Magnetic Characterization

### **Chapter 5**

Unraveling the Extraordinary Anisotropic Magnetoresistance in Antiferromagnetic Perovskite Heterostructures: A Case Study of CaMnO3/CaIrO3 Superlattice

*Suman Sardar*

#### **Abstract**

Antiferromagnetic (AFM) spintronics offers advantages over ferromagnetic (FM) spintronics, such as zero stray fields, closer packing, and imperviousness to disruptive fields. Anisotropic magnetoresistance (AMR) can be enhanced by materials with pronounced spin-orbit coupling (SOC) and magnetocrystalline anisotropies. AMR research aims to develop new materials and heterostructures with enhanced and tunable anisotropic transport properties for advanced electronic devices. The nonmagnetic ground state of iridium pseudospin moments in SrIrO3 and CaIrO3 is determined by SOC and electron correlations (U). This study shows that by coupling CaIrO3 with a severely distorted canted AFM manganite CaMnO3, the AMR can be increased by more than one order of magnitude, primarily due to interlayer coupling. Additionally, the spin-flop transition in a nearly Mott region contributes to an unprecedented AMR of 70%, two orders of magnitude larger than previously achieved. The study demonstrates that thin films of canted AFM phases of CaMnO3 and CaIrO3 exhibit dimensionality control, with a diminishing magnetic moment, and the valence state can be altered at interfaces in superlattices involving manganites.

**Keywords:** transition metal oxides and heterostructures, antiferromagnetic spintronics, anisotropic magnetoresistance, spin-orbit coupling, canted antiferromagnet, spin-flop transition

#### **1. Introduction**

Antiferromagnetic (AFM) spintronics has emerged as a promising alternative to ferromagnetic (FM) spintronics due to several advantages. AFM spintronics offers a significant advantage over other technologies as its ordered microscopic moments

alternate between individual atomic sites, resulting in zero stray fields and enabling closer packing of devices without interference. Thus, AFM materials possess a remarkable property of being externally invisible in magnetic fields, owing to their zero net magnetic moments, which implies that any information stored in their magnetic moments would be impervious to disruptive magnetic fields and beyond the detection capabilities of commonly used magnetic probes [1–6]. Antiferromagnets have been discovered to have greater potential than just being used as passive elements in exchange bias applications. When a soft ferromagnet is placed next to a thin antiferromagnet, and a feeble external magnetic field is applied, the ferromagnet can reposition itself, causing its interfacial moments to pull the adjacent antiferromagnetic moments via the interfacial exchange spring. Metal antiferromagnets, such as the Ir-Mn alloys, are versatile materials with various applications, ranging from serving as advantageous passive exchange-bias components to functioning as active electrodes in Tunneling Anisotropic Magnetoresistance (TAMR) devices [7–11]. Additionally, AFM spintronics devices require lower operational power, which makes them more energy-efficient. AFM spintronics allows for ultrafast control of the staggered spins at terahertz frequencies, which can enable faster and more efficient data processing. Current-induced spin-orbit torque (SOT) and anisotropic magnetoresistance (AMR) are two important phenomena used in AFM spintronics devices and in this way, the spin of the AFM material can be accessed for data writing and reading operations. SOT is a process that utilizes electric current to generate torque on the magnetization of a material, primarily used in AFM spintronic devices. The electron's spin polarization generates a spin current when a current is passed through a thin layer of heavy metal. The interaction of the spin current with the AFM moments at the interface generates a torque that can reorient the magnetic moments of the AFM layer, enabling precise data writing and reading operations by controlling the current's direction and magnitude. Moreover, the SOT-based devices have the advantage of low power consumption and fast switching speeds making them promising candidates for future high-density data storage and processing applications [6, 10, 12]. AMR is a phenomenon that causes the resistance of a material to change as a function of the angle between the direction of current flow and the magnetization direction. Overall, AFM spintronics has the potential to revolutionize the field of spintronics and enable the development of faster, more efficient, and more compact devices [13–15].

Here, a detailed discussion of AMR will be given in 3d/5d perovskite heterostructures. The origin of AMR depends on whether the material is crystalline or noncrystalline. In both cases, the AMR response arises from the anisotropy of the electron scattering or transport properties. In crystalline materials, AMR arises from the anisotropy of the electron scattering rate, which is influenced by the orientation of the magnetic field with respect to the crystal lattice [14, 16, 17]. As an example, a high electronic band coupling to crystal sites can lead to a stronger AMR response and itinerant electrons from higher energy bands typically contribute to the magnetic effects in AMR, resulting in a greater change in electrical resistance in LaAlO3/SrTiO3 (111) heterostructure [18]. On the other hand, in noncrystalline materials such as amorphous alloys, the AMR originates from the anisotropy of the electron transport properties. Researchers working on AMR seek to design heterostructures with specific properties that can enhance the AMR effect. One approach is to use materials with pronounced SOC and magnetocrystalline anisotropies. This can cause the anisotropies to manifest as anisotropic transport. In some cases, the magnetic field and weak magnetic moments of the canted AFM phase can couple together, resulting in

#### *Unraveling the Extraordinary Anisotropic Magnetoresistance in Antiferromagnetic… DOI: http://dx.doi.org/10.5772/intechopen.112252*

emergent magnetic and topological properties in oxide heterostructures. For example, 3d-5d oxide heterostructures such as epitaxial superlattices (SLs) of iridium oxides (Ca/SrIrO3)/SrTiO3 and manganite/iridate SLs, have been found to exhibit large atomic SOC and electron-correlation-dominated AMR [19]. Furthermore, currentdependent AMR and MR offer an opportunity to explore momentum-dependent scattering to elucidate the role of Rashba SOC. The Rashba SOC introduces spin splitting along the momentum axis, whereas atomic SOC does not [20]. However, a few research groups have proposed that besides the atomic SOC, the Rashba SOC also plays an important role in the AMR in transport. The primary focus of AMR research is to design and develop new materials and heterostructures that can exhibit enhanced and tunable anisotropic transport properties for use in advanced electronic devices.

The nonmagnetic ground state of iridium (Ir) pseudospin moments in SrIrO3 and CaIrO3 is determined by the interplay between SOC and electron correlations (U). The value of U, which represents the strength of the Coulomb interaction between electrons, affects the electronic and magnetic properties of the system. When U is large, the system tends to favor a Mott insulating state, which is characterized by the localization of electrons due to strong Coulomb repulsion. On the other hand, when U is small, the system can exhibit metallic behavior. In epitaxial thin films, the dimensionality of the system can be tuned by controlling the thickness of the film. It has been found that reducing the dimensionality in epitaxial thin films can increase U and induce pseudospin-based emergent magnetism in SrIrO3 and CaIrO3 [21–24]. This emergent magnetism arises from the system's delicate balance between SOC and U. In a low-bandwidth SL, i.e., CaIrO3/SrTiO3, the AMR effect is attributed to a combination of different factors including in-plane biaxial magnetic anisotropy, magnetoelastic coupling, and interlayer exchange coupling based on tilted oxygen octahedra with glazer notation (aac+ ) across the constituent layers [19, 25, 26]. Despite the concerted efforts to enhance the AMR effect in 3d-5d heterostructures, the maximum amplitude of the fourfold AMR signal is still limited to 1%. This limitation highlights the need for the development of new strategies for enhancing the AMR effect, such as the careful selection of constituent materials and the optimization of heterostructure architecture to get a larger AMR effect. This study shows that by coupling the CaIrO3 with a severely distorted canted AFM manganite CaMnO3 and using the same sense of (aac+ ) oxygen octahedra tilts, the AMR can be increased by more than one order of magnitude which is about 20%. This increase is mainly generated due to the interlayer coupling of the CaMnO3/CaIrO3 layer. Additionally, the spin-flop transition in a nearly Mott region triggers an additional two-order of AMR amplitude along with a four-fold symmetry component. By combining these two effects, an exceptional AMR of 70% has been achieved, surpassing the previous record by two orders of magnitude. The study also shows controls and other unique facets related to these effects. The study demonstrates that thin films of canted AFM phases of CaMnO3 and CaIrO3 exhibit dimensionality control, with a diminishing magnetic moment. The M-T curve shows a signature of a magnetic transition occurring around 70–100 K, representing an AFM phase transition in the CaMnO3/CaIrO3 SLs. The valence state can be altered at interfaces in SLs involving manganites, resulting in emergent magnetic phenomena through the transfer of charge. Research conducted on CaRuO3/CaMnO3 SLs has revealed that electron leakage into the CaMnO3 layer decreases exponentially from the interface to the bulk of the layer [27]. From the exchange bias data of CaMnO3/CaIrO3 SLs, it is clear that a charge transfer from the CaIrO3 to CaMnO3 layer near the interface develops FM and AFM phases at the interface and bulk of CaMnO3 layers, respectively.

#### **2. Experimental section**

#### **2.1 Sample synthesis and structural characterizations**

Pulsed laser deposition (PLD) is a valuable experimental technique in condensed matter physics for investigating interface properties [27, 28]. Creating a well-defined interface and high-quality thin film is essential, and PLD involves laser ablation of target material, plasma plume dynamics, and nucleation and growth of atoms on the substrate surface. Laser energy selection is critical based on the ablation threshold energy of bulk materials, and a KrF excimer laser with a wavelength of 240 nm is commonly used in lab experiments. The gas pressure is used to control plume dynamics and reduce its energy, resulting in a dense and unidirectional plume. The nucleation of atoms on the substrate is a crucial step in crystal formation, and the suitable combination of laser energy, gas pressure, and substrate temperature determines the mobility of surface atoms. Oxygen gas is supplied inside the PLD chamber from an external cylinder via an inlet to produce an oxide film, and different growth mechanisms, depending on the mobility of surface atoms and surface smoothness, occur on the surface (**Figure 1**).

Reflection high energy electron diffraction (RHEED) technology is used to study the growth mechanism, providing valuable information about the surface morphology and structure. RHEED enables the monitoring of various types of growth such as layer-by-layer (2D) growth and island (3D) growth. The process involves nucleation and growth of atoms on the substrate surface which can be visualized using the RHEED set-up. High-pressure RHEED has been developed to monitor surface structure during oxide deposition at higher pressures, opening up new possibilities for material synthesis. To obtain the atomically sharp TiO2-terminated surface which is essential for layer-by-layer growth, the substrates were treated in deionized water and buffered NH4F-HF (BHF) solution [30], followed by thermal annealing at 960°C for 1.5 hours. The SLs were grown on a substrate maintained at a temperature of 730°C and under an oxygen partial pressure of 6 Pa. Subsequently, the samples underwent a post-annealing process at identical temperature and pressure conditions for a duration of 30 minutes. The thickness of the SLs was precisely controlled and monitored by using in-situ RHEED. The high structural quality of the SLs was examined in detail by

#### **Figure 1.**

*Pulsed laser interval deposition [29]. (a) How the oscillation intensity changes with the increasing number of laser shots and the formation of each layer represented by one complete oscillation. (b) RHEED specular spot intensity and its surface plot in X-Y coordinates.*

*Unraveling the Extraordinary Anisotropic Magnetoresistance in Antiferromagnetic… DOI: http://dx.doi.org/10.5772/intechopen.112252*

**Figure 2.**

*(a, b) Scan of θ-2θ and X-ray reflectivity for (MIxy)z with x = y = 2–4, (MI22)10, (MI33)5, (MI44)5, and (MI84)5 SLs. (c) Cross-sectional HAADF-STEM image that exhibits the atomic level resolution of CaMnO3 and CaIrO3 layers in the (MI84)5 SLs is shown. (Reprinted from [14] © 2023 American Physical Society).*

performing room temperature X-ray diffraction (XRD) scans using a PANalytical X'pert Pro diffractometer. Finally, the thickness of the SLs was confirmed by using X-ray reflectivity (XRR).

