# Highly fcc-textured Pt-Al alloy films grown on MgO(001) showing enhanced
spin Hall efficiency

Yong-Chang Lau<EMAIL_ADDRESS>Institute for Materials
Research, Tohoku University, Sendai 980-8577, Japan  Center for Spintronics
Research Network, Tohoku University, Sendai 980-8577, Japan  Takeshi Seki
Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan
Center for Spintronics Research Network, Tohoku University, Sendai 980-8577,
Japan  Koki Takanashi  Institute for Materials Research, Tohoku University,
Sendai 980-8577, Japan  Center for Spintronics Research Network, Tohoku
University, Sendai 980-8577, Japan  Center for Science and Innovation in
Spintronics, Core Research Cluster, Tohoku University, Sendai 980-8577, Japan

###### Abstract

We report on a systematic comparative study of the spin Hall efficiency
between highly face-centered cubic (fcc)-textured Pt-Al alloy films grown on
MgO(001) and poorly-crystallized Pt-Al alloy films grown on SiO2. Using CoFeB
as the detector, we show that for Al compositions centering around $x=25$,
mainly L12 ordered Pt100-xAlx alloy films grown on MgO exhibit outstanding
charge-spin conversion efficiency. For Pt78Al22/CoFeB bilayer on MgO, we
obtain damping-like spin Hall efficiency as high as
$\xi_{\textrm{DL}}\sim+0.20$ and expect up to seven-fold reduction of power
consumption compared to the polycrystalline bilayer of the same Al composition
on SiO2. This work demonstrates that improving the crystallinity of fcc Pt-
based alloys is a crucial step for achieving large spin Hall efficiency and
low power consumption in this material class.

##  I Introduction

Current-induced spin-orbit torque (SOT) [1] is a promising means for
manipulating the magnetization of a nanomagnet [2, 3, 4, 5, 6, 7, 8, 9, 10,
11, 12, 13, 14, 15, 16, 17] and for developing next-generation magnetic
memories [18]. In a non-magnetic material (NM)/ferromagnetic material (FM)
bilayer heterostructure with strong spin-orbit coupling, application of an in-
plane charge current leads to the generation of a transverse spin current and
accumulation of non-equilibrium spin density near the NM/FM interface via
either the "bulk" spin Hall effect (SHE) [19] or interfacial Rashba-Edelstein
effect [20, 21] or spin-momentum locking of the topological surface states
[22]. The accumulated spin can be absorbed by the FM, exerting damping-like
and field-like SOT to the magnetization. Experimentally, this charge-to-spin
conversion process is commonly expressed by the relation:

$\displaystyle
j_{\mathrm{spin,FM}}^{\mathrm{DL(FL)}}=\frac{\hbar}{2e}\xi_{\mathrm{DL(FL)}}j_{\mathrm{charge,NM}}$
(1)

where $\hbar$ is the reduced Planck constant, $e$ the elementary charge,
$j_{\mathrm{charge,NM}}$ the charge current flowing within the NM layer,
$j_{\mathrm{spin,FM}}^{\mathrm{DL(FL)}}$ the equivalent spin current absorbed
by the FM layer for producing the measured damping-like (field-like) SOT, and
$\xi_{\mathrm{DL(FL)}}$ the damping-like (field-like) spin Hall efficiency.
Note that here $\xi_{\mathrm{DL(FL)}}$ describes phenomenologically the
conversion efficiency based on the total spin current eventually absorbed by
the FM for SOT generation, ignoring its origin (e.g. SHE or other interfacial
mechanisms) and its transmission probabilities across the interface (e.g. spin
backflow and spin memory loss) [23, 24, 25, 26, 27, 28]. Concerning the power
consumption, the figure of merit scales with
$\xi_{\textrm{DL}}^{2}\rho_{\textrm{NM}}$ or
$\xi_{\textrm{DL}}\sigma_{\textrm{SH}}$ where $\rho_{\textrm{NM}}$ is the
longitudinal resistivity and $\sigma_{\textrm{SH}}$ the spin Hall conductivity
of the NM of thickness $t_{\textrm{NM}}$. More rigorously, for NM/FM bilayer
relevant for most applications, one should include the power dissipation due
to the unavoidable current flow within the FM layer (with a thickness
$t_{\textrm{FM}}$ and resistivity $\rho_{\textrm{FM}}$), leading to the
following power efficiency parameter
$\eta\equiv\frac{1}{1+s}\xi_{\textrm{DL}}\sigma_{\textrm{SH}}$ with
$s=t_{\textrm{FM}}\rho_{\textrm{NM}}/(t_{\textrm{NM}}\rho_{\textrm{FM}})$.
Finding material combinations that maximize $\eta$ is of paramount importance
for improving the performance and competitiveness of any spintronic technology
involving SOT [29, 30, 31, 32].

