# Increased Gilbert damping in Yttrium Iron Garnet by low temperature vacuum
annealing

D. M. Cheshire  School of Physics, Engineering and Technology, University of
York, York, YO10 5DD, UK  D. Backes  Diamond Light Source, Harwell Science and
Innovation Campus, Chilton, Didcot, OX11 ODE, UK  L. Ishibe Veiga  Diamond
Light Source, Harwell Science and Innovation Campus, Chilton, Didcot, OX11
ODE, UK  S. S. Dhesi  Diamond Light Source, Harwell Science and Innovation
Campus, Chilton, Didcot, OX11 ODE, UK  S. A. Cavill<EMAIL_ADDRESS>School of Physics, Engineering and Technology, University of York, York, YO10
5DD, UK

###### Abstract

The effect of thermal surface cleaning on the Gilbert damping ($\alpha$) of
yttrium iron garnet (YIG), before capping with a metallic layer, has been
investigated. Our results show that $\alpha$ is strongly effected by
relatively mild annealing conditions ($T$ = 300 $\degree$ C) when performed in
a vacuum. This increase needs to be taken into account when obtaining the spin
mixing conductance from spin pumping measurements. We measure an increase in
$\alpha$ by a factor of $\times$8 when the YIG is vacuum annealed at 300
$\degree$ C. No such changes in $\alpha$ are observed when annealed at the
same temperature in 1$\times$10-1 mbar of oxygen.

##  I Introduction

Research in the sub-field of magnon spintronics, where magnons - the quanta of
spin waves - are used to carry and process information has gathered pace in
recent years Chumak2022 ; Flebus2024 ; Chumak2015453 . Magnons offer several
advantages over conventional spintronics, particularly in the development of
insulator-based devices with reduced energy consumption. In these devices, the
propagation of pure spin currents in magnetic insulators, where
dissipationless transport of the spin has been predicted Takei2014 ,
eliminates parasitic Joule heating. One magnetic insulator in particular,
yttrium iron garnet (YIG), is considered the most prominent material in this
field, being widely used in spin transport experiments Cornelissen20151022
due to its exceptionally low damping, even in thin films Onbasli2014 . In
order to combine magnon spintronics and charge based electronics, the latter
crucial for input - output functionality, it is necessary to create efficient
converters that transform magnon spin currents into conventional charge
currents. Typically, spin pumping, the generation of spin accumulation a metal
by the magnetization precession of an adjacent ferromagnetic, and the inverse
spin Hall effect (ISHE), that transforms a pure spin current into a charge
current, are used for the input and output conversion processes respectively.
According to spin-pumping theory Tserkovnyak20022244031 , the spin current
sunk by a layer adjacent to a ferromagnet (FM) leads to an increase in the
Gilbert damping such that $\alpha=\alpha_{intrinsic}+\alpha_{sp}$, with

$\alpha_{sp}=\frac{g\mu_{B}}{4\pi
M_{s}}g_{eff}^{\uparrow\downarrow}\frac{1}{d}$ (1)

where $M_{s}$ is the saturation magnetization of the FM, $d$ the FM layer
thickness, and $g_{eff}^{\uparrow\downarrow}$ is the effective spin-mixing
conductance that essentially governs the transfer of spin momentum across an
interface. Measuring the change in the Gilbert damping of the YIG due to spin
pumping into an adjacent metallic layer therefore allows a convenient
experimental determination of $g_{eff}^{\uparrow\downarrow}$.
Previous studies of the spin mixing conductance at a YIG/Pt interface
demonstrated an enhancement by more than two orders of magnitude by surface
treatments, such as Piranha etch and heating the sample at 500 °C in vacuum,
prior to Pt deposition Jungfleisch2013 . The authors considered that the
intrinsic Gilbert damping is the same for all samples, irrespective of
treatment method, so that changes in damping is solely related to changes in
$g_{eff}^{\uparrow\downarrow}$. In this paper, we report increases in the
Gilbert damping in YIG thin films, due to either being subjected to vacuum
thermal annealing, or the subsequent deposition of a thin (2 nm) weak spin-
orbit coupled aluminium capping layer. The Gilbert damping is observed to
increase significantly for YIG, vacuum annealed at 300 °C for as little as 15
minutes, whereas for YIG annealed at the same temperature in a 1$\times
10^{-1}$ mbar partial pressure of oxygen, $\alpha$ is unaffected. In addition,
we notice that the deposition of Al on the YIG, irrespective of film heat
treatment, also increases $\alpha$. We argue that such increases need to be
considered when forming spin pumping heterostructures as often the YIG films
are annealed in vacuum to remove physisorbed gas species (O2, air) from the
surface prior to heavy metal deposition. These increases in $\alpha$ may then
be incorrectly attributed to $\alpha_{sp}$, leading to errors in
$g_{eff}^{\uparrow\downarrow}$. We suggest that the main driver for the
increase in $\alpha$ is the reduction of Fe3+ to Fe2+, consistent with vacuum
annealing and / or a displacement reaction between Fe oxide and Al. Changes in
the Fe $L_{2,3}$ X-ray absorption spectra, with annealing conditions and
capping layer material, support this hypothesis.

