonances appear at θH < 20°. The relative intensity of the FMR signals is also angle dependent. As θH approaches 0°, the amplitude of the shoulder peaks increases at the cost of that of the main peak. The separation between the resonances also increases and the intensity of the FMR signal decreases as θH approaches 0°. This may be due to the prominent demagnetization effects in the perpendicular configuration. A similar behavior is exhibited by the ML with x = 86 nm. There are no multiple resonances for

Figure 5 is a representative plot of the angular dependence of A/B ratio. A/B is close to 2.1 for the perpendicular configuration and decreases as the ML approaches parallel configuration. A/B = 1 for θH ~ 30° showing that the spectra is symmetric at an orientation of 30° of the sample normal with the applied field. Below 30° A/B is < 1 and above 30° A/B is > 1 evidencing the variation in the intensity of the lower and upper part of the FMR spectra

pertaining to the interfacial region and the bulk of the magnetic layer.

FMR Studies of [SnO2/Cu-Zn Ferrite] Multilayers 119

� (2)

Here Hn is the position of the nth mode of the spin wave resonance, H0 is the position of the FMR resonance, L is the thickness of the sample, M0 is the magnetization of the film, n is an odd integer and A is the exchange constant. This relation is valid for uniformly magnetized film. The results obtained do not fit well into the Kittel model where Hn is plotted against n2.

According to Portis model [24] for films with non uniform magnetic profile, the magnetization shows a parabolic drop away from the center of the film. The spin wave

� �������� �� � �

�

�� � �� − ���

**Figure 7.** Variation of resonance field with the mode number according to Portis model.

Portis considered that the pinning in the film arises due to non uniform magnetization in the film. This model proposes a linear relation between Hn and n. Also from the above equation, the difference between the resonance modes decreases with decrease in magnetization.

Figure 7 shows the linear fits corresponding to Portis model. The exchange constant is proportional to the slope of the line. The slope of the line decreases with increasing temperature. Hence the exchange constant decreases with increasing temperature leading to

They rather exhibit a linear behavior with n.

modes are given by the following relation

Here � is the distortion parameter in the film.

**Figure 6.** Angle dependence of resonance field (1), resonance linewidth (2) and amplitude (3) of [SnO2(46 nm)CFZ(x nm)]5 for x = 249 (a), 83(b) and 42 nm (c).

Here Hn is the position of the nth mode of the spin wave resonance, H0 is the position of the FMR resonance, L is the thickness of the sample, M0 is the magnetization of the film, n is an odd integer and A is the exchange constant. This relation is valid for uniformly magnetized film. The results obtained do not fit well into the Kittel model where Hn is plotted against n2. They rather exhibit a linear behavior with n.

According to Portis model [24] for films with non uniform magnetic profile, the magnetization shows a parabolic drop away from the center of the film. The spin wave modes are given by the following relation

$$H\_n = H\_0 - \frac{4M\_0}{L} (4\pi\epsilon)^{1/2} \left(n + \frac{1}{2}\right) \tag{2}$$

Here � is the distortion parameter in the film.

118 Ferromagnetic Resonance – Theory and Applications

1

2

3

**Figure 6.** Angle dependence of resonance field (1), resonance linewidth (2) and amplitude (3) of

[SnO2(46 nm)CFZ(x nm)]5 for x = 249 (a), 83(b) and 42 nm (c).

**Figure 7.** Variation of resonance field with the mode number according to Portis model.

Portis considered that the pinning in the film arises due to non uniform magnetization in the film. This model proposes a linear relation between Hn and n. Also from the above equation, the difference between the resonance modes decreases with decrease in magnetization.

Figure 7 shows the linear fits corresponding to Portis model. The exchange constant is proportional to the slope of the line. The slope of the line decreases with increasing temperature. Hence the exchange constant decreases with increasing temperature leading to

weak coupling and hence lower magnetization. Also, the separation between the resonance modes decreases at higher temperatures, indicating a decreasing magnetization.

The effective magnetization (4πMeff) and effective g value (geff) calculated using the Kittel's relations are listed in table1. At room temperature 4πMeff increases and geff decreases with increasing CZF thickness. This may be due to increasing FM layer thickness [25]. The various factors which can account for deviation of geff from that of the free electron are spin orbit coupling, coupling at the interfaces etc [26].

**Table 1.** FMR parameters for [SnO2(46 nm)/ CZF (x)]5 ML for various values of x.

The perpendicular anisotropy field HK is obtained from the following equation [27]

$$H\_K = 4\pi M\_S - 4\pi M\_{eff} \tag{3}$$

FMR Studies of [SnO2/Cu-Zn Ferrite] Multilayers 121

**Figure 8.** (K..x) vs x plots for [SnO2(46 nm)CFZ(x nm)]5 ML for x = 43, 83 and 249 nm.

thickness indicates the increase in the damping of spins with increasing thickness.

