Variation of the giant intrinsic spin Hall conductivity of Pt with carrier lifetime

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Science Advances  19 Jul 2019:
Vol. 5, no. 7, eaav8025
DOI: 10.1126/sciadv.aav8025


More than a decade after the first theoretical and experimental studies of the spin Hall conductivity (SHC) of Pt, both its dominant origin and amplitude remain in dispute. We report the experimental determination of the rapid variation of the intrinsic SHC of Pt with the carrier lifetime (τ) in the dirty-metal regime by incorporating finely dispersed MgO intersite impurities into the Pt, while maintaining its essential band structure. This conclusively validates the theoretical prediction that the SHC in Pt in the dirty-metal regime should be dominated by the intrinsic contribution, and should decrease rapidly with shortening τ. When interfacial spin backflow is taken into account, the intrinsic SHC of Pt in the clean limit is at least 1.6 × 106 (ℏ/2e) ohm−1 m−1, more than 3.5 times greater than the available theoretical predictions. Our work also establishes a compelling spin Hall metal Pt0.6(MgO)0.4 with an internal giant spin Hall ratio of 0.73.


Since the first theoretical and experimental efforts on its spin Hall conductivity (SHC) a decade ago (14), platinum (Pt), the archetypal spin Hall material, has been central in generating and detecting pure spin currents and key in establishing most of the recent spin-orbit coupling phenomena (511). However, the correct physical understanding of the SHC of Pt has remained unresolved, both qualitatively and quantitatively, despite the extensive attention that has been given to this intriguing condensed matter physics problem (123). The bulk spin Hall effect (SHE) of a heavy metal (HM) can have three possible contributions, i.e., the intrinsic contribution from the Berry curvature of the band structure and the extrinsic skew-scattering and side-jump contributions from spin-orbit interaction–related defect and impurity scattering (24). Theoretically, the intrinsic contribution should dominate the SHC of Pt in the dirty-metal and clean regimes where the carrier lifetime (τ) is short, whereas the extrinsic contributions can become important only in the ultraclean regime where τ is very long (see fig. S1) (25). A tight-binding model calculation by Tanaka et al. (1) has specified that a Pt sample is in the dirty-metal regime when its resistivity (ρxx∝τ −1) is larger than ~30 microhm·cm. As a result, the intrinsic SHC of Pt, while being almost constant in the clean limit, is calculated to degrade rapidly with increasing ρxx or shortening τ in the dirty-metal regime [e.g., the calculated intrinsic SHC decreases from 2.6 × 105 to 1.6 × 105 then to 0.1 × 105 (ℏ/2e) ohm−1 m−1 as ρxx increases from 8 to 65 then to 200 microhm·cm (1)). Despite the consensus on the decrease of the SHC with τ in the dirty-metal regime, note that, quantitatively, the predicted clean-limit values of the intrinsic SHC (σSH) of Pt from the available theoretical calculations differ by more than a factor of 10 [i.e., σSH = (0.4 to 4.5) × 105 (ℏ/2e) ohm−1 m−1] (1, 2, 13, 18).

Experimentally, the characteristic variation of the intrinsic SHC with τ in the dirty-metal regime has never been quantified because it is a challenge to tune τ over a large range without varying the band structure and the Berry curvature. For example, in the composition-dependent studies on Pt-based binary alloys (e.g., Pd1−xPtx or Au1−xPtx) (14, 16, 18), the source of the SHC is the new alloy phase rather than Pt, as indicated by the greater SHC in the more resistive Au1−xPtx and Pd1−xPtx phases than that in Pt. Also, there is a substantial change in the lattice constant (tensile strain) of the material upon alloying (14, 16), which first-principles calculations (26) have indicated to significantly alter the SHC of Pt. In previous composition- or thickness-dependent studies (14, 16, 18, 23), the increase of the damping-like spin-orbit torque (SOT) efficiency per unit bias current density (ξDLj) with increasing ρxx was not a definitive indication of an intrinsic SHC because the side-jump contribution to ξDLj can also increase with ρxx. Since ξDLj = TintσSHρxx, with Tint being the spin transparency of the HM/ferromagnet (FM) interface, the experimental situation can also have an additonal complication when the HM layer is thinner than four times of its spin diffusion length (λs). This is because raising ρxx can increase Tint (see Eq. 3) by shortening λs of the HM (λs ∝ 1/ρxx in the Elliott-Yafet spin relaxation mechanism) (27, 28) and thus can affect spin backflow (SBF) when the HM thickness is not >>4λs (29, 30). Last, in a recent temperature-dependent nonlocal spin valve study of Pt with varying ρxx (15), the amplitudes and the variations of σSH are both comparable with the reported measurement uncertainty in the dirty-metal regime, preventing any examination of the variation of the intrisic σSH of Pt with ρxx and thus τ.