The samples are CaMnO3/CaIrO3 SLs with different configurations based on the periods of constituent layers. The SLs are coded as (MIxy)z, where M and I refer to CaMnO3 and CaIrO3 layers, respectively. The value of 'x' and 'y' represents the period or unit cell (u.c.) of the CaMnO3 and CaIrO3 layers, respectively, and 'z' represents the number of repetitions. The article discusses the structural properties and variations in AMR of CaMnO3/CaIrO3 SLs. The samples are categorized based on the period of constituent layers as (I) The first category involves the simultaneous variation of CaMnO3 and CaIrO3 u.c., with samples including (MIxy)z for x = y = 2–4, and (MI84)5 with a larger CaMnO3 period; (II) The second category involves the control of AMR by fixing CaIrO3 period while varying the CaMnO3 period, with samples (MIx2)5 for x = 2,4,6,8 and (MIx4)5 for x = 2,4,6; (III) The third category involves keeping the CaMnO3 period fixed and varying the CaIrO3 period, with samples (MI2y)z for y = 2,4,5 and (MI5y)z for y = 2,5,8. The SLs were formed by using a pulsed interval deposition technique and analyzed by using XRD and HAADF-STEM. In **Figure 1(a)**, the synthesis of (MI82)5 SL is shown, where one complete oscillation represents the formation of one u.c. Additionally, the Gaussian pattern of the specular spot intensity after finishing the deposition confirms sharp, layer-by-layer growth, as shown in **Figure 1(b)**. **Figure 2 (a)** and **(b)** provide XRD and XRR data, respectively, for the primary series and higher periodic SL, i.e., (MI84)5 SL. Also, **Figure 2 (c)** shows HAADF-STEM data for (MI84)5 SL. These data offer insights into the crystal structure, periodicity, and interface quality of the SLs.

#### **2.2 Investigating magnetic-properties of interface**

#### *2.2.1 Magnetization measurements, X-ray absorption study, and understanding charge transfer and spin canting mechanism across CaMnO3/CaIrO3 Heterointerface*

The magnetization (M) versus temperature (T) and magnetic field (H) data of (MIxy)z SLs with x = y = 2–4 are plotted in **Figure 3 (a)** and **(b)**. As the number of periods increases, there is a noticeable decrease in both the magnetic transition

#### **Figure 3.**

*Displays (a) the temperature (T), (b) field (H) dependence of magnetization (M), and (c) the strength of the exchange bias field (HEB) for (MIxy) SLs with varying stacking of CaMnO3 and CaIrO3 layers. X-ray absorption spectra around (d) the Mn L2,3 edge (TEY modes) and (e) Ir L3 edge (FY modes) are also presented for (MIxy)z SLs, where the insets show a comparison of the (MI25)5 SL with the IrO2 sample. (f) a schematic illustration is shown, demonstrating the spin canting in the CaIrO3 and CaMnO3 layers. CaIrO3 and CaMnO3 layers are organized into BO6 planes that are arranged in the ab plane and stacked along [001]. To simplify the explanation, a top-down view of the canted moments and net magnetic moment is shown along two in-plane directions, namely [010] and [100], with respect to the pseudocubic STO (100) substrate. The length of the arrows showing the net magnetic moment does not represent the relative size of the magnetic moment in CaIrO3 or CaMnO3 layers. (Reprinted from [14] © 2023 American Physical Society).*

temperature (Tc) and the saturation magnetic moment (Msat), as depicted in **Figure 3**. For example, the (MI22)10 SL exhibits Tc of approximately 100 K, while the Tc decreases to approximately 60 K for (MI44)5 SL and vanishes for the higher periodic (MI84)5 SL. This trend suggests that the magnetic properties of the SLs are strongly influenced by the periodicity of the constituent layers, with larger periods leading to weaker magnetism. The M-H data in **Figure 3 (b)** shows a saturation magnetic moment (Msat) of approximately 0.4 μB/f.u. for (MI22)10 SL, which value is consistent with the reported canted AFM state in CaIrO3/CaMnO3 heterostructures [31]. To further investigate the magnetic properties of the SLs, the exchange-bias fields (HEB) were measured by performing field-cooled M-H measurements, as shown in **Figure 3(c)**.

The interfacial charge transfer and electronic structure near the Fermi level were examined using x-ray absorption spectroscopy (XAS) at both the Mn and Ir L-edges. The spin-orbit coupled states are obtained in the spectra containing two features, the L3(2p3/2) and L2(2p1/2) edges, respectively, in Mn 2p core hole, as shown in **Figure 3 (d)**. A clear shift of the L3 edge of the spectra towards lower energy with respect to the other samples was observed in the (MI25)5 SL, indicating the presence of Mn3+ ions, which were likely formed by the transfer of charge from the Ir to the Mn at the interface. This shift was evident in both the surface-sensitive total electron yield

#### *Unraveling the Extraordinary Anisotropic Magnetoresistance in Antiferromagnetic… DOI: http://dx.doi.org/10.5772/intechopen.112252*

(TEY) and bulk-sensitive fluorescence yield (FY) mode for Mn-edge and Ir-edge spectra, respectively, as shown in **Figure 3(d, e)** and **4**. Thinner CaMnO3 layers in SLs receive a larger fraction of electrons, causing a larger shift in the Mn edge for (MI25)5 with 2 u.c. of CaMnO3 period compared to SLs with thicker CaMnO3 layers compared to CaIrO3, as shown in **Figure 3 (d)**. Additionally, the larger thickness/volume of CaIrO3 in (MI25)5 SL will transfer a larger number of electrons to CaMnO3. The observed minimal shift in the Ir edge, as shown in **Figures 3(e)** and **4**, suggests that the Ir4+ state is highly stable, and only a small amount of charge transfer occurs across the interface. Therefore, the remaining change in the Mn valency is assumed to arise from vacancies in the manganese layer. Approximately, 0.1 hole/electrons per Ir/Mn ion are transferred at CaMnO3/CaIrO3 interfaces for the (MI82)5 SL, while the remainder of the change in the Mn valence is due to vacancies in the manganese layer and, also, the charge transfer is sensitive to the constituent layer thickness, with a maximum of approximately 0.25 hole/electron per Ir/Mn ion transferred for the (MI25)5 SL, as shown in the table-**I**. It is observed from the table that there is charge transfer from Ir to Mn assuming a valency range of 3.8–3.95 for the bare CaMnO3 layer. As the CaIrO3 layer thickness increases and becomes comparable with CaMnO3 layer thickness, such as in MI25, MI44, and MI42 samples, the fraction of charge transfer increases, contributing to the larger conductivity and number of carriers available for charge-transfer in thicker CaIrO3 layers. This is evident in the comparison between MI25 and MI62 samples (**Table 1**).

#### **Figure 4.**

*XAS spectra around the Mn L2,3 edges for [(CaMnO3)x/(CaIrO3)y)]z measured in the (a) TEY and (b) TFY modes. XAS spectra of the Ir L2,3-edges for [(CMOx/CIOy)]z measured in the fluorescence yield modes. Insets depict the comparison view of [(CaMnO3)2/(CaIrO3)5)]5 with the reference IrO2 sample. (Reprinted from [14] © 2023 American Physical Society).*

#### **Table 1.**

*Charge transfer across CaMnO3/CaIrO3 interface.*

The charge transfer between CaIrO3 and CaMnO3 layers depends on the volume or the number of available carriers in CaIrO3 and the number of CaMnO3 layers. Due to the vacant 'eg' orbital near the Fermi level, CaMnO3 with a distorted lattice exhibits a significant attraction towards electrons. In another study on Ce4+ � doped CaMnO3, even a small electron doping induced canting of the AFM lattice resulting in a significant increase in magnetic moments [32]. Leakage of electrons into CaMnO3 decay exponentially from the interface to the bulk of the layer in CaRuO3/CaMnO3 SLs [27, 33]. The interface layer receives the maximum charge density, inducing a double-exchange governed FM phase or a largely canted AFM phase at the CaMnO3 interface layer. The deeper CaMnO3 layer tends to remain AFM. The formation of a magnetic gradient across the CaMnO3 layer is well supported by both theory and experiments [33]. The HEB is the signature of FM and AFM phases across the interface. As depicted in **Figure 3(c)**, the (MI22)10, (MI33)5, (MI44)5, and (MI84)5 SLs display HEB of 3, 15, 50, and 35 Oe, respectively. To achieve a higher HEB, a virtual arrangement of the FM/AFM interface is necessary, which is absent in the first SL since its CaMnO3 layers are only present at the interface. However, in the latter three SLs, the CaMnO3 layer thickness increases along with the FM interface, resulting in the manifestation of HEB which increases with the thickness of the CaMnO3 layer. This result can be used to look for the formation of such magnetic gradients also where the AFM state apart from the interface remains unchanged for both CaIrO3 and CaMnO3.

#### **2.3 Study on anisotropic magnetoresistance (AMR)**

#### *2.3.1 ϕ-AMR in (MIxy)z (x = y = 2: 4)*

The AMR, also referred to as angular dependent magnetoresistance, was measured in three different senses of rotations of the SLs with respect to the magnetic field, as shown in **Figure 5(a)**, and is calculated as

$$\text{AMR} = \frac{\rho[\text{B } (angle)] - \rho[\text{B } (angle = 90^{\circ})]}{\rho[\text{B } (angle = 90^{\circ})]} \tag{1}$$

Where 'angle' represents the angle between the magnetic field and the current direction.

In **Figure 5 (a)**, H rotates in the xy, yz, and zx planes while three rotation angles, namely ϕ, θ, and γ, are depicted. Additionally, the current direction is along the (100) axis of the sample. **Figure 5 (b**-**f)** depicts the magnetic and electrical behavior of (MIxy)z (x = y = 2–4), which can be explained by the enhancement of 'U' induced by dimensionality and the charge transfers. All SLs demonstrate diminishing AMR in the range of 70–100 K which is the same as the magnetic transition temperature (Tc) of the SLs. The sheet resistance was also measured, and it was found to increase with decreasing CaIrO3 period, as shown in **Figure 5 (b)**. The Mott state is characterized by a sudden increase in resistivity below 50 K. As the CaIrO3 period decreases, the sheet resistance increases and the resistance of a 10 nm CaIrO3 film is clearly distinct from the other SLs. In particular, (MI22)10 tends to exhibit a Mott-type state below 30 K. These SLs' emergent magnetic and transport properties are related to their AMR, which will be discussed further below. Now, it is important to investigate AMR properties of several 3d-5d SLs including (MI22)10, (MI33)5, (MI44)5, and (MI84)5 as *Unraveling the Extraordinary Anisotropic Magnetoresistance in Antiferromagnetic… DOI: http://dx.doi.org/10.5772/intechopen.112252*

#### **Figure 5.**

*(a) Three different rotational geometries schematically illustrating the measurements of AMR. (b) The impact of extended CaMnO3 and CaIrO3 periods on the sheet resistance was examined by plotting the temperaturedependent behavior of (MIxy)z (x = y = 2–4) SL and (MI84)5 SL. (c) Polar plots comparing the ϕ, θ, and γ AMRs are presented for (MI22)10 and (d) (MI33)5 SL. (e) The variation in ϕ-AMR at 30 K is demonstrated for both (MIxy)z (x = y = 2–4) and (MI84)5 SL. (f) The variation in the ϕ-AMR amplitude as a function of temperature for H = 9 T is shown. (Reprinted from [14] © 2023 American Physical Society).*

a function of temperature, magnetic field, and period of SLs. The AMR measurements reveal that the ϕ-AMR exhibits four-fold sinusoidal oscillations for both (MI22)10 and (MI33)5, with a subtle two-fold component superimposed on a dominant four-fold component, shown in **Figure 5 (e)**. In **Figure 5 (f)**, the ϕ-AMR in (MI22)10 SL is particularly striking, exhibiting an astounding 70% amplitude at 10 K, which decreases to 23% at 20 K and gradually ceases to manifest at 100 K. This is the largest amplitude of four-fold ϕ-AMR reported not only for 3d-5d SLs but also for other oxide heterostructures. Furthermore, the ability to tune the ϕ-AMR by two orders of magnitude is demonstrated by varying the period of the SLs. The θ- and γ-AMRs, shown in **Figure 5 (c, d)**, also show a phenomenal amplitude of 15% for (MI22)10, which is much larger than observed for any 3d-5d SL. The AMR decreases with increasing temperature and completely disappears around the transition temperature in the range of 70–100 K for all samples. The ϕ-AMR observed in (MI22)10 SL, as shown in **Figure 5 (f)**, is exceptional because it is much larger than what has been reported in any 3d-5d heterostructures so far, and it is the largest among complex oxide heterostructures. Additionally, the ϕ-AMR reduces by one order of magnitude as the period (x = y) increases from 2 to 4. This sensitivity to the constituent layer thickness suggests the presence of a unique phenomenon that promotes interlayer coupling.