##  II Methods

Crystalline YIG films were grown via pulsed laser deposition (PLD) on
(111)-oriented Gadolinium Gallium Garnet (GGG) substrates. Following
Hauser2016 ; Cheshire2024 , an amorphous YIG layer was deposited at room
temperature, in a partial oxygen pressure of 2.5$\times 10^{-3}$ mbar, by
ablating a stoichiometric polycrystalline YIG target. Ablation was performed
using a frequency quadrupled Nd:YAG laser ($\lambda$ = 266 nm) with a fluence
of approximately 1 Jcm-2, at a repetition frequency of 10 Hz. The sample was
rotated at 6 RPM during deposition. Following deposition, the amorphous YIG
samples were ex-situ annealed in atmospheric conditions, at 850 °C for 3
hours, to recrystallise the YIG. This technique was used to produce four YIG
films with nominal thicknesses of (65 $\pm$ 3) nm, for FMR measurements.
Post FMR, the four YIG films were then subjected to surface treatments, as
follows. Two films were placed into the PLD chamber, in vacuum (at a base
pressure of 5x10-8 mbar) and annealed at 150 °C and 300 °C respectively, for
15 minutes. In-situ annealing was performed with a pulsed 10.6 µm CO2 laser,
directed onto the back of the samples. The temperature of each film was ramped
at approximately 4 °C/min, by varying the laser’s duty cycle. The third film
was subjected to annealing at 300°C following the same procedure, but instead
in an oxygen partial pressure of 1$\times 10^{-1}$ mbar. The fourth film was
left untreated as a control. FMR measurements were then repeated on the
treated films to observe changes to the magnetic damping. The thermal
annealing treatments were repeated on 2 further sets of recrystallized YIG
films to ensure repeatability. An additional 2 nm aluminium capping layer was
deposited on three YIG films by sputtering a pure Al target at room
temperature. A final set of FMR measurements were performed on the aluminium
capped YIG films. The aluminium capping was also performed to allow total
electron yield (TEY) detection for XAS/X-ray magnetic circular dichroism
(XMCD) spectroscopy measurements. The fourth YIG film was grown and capped
with a 2nm platinum capping layer as a control. The Pt layer was deposited at
room-temperature using PLD, ablating a pure Pt target in vacuum (base pressure
of 5$\times 10^{-8}$ mbar).
The Gilbert damping of the YIG was measured using in-plane FMR spectroscopy by
mounting the samples face down onto a 50$\Omega$ coplanar waveguide (CPW),
connected to a two-port vector network analyser (VNA) and centred between the
poles of a 2D vector magnet. Details of the system can be found in Love2021 .
The microwave transmission S-wave parameter, S12, was measured over a
frequency range of 0.001-15 GHz. The applied magnetic field ranged from 0-4
kOe, with a field step of 0.5 Oe, producing a 2D frequency-field resonance
map. All FMR measurements were performed at an RF power of +7 dBm. Field
linescans at constant frequency were extracted from the FMR frequency-field
maps and fitted using an asymmetric Lorentzian function Love2023  to determine
the corresponding resonance field (Hr) and linewidth ($\Delta$H).
Fe $L_{2,3}$ x-ray absorption spectroscopy (XAS) and XMCD measurements were
performed on beamline I06 at the Diamond Light Source Dhesi2010311 . The XAS
was measured in normal incidence by total-electron yield (TEY) using the
sample drain current.

##  III Results

Resonant frequencies were extracted from the frequency-field maps for each
applied field and are plotted in Fig.1 for the YIG films prepared under
different conditions. The FMR resonance frequency as a function of field is
fit to the easy-axis in-plane Kittel equation for a (111) orientated film,
given by

$\omega=2\pi\gamma\sqrt{\big{(}H\big{(}H+4\pi M_{eff}\big{)}\big{)}}$ (2)

with the gyromagnetic ratio $\gamma=g\mu_{B}/\hbar$, and the effective
magnetisation $M_{eff}=4\pi M_{s}-K/M_{s}$ where $M_{s}$ is the saturation
magnetisation of the YIG, and K is the cubic magnetocrystalline anisotropy
constant (-6100 erg/cc for YIG) Hansen1974 .