There is also a strong disagreement between experiments on the amplitude of σSH in Pt in the clean limit. Direct SOT measurements (31) reveal a lower bound value of ≈1.5 × 106 (ℏ/2e) ohm−1 m−1 for the intrinsic σSH of Pt with ρxx ≈ 30 to 50 microhm·cm when the less than unitary Tint due to SBF (29, 30) and spin memory loss (SML) at the Pt/FM interfaces (3133) is taken into account. In contrast, the nonlocal spin valve study (15) where all the interfaces were assumed to be fully spin-transparent reported a small constant σSH of 0.3 × 106 (ℏ/2e) ohm−1 m−1 for both dirty and clean limits (ρxx = 6 to 80 microhm·cm). Generally, since the bare spin-mixing conductance at an HM/FM interface (GHM/FM) is only comparable to the spin conductance of the HM (GHM) rather being infinite, the drift-diffusion model (29, 30) predicts that an SBF will substantially reduce Tint, e.g., by more than 50% for Pt/FM interfaces. This has been unambiguously confirmed by the discovery of the spin Hall magnetoresistance in Pt/FM systems (34). Any SML due to substantial interfacial spin-orbit scattering (ISOC) at the interface (31) will further decrease Tint. Clarifying the underlying physics of the giant SHC of Pt is both of fundamental interest and of technological urgency (e.g., for maximizing ξDLjfor low-power devices). Arguably, Pt and certain Pt-rich alloys (14, 16) are the most attractive class of spin Hall metals for energy-efficient spin-torque applications because their combination of the highest SHC of any known class of metals with comparatively low ρxx provides a high ξDLj and minimal current shunting into an adjacent FM at the same time.

In this work, we report a substantial (×3) tuning of carrier mean lifetime τ in Pt films by varying the concentration of MgO intersite impurities (Fig. 1A) while maintaining the long-range face-centered-cubic (fcc) order of the Pt. From this, we observe a rapid degradation (×5) of the intrinsic SHC of Pt with decreasing τ in the dirty-metal regime, providing the first experimental validation of the tight-binding model prediction of the characteristic variation of the intrinsic SHC of Pt with carrier lifetime (1). We are also able to exclude both extrinsic and interfacial mechanisms as important contributions to the SHC of Pt over the investigated resistivity range (30 microhm·cm ≤ ρxx ≤ 240 microhm·cm). These results conclusively establish that the dominant source of the giant SHC in Pt in the dirty-metal regime is the bulk intrinsic SHE arising from the Berry curvature of its band structure. This also establishes the limit to which θSH can be increased by shortening the carrier lifetime of Pt. Moreover, the giant experimental SHC values for Pt (e.g., ≥1.6 × 106 (ℏ/2e) ohm−1 m−1 in the clean limit) indicate that the existing first-principles and tight-binding theories (1, 2, 12, 13, 18) are underestimating the true intrinsic SHC in Pt by more than a factor of 3.5. Last, we achieve a 100% enhancement in ξDLj by increasing ρxx via the incorporation of MgO impurities into Pt. This establishes a new ternary spin Hall material Pt0.6(MgO)0.4 that is very compelling for low-power SOT applications because of its combination of a giant θSH, a comparably low ρxx, a large Dzyaloshinskii-Moriya interaction (DMI), and easy growth on silicon substrates by sputtering.

Fig. 1 Sample structure.

(A) Schematic of enhanced impurity scattering in Pt by finely dispersed MgO molecules. (B) XPS spectrum for Pt 4f peaks in a Pt0.6(MgO)0.4 layer (black line) and a pure Pt layer (red line), indicating non-oxidation of Pt in both cases. a.u., arbitrary units. (C) XPS spectrum for Pt 4d and 4p peaks, Mg KLL peak, and O 1s, indicating that Pt atoms are not oxidized while Mg and O atoms coexist as MgO molecules in the Pt1−x(MgO)x layer peak. The solid lines represent the peak positions expected for nonbonding instances. Different from the Pt peaks, the Mg KLL and O 1s peaks show clear shifts of ±0.8 eV in binding energy, suggesting that Pt is not oxidized while Mg is oxidized. (D) Cross-sectional high-angle annular dark field scanning transmission electron microscopy (HAADF-STEM) image and energy-dispersive x-ray spectroscopy mapping of Pt, Mg, and O, showing no indication of Pt or MgO clusters. The two dotted lines represent the upper and lower interfaces of the Pt0.6(MgO)0.4 layer. (E) Cross-sectional high-resolution transmission electron microscopy image (bright field) of a magnetic stack of Ta 1/ Pt0.6(MgO)0.4 4/Co 1.4/MgO 2/TaOx 1.5. (F) XRD θ-2θ patterns for Pt1−x(MgO)x/Co bilayers with different x, indicating the robustness of the long-range fcc order of Pt (peak position) in the presence of increasing MgO impurities (peak weakening and broadening).