#### *2.3.2 The origin of the AMR*

One method for determining the origin of AMR is to compare the behavior of different types of AMRs and analyze their dependence with the magnetic field. In particular, the ϕ, θ, and γ AMRs have been studied extensively.

#### **3. Non-quadratic dependence of ϕ-AMR with field**

One observation that has been made is that none of the ϕ, θ, and γ AMRs follow a quadratic dependence on the magnetic field because ϕ-AMR does not vary linearly with B2 , as shown in **Figure 6**. These results rule out Lorentz scattering as the origin of the effect. Lorentz scattering is a mechanism in which the magnetic field causes the scattering of electrons, leading to a change in resistance [19]. Another observation that has been made is that the magnitude and phase of the θ and γ AMRs for the sample (MI22)10 are coincident. This eliminates the possibility of spin Hall MR or s-d scattering as the underlying mechanisms. Spin Hall MR is a mechanism in which the spin Hall effect causes a change in resistance, while s-d scattering is a mechanism in which the scattering of electrons between the spin-polarized d-band and s-band causes a change in resistance [34–37].

#### **3.1 Intra and interlayer coupling in ϕ-AMR for varying periodicity: (MIx2)z for x = 2, 4,6 and 8 and (MI2y)z for y = 2,4 and 5 SLs**

In the canted AFM phase of these SLs, interlayer coupling controls the domain scattering mechanism based on biaxial magnetic anisotropy, which is believed to be the underlying cause of the AMR. Domain scattering refers to the scattering of electrons as they pass through the domains (regions) with different magnetic orientations in a material. In this case, the domains are created by the canted AFM phase of the SLs, and the domain scattering is thought to be responsible for AMR observed in the material. The magnitude of interface coupling and the dimensions of the individual layers are determining factors in the strength of interlayer coupling. The magnetic interactions for intra- and interlayer bonds of neighboring iridium ions can be expressed in a common form [eq. (2)], with different coupling constants for inter- and intralayer bonds [38].

#### **Figure 6.**

*At various temperatures, the (MI22)10 and (MI33)5 SL display non-quadratic dependence of B as seen in the polar plots of ϕ, θ, and γ - AMRs presented. (Reprinted from [14] © 2023 American Physical Society).*

*Unraveling the Extraordinary Anisotropic Magnetoresistance in Antiferromagnetic… DOI: http://dx.doi.org/10.5772/intechopen.112252*

$$\mathbf{H}\_{\overrightarrow{\text{ij}}} = \mathbf{J}\_{\overrightarrow{\text{ij}}} \overrightarrow{\mathbf{S}}\_{\overrightarrow{\text{i}}} \overrightarrow{\mathbf{S}}\_{\overrightarrow{\text{j}}} + \mathbf{J}\_{\text{1c}} \overrightarrow{\mathbf{S}}\_{\overrightarrow{\text{i}}} \overrightarrow{\mathbf{S}}\_{\overrightarrow{\text{j}}} + \Gamma\_{\overrightarrow{\text{ij}}} \overrightarrow{\mathbf{S}}\_{\overrightarrow{\text{i}}}^{\texttt{z}} \overrightarrow{\mathbf{S}}\_{\overrightarrow{\text{j}}}^{\texttt{z}} + \overrightarrow{\mathbf{D}}\_{\overrightarrow{\text{ij}}} \overrightarrow{\left[\overrightarrow{\mathbf{S}}\_{\overrightarrow{\text{i}}} \times \overrightarrow{\mathbf{S}}\_{\overrightarrow{\text{j}}}\right]} \tag{2}$$

Where *Jij* is the in-plane isotropic Heisenberg exchange among pseudospin *S* ! *<sup>i</sup> and S*! *<sup>j</sup>*, and *J1c* represents the first interlayer interaction. In the case of 5d material, pseudospin is an entangled state of spin and orbital moment denoted as Jeff [39]. Γ*ij* represents symmetric exchange anisotropy that favors collinear c-axis spin order, and *D* ! *ij* whose direction is along the c-axis represents antisymmetric exchange anisotropy via Dzyaloshinskii-Moriya (DM) interaction that favors canting of in-plane spin order in the ab plane. Specifically, octahedral rotation and tetragonal distortion lead to symmetric and antisymmetric exchange anisotropy terms that are responsible for ϕ-AMR [38, 40]. This is due to the strong SOC that locks the staggered AFM pseudospins moments to the antiferrodistortive octahedral, and as a result, canted pseudospin as well as the net in-plane moment is obtained. To prevent the cancelation of canted moments, they must be aligned parallel to each other across the interlayer. The in-plane canted moments and their stability depend on the strength of interlayer AFM coupling as well. The Hamiltonian is originally proposed for layered Sr2IrO4 for explaining the strength of interlayer coupling between IrO2 layers separated by nonmagnetic SrO layer. In a different study, the theory of interlayer coupling is used to describe the magnetic properties of artificially synthesized SLs, i.e., SrIrO3/SrTiO3 [41]. Increasing the insulating SrTiO3 layer helps to reduce interlayer coupling and decrease magnetic transition temperature. The magnetic exchange interactions can be governed directly from one layer to another layer of the IrO2 plane separated by the SrO layer in Sr2IrO4 or can be governed by electron hopping through the SrTiO3 layer in SrIrO3/SrTiO3 SL. As the periodicity increases from (SrIrO3)1/ (SrTiO3)1 (1/1-SL) to (SrIrO3)1/(SrTiO3)2 (1/2-SL), the transition temperature is significantly reduced due to the decrease in interlayer exchange coupling. The insertion of additional insulating SrTiO3-blocking layers hinders the electronic hopping and exchange coupling along the c-axis, causing a decrease in interlayer coupling. Both Sr2IrO4 and 1/1-SL exhibit net magnetizations originating from the canting of the AFM moments within the IrO2 plane [22]. The coupling of LaNiO3 to the insulating FM LaMnO3 at the interface can lead to the stabilization of an induced AFM order in the [111] direction, which can generate interlayer AFM coupling between two LaMnO3 layers separated by 7 u.c of LaNiO3, as suggested by the authors in a separate study [21].

#### **3.2 CaMnO3 and CaIrO3 periodicity dependent AMR study in CaMnO3/CaIrO3 SLs**

In this section, we discuss a study conducted to understand further the role of individual layers in AMR. The study aims to determine the specific role of individual layers in achieving a large AMR in (CaIrO3)x/(CaMnO3)y SLs. The AMR of different sets of heterostructures is analyzed, and the results are presented in **Figure 7 (a**-**d)**.

i. (MIx2)5 for x = 4, 6, and 8 as (MI42)5, (MI62)5, and (MI82)5, with the CaIrO3 period fixed to 2 u.c.: The ϕ-AMR values of this series of SLs are plotted in **Figure 7(a)**. It is clear that, except for x = 2, the ϕ-AMR of all other SLs is in the range of 0.4–0.8%.

#### **Figure 7.**

*Exhibits the ϕ-AMR for (a) (MIx2)5 with x = 4, 6, and 8, and (b) (MIx4)5 with x = 2, 4, and 8, recorded at various temperatures with a 5 T magnetic field. Figures (c) and (d) display the ϕ-AMR for (MI2y)z with y = 4 and 5 and (MI5y)z with y = 2, 5, and 8, respectively, measured at different temperatures with a magnetic field of 5 T. (Reprinted from [14] © 2023 American Physical Society).*

*Unraveling the Extraordinary Anisotropic Magnetoresistance in Antiferromagnetic… DOI: http://dx.doi.org/10.5772/intechopen.112252*

> period increases. For (MI58)5, the AMR follows the behavior of a CaIrO3 film of the same thickness. The plot of the AMR data is given in **Figure 7(d)**.

v. It is found that the AMR of (MI58)5, having a large CaIrO3 period of 8 u.c., matches with that of a 10-nm-thick CaIrO3 film in terms of phase and amplitude.

The first three points suggest that a short CaMnO3 period contributes to a high AMR value when the CaIrO3 period is also small. However, when the maximum period of CaMnO3 and CaIrO3 in CaMnO3/CaIrO3 SLs is reached, the interlayer coupling necessary for biaxial anisotropy is lost, and the SL behaves like a single CaIrO3 film, as stated in the fifth point. SLs with a higher periodic thickness of CaMnO3 and CaIrO3, such as the (MI33)5 and (MI24)5 SLs, exhibit reduced octahedral distortion. As a result, these SLs demonstrate a decrease in AMR response compared to the (MI22)10 SL. This reduction results in a lower possibility of obtaining a net canted moment from each IrO2 plane, thereby reducing the AMR response of (MI33)5 and (MI24)5 SLs in comparison to the (MI22)10 SL. The AMR value of 1% for (MI24)5 and (MI52)5 SL confirms that the CaMnO3 and CaIrO3 periods have an equal impact on interlayer coupling in CaMnO3/CaIrO3 SLs. Therefore, in CaIrO3/ CaMnO3 SLs, the similarity of magnetic phase and structural distortion of (aac<sup>+</sup> ) type in low dimensions is a unique attribute and can be argued as a decisive factor for strong interlayer coupling. The structural distortion of both constituent layers in CaIrO3/CaMnO3 heterostructures contributes to a parallel interlayer alignment of moments, as shown in previous studies [19, 42]. This results in biaxial anisotropy and a large fourfold sinusoidal AMR in the heterostructures.

#### **3.3 Dynamics of ϕ-AMR in (MI22)z: Biaxial anisotropy and spin-flop transition**

The trough and crest of ϕ-AMR are assigned by the difference in scattering by soft (100) and hard (110) axes in (MI22)10 SL, a biaxial anisotropic system, as shown in **Figure 8 (a, b)**. There appears a transition from uneven scattering from (110) family of axes at 25 K to (100) axes at 14 K, as emphasized in **Figure 8 (c)**.