42 0.049 0.057 2.027 86 0.041 0.045 -1.989 249 0.053 0.146 -2.845,

**Table 2.** Damping and anisotropy parameters for or [SnO2(46 nm)/ CZF (x)]5 ML for various values of x.

The temperature dependent FMR studies in the temperature range 133- 473K were carried out on the ML. Figure 9 shows the FMR spectra of the ML at various temperatures. The change in

Figure 10 shows the variation of Ipp with temperature in the parallel configuration. Ipp increases with increasing temperature for all the ML. Ipp of the ML with x= 42 nm exhibits a linear trend. Whereas for ML with x=83 and 249 nm, the increase is not linear. It increases slowly from 133K to 298K (RT), followed by a rapid increase with temperature in the

line shape indicates change in the magnetic interaction with increasing temperature.

**x (nm)**

Gilbert damping is a spin relaxation phenomenon in magnetic systems which controls the rate at which the spins reach equilibrium. Spin-orbit coupling [32], non-local spin relaxations like spin wave dissipation [33,34] and disorder present in the materials are the major factors causing Gilbert damping. The damping parameter α values are 0.0096, 0.0083 and 0.0108 for x = 42, 83 and 249 nm respectively. The increase in α value with CZF

> **α K1 (103 erg/cm3** θH = 90° θH = 0° **)**

> > -1.254

The values of K are listed in table 2. In multilayers, there are two factors which contribute to the effective anisotropy – anisotropy due to the interfacial region (KS) and anisotropy due to the bulk volume of the magnetic layer (KV). The relation is given as follows [28]

$$K = K\_V + 2\frac{K\_S}{\varkappa} \tag{4}$$

Where x is the thickness of the magnetic layer. The factor of 2 in the second term on the (r. h.s) of the equation is due to an assumption that the magnetic layer is bound by identical interfaces on either side. When (K.x) is plotted against t (figure 8), the slope gives the value of KV and the intercept gives the value of KS. The negative slope indicates a negative volume anisotropy which tends to confine the magnetic moment in the plane of the film [29]. The intercept at x = 0 gives positive value of KS which tends to align the magnetic moment perpendicular to the surface of the film. The intercept on the x axis gives the thickness at which the contribution from KV outweighs that from KS. From the figure, the intercept on x axis is found to be 56 nm. Thus below 56nm, major contribution comes from interfaces. The KS and KV values obtained from the plot are 194980 and -3671 erg/cm3

The value of K changes from positive to negative as the thickness of CZF increases (figure 8). Negative values of K indicates in-plane anisotropy [30]. Thus with increasing CZF thickness, the direction of magnetization is confined to the plane of the sample surface. The thickness value at which the anisotropy changes sign is 56 nm. The perpendicular anisotropy for small values of x may be due to the lattice mismatch at the interfaces [31].

**Figure 8.** (K..x) vs x plots for [SnO2(46 nm)CFZ(x nm)]5 ML for x = 43, 83 and 249 nm.

orbit coupling, coupling at the interfaces etc [26].

4.173

ΔHres (kG)

1.107,

**Table 1.** FMR parameters for [SnO2(46 nm)/ CZF (x)]5 ML for various values of x.

The perpendicular anisotropy field HK is obtained from the following equation [27]

the bulk volume of the magnetic layer (KV). The relation is given as follows [28]

KS and KV values obtained from the plot are 194980 and -3671 erg/cm3

values of x may be due to the lattice mismatch at the interfaces [31].

Hres (kG)

249 2.526 3.633,

x (nm)

weak coupling and hence lower magnetization. Also, the separation between the resonance

The effective magnetization (4πMeff) and effective g value (geff) calculated using the Kittel's relations are listed in table1. At room temperature 4πMeff increases and geff decreases with increasing CZF thickness. This may be due to increasing FM layer thickness [25]. The various factors which can account for deviation of geff from that of the free electron are spin

g (± 0.01)

42 2.977 3.165 0.188 2.21 2.08 125.76 2.16 631 750 86 2.649 3.720 1.071 2.48 1.77 728.39 2.19 541 590

1.647 2.60 1.81, 1.58 754.41,

The values of K are listed in table 2. In multilayers, there are two factors which contribute to the effective anisotropy – anisotropy due to the interfacial region (KS) and anisotropy due to

���� + 2 ��

Where x is the thickness of the magnetic layer. The factor of 2 in the second term on the (r. h.s) of the equation is due to an assumption that the magnetic layer is bound by identical interfaces on either side. When (K.x) is plotted against t (figure 8), the slope gives the value of KV and the intercept gives the value of KS. The negative slope indicates a negative volume anisotropy which tends to confine the magnetic moment in the plane of the film [29]. The intercept at x = 0 gives positive value of KS which tends to align the magnetic moment perpendicular to the surface of the film. The intercept on the x axis gives the thickness at which the contribution from KV outweighs that from KS. From the figure, the intercept on x axis is found to be 56 nm. Thus below 56nm, major contribution comes from interfaces. The

The value of K changes from positive to negative as the thickness of CZF increases (figure 8). Negative values of K indicates in-plane anisotropy [30]. Thus with increasing CZF thickness, the direction of magnetization is confined to the plane of the sample surface. The thickness value at which the anisotropy changes sign is 56 nm. The perpendicular anisotropy for small

θH = 90° θH = 0° θH = 90° θH = 0° θH = 90° θH = 0°

4πMeff (Oe) geff

1132.88

�� � ���� � ������ (3)

2.28,

� (4)

ΔH (G)

2.14 703 1930

modes decreases at higher temperatures, indicating a decreasing magnetization.