Sample structure

Multilayer stacks of Ta 1.0/Pt1−x(MgO)x 4.0/Co 0.68 to 1.4/MgO 2.0/Ta 1.5 (numbers are thickness in nanometers) with MgO volume percentage x = 0, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3. 0.35, 0.4, and 0.5, respectively, were sputter-deposited on Si/SiO2 substrates. The Pt1−x(MgO)x layer was co-sputtered from a Pt target and a MgO target. The Co magnetization (Ms) for these samples was measured by a vibrating sample magnetometer to be ~1220 ± 85 electromagnetic unit/cm3, indicating the absence of an important magnetic proximity effect (22) in these as-grown samples. We find from x-ray photoemission spectroscopy (XPS) studies (Fig. 1B) that the Pt 4f7/2 and 4f5/2 peaks are located at 71.1 and 74.4 eV, respectively, in both a Pt0.6(MgO)0.4 and a pure Pt layer. In contrast, the binding energies of 4f7/2 and 4f5/2 peaks for Pt oxides are reported to be shifted to ~72.3 and ~75.8 eV for Pt2+ and to 74.0 and 77.5 eV for Pt4+, respectively (35, 36). Meanwhile, we find that the XPS peaks for Mg KLL and O 1s are shifted by ≈±0.8 eV, respectively (Fig. 1C). This indicates that, in the Pt1−x(MgO)x layers, the Pt atoms are not oxidized while the Mg atoms are oxidized, and Mg and O coexist as MgO molecules, consistent with the fact that Pt has a much stronger electronegativity than Mg. Figure 1D shows cross-sectional energy-dispersive x-ray spectroscopy (EDS) Pt, Mg, and O mapping of the composite material Pt0.6(MgO)0.4 under the high-angle annular dark field scanning transmission electron microscopy (HAADF-STEM) mode (a relatively low-resolution mode). This indicates, within the resolution, that the MgO molecules are finely dispersed within the Pt. High-resolution cross-sectional transmission electron microscopy (TEM) studies of the Pt(MgO) composites [see Fig. 1E for imaging of a Pt0.6(MgO)0.4 sample] show that the co-sputtered Pt1−x(MgO)x layer has a homogeneous polycrystalline texture where the grains are ~4 nm in vertical extent and that there is no indication of the presence of Pt or MgO clusters of observable size. The high-resolution transmission electron microscopy (TEM) result in Fig. 1E indicates that the long-range fcc order of Pt is essentially maintained despite the high-concentration MgO impurities (x = 0.4 in Fig. 1E). This is further reaffirmed by the x-ray diffraction (XRD) θ-2θ patterns of Pt1−x(MgO)x 4/Co 1.4 bilayers in Fig. 1F. The Pt1−x(MgO)x layer shows a broad fcc (111) peak due to the polycrystalline texture and the small thickness. However, unlike the case for Pt alloyed with another fcc metal (14, 16), the fcc (111) peak for all different values of x does not shift with x but is located at the Bragg angle of Pt for all different x, indicating that the diffraction is from the periodic Pt lattice and that the MgO molecules are primarily dispersed in the Pt as intersite impurities rather than being substituted into the Pt lattice. However, the Pt (111) peaks do show a marked broadening and weakening with increasing x (see fig. S3) due to the increasing presence of MgO impurities and the reducing Pt atomic volume. We also note here that, in this XRD measurement configuration where the grain size along the film normal is the film thickness (~4 nm; see Fig. 1E), the broadening of the Pt (111) peaks does not indicate a variation of the Pt grain size. It is somewhat unexpected that the lattice periodicity of Pt is so resilient against a large degree of MgO incorporation. A more detailed high-resolution analysis in the future can be useful for better understanding this material, but it is beyond the scope of the present work.