At 25 K, the stronger crest peaks at (110) and (1–10) axes suggest larger scattering compared to that at (110) and (1–10) peaks, despite the uniformity in scattering observed by the (100) family of axes, as shown in **Figure 8 (b, c)**. Similarly, at 14 K, crest peaks are uniform in magnitude whereas trough peaks are not uniform in magnitude. Hence, the ϕ-AMR in (MI22)10 SL deviates from regular four-fold sinusoidal symmetry. As scrutinized in very close temperature intervals in the range of 10–25 K, as shown in **Figure 8(c)**, as one moves from the (100) to the (110) crystal axes, a new superimposed feature in the form of a four-fold pattern of AMR kinks emerges alongside the underlying sinusoidal pattern. At 25 K, there is a clear and welldefined four-fold pattern of ϕ dependent AMR, but as the temperature decreases to 22 and 18 K, the pattern becomes more complex, with multiple kinks. Finally, at 15 K, the pattern reverts to a symmetric and sharp four-fold single kink configuration. The smooth pattern appears at 14 K which further transforms to a sharp step-like humungous amplitude of 70% at 10 K. The polarity of AMR peak amplitudes transforms for different fields, i.e., 9 and 5 T, as shown in **Figure 9 (a)**. This unprecedented ϕ-AMR is complex both in its pattern and amplitude. At 5 T, the smooth sinusoidal modulation of the ϕ-AMR displays a modest 10% increase, as shown in **Figure 9 (a)**. However, when the magnetic field is increased to 9 T, a remarkable metamagnetic

#### **Figure 8.**

*(a) The crystallographic in-plane directions for the (100) and (110) families are labeled as a, B, C, D, and A*<sup>0</sup> *, B*<sup>0</sup> *, C*<sup>0</sup> *, D*<sup>0</sup> *respectively. (b) The ϕ-AMR for (MI22)10 is shown at different temperatures between 25 K and 100 K with a magnetic field of 9 T. (c) The ϕ-AMR for (MI22)10 is displayed for the temperature range between 10 K and 22 K, showing a fourfold symmetry, and indicating the onset of the spin-flop transition at 22 K. (d) The field dependence of ϕ-AMR for (MI22)10 is presented at 15 K. (e) The spin arrangement in relation to the AMR is shown. The spins depicted in red and blue correspond to the two sublattices of the antiferromagnetic order. A subtle canting in AFM order at B = 0 is observed, which increases at a field of 9 T along the easy (100) axis (1 and 2), while the effect is less pronounced when B is applied along the (110) hard axis (panel 3). For B = 9 T along (010), the spin-flop arrangement at 10 K is depicted in the last panel (panel 4). (Reprinted from [14] © 2023 American Physical Society).*

transition occurs, which is responsible for generating a substantial 70% step-like AMR. This transition is identified as a spin-flop transition [43] since the trough of the ϕ-AMR at 5 T coincides with the crest at 9 T. By comparing the ϕ-AMR at these two fields, it is clear that there is an abrupt drop in resistance at 9 T when the sinusoidal ϕ-AMR peak starts appearing at 5 T, as shown in **Figure 9 (a)**. These observations establish that the spin-flop metamagnetic transition is responsible for the enormous ϕ-AMR at 9 T and 10 K. Magnetic-field dependence of ϕ-AMR was conducted at 15 and 25 K to investigate spin-flop-induced transition. **Figure 9 (b)** and **(c)** shows a kinklike transition indicative of the spin-flop transition only at 9 T and 15 K, absent at 25 K. Two primary phenomena are responsible for the diverse characteristics of the ϕ-AMR. Firstly, a robust biaxial magneto-crystalline anisotropy contributes to the sinusoidal ϕ-AMR, which can reach up to 20%. Secondly, the spin-flop transition induces kinkand step-like metamagnetic AMR of up to 70% at a maximum field of 9 T. To explain the anomalous AMR of CaIrO3/CaMnO3 SLs, a competition between pseudospin– lattice (S-L) coupling and field-pseudospin coupling is proposed. The S-L coupling in iridates is represented by Eq. (3) with the Hamiltonian Hs-ι [19, 38].

$$H\_{\mathfrak{r}-\mathfrak{r}} = \Gamma\_{(x^2-\mathfrak{r}^2)} \cdot \cos(2\mathfrak{a}) (\mathbb{S}\_i^x \, \mathbb{S}\_j^x - \mathbb{S}\_l^y \, \mathbb{S}\_j^y) + \Gamma\_{(xy)} \cdot \sin(2\mathfrak{a}) (\mathbb{S}\_i^x \, \mathbb{S}\_j^y + \mathbb{S}\_l^y \, \mathbb{S}\_j^x) \tag{3}$$

The energy scales of S-L coupling to the distortions along (100) and (110) are denoted by Γ *<sup>x</sup>*2�*y*<sup>2</sup> ð Þ and Γð Þ *xy* , respectively, while α represents the angle between the staggered moments and the (100) axis. As it is mentioned previously that AFM

*Unraveling the Extraordinary Anisotropic Magnetoresistance in Antiferromagnetic… DOI: http://dx.doi.org/10.5772/intechopen.112252*

#### **Figure 9.**

*Comparison of ϕ-AMR at T = 10 K for (MI22)10 reveals differences between measurements at 9 and 5 T. field dependence of ϕ-AMR for (MI22)10 is measured at 15 and 25 K. (Reprinted from [14] © 2023 American Physical Society).*

staggered pseudospins in ab plane are entangled to the antiferrodistortive octahedral via SOC, resulting canted pseudospin, hence, pseudospins have some special symmetric directions, i.e., *xy* and *<sup>x</sup>*<sup>2</sup> � *<sup>y</sup>*<sup>2</sup> quadruple symmetries. The competition between *xy* and *<sup>x</sup>*<sup>2</sup> � *<sup>y</sup>*<sup>2</sup> quadruple symmetries of pseudospins have two solutions: <sup>α</sup>=0 for Γ *<sup>x</sup>*2�*y*<sup>2</sup> ð Þ*<*Γð Þ *xy* and α=45° for Γ *<sup>x</sup>*2�*y*<sup>2</sup> ð Þ*>*Γð Þ *xy* .Sr2 IrO4 and an engineered SL, SrIrO3/ SrTiO3, both possess a similar magnetic structure and exhibit the former phenomenon, whereas the latter is observed in CaIrO3/SrTiO3 heterostructures. In both cases of SrIrO3 and Sr2IrO4, the ϕ-AMR phase lags by 45° compared with CaIrO3/CaMnO3 SL [19, 44]. In the case of CaIrO3/CaMnO3 SLs, the optimal solution is achieved at α=0 since the minimum of AMR oscillation aligns with the (100) axes, which is analogous to that of CaIrO3/SrTiO3 SLs. The difference in the phase lag between SrIrO3- and CaIrO3-based 3d-5d SLs is due to the different sense of octahedral rotations in their low-dimensiona limits (**Figure 10**).

#### **Figure 10.**

*Temperature dependence of the ϕ-AMR amplitude for (MIxy)z SLs at H = 5 T. (Reprinted from [14] © 2023 American Physical Society).*

#### **3.4 Temperature dependence of ϕ-AMR in the context of magneto-elastic coupling**

The behavior of solid-state materials in the vicinity of a magnetic transition is a complex and fascinating area of research. At such points, the coupling between the spin and lattice degrees of freedom, known as S-L coupling, plays a critical role, and its strength changes as the temperature decreases [38, 45]. One of the most striking manifestations of S-L coupling is the appearance of a sinusoidal ϕ-AMR due to the continuous lattice deformation under the influence of an external magnetic field. There are two ways in which S-L coupling can occur in CaMnO3/CaIrO3 SLs, namely, the coupling of pseudospins with octahedral distortion and the response of pseudospins to lattice vibrations or phonons that vary with temperature. It is noteworthy that the structural transition responsible for octahedral deformations has not been reported yet in layered systems, i.e., SrIrO3/SrTiO3 or CaIrO3/SrTiO3 SL.

As the temperature changes, the strength of S-L coupling can be described in two regimes based on the magnetic moment of the layered system. (i) In lower magnetic moment-based SLs such as (MIx2)5 (x = 4, 5, 8), the anisotropic scattering of electrons due to the orbital degree of freedom via lattice vibration is more prominent near the transition temperature, leading to strong pseudospin-lattice coupling. At lower temperatures, however, due to the stiffness of the lattice, the response of pseudospins with the lattice is low, and AMR is expected to be governed by field-pseudospin coupling only. (ii) In higher magnetic moment-based SL such as (MI22)10, at a temperature of 10 K, the (MI22)10 SL exhibits a sharp four-fold single kink separated by 90° with no sinusoidal variation observed in its ϕ-AMR. This suggests that the orbital degree of freedom of electrons contributed by lattice vibration is suppressed at this temperature, and the step-like AMR pattern in (MI22)10 SL is a result of fieldpseudospin coupling, facilitated by higher magnetic moment. In contrast, the absence of the kink pattern in (MIx2)5 (x = 4, 5, 8) represents the absence of fieldpseudospin coupling. Thus, the AMR mechanism in (MIx2)5 (x = 4, 5, 8) SLs is mainly governed by orthorhombic distortion through S-L coupling restoring the sinusoidal resistance [22].

Furthermore, it is noteworthy that the sinusoidal ϕ-AMR pattern with a kink observed in the temperature range of 15 to 22 K in the (MI22)10 SL indicates the coexistence of both S-L coupling and field pseudospin coupling. Additionally, in the cases of both (MI22)10 and (MI33)5 SLs, the amplitude of ϕ-AMR steadily increases with decreasing temperature. This suggests that the competition between these two couplings, which varies with temperature, ultimately determines the ϕ-AMR behavior in the (MI22)10 SL. Specifically, at high temperatures, the S-L coupling is responsible for the reorientation of moments, whereas at lower temperatures when the lattice is rigid but the moments are larger, the direct coupling of field pseudospin dominates.

#### **3.5 Metamagnetic transitions in perovskite manganites and iridates**

Metamagnetic transitions are a fascinating phenomenon that has been observed in a variety of materials including manganites and iridates. Over the past few decades, much attention has been focused on the ABO3 perovskite-type mixed valent manganites which have the general formula, i.e., R1-*x*A*x*MnO3, where 'R' represents a trivalent rare-earth cation and 'A' represents a divalent cation [46]. These materials have been extensively studied due to their intriguing properties arising from the interplay between the charge-orbital coupling. One of the most interesting features of these

*Unraveling the Extraordinary Anisotropic Magnetoresistance in Antiferromagnetic… DOI: http://dx.doi.org/10.5772/intechopen.112252*

compounds is the colossal magnetoresistance phase that emerges due to the interplay between charge and orbital ordering. The evolution of different magnetic ground states is also observed in these compounds as the value of '*x*' varies from 0 to 1. For instance, in Nd1*-x*Sr*x*MnO3, the magnetic phase transitions from FM metallic state to a C-type insulating phase as '*x*' increases from 0.3 to 0.8, via an A-type AFM metallic phase with a ferromagnetic plane featuring uniform dð*x*2�*y*2Þ-type orbital order. In another material, Pr1*-x*Ca*x*MnO3, a transition from a charge-orbital ordered AFM-CE type insulating state to FM metallic state is observed as the temperature decreases in the presence of an external magnetic field. Moreover, a larger field of 27 T is required to destabilize the charge-ordered insulating state via a metamagnetic transition at low temperatures in the half-doped Pr1*-x*Ca*x*MnO3 (*x* = 0.5) material [46, 47]. These results indicate that mixed valent manganites exhibit strong spin-charge-orbitallattice coupling, resulting in the field-induced metamagnetic transition [48]. More recently, materials based on late transition metal ions with strong SOC have come into focus. These compounds no longer treat spin-orbital separation as a separate entity that requires magnetism to be reformulated using pseudospin. Spin-flop-based metamagnetic transitions, which are the result of spin-lattice coupling, have been observed in these materials [45, 49]. As an example, the theoretical basis for the spinflop transition lies in the stronger interlayer coupling that varies from Sr2IrO4 to Sr3Ir2O7. Overall, the occurrence of metamagnetic transitions in manganites and iridates, as well as the diverse phenomena associated with these transitions, highlight the complex interplay between charge, orbital, and spin degrees of freedom in these materials.