Figure 1: Kittel curves (frequency vs field) for the (black) as-grown, (red)
annealed YIG films, and (blue) annealed YIG films after capping with 2nm metal
layer.

For three of the YIG films – untreated, oxygen annealed at 300°C, vacuum
annealed at 150 °C - the FMR resonant field (measured at 10 GHz) of all three
stages differ by less than 10 Oe, with the “Kittel” curves almost lying on top
of each other. However, for YIG vacuum annealed at 300 °C (Figure 1d), a more
significant decrease in resonant field ($H_{r}$) of 95 Oe is observed, with an
additional decrease of 18 Oe following aluminium capping. Nevertheless,
“Kittel” curve fits for all four films produce values for $M_{s}$ that agree
within error with independent measurements of the untreated YIG using
vibrating sample magnetometry, (131 $\pm$ 5) emu/cc. The three films with
similar Kittel curves also produce a similar $g$-factor of (2.02 $\pm$ 0.01)
across all stages of these three samples, close to the expected value of 2 for
a d5 ion Cheshire2022 . However, the 300 °C vacuum-annealed produces a larger
g-factor of (2.050 $\pm$ 0.005).

Figure 2: FMR linewidth ($\Delta$H) vs frequency for the (black) as-grown,
(red) annealed YIG films, and (blue) annealed YIG films after capping with 2nm
metal layer.

In samples where two-magnon scattering is negligible, the magnetic linewidth
($\Delta$H) of the FMR resonance follows a linear dependence with microwave
frequency, such that Parkes2013

$\Delta H(f)=\Delta H_{0}+\frac{2\pi\alpha f}{\gamma}$ (3)

where $\Delta H$ is the half width at half maximum (HWHM) of the resonance,
$\alpha$ is the intrinsic Gilbert damping, $\gamma$ the gyromagnetic ratio and
$\Delta H_{0}$ is the frequency independent extrinsic damping. The
experimental data for magnetic linewidth as a function of microwave frequency
are shown in Figure 2.

Fitting Eqn (3) to the data allows for the extraction of the Gilbert damping
($\alpha$) and frequency independent extrinsic damping ($\Delta H_{0}$), for
each of the treated YIG conditions. $\Delta H$ vs $f$ is linear for all
samples (prior to Al deposition), indicating that two-magnon scattering is not
significant in our samples, even those annealed in-vacuum. We observe no
significant increases in the Gilbert damping that arise from in-vacuum
annealing of the YIG at 150 °C. However, in-vacuum annealing at 300 °C – even
for only 15 minutes - dramatically raises the Gilbert damping, by almost an
order of magnitude upon re-measurement of the FMR: from (5.0 $\pm$ 0.6)$\times
10^{-4}$ to (38 ± 1)$\times 10^{-4}$. In contrast, for annealing performed at
300 °C in 1$\times 10^{-1}$ mbar of pure oxygen, the Gilbert damping was found
to be, within error, insignificantly changed. This is an important observation
and highlights the sensitivity of YIG FMR to preparation conditions, such as
thermal cleaning of physisorbed species, that may be used when depositing
multiple layers for magnonic devices.

Figure 3: Circular polarization-dependent XAS at the Fe $L_{2,3}$ edges for
the (a) YIG/Pt, (b) YIG(vac, 150°C)/Al, (c) YIG($O_{2}$, 300°C)/Al and (d)
YIG(vac, 300°C)/Al samples

No obvious relationship between annealing treatment and extrinsic damping was
inferred from the FMR data. In all three annealing treatments, the changes in
extrinsic damping are either within error, or insignificantly small, with
$\Delta H_{0}$ of (1.5 $\pm$ 0.5) Oe for all cases. This suggests that the
annealing temperatures used, despite being high enough to affect the Gilbert
damping when performed in vacuum, does not significantly impact the YIG/GGG
interface or promote the formation of defects in the bulk of the YIG film.
Interestingly, the addition of an aluminium layer causes a notable increase in
Gilbert damping for all the YIG films. At first consideration, this is not
expected as aluminium (Z = 13) is non-magnetic with a weak spin-orbit coupling
and therefore would not be a natural choice for a spin-sink. The low layer
thickness (2 nm) and natural oxidation, after removal from the sputtering
chamber, precludes significant eddy current damping as the cause. In addition,
we rule out radiative damping Qaid2017 ; Schoen2015  as significant, as we
obtain $\alpha^{rad}$ = 2 $\times$ 10-5 from Eqn. 6 in Schoen2015  for our
geometry. However, an unexpected second FMR resonance mode was observed in the
oxygen-annealed YIG film following aluminium deposition. The presence of this
second mode restricted the frequency range across which the HWHM linewidths of
the Kittel mode could be accurately determined, to below 10 GHz as reflected
in Figure 2(b), as above this frequency the two modes significantly overlapped
broadening the resonance. It is not clear the cause of this second resonance,
but we speculate that it may be due to an inhomogeneous Al layer or a slight
increases in the roughness of the YIG film at the YIG/Al interface, induced by
the sputtering process. However, it is clear from the slope of $\Delta H$ vs
frequency that there is little change in $\alpha$ after annealing at 300 °C in
oxygen.