Gilbert damping is a spin relaxation phenomenon in magnetic systems which controls the rate at which the spins reach equilibrium. Spin-orbit coupling [32], non-local spin relaxations like spin wave dissipation [33,34] and disorder present in the materials are the major factors causing Gilbert damping. The damping parameter α values are 0.0096, 0.0083 and 0.0108 for x = 42, 83 and 249 nm respectively. The increase in α value with CZF thickness indicates the increase in the damping of spins with increasing thickness.

**Table 2.** Damping and anisotropy parameters for or [SnO2(46 nm)/ CZF (x)]5 ML for various values of x.

The temperature dependent FMR studies in the temperature range 133- 473K were carried out on the ML. Figure 9 shows the FMR spectra of the ML at various temperatures. The change in line shape indicates change in the magnetic interaction with increasing temperature.

Figure 10 shows the variation of Ipp with temperature in the parallel configuration. Ipp increases with increasing temperature for all the ML. Ipp of the ML with x= 42 nm exhibits a linear trend. Whereas for ML with x=83 and 249 nm, the increase is not linear. It increases slowly from 133K to 298K (RT), followed by a rapid increase with temperature in the

temperature range RT- 473K. From 133K to 250K there is no significant difference in amplitude for ML with x= 83 and 249 nm. At temperatures above RT the amplitude of ML with x= 83 nm is higher than that of ML with x = 249 nm.

FMR Studies of [SnO2/Cu-Zn Ferrite] Multilayers 123

**Figure 10.** Temperature dependent amplitude of [SnO2(46 nm)CFZ(x nm)]5 for x = 249(a), 83(b) and 42

Variation of ΔH with temperature in the parallel configuration is displayed in figure 11. The width of the FMR spectra increases continuously with decreasing temperature for x= 42 nm. For x = 83 nm it decreases with temperature and saturates at ~ 215 K . Whereas for x = 249 nm it begins saturating at ~ RT presumably due to freezing of spins. The Hres increases with increasing temperature (figure 12) in all the ML presumably due to increasing internal field at low temperatures. The ML with x = 249 nm exhibits a linear dependence in the entire temperature range whereas the ML with x = 83 and 42 nm exhibit saturating tendency at higher temperatures in the parallel configuration. This may be an interfacial effect. For x = 42 nm the ratio of spins at the interfaces to the spins in the bulk is high. Whereas for x = 83 and 249 nm the ratio is lower. Hence the contribution from the bulk of the film becomes significant than that from the interfaces. The saturating tendency at high temperatures for the ML with x = 83 and 42 nm shows that even at higher temperatures, the thermal energy is

Similar behavior is observed for CZF thin films [12]. The increase in saturation temperature

The change of slope of ΔH indicates a change in the kind of magnetic interactions in the ML. The line shape of the FMR spectra also changes around the same temperature. The curvature of the temperature dependent of ΔH plot changes as x increases from 42 to 249 presumably due to increase in active to dead layer ratio. Decreasing trend in Ipp and Hres and increasing trend in ΔH with decreasing temperature is a signature of superparamagnetism [35]. The resonance field of a given particle includes contribution from magneto crystalline anisotropy

with increase in CZF thickness could be due to the interlayer coupling.

not sufficient to unlock the spins at the interfaces.

field and demagnetizing field.

nm (c).

**Figure 9.** FMR spectra of [SnO2(46 nm)CFZ(x nm)]5 ML at various temperatures for x = 249 (a), 83 (b) and 42 nm (c)in the parallel configuration.

with x= 83 nm is higher than that of ML with x = 249 nm.

temperature range RT- 473K. From 133K to 250K there is no significant difference in amplitude for ML with x= 83 and 249 nm. At temperatures above RT the amplitude of ML

**Figure 9.** FMR spectra of [SnO2(46 nm)CFZ(x nm)]5 ML at various temperatures for x = 249 (a), 83 (b)

and 42 nm (c)in the parallel configuration.

**Figure 10.** Temperature dependent amplitude of [SnO2(46 nm)CFZ(x nm)]5 for x = 249(a), 83(b) and 42 nm (c).

Variation of ΔH with temperature in the parallel configuration is displayed in figure 11. The width of the FMR spectra increases continuously with decreasing temperature for x= 42 nm. For x = 83 nm it decreases with temperature and saturates at ~ 215 K . Whereas for x = 249 nm it begins saturating at ~ RT presumably due to freezing of spins. The Hres increases with increasing temperature (figure 12) in all the ML presumably due to increasing internal field at low temperatures. The ML with x = 249 nm exhibits a linear dependence in the entire temperature range whereas the ML with x = 83 and 42 nm exhibit saturating tendency at higher temperatures in the parallel configuration. This may be an interfacial effect. For x = 42 nm the ratio of spins at the interfaces to the spins in the bulk is high. Whereas for x = 83 and 249 nm the ratio is lower. Hence the contribution from the bulk of the film becomes significant than that from the interfaces. The saturating tendency at high temperatures for the ML with x = 83 and 42 nm shows that even at higher temperatures, the thermal energy is not sufficient to unlock the spins at the interfaces.