Resistivity and carrier lifetime

We determined the average resistivity ρxx for the Pt1−x(MgO)x layers for each x by measuring the conductance enhancement of the corresponding stacks with respect to a reference stack with no Pt1−x(MgO)x layer. Note that the average resistivity ρxx best describes the effective scattering (by impurities, interfaces, and phonons) that a charge carrier experiences when flowing in the Pt1−x(MgO)x layer (see Fig. 1A and fig. S2) and directly determines the charge current density (je) via je = Exx for a given applied electric field E. As summarized in Fig. 2A, ρxx for the Pt1−x(MgO)x is enhanced by a factor of ~8, i.e., increases gradually from 33 microhm·cm at x = 0 (pure Pt) to 74 microhm·cm for x = 0.4, and then jumps up to 240 microhm·cm for x = 0.5. These high values of ρxx (>30 microhm·cm) place the Pt1−x(MgO)x films with 0 ≤ x ≤ 0.5 in the dirty-metal regime as calculated by Tanaka et al. (1) and as indicated by our experimental results discussed below. The increase in ρxx with x is due, in part, to the increase in carrier scattering rate (1/τ) and, in part, to the decrease in charge carrier density n = nPt (1−x). To separate these two contributions, we use the Drude model approximation for the resistivityρxx=1/σxx=m*/ne2τ(1)where σxx is the electrical conductivity and m* is the effective mass of the charge carriers. In this approximation, the carrier lifetime in Pt1−x(MgO)x isτ=σxxm*/ne2τPtσxx/σxx,Pt(1x)(2)where σxx,Pt and τPt = σxx,Ptm*/ne2 are the electrical conductivity and the carrier lifetime of the 4-nm pure Pt film (x = 0). As shown in Fig. 2B, with increasing impurity concentration x, τ for Pt1−x(MgO)x decreases monotonically from τPt for x = 0, moderately to 0.74τPt for x = 0.4, and then more abruptly to 0.27τPt for x = 0.5. We speculate that the modest increase in the carrier scattering rate with the MgO incorporation for x up to 0.4 is due to the very small scattering cross section of MgO molecules, while the substantial increase in scattering rate when x is increased from 0.4 to 0.5 may be due to an increase of very small MgO aggregates with a higher scattering cross section at that higher MgO content.

Fig. 2 Variation of the SHC with carrier lifetime.

The experimental values of (A) the average resistivity, (B) carrier lifetime, (C) the apparent SHC (σSH*) for Pt1−x(MgO)x 4/Co 1.4 bilayers plotted as a function of MgO concentration (x) of the Pt1−x(MgO)x layers. (D) Experimental and theoretical values for the (apparent) SHC of Pt plotted as a function of σxx/(1 − x), with σxx/(1 − x) being an approximate linear indicator of carrier lifetime. Inset: Nonlinear dependence of the experimental values of σSH* and σSH on σxx. In (D), the black dots, gray squares, and violet dot represent σSH of Pt predicted by the tight-binding model and first-principles calculations in the studies of Tanaka et al. (1), Guo et al. (2), and Obstbaum et al. (18), respectively. The red star represents the experimental value of σSH of Pt determined in (31). The dashed lines in (D) are solely to guide the eyes.

Physical origin of the giant SHC in Pt

In the following, we determine that the dominant source of the Pt SHC is the intrinsic SHE. We first calculated the apparent SHC σSH*TintσSH = (ℏ/2e)ξDLE as a function of x from our experimental results in Fig. 2C. Here, ξDLE = μ0MstHDL/E is the damping-like SOT per applied electric field (23), μ0 is the permeability of vacuum, t is the ferromagnetic layer thickness, and HDL is the damping-like SOT effective field for E = 66.7 kV/m as determined from harmonic response measurements (see figs. S4 and S5 and section S1) (14, 16, 31). Note that the thickness (d) and the carrier density (thus σxx) of the HM are not involved in the calculation of σSH* and ξDLE. In good accord with the changes in τ caused by the MgO addition, σSH* decreases only moderately from 4.9 × 105 (ℏ/2e) ohm−1 m−1 at x = 0 to 4.1 × 105 (ℏ/2e) ohm−1 m−1 at x = 0.4 and then sharply drops to 1.3 × 105 (ℏ/2e) ohm−1 m−1 at x = 0.5.

To obtain the internal values of σSH =σSH*/Tint, Tint of the Pt1−x(MgO)x/Co interfaces has to be calculated for each x. With the drift-diffusion analysis (29, 30), the interfacial spin transparency set by the SBF is given byTint=[1sech(d/λs)]/[1+GHMtanh(d/λs)/2GHM/FM](3)where GHM = σxxs is spin conductance of the HM. Because GHM/FM typically scales with the Sharvin conductance GSh of the HM and both GSh (37) and GHM are proportional to n and independent of τ, we have GPt−MgO = (1 − x)GPt and GPtMgO/Co = (1 − x)GPt/Co. Assuming a dominant Elliott-Yafet spin relaxation mechanism (λs ∝ σxx) (29, 30) and using the experimental value GPt ≈ 1.3 × 1015 ohm−1 m−2 (23) and the theoretical value GPt/Co ≈ 0.59 × 1015 ohm−1 m−2 (30), we estimated that λs of Pt1−x(MgO)x decreases monotonically from 2.35 nm for x = 0, to 1.73 nm for x = 0.4 and 0.64 nm for x = 0.5 (fig. S5B) and that Tint of the Pt1-x(MgO)x/Co interface increases monotonically from 0.32 for x = 0 to 0.39 for x = 0.4 and 0.47 for x = 0.5 (fig. S5C).

