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

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 SiO$_2$. Using CoFeB as the detector, we show that for Al compositions centering around $x = 25$, mainly L1$_{2}$ ordered Pt$_{100-x}$Al$_x$ alloy films grown on MgO exhibit outstanding charge-spin conversion efficiency. For Pt$_{78}$Al$_{22}$/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 SiO$_2$. 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 spinmomentum 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: spin,FM the equivalent spin current absorbed by the FM layer for producing the measured damping-like (field-like) SOT, and ξ DL(FL) the damping-like (field-like) spin Hall efficiency. Note that here ξ 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 ξ 2 DL ρ NM or ξ DL σ SH where ρ NM is the longitudinal resistivity and σ SH the spin Hall conductivity of the NM of thickness t 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 FM and resistivity ρ FM ), leading to the following power . Finding material combinations that maximize η 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 σ SH . Referring to η, however, elemental Pt with relatively small ξ DL is less attractive. Meanwhile, the large σ SH of Pt is mainly attributed to the intrinsic Berry curvature mechanism 33,34 , featuring σ SH that is independent of the carrier relaxation time, τ ∝ 1/ρ NM for the conduction in the "moderately dirty" regime. An immediate strategy for improving η would be to reduce τ while maintaining the high σ SH by alloying 35 . Following the pioneering demonstration of enhanced ξ DL and η 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 facecentered cubic (fcc) crystal structure such as Au 37,38 , Pd 39 , and Cu 41-43 tends to maintain or even slightly enhance σ SH over an extended alloying concentration of x 25 at.%. Intercalating thin Ti spacers in Pt to form a fcc(111)-textured multilayer is also effective for maintaining high σ SH while reducing τ (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 σ 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 η in Ptbased 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 η compared to their poorly-crystallized polycrystalline counterparts of the same composition grown on SiO 2 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
Thin film heterostructures consisting of MgO(001) or thermally-oxidized Si/SiO 2 (substrate)// Pt 100−x Al x (∼6)/Co 20 Fe 60 B 20 (2)/Al(3) (thicknesses in nanometer) were grown using an ultra-high vacuum magnetron sputtering tool with a base pressure better than 2 × 10 −7 Pa. Pt 100−x Al x alloy films of varying Al concentration x ranging from 0 to ∼ 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 nm s −1 . Al was used as the capping layer which naturally oxidized into AlO x . Deposition on MgO(001) was carried out by first heating the blank substrate to a substrate temperature T sub = 500°C for ∼ 1 hour to remove the magnesium hydroxide and other contaminations on the surface.
Next Pt 100−x Al x was deposited at T sub = 300°C followed by postannealing at the same T sub for ∼ 45 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 kV was observed for the Pt 100−x Al x surface of selected samples. The full stacks on SiO 2 were also grown at ambient temperature. Grazing-angle x-ray reflectivity (XRR)

A. Structural characterizations
The binary Pt-Al phase diagram for bulk 48 suggests that the solubility of Al in fcc-Pt is merely ∼ 10 at.%. On increasing the Al concentration, we encounter several ordered Pt-Al compounds that crystallize in cubic structures. We focus on fcc-based L1 2 Pt 3 Al 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 L1 2 Pt 3 Al. Based on the arguments elaborated in Sec. I, the formation of this fcc-ordered compound may help to maintain a higher σ SH , which is a main motivation of this study.
We first present the successful growth of epitaxial, nearly-stoichiometric L1 2 -ordered Pt 74 Al 26 .     a is compared with that of MgO. The mismatch in % and the strain are also given.   Fig. 1e and f. We further use ϕ scans to probe the epitaxial relationship between these films and the substrates. We found Pt 74 Al 26 film crystallizes in the cube-on-cube configuration on MgO, experiencing an in-plane tensile strain of ∼ 7% from the latter. Pt 52 Al 48 , upon making a 45°in-plane rotation, is facing an in-plane compressive strain of ∼ 1% from the MgO. The density deduced from x-ray reflectivity, the inplane (a) and out-of-plane (c) lattice parameters, and the tetragonal distortion (c/a) of these two compounds are summarized in Table I.