Similar behavior is observed for CZF thin films [12]. The increase in saturation temperature with increase in CZF thickness could be due to the interlayer coupling.

The change of slope of ΔH indicates a change in the kind of magnetic interactions in the ML. The line shape of the FMR spectra also changes around the same temperature. The curvature of the temperature dependent of ΔH plot changes as x increases from 42 to 249 presumably due to increase in active to dead layer ratio. Decreasing trend in Ipp and Hres and increasing trend in ΔH with decreasing temperature is a signature of superparamagnetism [35]. The resonance field of a given particle includes contribution from magneto crystalline anisotropy field and demagnetizing field.

FMR Studies of [SnO2/Cu-Zn Ferrite] Multilayers 125

For a system containing randomly oriented particles, the magnetic resonance signal is broad. At high temperatures where *k*b*T* is much greater than the anisotropy barriers the thermal fluctuations of the magnetic moments reduces the angular anisotropy of the resonance fields and the linewidth of individual nanoparticle [36] resulting in a superparamagnetic resonance (SPR) spectra in the case of nanoparticles. At low temperatures the particle moments are unable to overcome the local anisotropy barriers and, thus, become trapped in metastable states (blocking phenomenon). This results in broad

A characteristic feature of SPR is that at low temperatures, ΔH is almost equal to the value of Hres. For the ML with x = 42 nm around 40% of CZF layer is dead. The diffused region consists of fine particles of CZF dispersed in SnO2 matrix. Hence the SPR phenomenon is pronounced for this ML. Whereas for ML with x = 83 and 249 nm, the thickness of the diffused region is small compared to that of the bulk CZF layer. Hence the value of ΔH at

FMR susceptibility is estimated by calculating the double integrated intensity i.e. area under the absorption curve in FMR is proportional to the concentration of spins. Figure 13 shows temperature dependence of ESR susceptibility in the parallel configuration for *[SnO2(46 nm)CFZ(x nm)]5* ML. It initially increases with decreasing temperature, reaches a maximum and then decreases with further decrease in temperature evidencing the superparamagnetic behavior. The width of the transition is large due to the wide spread of blocking

**Figure 13.** Variation of FMR susceptibility, χFMR with temperature of [SnO2(46 nm)CFZ(x nm)]5 ML for x

For ML with x = 42 nm, χFMR decreases continuously with decrease in temperature down till 183 K. The negative absorption is due to the fact that the area under the lower part of the

resonance spectra with linewidth comparable to that of the resonance field.

low temperatures is not same as that of Hres.

temperatures.

= 249 (a), 83 (b) and 42 nm (c).

**Figure 11.** Temperature dependent resonance linewidth of [SnO2(46 nm)CFZ(x nm)]5 for x = 249(a), 83(b) and 42 nm (c).

**Figure 12.** Temperature dependent resonance field, Hres, in the parallel and perpendicular configuration of [SnO2(46 nm)CFZ(x nm)]5 for x = 249(a), 83(b) and 42 nm (c).

For a system containing randomly oriented particles, the magnetic resonance signal is broad. At high temperatures where *k*b*T* is much greater than the anisotropy barriers the thermal fluctuations of the magnetic moments reduces the angular anisotropy of the resonance fields and the linewidth of individual nanoparticle [36] resulting in a superparamagnetic resonance (SPR) spectra in the case of nanoparticles. At low temperatures the particle moments are unable to overcome the local anisotropy barriers and, thus, become trapped in metastable states (blocking phenomenon). This results in broad resonance spectra with linewidth comparable to that of the resonance field.

124 Ferromagnetic Resonance – Theory and Applications

83(b) and 42 nm (c).

**Figure 11.** Temperature dependent resonance linewidth of [SnO2(46 nm)CFZ(x nm)]5 for x = 249(a),

**Figure 12.** Temperature dependent resonance field, Hres, in the parallel and perpendicular

configuration of [SnO2(46 nm)CFZ(x nm)]5 for x = 249(a), 83(b) and 42 nm (c).

A characteristic feature of SPR is that at low temperatures, ΔH is almost equal to the value of Hres. For the ML with x = 42 nm around 40% of CZF layer is dead. The diffused region consists of fine particles of CZF dispersed in SnO2 matrix. Hence the SPR phenomenon is pronounced for this ML. Whereas for ML with x = 83 and 249 nm, the thickness of the diffused region is small compared to that of the bulk CZF layer. Hence the value of ΔH at low temperatures is not same as that of Hres.

FMR susceptibility is estimated by calculating the double integrated intensity i.e. area under the absorption curve in FMR is proportional to the concentration of spins. Figure 13 shows temperature dependence of ESR susceptibility in the parallel configuration for *[SnO2(46 nm)CFZ(x nm)]5* ML. It initially increases with decreasing temperature, reaches a maximum and then decreases with further decrease in temperature evidencing the superparamagnetic behavior. The width of the transition is large due to the wide spread of blocking temperatures.

**Figure 13.** Variation of FMR susceptibility, χFMR with temperature of [SnO2(46 nm)CFZ(x nm)]5 ML for x = 249 (a), 83 (b) and 42 nm (c).