Now, we can examine the effect of τ on the SHC. In Fig. 2D, we compare our experimental results of σSH* and σSH =σSH*/Tint for different x to the theoretical predictions of intrinsic SHC as a function of σxx/(1 − x). Here, we use σxx/(1 − x)∝τ as an approximate linear indicator of τ. Functionally, the scaling of σSH and σSH* with σxx(x)/(1 − x) and thus with τ is quite consistent with the tight-binding model prediction (1). The 4-nm-thick pure Pt sample with a relatively low σxx,Pt = 3 × 106 ohm−1 m−1 due to the strong scattering at its interfaces is just on the predicted crossover from the clean limit to the dirty-metal regime with respect to its intrinsic SHC behaviors. As τ is gradually decreased by increasing x, the intrinsic SHC decreases monotonically, in accord with the theoretical prediction (1, 25) (see also fig. S1) for the variation of σSH with electrical conductivity (τ) in the dirty-metal regime. The amplitude of the measured SHC is quite different from the predicted values, but if we rescale the magnitude of the tight-binding model result by a constant factor of 6 (Fig. 2D), then we find good agreement between the experiment and the prediction. Therefore, the tight-binding model captures the functional form, but not the magnitude, of the experimental behavior. More specifically, our experiment and the tight-binding model prediction (1) establish that the giant SHC of Pt is dominated by intrinsic Berry curvature contribution in the clean and dirty-metal regimes and that the intrinsic SHC varies strongly with the carrier lifetime τ in the dirty-metal regime. The good qualitative consistency of the experiment and theory also indicates that the topology of the Fermi surface of the fcc Pt is rather robust to the intersite impurities but is, as predicted, quite sensitive to τ in this high-resistivity regime. This establishes a practical limit to which θSH of pure Pt can be enhanced (i.e., θSH ≈ 0.65; see fig. S6) solely by reducing τ even if the structure order can be maintained while reducing τ. We do note that there is a minor difference between the experimental data of σSH and the rescaled tight-binding model prediction (×6) in the dirty-metal regime, which we tentatively attribute to a small SML at the Pt1−x(MgO)x/Co interfaces. As established previously (31), SML can result from ISOC of the HM/FM interface and increases linearly with the interfacial perpendicular magnetic anisotropy energy density of the HM/FM interface (KsHM/FM). Using the same method as in (31), we determined that KsPtMgO/Co for these unannealed in-plane Pt1−x(MgO)x/Co samples gradually decreases from ~0.66 erg/cm2 for x = 0 to be negligible for x = 0.5 (see fig. S7). These overall small amplitudes of ISOC [compared to the sample with a substantial SML in (31)] are well consistent with the high amplitude of σSH of the low-MgO concentration samples being close to that of Pt/Co samples after SML correction (the red star in the Fig. 2D). The MgO dopants may also interrupt the perfection of the long-range fcc order of Pt and thus may contribute to the difference between the measured and rescaled theoretical values of σSH. This, however, should be a minor effect compared to the dominant role of the carrier lifetime in determining the variation of σSH.

We now exclude the extrinsic skew scattering and side jump as important mechanisms in contributing to the SHC of Pt. As shown in the inset of Fig. 2D, the obvious nonlinear relations between σxx and σSH (with an SBF correction) and between σxx andσSH* (without an SBF correction) for different x obviously disagree with a dominant skew-scattering mechanism (σSH ∝ σxx). This is consistent with the theoretical expectation that the skew scattering should not be important in the dirty-metal regime. With regard to the possibility of a side-jump contribution to σSH of Pt and Pt1−x(MgO)x, we can draw from the conclusions of previous studies of side-jump contribution to the anomalous Hall conductivity (AHC) (38). Such research indicates that the side-jump contribution to σSH should scale inversely with the square of the residual resistivity ratio (RRR = ρxxxx0) of the metal, where ρxx0 is the residual, low-temperature resistivity due to elastic defect scattering. As shown in fig. S8, the RRR for our pure Pt sample (x = 0) is approximately 1.4, while RRR ≈ 1.1 for x = 0.4. Therefore, if the side jump was dominant, then we should expect a 60% increase in σSH as x increases from 0 to 1.1. In light of the decrease in σSH between x = 0 and x = 0.4, we can rule out side jump as an important contributor to the SHC of Pt and Pt1−x(MgO)x in the dirty-metal limit. The AHC of some FMs (e.g., L10-ordered MnGa, MnAl, or FePt) (3941) may have a distinguishable extrinsic SHC even in the “dirty-metal” regime, but in that case, the intrinsic AHC is very small—at least two orders of magnitude smaller than the intrinsic SHC of Pt. Therefore, we conclude that the intrinsic contribution is the dominant physical origin of the observed SHC in Pt.