B. Basic magnetotransport and magnetic properties
Magnetotransport was measured using the micro-fabricated Hall bar devices. Figure 3a plots   (2) bilayers are compared in Fig. 4b-h. The anomalous Hall resistance R AHE and the out-of-plane anisotropy field µ 0 H k are extracted from the anomalous Hall loop plotted in Fig. 4b. The extracted µ 0 H k are significantly lower than the demagnetizing field of CoFeB, indicating a non-negligible interface magnetic anisotropy contribution in Pt 100−x Al x /CoFeB/Al trilayers. Eq. 2 is used to fit the ϕ H -dependence of R ω to extract the planar Hall resistance R PHE , as shown in Fig. 4c and e. ϕ H -dependence of R 2ω (Fig. 4d and f)  We assume an in-plane anisotropy field µ 0 H in-plane = 0.05 mT which mainly arises from the fourfold symmetry of the Pt 100−x Al x . 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 ξ DL and ξ FL are estimated based on the following equation: where M 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 σ SH and the power efficiency η. Similar analyses were repeated for the two series of x-varying samples grown on MgO and SiO 2 to establish the substrate and x-dependence of these quantities. Results are summarized in Fig. 5.
R AHE and R 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 Pt 100−x Al x films grown on SiO 2 are typically more conducting and should shunt more current from the CoFeB, we surprisingly found higher R AHE for SiO 2 //Pt 100−x Al x /CoFeB series. Instead, x-dependence of R 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 Pt 100−x Al x /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 30, we found striking enhancement for structures on MgO over structures on SiO 2 across all aspects, including ξ DL (Fig. 5c), ξ FL (Fig. 5d), σ SH (Fig. 5e), and η (Fig. 5f). For example, for Pt 78 Al 22 /CoFeB bilayer on MgO, with ρ PtAl = 105 µΩ cm, we found ξ DL ∼ +0.20 and σ SH ∼ 1900(h/2e)Ω −1 cm −1 , whereas we only obtained ξ DL ∼ +0.06 and σ SH ∼ 770(h/2e)Ω −1 cm −1 for the structure of the same x on SiO 2 with a lower degree of crystallinity and exhibiting a slightly lower ρ PtAl = 81 µΩ cm. This represents up to seven-fold increase in η, hence a seven-fold reduction of power consumption is expected. Compared to a previous work 36  The strongly fcc(111)-textured Pt (i.e. x = 0) on MgO also exhibits a relatively large σ SH ∼ 2600(h/2e)Ω −1 cm −1 with a low ρ Pt = 17.6 µΩ cm. This is to be compared with the relatively poorly crystallized, also fcc(111)-textured Pt on SiO 2 , with σ SH ∼ 1300(h/2e)Ω −1 cm −1 and ρ Pt = 27.8 µΩ cm. Here, the effect of crystallinity may also present. However, in view of the low ρ Pt , additional σ SH contribution due to extrinsic skew scattering mechanism cannot be excluded.
Careful evaluation of SOT at various temperatures may allow separation of the two σ SH contributions. Finally, the rapid decrease of the charge-to-spin conversion efficiency in bcc Pt 100−x Al x with x > 32 suggests for Pt-rich alloys the fcc crystal structure and σ SH are strongly correlated.
The high crystallinity alone is a necessary but not a sufficient condition for obtaining large σ SH .
We also found large positive ξ FL with a maximum at x = 0.22, which exhibits similar xdependence as ξ DL . The observed ξ FL is opposing the Oersted field with a ξ FL /ξ DL ratio up to 0.7, suggesting the two quantities are strongly correlated. We consider the bulk spin Hall effect contribution to ξ FL scales with ξ DL and is responsible for the large ξ FL in Pt-Al/CoFeB bilayers with ξ DL up to 0.20. In contrast, the ξ FL contribution from the interfacial Rashba-Edelstein effect should be negligible in these more resistive heterostructures because of its small size of ≈ 0.02, which does not scale with ρ PtAl 59 .
We have also investigated the PtAl thickness t PtAl dependence of SOT for Pt 78 Al 22 (t PtAl )/CoFeB structures grown on MgO, which exhibits the highest η. The sheet conductance 1/R sq against t PtAl is plotted in Fig. 6a. Assuming a fixed CoFeB resistivity (ρ CoFeB = 150 µΩ cm), the extracted resistivity of PtAl ρ PtAl is shown in Fig. 6b. The strong enhancement of ρ PtAl for low t 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 PtAl dependence of σ SH as shown in Fig. 6c. For the structure on MgO with t PtAl as thin as ∼ 2 nm, we found a relatively large σ SH ∼ 1350(h/2e)Ω −1 cm −1 .
The fact that all the four data points for structures on MgO clearly exhibit higher σ SH than the structure of the same x grown on SiO 2 (red symbol) confirms the robustness of our results. Within a drift-diffusion model, for t PtAl comparable to the spin diffusion length λ , σ SH can be described by 60 : Black curve in Fig. 6c is calculated using Eq. 5 with σ SH = 1600(h/2e)Ω −1 cm −1 and λ = 0.8 nm.
The thickness dependence of the SMR is also consistent with such a short λ (See the supplementary material). The red dashed curve shows that one needs to assume a much longer λ ∼ 4.5 nm for the structure on SiO 2 to account for the σ SH gap between the two sample sets. If the spin relaxation is governed by the Elliott-Yafet mechanism 61,62 , λ should be inversely proportional to ρ PtAl . Yet, 2 nm Pt 78 Al 22 layer on MgO with the highest ρ PtAl is only about twice more resistive than Pt 78 Al 22 layer grown on SiO 2 . Therefore, we conclude that the potential change of λ alone cannot explain the dramatic enhancement of ξ DL and σ SH for highly fcc-textured Pt-Al alloys.

IV. DISCUSSION
First-principles calculations suggest the exceptionally high intrinsic σ SH of fcc-Pt is mainly due to the double degeneracies near the Fermi level E F at the high-symmetry L and X points of the fcc lattice 33 . Notably, E F of fcc-Pt falls practically on the summit of a high σ SH peak with a broad full-width at half maximum (FWHM) of the order of 1 eV. Although this SHE contribution is robust against impurities due to its intrinsic nature, introducing dopants unavoidably modulate σ SH via three mechanisms. Firstly, alloying may induce carrier doping that shifts the E F of the doped Pt alloy away from this optimum position, leading to a reduction of σ SH . Secondly, alloying with a lighter element will weaken the average spin-orbit coupling and distort the critical nearlydegenerated 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 σ SH with increasing x. In principle, all the three mechanisms may be relevant and are hardly distinguishable. Here, the comparison of σ SH for fcc-Pt 100−x Al x (grown on different substrates) exhibiting different degree of crystallinity allows us to extract the net σ SH gain which is correlated with the high-quality fcc texture of the Furthermore, we note that fully epitaxial films are not required for observing such an enhancement as demonstrated by MgO//Pt 78 Al 22 /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 σ SH , as B2 Pt 52 Al 48 with relatively high crystallinity only exhibit low σ SH . The band structure of bcc-based Pt compounds may not possess nearly-degenerated nodes/lines near E F that can host large spin Berry curvature.
Finally, from the applications point of view, protocols for growing at ambient temperature 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.