Pt is an archetypal NM for efficient charge-to-spin conversion and is well-
known for being the elemental material exhibiting the largest
$\sigma_{\textrm{SH}}$. Referring to $\eta$, however, elemental Pt with
relatively small $\xi_{\textrm{DL}}$ is less attractive. Meanwhile, the large
$\sigma_{\textrm{SH}}$ of Pt is mainly attributed to the intrinsic Berry
curvature mechanism [33, 34], featuring $\sigma_{\textrm{SH}}$ that is
independent of the carrier relaxation time, $\tau\propto 1/\rho_{\textrm{NM}}$
for the conduction in the "moderately dirty" regime. An immediate strategy for
improving $\eta$ would be to reduce $\tau$ while maintaining the high
$\sigma_{\textrm{SH}}$ by alloying [35]. Following the pioneering
demonstration of enhanced $\xi_{\textrm{DL}}$ and $\eta$ in polycrystalline
Pt-Al and Pt-Hf alloys [36], considerable research efforts have been devoted
to investigate the SOT in Pt-based alloys [37, 38, 39, 40, 41, 42, 43, 44, 45,
46]. It is worth pointing out that among these attempts, alloying Pt with an
element of identical face-centered cubic (fcc) crystal structure such as Au
[37, 38], Pd [39], and Cu [41, 42, 43] tends to maintain or even slightly
enhance $\sigma_{\textrm{SH}}$ over an extended alloying concentration of
$x\gtrsim 25$ at.%. Intercalating thin Ti spacers in Pt to form a
fcc(111)-textured multilayer is also effective for maintaining high
$\sigma_{\textrm{SH}}$ while reducing $\tau$ (Ref. [47]). In contrast,
introducing dopants of different crystal structures and with limited
solubility (e.g. Al, Hf [36], MgO [40], Cr [45], and Mn [46]) in Pt typically
results in a rapid reduction of $\sigma_{\textrm{SH}}$ and deterioration of
the fcc lattice. These observations seem to suggest increasing the resistivity
while maintaining the fcc crystal structure is beneficial for achieving large
$\eta$ in Pt-based alloys. Here, by revisiting the charge-to-spin conversion
in Pt-Al binary alloys, we show that highly fcc-textured Pt-Al alloy films
grown on MgO(001) single crystal substrates exhibit up to seven-fold
enhancement of $\eta$ compared to their poorly-crystallized polycrystalline
counterparts of the same composition grown on SiO2 substrates. Our results
highlight the central role of high fcc crystallinity and atomic ordering that
govern the efficiency of charge-to-spin conversion in these binary alloys.

##  II Experimental Methods

Figure 1:  (a-b) Illustrations of the crystal structure for (a) face-centered
cubic (fcc) L12-ordered Pt3Al and (b) body-centered cubic B2-ordered PtAl.
(c-f) Reflection high-energy electron diffraction (RHEED) patterns of (c-d)
Pt74Al26 and (e,f) Pt52Al48 films grown on MgO(001) substrates. (c, e) and (d,
f) were observed with the electron beam along the MgO[110] and MgO[100]
azimuths, respectively. White arrows in (d) indicate superlattice streaks due
to the L12 ordering. (g-h) $$1\text{\,}\mathrm{\SIUnitSymbolMicro
m}$\times$1\text{\,}\mathrm{\SIUnitSymbolMicro m}$$ atomic force microscopy
images of uncapped (g) Pt74Al26 and (h) Pt52Al48 films showing low root mean
square (r.m.s.) roughness of $\sim$0.1\text{\,}\mathrm{nm}$$.

Thin film heterostructures consisting of MgO(001) or thermally-oxidized
Si/SiO2 (substrate)//Pt100-xAlx($\sim$6)/Co20Fe60B20(2)/Al(3) (thicknesses in
nanometer) were grown using an ultra-high vacuum magnetron sputtering tool
with a base pressure better than
$2\text{\times}{10}^{-7}\text{\,}\mathrm{Pa}$. Pt100-xAlx alloy films of
varying Al concentration $x$ ranging from 0 to $\sim 48$ at.% were obtained by
tuning the sputtering power of elemental Pt and Al targets. The growth rate of
these Pt-Al alloys was around
$0.03\text{\,}\mathrm{nm}\text{\,}{\mathrm{s}}^{-1}$. Al was used as the
capping layer which naturally oxidized into AlOx. Deposition on MgO(001) was
carried out by first heating the blank substrate to a substrate temperature
$T_{\textrm{sub}}=$500\text{\,}\mathrm{\SIUnitSymbolCelsius}$$ for $\sim$ 1
hour to remove the magnesium hydroxide and other contaminations on the
surface. Next Pt100-xAlx was deposited at
$T_{\textrm{sub}}=$300\text{\,}\mathrm{\SIUnitSymbolCelsius}$$ followed by
postannealing at the same $T_{\textrm{sub}}$ for
$\sim$45\text{\,}\mathrm{min}$$. The remaining CoFeB/Al layers were grown
after cooling down the substrate to near ambient temperature. Prior to this
deposition, reflection high-energy electron diffraction (RHEED) with a beam
energy of $20\text{\,}\mathrm{kV}$ was observed for the Pt100-xAlx surface of
selected samples. The full stacks on SiO2 were also grown at ambient
temperature. Grazing-angle x-ray reflectivity (XRR) was used to measure the
thickness and estimate the density of Pt100-xAlx. The Al concentration $x$ of
the films were estimated by extrapolating the obtained x-ray density to those
of the three known compounds: Pt (Density = 21.45), L12 Pt3Al (Density =
17.58) and B2 PtAl (Density = 13.13). From the XRR, we found no noticeable
change of the growth rate for the two sample series, albeit with different
substrates and $T_{\textrm{sub}}$ (See the supplementary material). Out-of-
plane and in-plane x-ray diffraction (XRD) were measured to study the
structure and the epitaxial relationship of Pt100-xAlx with respect to the
substrate. CoFeB and Al are practically amorphous showing negligible
contribution to the XRD spectra. Surface morphology was characterized by
atomic force microscopy (AFM) on Pt100-xAlx films without CoFeB and Al
capping. Magnetic properties of Pt100-xAlx/CoFeB bilayers were measured using
a vibrating sample magnetometer (VSM) at room temperature.