#### *3.5.1 Metamagnetic transition in thin-film*

Obtaining a spin-flop transition in thin films can pose a significant challenge due to the reduced thickness of the film. However, in a thin film, the magnetic moments are often constrained by the surface and interface effects as well as defects [48, 50–53]. These effects can create a preferential orientation for the magnetic moments, hindering their ability to rotate easily in response to an external magnetic field. It is crucial to have a strong SOC effect to effectively leverage large magnetoresistance anisotropy. However, if the magnetic moments are aligned along an easy axis that is perpendicular to the film plane, it becomes quite challenging to rotate them away from this easy axis and towards the basal plane. As a result, utilizing TAMR effects may be impossible. On the other hand, in Mn2Au, the magnetic moments are oriented in the basal plane of the structure. This makes it relatively easy to rotate them from one easy in-plane direction to another with the aid of a relatively small external excitation [54]. Defects and imperfections in thin films can also have a considerable impact on the spin-flop transition based on the rotation of spin [55]. These defects can act as pinning sites for the magnetic moments, impeding their motion. Thus, a sharp interface is essential for achieving a spin-flop transition. Careful consideration of the film thickness, interface effects, shape anisotropy, and defects, among other factors, is necessary to optimize the magnetic properties and achieve the desired behaviors. The resistance oscillations in the current CaIrO3/CaMnO3 SLs stem from a magnetic moment that oscillates with respect to the crystallographic axis embedded in a system with in-plane biaxial magnetic anisotropy. Along with these oscillations, there are sharp kink- and steplike transitions that induce an additional large component ϕ-AMR and originate from spin-flop metamagnetic transition. In **Figure 8 (e)**, there is a depiction of a

pseudospin arrangement that corresponds to the crest and trough of the spin-flopbased AMR. When a field of 9 T is applied along the (100) easy axis, the canting angle and magnetic moment increase. The canting effect is less pronounced when the field is applied along the (110) hard axes, where the AFM spin arrangement is rotated along the direction of the field. When the magnetic moments are tilted at larger angles along the (100) and (010) directions, the material shows less resistance to the flow of electric current compared to when the magnetic moments are tilted along the (110) direction. Additionally, **Figure 8 (e)** illustrates a spin-flop transition that occurs at 10 K in a field of 9 T.

#### **4. Conclusion**

Ultimately, it should be highlighted that the selection of a suitable 3d compound is crucial for achieving efficient interlayer coupling and distortion, which are necessary to adjust a significant ϕ-AMR. In the case of CaIrO3/SrTiO3 SLs, the CaIrO3 layers with distorted (a˗˗a˗˗c+ ) octahedral as per Glazer notations convey this distortion between them via distortion of the mediating SrTiO3 layer octahedra, only for one layer thickness of the latter [19]. In present CaIrO3/CaMnO3 SLs, in contrast, the presence of AMR in (MI82)5 SL, 8 u.c.s thick CaMnO3 mediating SL, suggests that CaMnO3 is the most suitable candidate known so far to promote interlayer exchange coupling. Here, the coupling is such long-range that the CaIrO3 layers separated by even eight u.c.s of CaMnO3 in (MI82)5 SL are capable of inducing a ϕ-AMR of 0.25% at 5 T and 50 K. The reason for this is that when few unit cells are considered, both CaMnO3 and CaIrO3 films exhibit orthorhombic distortion with the same octahedral rotation pattern (a˗˗a˗˗c+ ) according to Glazer's notations. Moreover, they also share a similar in-plane DM-type canted AFM phase. This similarity of distortion of both the constituents is key for phenomenal CaIrO3 interlayer coupling, and, hence, a large biaxial anisotropy is obtained. The presence of a stronger HEB, as observed in (MI44)5 and (MI84)5, leads to the formation of a graded AFM/FM phase within the CaMnO3 layer, which acts as a hindrance to a uniform interlayer coupling of CaIrO3. The impact is evident in the comparison between (MI22)10, which has an AMR of 23% in the absence of HEB, and (MI33)5, which has a moderate HEB and a reduced AMR of just 3%.

The CaIrO3/CaMnO3 SLs prove to be the most potent 3d-5d heterostructures for achieving an unprecedented AMR of about 70%, utilizing two key factors of a strong biaxial anisotropy and a spin-flop metamagnetic transition. On the fundamental side, employing the tolerance factor to appropriately manage the structural and surface layer construction of a large bi-axial magnetic anisotropy, fine-tuning the interlayer coupling facilitated by an exceptionally thick layer, and showcasing the spin-flop transition to enhance the degree of anisotropic AMR are all significant advancements in the realm of 3d-5d SLs. These developments hold immense promise in the field of contemporary quantum materials and their application in technological advancements. This proof-of-concept study opens new avenues for designing highly sensitive AMR readout devices for emerging AFM spintronics.

#### **Acknowledgements**

The authors extend their gratitude to several organizations for their financial support and provision of research facilities. Specifically, D.S.R. expresses thanks to the Department of Science and Technology (DST) Nanomission and the Science and

*Unraveling the Extraordinary Anisotropic Magnetoresistance in Antiferromagnetic… DOI: http://dx.doi.org/10.5772/intechopen.112252*

Engineering Research Board Technology, New Delhi for their financial support through Research Project No. SM/NM/NS-84/2016 and Project No. CRG/2020/ 002338, respectively. XAS measurements were performed at UC San Diego as part of a search for materials for spin-torque oscillators, which was supported by Quantum Materials for Energy Efficient Neuromorphic Computing, an Energy Frontier Research Center funded by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences under Award No. DE-SC0019273. Also, Resources for this research were made available through the Advanced Photon Source, which is operated by Argonne National Laboratory for the DOE Office of Science under Contract No. DE-AC02-06CH11357, with supplementary support from the National Science Foundation under Grant No. DMR-0703406. The authors also acknowledge the DOE Office of Science for supporting extraordinary facility operations through the National Virtual Biotechnology Laboratory. The authors express their appreciation to various individuals for their assistance in performing magnetization, transport, and x-ray diffraction characterizations, as well as in the preparation of transmission electron microscopy specimens. Finally, the authors express their gratitude for the utilization of the HZDR Ion Beam Center TEM facilities and the financial support provided by the German Federal Ministry of Education and Research (Grant No. 03SF0451) through the Helmholtz Energy Materials Characterization Platform for the funding of TEM Talos.

### **Author details**

Suman Sardar Department of Physics, Garhbeta College, India

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[50] Veremchuk I et al. Defect nanostructure and its impact on magnetism of α-Cr2O3 thin films. Small. 2022;**18**:1-10

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#### **Chapter 6**

## Growth and Interfacial Emergent Properties of Complex Oxide Thin Film Heterostructures

*Snehal Mandal*

#### **Abstract**

Non-trivial/chiral spin textures like skyrmions originate from inversion symmetry breaking. Moreover, inversion symmetry breaking combined with strong spin-orbit coupling (SOC) can lead to a large Dzyaloshinskii-Moriya interaction (DMI). Electrically, these phenomena can be detected through what is called the topological Hall effect (THE). In artificially layered complex oxide thin film heterostructures composed of ferromagnetic or antiferromagnetic layers, this THE appears as an emergent property at the interfaces because it is not intrinsic to the bulk layer of such oxides. Thus these heterostructures provide a playground for the competition among DMI, exchange interaction, and magnetic anisotropy to produce novel non-coplanar spin textures and THE in a designable way due to inversion symmetry breaking at the interfaces. With the advancement in modern fabrication techniques, these properties can be tuned at will by engineering the interfaces of the heterostructures, especially due to crystal structure compatibility of these materials. In this chapter, growth, detection and manipulation of interfacial emergent phenomena in complex oxide heterostructures will be discussed.

**Keywords:** complex oxide heterostructures, interfaces, magnetism, topological Hall effect, Dzyaloshinskii-Moriya interaction

#### **1. Introduction**

Magnetism and magnetic materials lie at the heart of all the electronic storage devices that we all know of (like, magnetic random access memory (MRAM), harddisk drives (HDD), pen-drives). However, the ever-shrinking dimensions and everincreasing demands in the storage areal density limit the data transfer rate in the present-day magnetic materials based devices.

Magnetic skyrmions (or simply, skyrmions), which are nanoscale swirling or chiral spin textures arising out of non-trivial real-space topology, are argued to have the potential to be the basis for next-generation magnetic storage devices. Because of the topological protection, these spin textures cannot be unwound without forming a discontinuity, providing them with high stability against external perturbations, even at small sizes. Along with skyrmions, there are other various chiral topological

textures that are stabilized due to various magnetic interactions and can be classified by their unique topological properties. The basic requirement for such textures is to have strong spin-orbit coupling (SOC) along with inversion symmetry breaking, which gives rise to Dzyaloshinskii-Moriya interaction (DMI) [1, 2]. Interestingly, this DMI shows up as an anomalous topological contribution to the Hall effect, which thus is called the topological Hall effect (THE), and provides a tell-tale sign of the existence of chiral textures. Although many direct imaging techniques have been developed over the last few years, electrical detection by means of THE has also become a promising technique.

To harness topological textures practically, it is important to develop materials that can stabilize these textures across a wide range of temperatures, and develop allelectrical pathways to manipulate them. A large family of topological textures and control mechanisms have been discovered in magnetic metal-based heterostructures, or chiral magnets such as Heusler compounds [3] and *B*<sup>20</sup> systems [4, 5], making them favorites for developing skyrmionics. However, to no wonder, in nature only a few bulk materials have crystal structures that intrinsically aids to the formation of skyrmions. One way out is to design systems in such a manner that these phenomena can "emerge" due to some new interactions, which otherwise are absent in the bulk. Thin films offer this extra space where one can utilize the interfaces and surfaces to modify/tune the interactions separately from their bulk counterparts. Most often, these phenomena emerge at or near the surfaces/interfaces of thin films/ heterostructures that are designed at will; due to which they are called "interfacial emergent phenomena".

Correlated oxide magnets have sparked great attention because they provide the following specific advantages: **(i)** They host myriad of phases (like, magnetic, multiferroic, *etc.*) due to strong correlations among various degrees-of-freedom (*i.e.*, charge, spin, orbital and lattice), which are quite susceptible to external perturbations. These couplings provide innovative practical avenues for controlling both intrinsic and emergent magnetic characteristics, such as anisotropy, symmetric exchange interactions, and DMI [6]. **(ii)** Because of their lower and configurable charge carrier densities, oxides are very responsive to electric fields, making them excellent candidates for non-volatile control. **(iii)** Additionally, using standard growth techniques, high-quality crystalline oxide thin films with carefully regulated interfaces and/or surfaces and heterostructures thereof, permitting spatial inversion symmetry breaking (with extremely low defects), can be fabricated at will. This chapter focuses on the two key proponents in the field of oxide skyrmionics: the creation of oxide heterostructures and detection and tuning mechanisms, which might set the course for practical oxide-based devices.

We start with a brief discussion on the basic physical interactions that can generate non-collinear or chiral spin textures, followed by their notions in electrical/ magnetotransport properties. As a prelude to the electrical detection of such interactions/spin textures, we then discuss the various types of Hall effects and their phenomenological origin that show up in the experiments and cover a large part of the chapter on how to extract (from raw data) the topological Hall effect (THE), *i.e.* associated with such chiral spin structures. Finally, we discuss the ways one can harness these properties in complex oxide heterostructures. We go straight into the growth/development part of complex oxide heterostructures, followed by the detection and manipulation of the interfacial emergent properties in them. The recent progress in this field of research along with some future outlook is also concluded.