An interfacial origin of the SHC can also be safely ruled out as a significant factor in the Pt/Co and Pt1−x(MgO)x/Co systems. The clear qualitative correlation between the evolution of σSH* over the entire range (0 < x ≤ 0.5) and the changes in carrier lifetime of the Pt films confirms that the SOTs that we observe in this system are the result of a bulk effect [i.e., due to the SHC from the long-range fcc order of Pt in the Pt1−x(MgO)x layer] rather than an interfacial effect. This conclusion of a predominant bulk origin of the SOTs in our doped Pt system is consistent with the previously reported rapid decrease of the SOT strength (σSH*) when the Pt or Pt alloy thickness becomes less than 4λs (14, 16, 23). Here, we take note of a recent report of a strong SOT from a Pt oxide/NiFe interface (35). In that case, there was no current flow in the insulating Pt oxide (ρxx = 2.2 × 107 microhm·cm), which is in sharp contrast to our case where the current is flowing in the conductive Pt1−x(MgO)x layer. Thus, the Pt oxide/NiFe does not have any connection to our Pt1−x(MgO)x/Co study.

After having established the intrinsic nature of the Pt SHC, we return to the quantitative comparison of the measured SHC results to the available theoretical predictions. Even before we make any corrections for the effect of the thickness of the sample compared to its λs and less than perfect Tint, the experimental values that we obtain for σSH* are equal to or larger than the available theoretical predictions for Pt from first-principles or tight-binding calculations (see the comparison in Fig. 2D). If we only consider the ideal situation of SBF being important, with no additional SML (3133), then the experiments determine the actual intrinsic SHC of 1.1 × 106 to 1.6 × 106 (ℏ/2e) ohm−1 m−1 for σxx > 2.2 × 105 ohm−1 m−1(or ρxx ≤ 74 microhm·cm) (see Fig. 2D). In the clean limit (e.g., ρxx ≤ 32 microhm·cm), the actual intrinsic SHC of Pt is then at least ~1.6 × 106 (ℏ/2e) ohm−1 m−1. This is significantly larger than any of the existing theoretical predictions, that is, 0.4 × 105 to 4.5 × 105 (ℏ/2e) ohm−1 m−1 (1, 2, 12, 13, 18), indicating that the available theoretical calculations are underestimating the true intrinsic SHC of Pt by more than a factor of 3.5, most likely more because there can be SML at Pt/Co interfaces (3133). We infer that there is still important underlying physics related to the generation of spin currents by intrinsic effects in Pt that is yet to be fully understood and that could benefit from the additional theoretical investigation.

Practical impact for low-power SOT devices

θSH and ξDLj are the most direct parameters that characterize the useful strength of the phenomenon. Figure 3A shows the results for θSH = (2e/ℏ)σSHρxx for the Pt1−x(MgO)x layers and ξDLj= TintθSH = ξDLEρxx for the Pt1−x(MgO)x 4/Co 1.4 bilayers, where the HM thickness of 4 nm is chosen from the viewpoint of the optimized current efficiency of a SOT switching of magnetic tunneling junctions (42). In consistence with the bulk intrinsic SHE, θSH increases monotonically from 0.51 for pure Pt to 0.73 for x = 0.4 and then slightly drops back to 0.66 for x = 0.5 because of the strong decrease in σSH as the result of the sharp decrease in carrier lifetime. We note that θSH = 0.73 is still a low bound value for Pt0.6(MgO)0.4 as there is still SML. The internal value of θSH for Pt0.6(MgO)0.4 would be ≈0.95 if the difference between the experimental and rescaled tight-binding model values of σSH in Fig. 2D is attributed solely to the SML. Note that θSH ≈ 0.95 should be the upper bound for the case where Pt is diluted by an insulator (e.g., MgO here) that does not alter the band structure. This upper limit (θSH ≈ 0.95) is higher than that for pure Pt (θSH ≈ 0.65) because, for the same σSH and τ, the enhancement of ρxx for Pt0.6(MgO)0.4 is more significant than that in pure Pt because of the additional dilution effect of the carrier density in Pt0.6(MgO)0.4. Benefiting from the increase of both θSH and Tint (fig. S5) with x, ξDLj increases from 0.16 at x = 0 (33 microhm·cm) to 0.28 at x = 0.4 (74 microhm·cm). At x = 0.5, despite the result that ρxx increases sharply to 240 microhm·cm, ξDLj only slightly increases to 0.31. The giant ξDLj of ≈0.3 that we obtained with the 4-nm Pt0.6(MgO)0.4xx = 74 microhm·cm) is comparable to the high value reported for fcc-Au0.25Pt0.75xx ≈ 83 microhm·cm) (16) and β-W (ρxx ≈ 300 microhm·cm) (43) and three times higher than that of β-Ta (ρxx ≈ 190 microhm·cm) (44). The SHE in those HMs has been demonstrated to enable sub-nanosecond deterministic magnetic memories (8, 42), gigahertz and terahertz oscillators (9, 10), and fast skyrmion/chiral domain wall devices (11, 44). However, for low-power device applications, new HMs that simultaneously combine a giant ξDLj with a low ρxx and a good compatibility for device integration are still urgently required (14, 16). In that regard, we first point out that Pt0.6(MgO)0.4 (ξDLj = 0.28 and ρxx = 74 microhm·cm) is as efficient as Pd0.25Pt0.75 (14) and Au0.25Pt0.75 (16) and progressively more so than Pt, β-W (43), β-Ta (44), and the topological insulator BixSe1−x (ξDLj = 3.5 to 18.6) (46, 47) for SOT applications with metallic magnets, e.g., in-plane magnetized FeCoB/MgO magnetoresistive random access memories (MRAMs; see the quantitative comparison in Table 1), after taking into account the current shunting into the ferromagnetic layer (see fig. S9 and section S2 for details on the power calculations). The Pt0.6(MgO)0.4 is also better than Pt, β-W, and β-Ta in current efficiency. The relatively small ρxx of the Pt0.6(MgO)0.4 is also highly desirable for applications that require high energy/current efficiencies but small write impedance, e.g., the prospective implementation of SOT devices in cryogenic computing systems (48). In that case, the very resistive spin Hall materials of β-W (43), β-Ta (44), and BixSe1−x (46, 47) are all problematic.