Micron-sized Hall bar devices were fabricated using standard optical
lithography and Ar ion milling. The distance between the two longitudinal
voltage probes $L$ and the width of the Hall bar $w$ are 25 and
$10\text{\,}\mathrm{\SIUnitSymbolMicro m}$, respectively. Cr(10)/Au(100)
contact pads were formed using ion beam sputtering and standard lift-off
process. The variable-temperature magnetotransport was measured in a Quantum
Design Physical Property Measurement System (PPMS) equipped with a horizontal
rotator using the built-in resistivity bridge. Harmonic Hall measurements were
also carried out in the PPMS at $300\text{\,}\mathrm{K}$ via a home-made
external measurement platform for quantifying the spin Hall efficiency. A
sinusoidal current of frequency $172.1\text{\,}\mathrm{Hz}$ was applied using
a Keithley 6221 dc and ac current source meter while the first and second
harmonic Hall resistances were simultaneously measured using two LI5660 lock-
in amplifiers.

##  III Experimental Results

###  III.1 Structural characterizations

The binary Pt-Al phase diagram for bulk [48] suggests that the solubility of
Al in fcc-Pt is merely $\sim$ 10 at.%. On increasing the Al concentration, we
encounter several ordered Pt-Al compounds that crystallize in cubic
structures. We focus on fcc-based L12 Pt3Al and body-centered cubic
(bcc)-based B2 PtAl, for which the structures are illustrated in Fig. 1a and
b, respectively. Of particular interest is the fcc-based L12 Pt3Al. Based on
the arguments elaborated in Sec. I, the formation of this fcc-ordered compound
may help to maintain a higher $\sigma_{\textrm{SH}}$, which is a main
motivation of this study.

Figure 2:  (a-b) Out-of-plane 2$\theta$-$\theta$ x-ray diffraction (XRD)
spectra of Pt100-xAlx films with varying Al concentration $x$, grown on (a)
MgO(001) and (b) thermally oxidized Si substrates. (c-d) In-plane
$2\theta\chi/\varphi$ scans of (c) Pt74Al26 and (d) Pt52Al48 films on MgO
(i.e. MgO//Pt74Al26 and MgO//Pt52Al48), probing lattice planes along MgO[100]
(upper panels) and MgO[110] (lower panels). (e-f) In-plane $\varphi$ scans
showing the four-fold symmetry of the films and the MgO substrate. The
thicknesses of these Pt100-xAlx films are approximately
$6\text{\,}\mathrm{nm}$.

We first present the successful growth of epitaxial, nearly-stoichiometric
L12-ordered Pt74Al26. Figure 1c and d show the RHEED patterns of the Pt74Al26
film with electron beam along the MgO[110] and MgO[100]. The clear streak
patterns that systematically change with the substrate rotation imply that the
film was epitaxially grown on MgO with a flat surface. Furthermore, the
appearance of streaky satellite pattern (indicated by white arrows) along the
MgO[100] is consistent with L12 ordering. In contrast, the corresponding RHEED
patterns for Pt52Al48, depicted in Fig. 1e and f, are more complicated,
suggesting a mixture of several crystal orientations. AFM images of these two
films are compared in Fig. 1g and h. Both films exhibit very low surface
roughness with a root-mean-square (r.m.s.) roughness of the order of
$0.1\text{\,}\mathrm{nm}$. The flat surface morphology cannot explain the
spot-like RHEED patterns for Pt52Al48.

Table 1: Density, out-of-plane lattice parameter $c$, in-plane lattice parameter $a$, and tetragonal distortion $c/a$ extracted from the x-ray measurements for $\sim$6\text{\,}\mathrm{nm}$$ L12 Pt74Al26 and B2 Pt52Al48 films grown on MgO. $a$ is compared with that of MgO. The mismatch in % and the strain are also given. Compound | Density | Out-of-plane, $c$ (Å) | In-plane, $a$ (Å) | $c/a$ | In-plane MgO (Å) | Mismatch
---|---|---|---|---|---|---
L12 Pt74Al26 | 17.4 | 3.84 | 3.91 | 0.98 |  $a_{\textrm{MgO}}$ = 4.21 | 7% tensile
B2 Pt52Al48 | 13.5 | 3.12 | 3.01 | 1.04 |  $a_{\textrm{MgO}}/\sqrt{2}$ = 2.98 | 1% compressive

We next track the structural change of MgO//Pt100-xAlx based on the
$x$-dependence of the XRD spectra plotted in Fig. 2a. The sputtered Pt film
tends to assume fcc(111) texture on MgO(001) for a moderate
$T_{\textrm{sub}}$, which is consistent with a previous work [49]. Despite the
lack of clear epitaxial relationship with the substrate, the strong fcc(111)
diffraction peak and the clear Laué fringes both imply the high crystallinity
of the Pt film with sharp interfaces. Introducing Al changes the preferred
orientation and texture of the alloy film to fcc(001) while drastically
attenuates the Bragg diffraction of fcc(111). L12-ordered Pt100-xAlx with no
observable secondary phase was obtained for $x=26$. Further increase of $x$
leads to a rapid decrease of the out-of-plane lattice parameter $c$, as shown
by the shift of the Bragg peaks towards higher $2\theta$ angles. After going
through a fcc to bcc transition, single-phase B2-PtAl with clear Laué fringes
was eventually formed for $x=48$. In contrast, the XRD spectra of
SiO2//Pt100-xAlx deposited at ambient temperature (Fig. 2b) show monotonic
decrease of the fcc(111) peak intensity with increasing $x$, suggesting the
non-equilibrium [50] fcc Pt-Al alloy gradually becomes amorphous upon
incorporating more and more Al.