For ML with x = 42 nm, χFMR decreases continuously with decrease in temperature down till 183 K. The negative absorption is due to the fact that the area under the lower part of the

FMR curve is greater than that of the upper part. The Curie- Weiss law does not fit 1/ χ FMR vs T plot due to the continuous curvature in the entire temperatures range.

FMR Studies of [SnO2/Cu-Zn Ferrite] Multilayers 127

**Figure 15.** FMR spectra of [SnO2(46 nm)CFZ(x nm)]5 at various temperatures in the perpendicular

configuration for x = 249 (a), 83 (b) and 42 nm (c).

**Figure 14.** Variation A/B ratio with temperature of [SnO2(46 nm)CFZ(x nm)]5 ML for x = 249(a), 83(b) and 42 nm (c).

Figure 14 shows the A/B ratio with temperature for these ML. It decreases almost linearly with decreasing temperature from 400 to 200 K for the ML with x = 42 nm. Below 200 K there is a change in slope. The temperature dependence of A/B ratio exhibits different slopes in different temperature region for the ML with x = 83 nm. Whereas for the ML with x = 249 nm, there is no significant change in the A/B ratio in the temperature range between 500 and 350 K. Below 350 K the ratio decreases continuously. The temperature at which the slope for A/B ratio changes matches with that of temperature dependence of linewidth.

Temperature dependence of FMR spectra of these ML in the perpendicular configurations is displayed in figure 15. The resonance field shifts towards higher values with decreasing temperature. This is accompanied with decrease in intensity and increase in line width. This indicates that AFM interactions dominate as temperature decreases in the perpendicular configuration.

#### FMR Studies of [SnO2/Cu-Zn Ferrite] Multilayers 127

126 Ferromagnetic Resonance – Theory and Applications

and 42 nm (c).

configuration.

FMR curve is greater than that of the upper part. The Curie- Weiss law does not fit 1/ χ FMR

**Figure 14.** Variation A/B ratio with temperature of [SnO2(46 nm)CFZ(x nm)]5 ML for x = 249(a), 83(b)

Figure 14 shows the A/B ratio with temperature for these ML. It decreases almost linearly with decreasing temperature from 400 to 200 K for the ML with x = 42 nm. Below 200 K there is a change in slope. The temperature dependence of A/B ratio exhibits different slopes in different temperature region for the ML with x = 83 nm. Whereas for the ML with x = 249 nm, there is no significant change in the A/B ratio in the temperature range between 500 and 350 K. Below 350 K the ratio decreases continuously. The temperature at which the slope for

Temperature dependence of FMR spectra of these ML in the perpendicular configurations is displayed in figure 15. The resonance field shifts towards higher values with decreasing temperature. This is accompanied with decrease in intensity and increase in line width. This indicates that AFM interactions dominate as temperature decreases in the perpendicular

A/B ratio changes matches with that of temperature dependence of linewidth.

vs T plot due to the continuous curvature in the entire temperatures range.

**Figure 15.** FMR spectra of [SnO2(46 nm)CFZ(x nm)]5 at various temperatures in the perpendicular configuration for x = 249 (a), 83 (b) and 42 nm (c).

Figure 15(a) also shows the variation in the positions of the multiple resonances for x = 249. They are narrow and closely spaced at 473 K. As temperature decreases, the FMR peaks broaden and move away from each other with decreasing temperature. The peak at the lower field moves further towards lower field and the one at the higher field moves further towards higher field. This is a clear indication of existence of both FM and AFM phase. The relative intensity of the peak at higher field decreases and that of the one at lower field increases with decreasing temperature. The distance between the peaks increases with decreasing temperature. This indicates increase in phase separation with decrease in temperature.

FMR Studies of [SnO2/Cu-Zn Ferrite] Multilayers 129

(a)

(b)

(c)

**Figure 17.** Temperature dependent resonance field, Hres, in the parallel and perpendicular

configuration of [SnO2(46 nm)CFZ(x nm)]5 for x = 249 (a), 83 (b) and 42 nm (c).

Ipp value in the perpendicular configuration is lower than that in the parallel configuration at all temperatures. However, the trend remains the same in both parallel and perpendicular configurations. The ΔH value in the perpendicular configuration is not very much different from that in the parallel configuration for the ML with x = 42 and 83 nm (figure 16). On the other hand, ΔH for x = 249 ML is much higher in the perpendicular configuration.

**Figure 16.** Temperature dependent resonance linewidth in the parallel (full circle) and perpendicular (open circle) configuration of [SnO2 (46 nm)CFZ(x nm)]5 for x = 249(a), 83(b) and 42 nm (c).

Figure 17 shows the variation of Hres in the parallel and perpendicular configuration. Unlike the parallel configuration, the resonance field increases with decreasing temperature in the perpendicular configuration for ML with x = 249 and 83 nm. Hres remains insensitive to temperature in the range 300- 473K. Below 300 K it increases with further decrease in temperature.

temperature.

temperature.