Fig. 3 Spin Hall ratio, damping-like SOT efficiency, and current-induced switching of perpendicular magnetization.

(A) The MgO concentration dependence of θSH and ξDLj for the Pt1−x(MgO)x 4/Co 1.4 bilayers. (B) VAH versus I (Hx = −1500 Oe), (C) VAH versus I (Hx = 1500 Oe), (D) VAH versus Hz, and (E) VAH versus Hx for the Pt0.7(MgO)0.3 4/Co 0.68 bilayers. The Hall bar dimension is 5 μm by 60 μm. The applied electric field is E = 1.67 kV/m for (B) to (E).

Table 1 Comparison of ξDLj, θ, ρxx, σSH*(x) and calculated power and current consumption of SOT-MRAM devices for various strong spin current generators.

Here, we use a spin Hall channel (600 nm by 300 nm by 4 nm), an FeCoB free layer (190 nm by 30 nm by 1.8 nm; resistivity ≈ 130 microhm·cm), and the parallel resistor model for the illustrative calculation (see the Supplementary Materials for details on the power and current calculations). Power and current are normalized to that of the Pt0.6(MgO)0.4-based device. n.a., not applicable.

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As an independent check of the validity of the strong damping-like SOT generated by the Pt1−x(MgO)x, we show in Fig. 3, B and C the sharp deterministic switching of a perpendicularly magnetized Co layer through domain wall depinning driven by the strong damping-like SOT generated by the SHE in a 4-nm Pt0.7(MgO)0.3 layer [we use Pt0.7(MgO)0.3 rather than Pt0.6(MgO)0.4 to provide a stronger perpendicular magnetic anisotropy and a larger coercivity]. The Co layer has a thickness of 0.68 nm, a coercivity (Hc) of ~80 Oe (Fig. 3D), and an effective perpendicular anisotropy field (Hk) of ~2.0 T as determined by fitting the dependence of V on the in-plane bias field Hx following the parabolic relation V = ±VAH(1 − Hx2/2Hk2) (see Fig. 3E). The switching current of ~2.7 mA (Fig. 3, B and C) corresponds to a critical switching current density of je = 1.15 × 107 A/cm2 in the Pt0.7(MgO)0.3 layer. To obtain reliable switching in this configuration, it was necessary to apply an in-plane magnetic field of >1000 Oe along the current direction to overcome the domain wall chirality imposed by the DMI at the HM/Co interface (49).

Here, we also note that the requirement of a large in-plane bias field (>1000 Oe) for switching perpendicular magnetization indicates a strong DMI at the Pt1−x(MgO)x /FM interface, which, together with the high ξDLj, makes Pt1−x(MgO)x particularly attractive for energy-efficient skyrmion and chiral domain wall devices driven by SHE-governed domain wall depinning (11, 49). However, such a bias field is not required for the anti-damping SOT switching of collinear or “y-type” in-plane magnetized magnetic memories (50), which have been demonstrated to be unexpectedy efficient and fast [e.g., critical switching current (density) of ~110 μA (~5 × 106 A/cm2) and ~200 ps for W-based FeCoB-MgO MRAM devices (42)].