Figure 3:  (a) $x$-dependence of longitudinal resistivity
$\rho_{\textrm{PtAl}}$ for $\sim$6\text{\,}\mathrm{nm}$$ Pt100-xAlx extracted
from Pt100-xAlx($\sim$6)/CoFeB(2) bilayers. Data for samples on MgO are in
black and those for samples on SiO2 are in red. (b) Temperature dependence of
longitudinal resistance $R_{\textrm{xx}}$ normalized by its value at
$300\text{\,}\mathrm{K}$ for Pt100-xAlx($\sim$6)/CoFeB(2) bilayers of selected
Al compositions on MgO. The residual resistivity ratio (RRR) is defined as
$R_{\textrm{xx}}(T=$300\text{\,}\mathrm{K}$)$/$R_{\textrm{xx}}(T=$10\text{\,}\mathrm{K}$)$.
(c) $x$-dependence of saturation magnetization $M_{\textrm{s}}$. Blue line is
a linear fit combining all the data.

Focusing on MgO//Pt74Al26 and MgO//Pt52Al48, we measured the in-plane XRD
($2\theta\chi/\varphi$ scan; Fig. 2c and d) to reveal the tetragonal
distortion of these compounds, which mainly arises from the substrate-induced
in-plane biaxial strain. For MgO//Pt52Al48, we found an additional diffraction
peak corresponding to bcc-PtAl(211) for the scan along MgO[100]. This
parasitic orientation may partially explain the complicated RHEED patterns
shown in Fig. 1e and f. We further use $\varphi$ scans to probe the epitaxial
relationship between these films and the substrates. We found Pt74Al26 film
crystallizes in the cube-on-cube configuration on MgO, experiencing an in-
plane tensile strain of $\sim~{}7\%$ from the latter. Pt52Al48, upon making a
$45\text{\,}\mathrm{\SIUnitSymbolDegree}$ in-plane rotation, is facing an in-
plane compressive strain of $\sim 1\%$ from the MgO. The density deduced from
x-ray reflectivity, the in-plane ($a$) and out-of-plane ($c$) lattice
parameters, and the tetragonal distortion ($c/a$) of these two compounds are
summarized in Table 1.

###  III.2 Basic magnetotransport and magnetic properties

Magnetotransport was measured using the micro-fabricated Hall bar devices.
Figure 3a plots the $x$-dependence of the longitudinal resistivity
$\rho_{\textrm{PtAl}}$ extracted from Pt100-xAlx/CoFeB bilayers using parallel
circuit model and assuming
$\rho_{\textrm{CoFeB}}=$150\text{\,}\mathrm{\SIUnitSymbolMicro\SIUnitSymbolOhm}\text{\,}\mathrm{cm}$$.
In general, $\rho_{\textrm{PtAl}}$ for the two sample sets tend to increase
with increasing $x$, reflecting the modulation of $\tau$ by tuning the alloy
composition. $\rho_{\textrm{PtAl}}$ shows a pronounce local maximum for
$x=0.32$. We tentatively attribute this to the enhanced scattering due to the
formation of many grain boundaries for this particular composition at the
vicinity of fcc-bcc structural transition. Despite having higher
crystallinity, Pt100-xAlx layers grown on MgO tend to be more resistive than
those grown on SiO2. We consider the defects and dislocations due to epitaxial
strain relaxation in these films can enhance the scattering.

The temperature $T$-dependence of $\rho_{\textrm{PtAl}}$ sheds light on the
defects and impurities in these Pt100-xAlx alloy films. Neglecting the $T$
dependence of $\rho_{\textrm{CoFeB}}$, we attribute the overall temperature
change of the bilayer longitudinal resistance $R_{xx}$ to that of
$\rho_{\textrm{PtAl}}$. The normalized
$R_{xx}(T)/R_{xx}(T=$300\text{\,}\mathrm{K}$)$ for selected samples on MgO are
shown in Fig. 3b. We further define the residual resistivity ratio,
$\mathrm{RRR}\equiv
R_{xx}(T=$300\text{\,}\mathrm{K}$)/R_{xx}(T=$10\text{\,}\mathrm{K}$)$. On
increasing $x$, RRR reduces and crosses 1 at $x\sim 0.26$, reflecting a change
from metallic-like (with a positive temperature coefficient of the
resistivity) to semiconducting-like conduction (with a negative temperature
coefficient of the resistivity). A dramatic enhancement of
$\rho_{\textrm{PtAl}}$ for bcc-Pt52Al48 grown on MgO may reflect the intrinsic
transport characteristics of this exotic metastable compound, although further
optimization of the film growth is necessary to exclude the extrinsic
transport contributions from the defects and impurities.

The Al concentration $x$-dependence of the saturation magnetization
$M_{\textrm{s}}$ extracted from VSM for selected samples are plotted in Fig.
3c. Within experimental error (estimated to be $\sim 5\%$), no obvious
substrate dependence of $M_{\textrm{s}}$ is observed. Instead,
$M_{\textrm{s}}$ systematically decreases with increasing $x$, which may be
related to the weakening of the proximity-induced magnetism at
Pt100-xAlx/CoFeB interface, as Pt atoms at interface are gradually replaced by
Al. Combining the two data sets, linear fit yields a slope of
$-264.1\text{\,}\mathrm{kA}\text{\,}{\mathrm{m}}^{-1}\text{\,}{\mathrm{at.\%}}^{-1}$
and a $y$-intercept of
$M_{\textrm{s,Pt}}=$1040\text{\,}\mathrm{kA}\text{\,}{\mathrm{m}}^{-1}$$.
Hereafter, we use the interpolated $M_{\textrm{s}}$ for the SOT quantification
in these heterostructures.