Figure 15(a) also shows the variation in the positions of the multiple resonances for x = 249. They are narrow and closely spaced at 473 K. As temperature decreases, the FMR peaks broaden and move away from each other with decreasing temperature. The peak at the lower field moves further towards lower field and the one at the higher field moves further towards higher field. This is a clear indication of existence of both FM and AFM phase. The relative intensity of the peak at higher field decreases and that of the one at lower field increases with decreasing temperature. The distance between the peaks increases with decreasing temperature. This indicates increase in phase separation with decrease in

Ipp value in the perpendicular configuration is lower than that in the parallel configuration at all temperatures. However, the trend remains the same in both parallel and perpendicular configurations. The ΔH value in the perpendicular configuration is not very much different from that in the parallel configuration for the ML with x = 42 and 83 nm (figure 16). On the

**Figure 16.** Temperature dependent resonance linewidth in the parallel (full circle) and perpendicular

Figure 17 shows the variation of Hres in the parallel and perpendicular configuration. Unlike the parallel configuration, the resonance field increases with decreasing temperature in the perpendicular configuration for ML with x = 249 and 83 nm. Hres remains insensitive to temperature in the range 300- 473K. Below 300 K it increases with further decrease in

(open circle) configuration of [SnO2 (46 nm)CFZ(x nm)]5 for x = 249(a), 83(b) and 42 nm (c).

other hand, ΔH for x = 249 ML is much higher in the perpendicular configuration.

**Figure 17.** Temperature dependent resonance field, Hres, in the parallel and perpendicular configuration of [SnO2(46 nm)CFZ(x nm)]5 for x = 249 (a), 83 (b) and 42 nm (c).

Whereas for the ML with x = 42 nm, initially there is a small increase in Hres as temperature decreases from 473 to 433 K. Below 433 K it decreases continuously. At all temperatures, Hres is less sensitive to temperature in the perpendicular configuration than in the parallel configuration.

FMR Studies of [SnO2/Cu-Zn Ferrite] Multilayers 131

decreasing temperature. This shows increasing anisotropy with decreasing temperature. The multiple resonance for the ML with x = 249 is prominent at 298 and 473 K (figure 20(a)). For ML with x < 249 nm, the absence of multiple resonances even at high temperatures indicates absence of interlayer coupling. At all temperatures the ΔHres is highest for the ML with x =

**Figure 19.** Representative plot of the FMR susceptibility, FMR of [SnO2 (46 nm)CFZ(249 nm)]5 ML in

At room temperature, ΔH shows a minimum ~ 30-40° (figure 21). Ipp shows maximum around the same value. Hence the sample has an easy axis of magnetization at that inclination. At 473 and 298 K its intensity initially increases, reaches a maximum and then decreases with decreasing θH. Whereas at 133 K, Ipp values remains constant initially then

Another evidence for decreasing anisotropy with decreasing x is shown in figure 21. At 473 K, ΔH for the ML with x = 249 nm initially increases, exhibits a minimum ~ 40° and then increases continuously with further increase in θH . Whereas for the ML with x = 83 nm, with increasing θH, ΔH value remains constant till certain angle then decreases continuously. On the other hand the ΔH value for the ML with x = 42 nm, the ΔH value continuously decrease reaches a minimum and then increases with increasing θH. The occurrence of minimum in ΔH may be due to existence of regions with different effective magnetization values due to inhomogeneous nature of the sample [37]. The minimum in ΔH shifts towards higher angle with decreasing x. Similar behavior is observed at 298 K for all the ML. With decreasing

parallel and perpendicular configuration.

decreases continuously with decreasing value of θH.

249 nm. These multiple resonances disappear with decreasing temperature.

For all the ML, the FMR susceptibility increases with decreasing temperature in the perpendicular configuration. The effective magnetization is a measure of net magnetization within the ML. Figure 18 shows the variation of effective magnetization with temperature. It increases with decreasing temperature for all ML.

**Figure 18.** Variation of effective magnetization with temperature for [SnO2 (46 nm)CFZ(x nm)]5 ML for x = 249(a), 83(b) and 42 nm (c).

Figure 19 is a representative graph of [SnO2 (46 nm)/ CZF(249 nm)]5 ML showing the variation of FMR susceptibility with temperature in both parallel and perpendicular configurations. Unlike the parallel configuration, χFMR in the perpendicular configuration increases continuously with decreasing temperature.

The FMR spectra were recorded at different orientations of the normal to the sample with the applied field (θH). The rotational dependence of FMR spectra was measured at 133, 298 (room temperature) and 473 K. At all temperatures the resonance field increases continuously as θH decreases exhibiting uniaxial anisotropy. For the ML, the difference between ΔH values in the parallel and perpendicular configuration increases with decreasing temperature. This shows increasing anisotropy with decreasing temperature. The multiple resonance for the ML with x = 249 is prominent at 298 and 473 K (figure 20(a)). For ML with x < 249 nm, the absence of multiple resonances even at high temperatures indicates absence of interlayer coupling. At all temperatures the ΔHres is highest for the ML with x = 249 nm. These multiple resonances disappear with decreasing temperature.

130 Ferromagnetic Resonance – Theory and Applications

increases with decreasing temperature for all ML.

configuration.

x = 249(a), 83(b) and 42 nm (c).

increases continuously with decreasing temperature.