#### **2. Brief basics of Skyrmions**

#### **2.1 Skyrmions**

A magnetic skyrmion (or simply skyrmion) is a collection of magnetic moments forming non-coplanar/chiral texture. Mathematically it can be described by the topological skyrmion number (*Nsk*), which counts the times magnetic moments wraps a unit sphere, and is given by the following expression:

$$N\_{sk} = \frac{1}{4\pi} \left[ \left| \vec{m} \left( \vec{r} \right) \cdot \left( \frac{\partial \vec{m} \left( \vec{r} \right)}{\partial \mathbf{x}} \times \frac{\partial \vec{m} \left( \vec{r} \right)}{\partial \mathbf{y}} \right) \right| d^2 \vec{r} \right] \tag{1}$$

where *m* !( *r* !) is the magnetic moment. For trivial spin arrangements/textures, like ferromagnet or antiferromagnet, *Nsk* = 0. For magnetic vortices (as in magnetic nanostructures), *Nsk* ¼ � <sup>1</sup> 2 . For non-trivial spin textures like skyrmions, *Nsk* = 1. There are two basic variations of skyrmions with different spin arrangements along the radial direction, *viz.*, Bloch-type skyrmions and Néel-type skyrmions. In Bloch-type skyrmions, the spins rotate in the tangential planes (that is perpendicular to the radial directions), when moving from the Center to the circumference (periphery). Whereas, in a Néel-type skyrmions, the spins rotate in the radial planes when moving from the Center to the circumference. These are schematically shown in **Figure 1**. It is worth mentioning that there are other types of chiral spin textures apart from skyrmions and the skyrmion number topological charge can be used to identify the topological distinction of these different types of spin textures.

The type of chiral spin texture formation depends on the interplay of different magnetic interactions in a material.

#### **2.2 Interactions involved in stabilizing chiral spin textures**

There are various magnetic interactions that can generate skyrmions in magnetic systems, and at times, multiple such mechanisms may contribute simultaneously.

#### *2.2.1 Dzyaloshinskii-Moriya interaction (DMI)*

The Dzyaloshinskii-Moriya interaction (DMI) is an asymmetric exchange interaction that favors canting of spins in materials that would, in contrary, be ferromagnetic (FM) or antiferromagnetic (AF) with collinearly aligned spins (either parallel or anti-

**Figure 1.**

*Schematic of spin textures in two types of skyrmions: (a) Bloch-type skyrmion, (b) Néel-type skyrmion.*

parallel). The DMI originates from spin-orbit coupling (SOC) and inversion symmetry breaking (typically through bulk crystal structure or multilayer heterostructure). Its Hamiltonian is written as:

$$H\_{\rm DMI} = \sum\_{i,j} \overrightarrow{D}\_{ij} \cdot \left(\overrightarrow{S}\_i \times \overrightarrow{S}\_j\right) \tag{2}$$

where *D* ! *ij* is the DMI vector. The direction of the DMI vector depends on the symmetry of the system. For bulk material with no inversion symmetry such as *B*<sup>20</sup> compounds, the *D* ! *ij* is parallel to the vector that connects *S* ! *<sup>i</sup>* and *S* ! *<sup>j</sup>* [4, 7]. On the other hand, in multilayer heterostructure composed of a FM layer and a layer with strong SOC, the *D* ! *ij* is often parallel to the interface [8], as shown in **Figure 2**.

#### *2.2.2 Magnetic dipolar interaction*

In magnetic thin films with perpendicular easy-axis anisotropy, the dipolar interaction favors an in-plane magnetization, whereas the anisotropy prefers an out-ofplane magnetization. The competition between these two interactions results in periodic stripes in which the magnetization rotates in the plane perpendicular to the thin film. An applied magnetic field perpendicular to the film turns the stripe state into a periodic array of magnetic bubbles or skyrmions.

Apart from these, **frustrated exchange interactions** and **four-spin exchange interactions** can also aid to the formation of chiral spin structures. However, in these two cases, the skyrmions are of atomic size length scales (often of the order of the lattice constant �1 nm).

In case of dipolar interactions, skyrmions are typically of the order of 100 nm to 1 *μ*m, which is comparable to the period of the spiral determined by the ratio of the dipolar and exchange interactions. In case of DMI, the size is determined by the strength of DMI and is typically 5 nm – 100 nm. As a result, skyrmions in skyrmion crystals in cases (1) and (2) are larger than the lattice constant, and therefore the continuum approximation is justified. In these two cases, the energy density of the skyrmions is much smaller than the atomic exchange energy J, and the topological protectorate holds. In other words, discontinuous spin configurations — called monopoles — with energy of the order of J can create or annihilate the skyrmions.

In complex oxide based thin film heterostructures, one can easily comply with the dipole exchange interaction as well as the DMI interaction by harnessing the inversion

#### **Figure 2.**

*Schematic of the interfacial DMI mechanism that gives rise to emergent phenomena in thin film heterostructures.*

symmetry breaking at the interfaces and/or surfaces of the heterostructures, using heavy Z-based elements (Z = atomic number) for strong SOC and of course the thickness to generate anisotropy along various directions with respect to the film plane.

#### **2.3 Detection techniques**

There are many various techniques for detection of skyrmions. These include advanced imaging techniques like magnetic force microscopy (MFM), Lorentz transmission electron microscopy (LTEM), spin polarized scanning tunneling microscopy (SP-STM), photoemission electron microscopy (PEEM), *etc.*; synchrotron radiation based techniques like x-ray magnetic circular dichroism (XMCD). But very intriguing and easy technique is the electrical one, the topological Hall effect (THE). Electrical detection can be easily performed nowadays with the available cryogenic and magnet based systems in any condensed matter physics laboratory.

#### **3. Magnetotransport properties: the family of Hall effect**

The Hall effect was discovered by Edwin Hall in 1879 (even before the discovery of the electron) when he observed the evolution of a transverse voltage in conductors for applied electric and magnetic fields which were mutually perpendicular (schematically shown in **Figure 3(a)**) [9]. Couple of years later, he again reported that the effect was ten times larger in ferromagnetic conductors than in non-magnetic conductors [10], which was hence termed as the "Anomalous" Hall effect (AHE). Then, about a century later, other members started to appear in the family, like the spin Hall effect (SHE), quantum Hall effect (QHE), planar Hall effect (PHE), quantum spin Hall effect (QSHE), to name a few. A recent addition to the family is the topological Hall effect (THE) that is related to the chiral spin textures in materials. All of these effects have different origin in themselves, except for the fact that the experimental arrangements remain same (and hence this arrangement is commonly called the "Hall configuration"). For simplicity and distinguishablity, the original Hall effect is often

#### **Figure 3.**

*Basic configuration for Hall effect measurement: (a) for bulk or layered (thin film) samples, (b) for patterned thin film samples in the form of "Hall bar".*

called as the ordinary Hall effect (OHE). The schematic of the Hall configuration is shown in **Figure 3**.

Needless to say that this section can form a chapter in itself; so we will try to keep it simple for the readers and discuss phenomenologically some of the important Hall effects, *i.e.*, OHE, AHE, and ofcourse THE, those are of interest for this chapter.

#### **3.1 Ordinary Hall effect (OHE)**

When electric current (*I*) flows (say along *x*-direction) through a metal or a semiconductor placed in a perpendicular magnetic field (*μ*0*H*, say along *z*-direction), the charge carriers inside the material are deflected from the straight path by the magnetic field as per the Lorentz force (given by Eq. (3)).

$$
\overrightarrow{F} = q \left[ \overrightarrow{E} + \left( \overrightarrow{\nu} \times \overrightarrow{B} \right) \right] \tag{3}
$$

This results in charge accumulation on the sides (in *y*-direction) preferably depending on the type of charge carrier, giving rise to a transverse voltage along the *y*direction (*i.e.*, mutually perpendicular to that of both *I* and *μ*0*H*). This voltage is called the Hall voltage (*Vxy*); and in a non-magnetic material it is proportional to the applied magnetic field. The Hall resistance (*Rxy* = *Vxy*/*Ixx*) due to OHE is expressed as *ROHE* = *μ*0*R*0*H*, where *R*<sup>0</sup> is the ordinary Hall coefficient.

#### **3.2 Anomalous Hall effect (AHE)**

In conducting magnetic materials with uniform magnetization (*M*), like ferromagnets, an anomalous contribution to the Hall signal is often observed in addition to the OHE, which is called "anomalous" Hall effect (AHE). AHE occurs intrinsically due to the spin-orbital coupling as a result of the "fictitious" magnetic field added by the magnetization and thus the anomalous Hall resistance is proportional to the magnetization *Mz*, expressed as:

$$R\_{AHE} = R\_A M\_x \tag{4}$$

where *RA* is the anomalous Hall coefficient. However, apart from intrinsic source (i.e., *M*), there can be extrinsic sources (impurity scattering like, side-jump or skew scattering) can contribute to the anomalous Hall signal. Information of the contributing source (intrinsic or extrinsic) is generally contained in the *RA*: For intrinsic sources, *RA* ∝ *R*<sup>2</sup> *xx*; and for extrinsic sources *RA* ∝ *Rxx* (where *Rxx* is the longitudinal resistance of the sample).

Thus AHE basically occurs due to the effect of magnetic field on the spin orientation in momentum (reciprocal) space and not in position (real) space that makes it different from topological Hall effect which is associated with spin arrangements in real space (**Figure 4**).

#### **3.3 Topological Hall effect (THE)**

In materials with topologically protected real space chiral spin textures, such as skyrmions, strong exchange coupling occurs between the moments of the conduction electrons and the local magnetic moments at each sites. The spin of the electrons

*Growth and Interfacial Emergent Properties of Complex Oxide Thin Film Heterostructures DOI: http://dx.doi.org/10.5772/intechopen.110885*

**Figure 4.**

*Schematics of THE typical signatures of Hall resistances arising from different types of Hall effects: (a) OHE only, (b) AHE only, and (c) THE only.*

adiabatically follow the spin texture and thus pick up a quantum-mechanical Berry phase, which obviously is sensitive to the topology of the texture. The Berry phase is considered to give rise to another "virtual" (or emergent, or effective) spatially varying magnetic field, *beff* . As a result, the conduction electrons "feel" the emergent virtual magnetic field (*beff* ) arising from the spin textures and are deflected perpendicularly to the applied current direction, resulting in the so-called topological Hall effect (THE). This THE appears as a bump or dip during the hysteretic Hall resistivity measurements. Thus, unlike OHE or AHE, it is obviously neither proportional to external magnetic field (*μ*0*H*) nor to the magnetization (*M*) of the sample.

In contrast, the topological Hall voltage signal is proportional to emergent magnetic field (*beff* ). In case of skyrmions, the *beff* contains the information of the skyrmion density; it is proportional to *nsk*, and hence for skyrmions, the THE voltage is inversely proportional to the size of the skyrmions. The topological Hall resistivity can be given by the following equation [11]:

$$
\rho\_{\rm THE} = \frac{PR\_0 b\_{\rm eff}}{en} = \frac{P\Phi\_0}{d\_{\rm sk}^2 en} \tag{5}
$$

Here, *P*- spin polarization of carriers, *dsk*- distance between skyrmions, *n*- carrier density and Φ<sup>0</sup> is the quantum flux (*h=e*). The skyrmion density (*nsk*) gives rise to the emergent magnetic field as *beff* = *nsk*Φ0. Thus from Eq. (5), one can say that separation of skyrmions (*dsk*) varies as *n*�1*=*<sup>2</sup> *sk* . Eq. (5) can thus also be re-written as

$$
\rho\_{\rm THE} = \boldsymbol{PR}\_0 \boldsymbol{n}\_{sk} \boldsymbol{\Phi}\_0 \tag{6}
$$

It must be mentioned here, that, in case of skyrmions, the emergent magnetic field (*beff* ) is expected to be independent of temperature and often is very high (may range from few tens of Tesla to few hundreds of Tesla) [12].

It is highlighted here that the appearance of distinctive bumps or dips in Hall resistivity signal of such chiral magnetic systems is a direct consequence of stabilization of non-collinear topological spin textures. However, it should be noted that complications in AHE, *e.g.*, arising from the electronic band structure or sign change of the dominant scattering mechanism might influence the Hall resistivity signal equivalently [13], resulting in similar transport features. The emergence of a bump/ dip characteristic in the Hall effect, for example, may not hold strict for skyrmions; and thus cannot always suffice as an unambiguous evidence for identifying noncollinear "topological" spin textures [14, 15]. Hence, along with THE detection, other imaging/x-ray based techniques (as mentioned above) might be required to support the claim of skyrmions as the origin of THE.