We have presented the first experimental observation of the rapid variation of the intrinsic SHC of Pt with the carrier lifetime in the dirty-metal regime, a characteristic of the intrinsic SHC as theoretically predicted more than a decade ago. Via tuning the scattering from the finely dispersed MgO intersite impurities, the carrier lifetime τ and intrinsic SHC were varied by factors of 3 and 5, respectively, while the basic fcc order of Pt was maintained. We have also excluded any important skew-scattering, side-jump, or interfacial contributions to the SHE in this system. These results unambiguously determine the dominant intrinsic nature of the giant SHE in the archetypal material of Pt and establish the limit to which the spin Hall efficiency of Pt can be enhanced by shortening τ (i.e., θSH ≈ 0.65 for pure Pt). Moreover, the internal intrinsic SHC in the clean limit is experimentally found to be >1.6 × 106 (ℏ/2e) ohm−1 m−1, a value that is considerably underestimated by the existing first-principles and tight-binding theories. Our effort in shortening τ via MgO incorporation into Pt also enables a 100% enhancement of ξDLjfor the Pt0.6(MgO)0.4/Co bilayers compared to the Pt/Co bilayer. This establishes a new spin Hall material Pt0.6(MgO)0.4 that is very compelling for low-power SOT applications in magnetic memories, oscillators, and skyrmion/chiral domain wall devices because of its combination of a giant spin Hall ratio (θSH = 0.73 with a upper bound of ≈0.95 if the SML is diminished) with a relatively low resistivity (~74 microhm·cm), a strong DMI, and a good compatibility with the fabrication requirements for integrated circuit technologies.


All the samples were sputter-deposited at room temperature on Si/SiO2 substrates with an argon pressure of 2 mtorr and a base pressure of below 1 × 10−8 torr. The volume percentage (x) of MgO in the Pt1−x(MgO)x layers was determined using the calibrated growth rates of Pt and MgO. The 1-nm Ta underlayer was introduced to improve the adhesion and the uniformity of the stack. The 1.5-nm Ta capping layer was fully oxidized upon exposure to the atmosphere. The magnetization of Co layers and the chemical bond information in the Pt1−x(MgO)x layers were measured by a vibrating sample magnetometer and XPS, respectively. The sample structure was also characterized by combining cross-sectional high-resolution TEM imaging, HAADF-STEM imaging, and EDS mapping in a spherical aberration–corrected (Cs-corrected) 300-kV FEI Titan G2 microscope equipped with a Super-X detector. A focused ion beam (FEI Helios Nanolab 600i) was used during the preparation of the STEM samples. The stacks were patterned into Hall bars with a dimension of 5 μm by 60 μm by ultraviolet photolithography and argon ion milling for harmonic response measurements and direct current switching experiments. In the magnetization switching experiment, the dc current was sourced by a Yokogawa 7651, and the differential Hall resistance was detected by the lock-in amplifier (E = 1.67 kV/m).


Supplementary material for this article is available at

Fig. S1. Evolution of SHC with carrier lifetime.

Fig. S2. Three carrier scattering schemes.

Fig. S3. Composition dependence of the intensity and the full width at half maximum of the XRD patterns.

Fig. S4. Determination of SOT effective fields.

Fig. S5. MgO concentration dependence of spin-torque fields, spin diffusion length, and interfacial spin transparency.

Fig. S6. Enhancement of the spin Hall ratio in Pt by shortening carrier lifetime.

Fig. S7. MgO concentration dependence of interfacial magnetic anisotropy energy density.

Fig. S8. Temperature dependence of resistivity for 4-nm-thick Pt and Pt0.6(MgO)0.4 films.

Fig. S9. Schematics of a SOT-MRAM device.

Section S1. In-plane harmonic response measurements

Section S2. Calculation of power consumption of SOT-MRAM devices

This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial license, which permits use, distribution, and reproduction in any medium, so long as the resultant use is not for commercial advantage and provided the original work is properly cited.


Acknowledgments: Funding: This work was supported, in part, by the Office of Naval Research (N00014-15-1-2449), by the NSF MRSEC program (DMR-1719875) through the Cornell Center for Materials Research and by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA), via contract W911NF-14-C0089. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the ODNI, IARPA, or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright annotation thereon. The devices were fabricated, in part, at the Cornell NanoScale Facility, an NNCI member supported by NSF Grant No. ECCS-1542081. The TEM measurements performed at Shaanxi Normal University and Beijing University of Technology were supported by the Science and Technology Program of Shaanxi Province (Grant No. 2019JQ-433) and the Fundamental Research Funds for the Central Universities (Grant No. GK201903024). Author contributions: Lijun Zhu and R.A.B designed the project. Lijun Zhu, R.A.B., and D.C.R. wrote the manuscript draft. Lijun Zhu fabricated the samples and performed the sample fabrication, vibrating sample magnetometry, XRD, XPS, and spin-torque measurements. Lujun Zhu and M.S. performed the TEM measurements. All the authors contributed to discussing the results and writing the manuscript. Competing interests: The authors declare that they have no competing interests. Data and materials availability: All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials. Additional data related to this paper may be requested from the authors.

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