Figure 4:  (a) Schematic illustration of the harmonic Hall measurement setup
for quantifying the spin Hall efficiency of Pt100-xAlx/CoFeB bilayers with
easy-plane magnetic anisotropy. An external magnetic field
$\mu_{0}H_{\textrm{ext}}$ is rotated within the azimuthal plane, making an
angle $\varphi_{\textrm{H}}$ with the current $I$. (b) Hall resistance
$R_{xy}$ against an out-of-plane external field $\mu_{0}H_{z}$. (c) and (e)
$\varphi_{\textrm{H}}$ dependence of the first harmonic Hall resistance
$R_{\omega}$ with $\mu_{0}H_{\textrm{ext}}=$0.2\text{\,}\mathrm{T}$$. (d) and
(f) $\varphi_{\textrm{H}}$ and $\mu_{0}H_{\textrm{ext}}$ dependence of the
second harmonic Hall resistance $R_{2\omega}$. (g)
$\cos{\varphi_{\textrm{H}}}$ component ($A$) and (h)
$\cos{2\varphi_{\textrm{H}}}\cos{\varphi_{\textrm{H}}}$ component of
$R_{2\omega}$ plotted against
$1/(\mu_{0}H_{\textrm{k}}+\mu_{0}H_{\textrm{ext}})$ and
$1/(\mu_{0}H_{\textrm{in-plane}}+\mu_{0}H_{\textrm{ext}})$, respectively. All
the data were measured at $300\text{\,}\mathrm{K}$ for Pt78Al22( 6)/CoFeB(2)
structures grown on MgO and SiO2.

###  III.3 Harmonic Hall measurements

Figure 5:  Al concentration $x$ dependence of (a) anomalous Hall resistance
($R_{\textrm{AHE}}$), (b) planar Hall resistance ($R_{\textrm{PHE}}$), (c)
damping-like spin Hall efficiency ($\xi_{\textrm{DL}}$), (d) field-like spin
Hall efficiency ($\xi_{\textrm{FL}}$), (e) spin Hall conductivity
($\sigma_{\textrm{SH}}$), and (f) the power efficiency $\eta$. Black and red
symbols represent Pt100-xAlx/CoFeB bilayers grown on MgO and SiO2 substrates,
respectively.

The harmonic Hall technique [51, 52, 53, 54, 55] was used to quantify the SOT
in Pt100-xAlx/CoFeB bilayers with in-plane magnetization. The experimental
setup is schematically depicted in Fig. 4a. An external field
$\mu_{0}H_{\textrm{ext}}$ is applied in the PPMS while rotating the sample.
The field vector is making a rotation within the sample azimuthal plane,
making an angle $\varphi_{\textrm{H}}$ with the current, $I$. We measured the
$\varphi_{\textrm{H}}$ angular dependence of the in-phase first harmonic
($R_{\omega}$) and out-of-phase second harmonic Hall resistances
($R_{2\omega}$) at various $\mu_{0}H_{\textrm{ext}}$ ranging from
$0.1\text{\,}\mathrm{T}$ to $4.0\text{\,}\mathrm{T}$. Including thermoelectric
contributions, $R_{\omega}$ and $R_{2\omega}$ are of the form:

$\displaystyle R_{\omega}=R_{\mathrm{PHE}}\sin 2\varphi_{\mathrm{H}}$ (2)
$\displaystyle R_{2\omega}=$
$\displaystyle\left(R_{\mathrm{AHE}}\dfrac{H_{\mathrm{DL}}}{H_{\mathrm{ext}}+H_{\mathrm{k}}}+R_{\mathrm{const}}\right)\cos\varphi_{\mathrm{H}}$
$\displaystyle-2R_{\mathrm{PHE}}\dfrac{H_{\mathrm{FL}}+H_{\mathrm{Oe}}}{H_{\mathrm{ext}}+H_{\mathrm{in-
plane}}}\cos 2\varphi_{\mathrm{H}}\cos\varphi_{\mathrm{H}}$
$\displaystyle=A\cos\varphi_{\mathrm{H}}+B\cos
2\varphi_{\mathrm{H}}\cos\varphi_{\mathrm{H}}$

Harmonic Hall data collected for MgO//Pt78Al22(6)/CoFeB(2) and
SiO2//Pt78Al22(6)/CoFeB(2) bilayers are compared in Fig. 4b-h. The anomalous
Hall resistance $R_{\textrm{AHE}}$ and the out-of-plane anisotropy field
$\mu_{0}H_{\textrm{k}}$ are extracted from the anomalous Hall loop plotted in
Fig. 4b. The extracted $\mu_{0}H_{\textrm{k}}$ are significantly lower than
the demagnetizing field of CoFeB, indicating a non-negligible interface
magnetic anisotropy contribution in Pt100-xAlx/CoFeB/Al trilayers. Eq. 2 is
used to fit the $\varphi_{\mathrm{H}}$-dependence of $R_{\omega}$ to extract
the planar Hall resistance $R_{\textrm{PHE}}$, as shown in Fig. 4c and e.
$\varphi_{\textrm{H}}$-dependence of $R_{2\omega}$ (Fig. 4d and f) can be
decomposed into two parts according to Eq. III.3. The prefactors $A$
(corresponding to $\cos\varphi_{\mathrm{H}}$ component) and $B$ (corresponding
to $\cos 2\varphi_{\mathrm{H}}\cos\varphi_{\mathrm{H}}$ component) of
$R_{2\omega}$ are plotted against
$1/(\mu_{0}H_{\textrm{k}}+\mu_{0}H_{\textrm{ext}})$ and
$1/(\mu_{0}H_{\textrm{in-plane}}+\mu_{0}H_{\textrm{ext}})$, respectively. We
assume an in-plane anisotropy field $\mu_{0}H_{\textrm{in-
plane}}=$0.05\text{\,}\mathrm{mT}$$ which mainly arises from the four-fold
symmetry of the Pt100-xAlx. The slopes of the linear fits in Fig. 4g and Fig.
4h were used to extract the damping-like and the field-like spin-orbit
effective fields. The corresponding spin Hall efficiencies $\xi_{\textrm{DL}}$
and $\xi_{\textrm{FL}}$ are estimated based on the following equation:

$\displaystyle\xi_{\mathrm{DL(FL)}}=\frac{2e}{\hbar}\frac{\mu_{0}H_{\mathrm{DL(FL)}}M_{\mathrm{s}}t_{\mathrm{CoFeB}}}{j_{\mathrm{PtAl}}}$
(4)

where $M_{\mathrm{s}}$ is the interpolated saturation magnetization of the
CoFeB layer obtained from Fig. 3c. Knowing the resistivity of each layer, we
can now calculate the spin Hall conductivity $\sigma_{\textrm{SH}}$ and the
power efficiency $\eta$. Similar analyses were repeated for the two series of
$x$-varying samples grown on MgO and SiO2 to establish the substrate and
$x$-dependence of these quantities. Results are summarized in Fig. 5.

$R_{\textrm{AHE}}$ and $R_{\textrm{PHE}}$ are plotted against $x$ in Fig. 5a
and b, respectively. The anomalous Hall loops of all the samples can be found
in the Supplementary Material. Although Pt100-xAlx films grown on SiO2 are
typically more conducting and should shunt more current from the CoFeB, we
surprisingly found higher $R_{\textrm{AHE}}$ for SiO2//Pt100-xAlx/CoFeB
series. Instead, $x$-dependence of $R_{\textrm{PHE}}$ for the two sample
series are quite similar. This can be understood because CoFeB has a
relatively small anisotropic magnetoresistance and the planar Hall effect in
Pt100-xAlx/CoFeB should mainly originate from the spin Hall magnetoresistance
(SMR) [56, 57, 58]. Details on the SMR of these samples are elaborated in the
Supplementary Material.

The primary results of this work are shown in Fig. 5c-f. For $x\lesssim 30$,
we found striking enhancement for structures on MgO over structures on SiO2
across all aspects, including $\xi_{\mathrm{DL}}$ (Fig. 5c),
$\xi_{\mathrm{FL}}$ (Fig. 5d), $\sigma_{\textrm{SH}}$ (Fig. 5e), and $\eta$
(Fig. 5f). For example, for Pt78Al22/CoFeB bilayer on MgO, with
$\rho_{\textrm{PtAl}}=$105\text{\,}\mathrm{\SIUnitSymbolMicro\SIUnitSymbolOhm}\text{\,}\mathrm{cm}$$,
we found $\xi_{\textrm{DL}}\sim+0.20$ and $\sigma_{\textrm{SH}}\sim
1900(\hbar/2e)\Omega^{-1}\text{cm}^{-1}$, whereas we only obtained
$\xi_{\textrm{DL}}\sim+0.06$ and $\sigma_{\textrm{SH}}\sim
770(\hbar/2e)\Omega^{-1}\text{cm}^{-1}$ for the structure of the same $x$ on
SiO2 with a lower degree of crystallinity and exhibiting a slightly lower
$\rho_{\textrm{PtAl}}=$81\text{\,}\mathrm{\SIUnitSymbolMicro\SIUnitSymbolOhm}\text{\,}\mathrm{cm}$$.
This represents up to seven-fold increase in $\eta$, hence a seven-fold
reduction of power consumption is expected. Compared to a previous work [36],
similar $\xi_{\textrm{DL}}$ and $\sigma_{\textrm{SH}}$ can only be achieved in
Pt85Hf15(5.5)/Pt(0.5)/Co trilayer with carefully engineered interface. We may
thus expect further enhancement of $\sigma_{\textrm{SH}}$ and $\eta$ for well-
ordered Pt78Al22/CoFeB upon optimizing the interface.

The strongly fcc(111)-textured Pt (i.e. $x=0$) on MgO also exhibits a
relatively large $\sigma_{\textrm{SH}}\sim
2600(\hbar/2e)\Omega^{-1}\text{cm}^{-1}$ with a low
$\rho_{\textrm{Pt}}=$17.6\text{\,}\mathrm{\SIUnitSymbolMicro\SIUnitSymbolOhm}\text{\,}\mathrm{cm}$$.
This is to be compared with the relatively poorly crystallized, also
fcc(111)-textured Pt on SiO2, with $\sigma_{\textrm{SH}}\sim
1300(\hbar/2e)\Omega^{-1}\text{cm}^{-1}$ and
$\rho_{\textrm{Pt}}=$27.8\text{\,}\mathrm{\SIUnitSymbolMicro\SIUnitSymbolOhm}\text{\,}\mathrm{cm}$$.
Here, the effect of crystallinity may also present. However, in view of the
low $\rho_{\textrm{Pt}}$, additional $\sigma_{\textrm{SH}}$ contribution due
to extrinsic skew scattering mechanism cannot be excluded. Careful evaluation
of SOT at various temperatures may allow separation of the two
$\sigma_{\textrm{SH}}$ contributions. Finally, the rapid decrease of the
charge-to-spin conversion efficiency in bcc Pt100-xAlx with $x>32$ suggests
for Pt-rich alloys the fcc crystal structure and $\sigma_{\textrm{SH}}$ are
strongly correlated. The high crystallinity alone is a necessary but not a
sufficient condition for obtaining large $\sigma_{\textrm{SH}}$.