In any case, the acquired total Hall resistance signal contains the three components: OHE, AHE and THE. It is thus necessary to discuss in detail how to extract individual components in order to eliminate any experimental artifacts [16].

#### *3.3.1 THE signal extraction technique*

**Step-1:** During experiments with unpatterned thin film samples (say, as in **Figure 2(a)**), electrical four-probe (or van der Pauw) contacts are often made with conductive paints or solders by eye estimation, which adds the longitudinal magnetoresistance (MR) component in the Hall resistance due to the inevitable misalignment of the electrodes. This has to be removed, first, by using *Rxy*(*H*)↑ = [*Rraw xy* (*H*)↑ - *Rraw xy* (*<sup>H</sup>*)↓]/2, where *Rraw xy* (*H*)↑ stands for the measured raw data in the 4*th* and 1*st* quadrants with the magnetic field scanning from -∣*μ*0*Hmax*∣ to +∣*μ*0*Hmax*∣ and *Rraw xy* (*<sup>H</sup>*)<sup>↓</sup> the measured raw data in the 2*nd* and 3*rd* quadrant for the reversed field scanning. Similarly, the *Rxy*(*H*)↓ branch was extracted using [*Rraw xy* (*H*)↓ - *Rraw xy* (*H*)↑]/2. In this way one can eliminate the longitudinal (MR) contribution due to misalignment of electrodes. Apart from this, another way to eliminate it from appearing in the Hall data is by pattering the thin film samples in the form of Hall bar. This leaves us with pure Hall signal (*Rxy*) which contains the contributions: *Rtotal xy* = *μ*0*R*0*H* + *RAMz* + *PR*0*beff* .

**Step-2:** The ordinary Hall resistance component (which varies linearly with the applied magnetic field) is subtracted from the total Hall resistance loop by slopededuction method at the high field region. This leaves us with the AHE and THE components: *Rtotal xy* - *ROHE* = *RAHE* + *RTHE*.

**Step-3:** Finally the AHE component (*RAHE*) is subtracted from the above equation to obtain only *RTHE* contribution. There are two methods to find *RAHE*: one is by measuring out-of-plane magnetization (*Mz*) and the *RA* from longitudinal resistivity (as mentioned in Section 3.2). The other method is by fitting with trial *tanh* or Langevin functions to estimate the AHE, which though is a crude method. Finally what remains is the *RTHE* signal only. The complete process is shown schematically in **Figure 5**. In the next sections we discuss the origin of and ways to manipulate the topological Hall effect in complex oxide heterostructures.

#### **4. Oxide Heterostructures**

The quest for magnetic textures in oxides have taken new thrust very recently after the celebrated discovery of chiral spin texture in La1.37Sr1.63Mn2O7 compound [17]. In this manganite compound, promisingly low threshold current density (*Jc* <sup>10</sup><sup>7</sup> A/m2 ) was recorded for their electrically driven motion. Since then, over the years, various layer-by-layer or step-flow oxide growth techniques have emerged, which have enabled the creation of high-quality interfaces for novel heterostructure design. Interface engineering in complex oxide heterostructures has developed into a flourishing field as various intriguing physical phenomena can be demonstrated which *Growth and Interfacial Emergent Properties of Complex Oxide Thin Film Heterostructures DOI: http://dx.doi.org/10.5772/intechopen.110885*

**Figure 5.**

*Steps for extracting THE THE signal from typical Hall data:- (a) gray curve: Rtotal xy . Find OHE by slope-deduction method (red curve) at high field region. (b) after performing Step-2 (mentioned in text), dark gray curve: RAHE + RTHE. (c) RAHE determined from magnetization (M H) data. (d) Finally after performing Step-3 (as in text), what remains is THE pure THE resistivity signal (black curve).*

are otherwise absent in their constituent bulk compounds [18]. Such capability has opened doors for stabilizing Néel-type skyrmions by engineering the interfacial DMI.

#### **4.1 Growth of oxide heterostructures**

Practical applications demand high-quality thin film growth. Owing to some significant advances in the fabrication techniques of high quality oxide heterostructures and the structural compatibility of these kind of complex oxides, the minute tuning of interfacial properties can be routinely achieved. Advanced techniques such as sputtering, pulsed laser deposition (PLD), and molecular beam epitaxy (MBE) have been successfully used to produce high-quality crystalline manganite thin films. Moreover, the presence of a substrate adds another degree of freedom, the external pressure in the form of stress. This is why one of the major characteristics of epitaxial thin films is the strain, which induces modifications in the physical properties (structure, transport and magnetic order) with respect to the bulk.

On the other hand, most of the interfacial emergent properties are highly sensitive to the structure of the interfaces/surfaces, since they arise out of various modified exchange interactions across the interfaces or at the surfaces/terminations (as we will soon explore in upcoming sections of this chapter), and may easily get lost due to presence of slightest of defects.

Intuitively, one has to create a very clean engineered surface or interface to play with such emergent phenomena.

#### **5. Interfacial emergent properties of oxide Heterostructure**

As discussed in earlier sections that THE arising from stabilized chiral spin structures or skyrmions require DMI. Considering that the DMI arises from spin-orbit coupling combined with broken inversion symmetry, it is possible to artificially introduce DMI at the surface/interface of complex oxide heterostructures, as discussed below.

Although the individual layers as whole may not show exotic/non-trivial spin structures, various mechanisms like strain, exchange interaction, proximity effect, *etc.*, at the interfaces or surfaces may induce such phenomena and hence, in these heterostructures these properties are called "interfacial emergent" properties.

#### **5.1 Origin and tuning of interfacial DMI**

Skyrmions were observed in epitaxial ultrathin ferromagnetic films in the proximity of heavy metal layers, which are subject to giant "emergent" DMIs induced at the interface that breaks inversion symmetry and the strong SOC with neighboring heavy metal. The first investigated system in this class showing "emergent" DMI was heterostructure of Fe monolayer grown on Ir(111) [19].

It is well know that 3*d* transition metal ions rarely show any SOC effect and thus are unlikely to show DMI alone. Rather 4*d* and 5*d* ions are a very good candidate for DMI as they bear inherent strong SOC. For example, SrRuO3 (SRO) (a 4*d* transition metal oxide) has a SOC strength of 150 m*e*V, while 5*d* transition metal oxide SrIrO3 (SIO) has SOC strength of 450 m*e*V, 3 times larger than that of SRO [20].

Thus 4*d* and 5*d* based oxides provide platform for engineering the interfacial DMI along with the manganites (Mn based (3*d*) oxides), which have myriad of magnetic phases. The most versatile candidates are SrRuO3 (SRO), SrIrO3 (SIO), BaTiO3 (BTO) and La2/3Sr1/3MnO3 (LSMO); additionally, they posses very common crystal structure- the ABO3 Perovskite structure and hence high quality layer-by-layer growth can be easily achieved. In the following sub-sections, some recent progress in this field is presented, highlighting the origin and tuning mechanisms of the interfacial DMI, detected electrically through topological Hall effect.

#### *5.1.1 Bilayer structures with strong SOC based oxide*

The first investigated system in this class was epitaxial bilayer heterostructure of SRO and SIO in 2016 [11]. SIO is a paramagnet which can host 5*d* electrons with strong spin-orbit coupling [21], and SRO is an itinerant ferromagnet with a Curie temperature (*T*C) of 160 K [22]. The bilayers were grown by PLD on SrTiO3 (STO) substrate with different SRO layer thickness (*m*, basically the number of unit cells) ranging from 4 to 7 unit cells, while keeping the SIO layer thickness fixed at 2 unit cells (uc). So in the layered structure STO//SRO (*m* uc)/SIO (2 uc), the interface between SRO and SIO provided the broken inversion symmetry and the SIO layer provided the strong SOC, mimicking an effective "heavy metal" layer. The systematics of the magnetic and transport properties of the bilayers were governed by SRO and could be precisely controlled by tuning SRO layer thickness, *m*.

Using techniques mentioned as in Section 3.3.1 above, THE component was extracted from the Hall resistivity data for each measurements, where AHE components were derived by measuring the Kerr rotation angle (the Kerr signal magnitude is proportional to *M* and thus to AHE as well). Among the samples, the THE was highest for *m* = 4 uc. With increasing *m* to 5 uc, similar peak structure related to THE could be observed, however, the THE component decreased. Upon further increasing *m*, THE decreased and vanished at only *m*=7 uc.

At the high magnetic field regions (say 9 T) where the magnetization gets saturated, the spins at the Ru sites align ferromagnetically (in corresponding directions depending on field), which lead to absence of spin chirality and the Hall resistivity in those high field regions could be attributed to AHE only. Decreasing the field from 9 T to 0 T, it remains in the ferromagnetic (FM) state with positive magnetization, which corresponds to the observed finite AHE and the negligible THE. With

#### *Growth and Interfacial Emergent Properties of Complex Oxide Thin Film Heterostructures DOI: http://dx.doi.org/10.5772/intechopen.110885*

further decrease of the magnetic field from 0 to 0.8 T, absolute value of THE sharply increases upto 0.06 T and then gradually decreases to zero at around 0.4 T. This field (0.4 T) coincides with the field at which the hysteresis in *M* vs. *μ*0*H* loop closes. This is indicative of the fact that some specific spin structure with finite scaler spin chirality might have been induced when the FM spins started to reverse. The appearance of hysteresis in magnetization and THE in Hall resistivity at simultaneous field range indicates a coexistence between co-planar FM phase and the scalar spin chiral phase.

As discussed earlier, the most plausible chiral spin texture responsible for THE is magnetic skyrmion which gives rise to the emergent magnetic field. This emergent magnetic field strongly affects the electron transport and marginally affects the magnetization.

Due to the broken inversion symmetry at SRO/SIO interface and the strong SOC of SIO, the finite DM vector pointed in the in-plane direction, which might give rise to a Néel-type magnetic skyrmion. The fact, THE appeared only when 4 ≥ *m* ≤ 6, suggests that it was derived from interfacial DMI.

It is worth mentioning that in contrast to the very narrow *T H* window of THE in bulk *B*<sup>20</sup> compounds (which exhibit Bloch type skyrmions), the THE in oxide bilayer heterostructures was found within a wide *T* range upto around 90 K. The thickness variation also revealed the stabilization of 2-D nature of the Néel-type skyrmions.

Moreover, utilizing Eqs. (5) and (6) with P -9.5 % for SRO [23], the distance between skyrmions in these bilayers was approximately estimated to be around 10 nm to 20 nm. This provided an estimation of the length scales of the skyrmions, which was always larger than the film thickness (2 nm in this case) and confirmed the twodimensional nature of the skyrmions.

#### *5.1.2 Single layer ultrathin film*

In another contrasting work, a few years ago, THE was observed in a single layer SRO film grown on STO insulating substrate; but this time, astonishingly, without the presence of any 5*d* based metal oxides like SrIrO3 [24]. Here the thickness of SRO films ranged from 3 nm to 10 nm, all having tetragonal structure. From structural characterizations it was observed that the strained SRO films in tetragonal phase showed rotation of the RuO2 octahedra about the c-axis, which could persist upto several tens of nm.

In this case also, the THE appeared in the vicinity of the magnetization reversal, which was consistent with the previous result as mentioned above. Furthermore, the amplitude of the THE resistivity increased with increasing *T* from 20 K to 80 K, and above 85 K, THE signal vanished. The itinerant magnetic property and the strong perpendicular magnetic anisotropy in these single layer SRO films are indicative of the fact that the non-trivial topological spin texture responsible for the THE must be the Néel skyrmion.