Figure 4: XMCD spectra at the Fe $L_{2,3}$ edges for: (a) YIG/Pt, (b) YIG(vac,
150°C)/Al, (c) YIG($O_{2}$, 300°C)/Al and (d) YIG(vac, 300°C)/Al samples.

To gain a detailed understanding of the annealed YIG, XAS/XMCD measurements
were performed at the Fe $L_{2,3}$ absorption edges in order to determine the
valency, coordination, and magnetic properties of the Fe cations. In L-edge
XAS, electrons are excited from a 2p core level to the unoccupied 3d valence
states of the element of interest by circularly polarized x-rays at the
resonance energy of the transition. The difference in absorption for opposite
chirality of the polarizations (XMCD) gives a direct and element-specific
measurement of the projection of the 3d magnetic moment along the x-ray
helicity vector vanderLaan2014X-rayMagnetism . At the $L_{2,3}$ absorption
edges of 3d transition metals, the probing depth for TEY detection is
approximately 6 nm. All measurements were performed at normal incidence, which
reduces the effect of self-absorption on the spectra Nakajima1999 , in a 6 T
field applied collinear to the x-ray helicity vector. Figure 3 shows XAS data
for the (a) YIG/Pt, (b) YIG(vac, 150°C)/Al, (c) YIG($O_{2}$, 300°C)/Al and (d)
YIG(vac, 300°C)/Al samples at the Fe $L_{2,3}$ edges. The XAS shows multiplet
structure typical of YIG Cheshire2022 . Two main peaks, one negative and one
positive, are present in the XMCD spectra at the $L_{3}$ edge, identical to
that found in other XMCD studies of YIG Cheshire2022 . These peaks correspond
to contributions from Fe3+ in octahedral ($O_{h}$) and Fe3+ in tetrahedral
($T_{d}$) sites. For the ferrimagnetic garnet structure, spins located on the
$T_{d}$ sites are aligned antiparallel to the spins on the $O_{h}$ sites in a
ratio of 3:2. Hence, the negative peak in the XMCD at the $L_{3}$ edge is due
to tetrahedrally coordinated Fe3+. However, on annealing in an increasingly
reducing environment we notice a change in both the XAS and XMCD close to the
pre-edge region of both the $L_{3}$ and $L_{2}$ edges, as shown in the grey
boxed regions of Figs.3,4. The clear increase in spectral weight that occurs
towards lower photon energies is indicative of an increase in Fe2+, consistent
with annealing in a reducing vacuum environment and / or a displacement
reaction between iron oxide and metallic aluminium. To further demonstrate
this, we integrate the XMCD in the pre-edge region of the $L_{3}$ edge (grey
box). For the Pt capped sample the integral is slightly positive, shown in
Fig. 4, but becomes increasingly negative as the samples are progressively
reduced. This indicates an increasing amount of Fe2+, aligned parallel to the
$T_{d}$ Fe3+ in the near surface region. As Fe2+ has a larger orbital moment
compared to Fe3+, any increase in the former would provide an additional
relaxation mechanism to the lattice, thereby enhancing the Gilbert damping,
consistent with the FMR results.

##  IV Conclusion

In conclusion, we demonstrate that moderate vacuum annealing of YIG or the
addition of an aluminium capping layer significantly increases the Gilbert
damping. For the former case, this increase needs to be taken into account
when obtaining the spin mixing conductance from spin pumping measurements. We
suggest that the main driver for the increase in $\alpha$ is the reduction of
Fe3+ to Fe2+, as demonstrated by soft X-ray magnetic spectroscopy.

##  V Acknowledgments

The authors acknowledge Diamond Light Source for time on Beamline I06 under
proposal MM32492.

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