Whereas for the ML with x = 42 nm, initially there is a small increase in Hres as temperature decreases from 473 to 433 K. Below 433 K it decreases continuously. At all temperatures, Hres is less sensitive to temperature in the perpendicular configuration than in the parallel

For all the ML, the FMR susceptibility increases with decreasing temperature in the perpendicular configuration. The effective magnetization is a measure of net magnetization within the ML. Figure 18 shows the variation of effective magnetization with temperature. It

**Figure 18.** Variation of effective magnetization with temperature for [SnO2 (46 nm)CFZ(x nm)]5 ML for

Figure 19 is a representative graph of [SnO2 (46 nm)/ CZF(249 nm)]5 ML showing the variation of FMR susceptibility with temperature in both parallel and perpendicular configurations. Unlike the parallel configuration, χFMR in the perpendicular configuration

The FMR spectra were recorded at different orientations of the normal to the sample with the applied field (θH). The rotational dependence of FMR spectra was measured at 133, 298 (room temperature) and 473 K. At all temperatures the resonance field increases continuously as θH decreases exhibiting uniaxial anisotropy. For the ML, the difference between ΔH values in the parallel and perpendicular configuration increases with

**Figure 19.** Representative plot of the FMR susceptibility, FMR of [SnO2 (46 nm)CFZ(249 nm)]5 ML in parallel and perpendicular configuration.

At room temperature, ΔH shows a minimum ~ 30-40° (figure 21). Ipp shows maximum around the same value. Hence the sample has an easy axis of magnetization at that inclination. At 473 and 298 K its intensity initially increases, reaches a maximum and then decreases with decreasing θH. Whereas at 133 K, Ipp values remains constant initially then decreases continuously with decreasing value of θH.

Another evidence for decreasing anisotropy with decreasing x is shown in figure 21. At 473 K, ΔH for the ML with x = 249 nm initially increases, exhibits a minimum ~ 40° and then increases continuously with further increase in θH . Whereas for the ML with x = 83 nm, with increasing θH, ΔH value remains constant till certain angle then decreases continuously. On the other hand the ΔH value for the ML with x = 42 nm, the ΔH value continuously decrease reaches a minimum and then increases with increasing θH. The occurrence of minimum in ΔH may be due to existence of regions with different effective magnetization values due to inhomogeneous nature of the sample [37]. The minimum in ΔH shifts towards higher angle with decreasing x. Similar behavior is observed at 298 K for all the ML. With decreasing

FMR Studies of [SnO2/Cu-Zn Ferrite] Multilayers 133

(a)

(c)

**Figure 21.** Rotational dependence of resonance linewidth, ΔH, at various temperatures for [SnO2 (46

(b)

nm)CFZ(x nm)]5 ML for x = 42(a), 83(b) and 249 nm (c).

**Figure 20.** Rotational dependence of resonance field, Hres, at various temperatures for [SnO2 (46 nm)CFZ(x nm)]5 ML where x = 249(a), 83(b) and 42 nm (c).

**Figure 20.** Rotational dependence of resonance field, Hres, at various temperatures for [SnO2 (46

nm)CFZ(x nm)]5 ML where x = 249(a), 83(b) and 42 nm (c).

**Figure 21.** Rotational dependence of resonance linewidth, ΔH, at various temperatures for [SnO2 (46 nm)CFZ(x nm)]5 ML for x = 42(a), 83(b) and 249 nm (c).

temperature, the curvature of the angle dependent linewidth changes. At 133 K, for x = 249 nm, the minima vanishes and ΔH increases continuously with increasing θH. For the ML with x = 83 nm, the curvature is reversed at 133 K. It increases with increasing θH, attains a maximum value at ~ 40° and then decreases. On the contrary there is no significant change in ΔH for the ML with x = 42 nm. Thus at 133 K, x = 249 nm ML is more anisotropic than the ML with x = 42 and 83 nm.

FMR Studies of [SnO2/Cu-Zn Ferrite] Multilayers 135

FMR studies were carried out at different temperatures and by varying the angle θH between the film normal and the direction of the applied field. Figure 23 shows the first derivative of the FMR absorption spectra of the ML at room temperature in parallel (θH = 90°) and perpendicular (θH = 0°) geometry, normalized to the volume of the CZF layers. Ipp increases as the spacer (SnO2) thickness increases from x = 46 to 115 nm followed by a decrease for x = 184 nm. The peak to peak linewidth (∆H) is sensitive to inhomogenieties, surface roughness, internal field etc. The χ FMR is estimated by calculating double integrated intensity (DI). Both ∆H and DI follow a trend similar to that of Ipp with increase in spacer layer thickness. This behavior may be attributed to the oscillation in the exchange coupling across the NM layer due to quantum interference of the electron waves reflected from the interfaces. The A/B ratio is 0.82, 0.74 and 0.79 for x = 46, 115 and 184 nm respectively. The asymmetry ratio is not very different from each other. For the ML with x = 115 nm, the upper part of the FMR signal rises steeply whereas the rise is relatively slow for the lower

**Figure 23.** Room temperature FMR spectra of [SnO2(x nm) CZF(83 nm)]5 ML in the parallel and

table 3. The effective magnetization decreases with increasing SnO2 thickness.