Needless to say, the terminating surface provides the broken symmetry for this single layer system, while Ru ions at the surfaces are the sources of SOC. This gave rise to the DMI, where DM vector also point along the film plane. The oxygen octahedral rotation due to combination of substrate induced strain and natural termination of top layer has a significant effect on THE of the SRO single layer.

Further, in order to elucidate on the origin of SOC of Ru ions at the surface layers, Hall transport was measured in presence of extra electric field, provided by ionic

liquid gating. Although the electric field generated from the ionic liquid could be much higher as compared to that with conventional voltage gating, the penetration depth of the electric field might only be a nm or less due to the high carrier density of the SRO. It was observed that upon applying negative gate bias, the THE diminished. The reason is as follows: Upon applying gate bias, the momentum space around the Fermi level of SRO changed [25]. The electric potential gradient near the SRO surface resulted in a change in the inversion asymmetry, which modulated the SOC in that region. This is reminiscent of the phenomenon observed in case of Rashba-type band splitting and spin splitting [26, 27]. The combined contribution of change in SOC and change in inversion asymmetry affected the DMI, which resulted in the enhancement or suppression of THE with the polarity of gate bias.

As earlier, in the single layer SRO films, the emergence of the THE was observed at reduced dimensions, for thickness 3 nm to 6 nm but not in 10 nm film. This, along with the gate voltage modulation of the THE indicated that 2-D Néel skyrmions formed at the surface of the SRO single layer films.

#### *5.1.3 Bilayer heterostructure with ferroelectric layer*

Now that we have explored the idea of tuning the THE by applying electric field through ionic gating on SRO single layer films, one might be intuitively tempted to utilize ferroelectric materials in the proximity of SRO layers, as ferroelectric materials could be easily manipulated by electric field since they have the added advantage of inherent inversion symmetry breaking.

Heretofore, tuning of interfacial DMI due to lattice distortions driven by ferroelectricity at the SrRuO3/BaTiO3 (BTO) interface was investigated in detail [28]. Ultrathin bilayer heterostructures of SRO/BTO were prepared on STO substrate with SRO as the bottom layer. The SRO layer thickness *tSRO* was varied between 4 and 8 uc and BTO layer thickness *tBTO* was varied between 3 and 20 uc.

FE-driven ionic displacements in BTO could cross the interface and continue for several unit cells into SRO, a phenomenon what is known as the FE proximity effect [29]. The inevitable lattice distortion due to FE proximity effect could break the inversion symmetry of the SRO structure near SRO/BTO interface. The degree of this inversion symmetry breaking in SRO could be elucidated as the vertical ionic displacement between Ru and O (*δRu<sup>O</sup>*) ions in the RuO2 plane, taking into account a caxis-oriented FE polarization. In such a case also, one can expect a emergent DMI in the ferroelectrically distorted SRO lattice, where DM vector should lie in-plane, perpendicular to the Ru-O-Ru chains. Accordingly, it is expected that this in-plane DMI at the vicinity of SRO/BTO interface might stabilize Néel-type magnetic skyrmions, giving rise to emergent THE.

As obvious, The Hall signals of SRO/BTO samples depend strongly on the individual layer thicknesses. In this case, the THE signal persisted upto *T* 80 K, but for a much larger field range, with peak around 1.65 T and vanished at around 3.9 T.

To estimate the basic skyrmionic properties from the THE signal, the evolution of *nsk* (estimated from Eq. (6)) with sample structures (basically *tSRO* and *tBTO*). With increasing *tSRO* from 4 to 6 uc, *nsk* decreased rapidly by almost an order of magnitude, which implied that the DMI was stronger in the vicinity of the SRO/BTO interface. On the other hand, *nsk* also decreased with decreasing *tBTO* below 8 uc due to suppression of the FE polarization. This trend further demonstrated that skyrmions could be driven by FE, through the proximity effect.

#### *Growth and Interfacial Emergent Properties of Complex Oxide Thin Film Heterostructures DOI: http://dx.doi.org/10.5772/intechopen.110885*

Further, because of a strong correlation between the interfacial DMI and FE, the manipulation of skyrmions with changes in ferroelectric polarization of BTO layer was also explored. For this, the BTO layer had to be electrically poled into pre-designed domain structures which led to local switching of the BTO polarization in the patterned Hall bars of the bilayer structures. This was performed using a conducting AFM tip at room temperature; voltage bias of -(+)8 V led to upward (downward) poling; and then the Hall measurements were performed at low temperatures. The local switching of the BTO polarization (in the out-of-plane/c-axis direction in this case) due to poling led to changes in the *δSrRu* near the SRO/BTO interface. This further led to changes in *δRu<sup>O</sup>* from the pristine state, which remarkably affected the THE signal. It was observed that the uniformly upward-poled Hall bar exhibited enhancement in polarization which slightly enhanced the *ρTHE* as compared with that in pristine FE state. However, upon complete downward poling, polarization changed and as a result *ρTHE* decreased by about 80 %. The magnetic field and temperature range of THE also got reduced due to downward poling which signified a substantial reduction in *nsk*.

Thus, by downscaling the FE domain size in the above procedures, one might not only be able to tune the overall skyrmion properties microscopically but also could control the nucleation/deletion of individual skyrmions.

#### *5.1.4 Bilayers heterostructures composed of manganites*

Enlightened by the observations thin films and heterostructures as mentioned in previous sub-sections, an intuitive question appears: whether the emergent THE observed in these complex oxide heterostructures only appear specifically in the presence of SRO, which itself exhibits a relatively large SOC with 4*d* transition-metal Ru? Hence, it became desirable to investigate the magnetotransport properties in heterostructures composed of SIO and other magnetic oxides. In this subsection, we discuss briefly the emergent THE observed for the first time in the 3*d* perovskite La0.7Sr0.3MnO3 (LSMO) in SIO/LSMO heterostructures deposited epitaxially on the (001) STO substrates [30].

Although the magnetic easy axis of LSMO is commonly known to lie in-plane along < 110> direction on STO (001)-oriented substrate, it was reported that the easy axis could shift to <100 > direction when interfaced with a SIO layer of thickness < 5 uc due to strong SOC of SIO layer [31]. Hence the heterostructures used for the study of THE were composed of 2 uc SIO followed by 6–10 uc LSMO; the final structure being STO//SIO (2 uc)/LSMO (*m* uc), *m* = 6,8,10.

As shown in **Figure 6**, the emergent THE peak appeared in a wide temperature range of upto 200 K, and exhibited a gradual broadening with decreasing temperature, very similar trend seen in other oxide heterostructure systems as mentioned above and in typical skyrmion hosting materials like the *B*<sup>20</sup> alloys [7]. Moreover, the giant THE resistivity of 1.0 *μ*Ω.cm (in average) was significantly higher than those reported in complex oxide heterostructures composed of SRO/SIO, SRO/BTO or SRO films, demonstrating the feasibility of using the proximity effect of SIO to create novel spin textures in oxide magnetic heterostructures.

To confirm the interfacial origin of the THE observed in the LSMO/SIO heterostructures, Hall effect measurements were performed on separate LSMO single layer films and on LSMO (8 uc)/STO (2 uc)/SIO (2 uc) trilayer heterostructures, both

#### **Figure 6.**

*(a) Upper panel: AHE + THE combined signal at 200 K for SIO (2 uc)/LSMO (8 uc) heterostructure; lower panel: Only THE resistivity at 200 K for THE same sample. (b) H-T phase diagram of THE THE resistivity for same heterostructure generated from Hall measurements at various temperatures. (c) Ordinary Hall co-efficient at various temperatures obtained from Hall measurements for THE same heterostructure. (d) Upper panel: Peak value of THE THE resistivity at various temperatures measured several times and on several samples of THE same heterostructure SIO (2 uc)/LSMO (8 uc), that showed THE reproducibility of THE THE signal; lower panel: The effective fictitious magnetic field obtained from Eq. (5), which was almost constant with temperature, confirmed that the emergent THE was due to formation of skyrmions as a result of interfacial DMI. [reprinted (adapted) with permission from [30]. Copyright (2019), American Chemical Society.]*

grown on STO substrates. Distinctively, no THE signals were observed in those two samples (single layer and trilayer). Although the absence of THE in LSMO single layer films was upto expectation, the absence of THE in the trilayer samples could only be ascribed to the inserted non-magnetic insulating STO layer, which interrupted the strong interfacial DMI between the LSMO and SIO layers.

The effective emergent magnetic field *beff* , associated with the real space Berry phase, was also found to be independent of temperature upto 200 K as shown in **Figure 6(d)**, with an average value of around 12 Tesla. Such a strong stability against temperature indicated that the origin of emergent THE might be due to skyrmions.

In another work, interfacial atomic layer control of THE by deliberately controlling the competition between chiral DMI and intrinsic collinear FM in 3*d*-5*d* heterostructures composed of LaMnO3/SrIrO3 was demonstrated [32]. This interfacial symmetry control led to a large THE, which was believed to be originated from a highly robust chiral magnetic phase, potentially hosting skyrmions.

*Growth and Interfacial Emergent Properties of Complex Oxide Thin Film Heterostructures DOI: http://dx.doi.org/10.5772/intechopen.110885*

#### **6. Further scope**

Heterostructure engineering in complex oxide systems with polycrystalline heavy metal layers like, Pt or W instead of strong SOC based oxides is now an active subdomain of research which is worth investigating, since the interfacial DMI is key for stabilization of Néel type skyrmions.

It has long been felt for the utilization of oxides in the field of flexible electronics. This requirement has triggered the research on growth and characterization of complex oxide thin films like on various flexible substrates like, mica, polymide tapes, *etc.* [33, 34] using common epitaxial lift-off techniques with the aid of sacrificial layers. A thorough and exhaustive study on the film growth and transfer on flexible substrates, their characterization (using AFM or electron microscopy techniques) and further establishing a direct relationship between strain and magnetic, magnetotransport properties are now being investigated in details.

#### **7. Conclusions**

To conclude, we presented the detection technique of interfacial emergent phenomena like interfacial DMI by means of topological Hall effect (THE) in complex oxide heterostructures, which only provides a tell-tale sign of the existence of chiral textures.

We also presented recent progresses towards various methods of achieving and tuning the inversion asymmetry and spin-orbit coupling to tailor minutely the interfacial DMI in those kind of thin film heterostructures, based on some recent works. To illustrate, we presented examples from each of the following methods: tuning the structure through atomic (unit cell) layer control at interface of 4*d*/5*d* based heterostructures (SRO/SIO); harnessing octahedral rotation due to strain in ultrathin single layer SRO films; utilizing ferroelectric polarization to tune the RuO2 octahedra in SRO/BTO heterostrcutures; using the exchange interactions among the Mn spins in (3*d*-5*d*) based heterostrcutures (LSMO/SIO) and superlattices (LMO/SIO) by means of unit cell modification along with the strong SOC of the 5*d* layers at the interfaces.

For the device application thin film heterostructures are very important. We expect that the recent progresses will aid to the future skyrmion based devices for the manipulation by current, electric field and/or by some other techniques as well, so that the information can be used for the memory devices and logic implementation.

#### **Acknowledgements**

The author acknowledges Dr. Samik DuttaGupta and Mr. Arnab Bhattacharya of SINP, Kolkata, for scientific discussions. Finally, the author acknowledges TCG CREST, Kolkata, for the Post-Doctoral fellowship.

#### **Conflict of interest**

The author declares no conflict of interest.

### **Author details**

Snehal Mandal Centre for Quantum Engineering, Research and Education (CQuERE), TCG Centres for Research and Education in Science and Technology (TCG-CREST), Kolkata, India

\*Address all correspondence to<EMAIL_ADDRESS>
© 2023 The Author(s). Licensee IntechOpen. 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.

*Growth and Interfacial Emergent Properties of Complex Oxide Thin Film Heterostructures DOI: http://dx.doi.org/10.5772/intechopen.110885*

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Section 3