We also found large positive $\xi_{\mathrm{FL}}$ with a maximum at $x=0.22$,
which exhibits similar $x$-dependence as $\xi_{\mathrm{DL}}$. The observed
$\xi_{\mathrm{FL}}$ is opposing the Oersted field with a
$\xi_{\mathrm{FL}}/\xi_{\mathrm{DL}}$ ratio up to 0.7, suggesting the two
quantities are strongly correlated. We consider the bulk spin Hall effect
contribution to $\xi_{\mathrm{FL}}$ scales with $\xi_{\mathrm{DL}}$ and is
responsible for the large $\xi_{\mathrm{FL}}$ in Pt-Al/CoFeB bilayers with
$\xi_{\mathrm{DL}}$ up to 0.20. In contrast, the $\xi_{\mathrm{FL}}$
contribution from the interfacial Rashba-Edelstein effect should be negligible
in these more resistive heterostructures because of its small size of $\approx
0.02$, which does not scale with $\rho_{\textrm{PtAl}}$ [59].

Figure 6:  (a) Sheet conductance $1/R_{\textrm{sq}}$ against Pt78Al22 layer
thickness $t_{\textrm{PtAl}}$ for Pt78Al22($t_{\textrm{PtAl}}$)/CoFeB
bilayers. Blue horizontal dashed line represents the expected sheet
conductance of the CoFeB layer. (b) Resistivity of Pt78Al22 layer
$\rho_{\textrm{PtAl}}$ assuming a fixed CoFeB resistivity
$\rho_{\textrm{CoFeB}}=$150\text{\,}\mathrm{\SIUnitSymbolMicro\SIUnitSymbolOhm}\text{\,}\mathrm{cm}$$.
(c) $t_{\textrm{PtAl}}$ dependence of spin Hall conductivity
$\sigma_{\textrm{SH}}$. Black and red curves are calculated from Eq. 5 using
the same $\overline{\sigma}_{\mathrm{SH}}$ in the bulk limit and different
spin diffusion length $\lambda$.

We have also investigated the PtAl thickness $t_{\textrm{PtAl}}$ dependence of
SOT for Pt78Al22($t_{\textrm{PtAl}}$)/CoFeB structures grown on MgO, which
exhibits the highest $\eta$. The sheet conductance $1/R_{\textrm{sq}}$ against
$t_{\textrm{PtAl}}$ is plotted in Fig. 6a. Assuming a fixed CoFeB resistivity
($\rho_{\textrm{CoFeB}}=$150\text{\,}\mathrm{\SIUnitSymbolMicro\SIUnitSymbolOhm}\text{\,}\mathrm{cm}$$),
the extracted resistivity of PtAl $\rho_{\textrm{PtAl}}$ is shown in Fig. 6b.
The strong enhancement of $\rho_{\textrm{PtAl}}$ for low $t_{\textrm{PtAl}}$
may be attributed to interfacial scattering and defects in ultrathin films.
Since the intrinsic mechanism is expected to dominate, we focus on the
$t_{\textrm{PtAl}}$ dependence of $\sigma_{\textrm{SH}}$ as shown in Fig. 6c.
For the structure on MgO with $t_{\textrm{PtAl}}$ as thin as
$\sim$2\text{\,}\mathrm{nm}$$, we found a relatively large
$\sigma_{\textrm{SH}}\sim 1350(\hbar/2e)\Omega^{-1}\text{cm}^{-1}$. The fact
that all the four data points for structures on MgO clearly exhibit higher
$\sigma_{\textrm{SH}}$ than the structure of the same $x$ grown on SiO2 (red
symbol) confirms the robustness of our results. Within a drift-diffusion
model, for $t_{\textrm{PtAl}}$ comparable to the spin diffusion length
$\lambda$, $\sigma_{\textrm{SH}}$ can be described by [60]:

$\displaystyle\sigma_{\mathrm{SH}}(t_{\mathrm{PtAl}})=\overline{\sigma}_{\mathrm{SH}}\left[1-\mathrm{sech}{\frac{t_{\mathrm{PtAl}}}{\lambda}}\right]$
(5)

Black curve in Fig. 6c is calculated using Eq. 5 with
$\overline{\sigma}_{\mathrm{SH}}=1600(\hbar/2e)\Omega^{-1}\text{cm}^{-1}$ and
$\lambda=$0.8\text{\,}\mathrm{nm}$$. The thickness dependence of the SMR is
also consistent with such a short $\lambda$ (See the supplementary material).
The red dashed curve shows that one needs to assume a much longer
$\lambda\sim$4.5\text{\,}\mathrm{nm}$$ for the structure on SiO2 to account
for the $\sigma_{\textrm{SH}}$ gap between the two sample sets. If the spin
relaxation is governed by the Elliott-Yafet mechanism [61, 62], $\lambda$
should be inversely proportional to $\rho_{\textrm{PtAl}}$. Yet,
$2\text{\,}\mathrm{nm}$ Pt78Al22 layer on MgO with the highest
$\rho_{\textrm{PtAl}}$ is only about twice more resistive than Pt78Al22 layer
grown on SiO2. Therefore, we conclude that the potential change of $\lambda$
alone cannot explain the dramatic enhancement of $\xi_{\textrm{DL}}$ and
$\sigma_{\textrm{SH}}$ for highly fcc-textured Pt-Al alloys.