The resonance field (Hres) increases from 2.65 to 2.78 kG and the g value decreases from 2.47 to 2.36 with increase in SnO2 layer thickness in parallel geometry. The shift in Hres to higher values might be due to the decrease in interlayer coupling strength. The Hres decreases and g values increases from 1.77 to 1.96 with increasing spacer layer thickness in the perpendicular geometry. This might be attributed to lower perpendicular anisotropy for well separated films [38]. The FMR parameters in the parallel and perpendicular configurations are listed in

perpendicular configuration for x = 46 (a), 115 (b) and 184 nm (c)..

part indicating a negative anisotropy.

### **3.2. Effect of spacer layer thickness**

The effect of thickness of spacer (SnO2) layer was studied on 3 sets of samples with varying thickness of the SnO2 layer. The total number of bilayers is 5 and individual CZF layer thickness is 83 nm for all the samples. The ML samples were [SnO2(x nm) CZF(83 nm)]5 ML for x = 46 , 115 and 184 nm .

Stack of alternate dark and light layers are evident from the FESEM images (figure 22). The dark columnar layers correspond to CZF and the light layers correspond to SnO2. The variation in the thickness ratio between SnO2 and CZF is also clearly visible from these images. The absence of fringes in XRR spectra may be due to large thickness of the ML stack.

**Figure 22.** FESEM images of [SnO2(x nm) CZF(83 nm)]5 ML for x = 46 (a), 115 (b) and 184 nm (c).

FMR studies were carried out at different temperatures and by varying the angle θH between the film normal and the direction of the applied field. Figure 23 shows the first derivative of the FMR absorption spectra of the ML at room temperature in parallel (θH = 90°) and perpendicular (θH = 0°) geometry, normalized to the volume of the CZF layers. Ipp increases as the spacer (SnO2) thickness increases from x = 46 to 115 nm followed by a decrease for x = 184 nm. The peak to peak linewidth (∆H) is sensitive to inhomogenieties, surface roughness, internal field etc. The χ FMR is estimated by calculating double integrated intensity (DI). Both ∆H and DI follow a trend similar to that of Ipp with increase in spacer layer thickness. This behavior may be attributed to the oscillation in the exchange coupling across the NM layer due to quantum interference of the electron waves reflected from the interfaces. The A/B ratio is 0.82, 0.74 and 0.79 for x = 46, 115 and 184 nm respectively. The asymmetry ratio is not very different from each other. For the ML with x = 115 nm, the upper part of the FMR signal rises steeply whereas the rise is relatively slow for the lower part indicating a negative anisotropy.

134 Ferromagnetic Resonance – Theory and Applications

**3.2. Effect of spacer layer thickness**

ML with x = 42 and 83 nm.

for x = 46 , 115 and 184 nm .

temperature, the curvature of the angle dependent linewidth changes. At 133 K, for x = 249 nm, the minima vanishes and ΔH increases continuously with increasing θH. For the ML with x = 83 nm, the curvature is reversed at 133 K. It increases with increasing θH, attains a maximum value at ~ 40° and then decreases. On the contrary there is no significant change in ΔH for the ML with x = 42 nm. Thus at 133 K, x = 249 nm ML is more anisotropic than the

The effect of thickness of spacer (SnO2) layer was studied on 3 sets of samples with varying thickness of the SnO2 layer. The total number of bilayers is 5 and individual CZF layer thickness is 83 nm for all the samples. The ML samples were [SnO2(x nm) CZF(83 nm)]5 ML

Stack of alternate dark and light layers are evident from the FESEM images (figure 22). The dark columnar layers correspond to CZF and the light layers correspond to SnO2. The variation in the thickness ratio between SnO2 and CZF is also clearly visible from these images. The absence of fringes in XRR spectra may be due to large thickness of the ML stack.

**Figure 22.** FESEM images of [SnO2(x nm) CZF(83 nm)]5 ML for x = 46 (a), 115 (b) and 184 nm (c).

**Figure 23.** Room temperature FMR spectra of [SnO2(x nm) CZF(83 nm)]5 ML in the parallel and perpendicular configuration for x = 46 (a), 115 (b) and 184 nm (c)..

The resonance field (Hres) increases from 2.65 to 2.78 kG and the g value decreases from 2.47 to 2.36 with increase in SnO2 layer thickness in parallel geometry. The shift in Hres to higher values might be due to the decrease in interlayer coupling strength. The Hres decreases and g values increases from 1.77 to 1.96 with increasing spacer layer thickness in the perpendicular geometry. This might be attributed to lower perpendicular anisotropy for well separated films [38]. The FMR parameters in the parallel and perpendicular configurations are listed in table 3. The effective magnetization decreases with increasing SnO2 thickness.

FMR Studies of [SnO2/Cu-Zn Ferrite] Multilayers 137

The angle dependent FMR spectra are shown in figure 24. The symmetry in the FMR spectra increases as θH decreases from 90° to 40°. For θH > 40° the spectra becomes asymmetric and the single FMR peak splits into two resonance peaks. With decreasing θH the separation of