##  IV Discussion

First-principles calculations suggest the exceptionally high intrinsic
$\sigma_{\mathrm{SH}}$ of fcc-Pt is mainly due to the double degeneracies near
the Fermi level $E_{\textrm{F}}$ at the high-symmetry $L$ and $X$ points of
the fcc lattice [33]. Notably, $E_{\textrm{F}}$ of fcc-Pt falls practically on
the summit of a high $\sigma_{\textrm{SH}}$ peak with a broad full-width at
half maximum (FWHM) of the order of $1\text{\,}\mathrm{eV}$. Although this SHE
contribution is robust against impurities due to its intrinsic nature,
introducing dopants unavoidably modulate $\sigma_{\mathrm{SH}}$ via three
mechanisms. Firstly, alloying may induce carrier doping that shifts the
$E_{\textrm{F}}$ of the doped Pt alloy away from this optimum position,
leading to a reduction of $\sigma_{\textrm{SH}}$. Secondly, alloying with a
lighter element will weaken the average spin-orbit coupling and distort the
critical nearly-degenerated nodes/lines in the band structure. Thirdly,
alloying can deform the lattice and even induce structural change that will
significantly alter the band structure. We note that rigid-band approximations
may be valid for the first mechanism whereas the later two are clearly beyond
this simple picture. Based on these three mechanisms, we can now comment on
our experimental observations.

In Fig. 5e, we have observed a monotonic decrease of $\sigma_{\textrm{SH}}$
with increasing $x$. In principle, all the three mechanisms may be relevant
and are hardly distinguishable. Here, the comparison of $\sigma_{\textrm{SH}}$
for fcc-Pt100-xAlx (grown on different substrates) exhibiting different degree
of crystallinity allows us to extract the net $\sigma_{\textrm{SH}}$ gain
which is correlated with the high-quality fcc texture of the L12-ordered Pt3Al
alloy. In such an ordered alloy, the Al atoms selectively substitute Pt atoms
of the parent fcc-Pt lattice which helps to maintain the fcc structure
throughout and minimize the band structure distortion. Instead, if the same
amount of Al is randomly distributed in Pt (the film grown on SiO2), due to
their small atomic radius, Al atoms are more likely occupying interstitial
sites, resulting in a rapid degradation of the fcc structure. The unique
degenerated bands with large spin Berry curvature in the electronic band
structure of fcc-Pt may be strongly perturbed and one may expect a faster
reduction of $\sigma_{\textrm{SH}}$ in this case. Having established the
tunability of $\sigma_{\textrm{SH}}$ with the degree of crystallinity, it
would be interesting to check whether the performance of other Pt-based fcc
alloys (e.g. Pt-Au, Pt-Pd and Pt-Cu) can be further enhanced by improving the
film texture or atomic ordering.

Furthermore, we note that fully epitaxial films are not required for observing
such an enhancement as demonstrated by MgO//Pt78Al22/CoFeB which, according to
the XRD spectrum, is consisted of a mixture of fcc(111) and fcc(100) textured
crystallites. We believe this is partially due to the fact that the measured
spin current is flowing along the film normal. In this geometry, the long-
range atomic order within the film plane is less critical. We should also note
that the high crystallinity alone is not a sufficient condition for obtaining
large $\sigma_{\textrm{SH}}$, as B2 Pt52Al48 with relatively high
crystallinity only exhibit low $\sigma_{\textrm{SH}}$. The band structure of
bcc-based Pt compounds may not possess nearly-degenerated nodes/lines near
$E_{\textrm{F}}$ that can host large spin Berry curvature.

Finally, from the applications point of view, protocols for growing at ambient
temperature L12 Pt3Al (or other fcc-based Pt compounds) of similar quality on
amorphous or polycrystalline substrates are highly desirable. Inspired by the
successful growth of L10-ordered FePt [63, 64] and tetragonal Mn-based Heusler
compounds [65, 66] on SiO2, we believe some of these strategies may be applied
to L12 Pt3Al. Furthermore, the fcc(100) texture of L12 Pt3Al with four-fold
in-plane symmetry is compatible with the coherent tunneling across the
crystalline MgO(001) barrier, a prerequisite for large tunneling
magnetoresistance readout [67].

##  V Summary

In summary, we have studied the Al concentration $x$ dependence of spin Hall
efficiency and power consumption efficiency for Pt100-xAlx/CoFeB bilayers
grown on two different substrates (MgO or SiO2). For $x\lesssim 30$,
systematic enhancement over all aspects was found for structures grown on MgO,
which we attribute to the ideal positioning of Al atoms substituting Pt in the
fcc lattice. The fcc crystal structure critical for large spin Berry curvature
can be maintained with better crystallinity and higher ordering compared to
similar structures grown on SiO2. This work uncovers the essential role of the
structural aspect for modulating the spin Hall efficiency in Pt-based fcc
alloys, pointing to a new direction for further improving state-of-the-art
materials for spin current generation via the spin Hall effect.

## Supplementary Material

See supplementary material for the comparison of x-ray reflectivity, spin Hall
magnetoresistance, and anomalous Hall effect for samples grown on MgO and SiO2
substrates.

###### Acknowledgements.

This work was supported by JSPS KAKENHI Grant-in-Aid for Scientific Research
(S) (JP18H05246), Grant-in-Aid for Early-Career Scientists (JP20K15156) and
Grant-in-Aid for Scientific Research (A) (JP20H00299). The structural
characterizations and device fabrication were carried out at the Cooperative
Research and Development Center for Advanced Materials, IMR, Tohoku
University. The authors thank T. Sasaki for her help to do the film deposition
by ion beam sputtering.

## Data Availability Statement

The data that support the findings of this study are available from the
corresponding author upon reasonable request.

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