We investigate the Pt thickness dependence of spin–orbit torques (SOTs) in Co/Pt layers grown on single crystalline SrTiO3 and LaAlO3 and amorphous SiO2 substrates. We measure the SOT-induced effective damping-like fields and spin Hall magnetoresistances of the Co/Pt (tPt) samples, where tPt varies from 0.5 to 5.5 nm. We find that the Co/Pt layers grown on the single crystalline substrates show weaker thickness dependence of the SOT than the samples on the SiO2 substrate, which cannot be explained by the conventional bulk spin Hall effect in the Pt layer. This indicates that there is a non-negligible interfacial SOT originating from the Pt/substrate interface, which is more pronounced for thinner Pt. These results provide a way to design SOT material structures with enhanced SOT efficiency by incorporating interfacial SOT.

Spin–orbit coupling in ferromagnet (FM)/heavy metal (HM) bilayers converts charge currents into spin currents, which exert spin–orbit torques (SOTs) on the magnetization of the FM that can control its orientation.1–9 Current-induced SOT has been widely investigated as an efficient means of switching the magnetization direction in spintronic device applications because of the following advantages: First, SOT spin currents carry in-plane spin polarization, enabling ultrafast switching of perpendicular magnetizations.10–13 Second, SOT utilizes a three-terminal device geometry, in which the magnetization switching is done using in-plane current, enhancing device stability.1,2,14–16 Furthermore, the spin angular momentum is supplied by the lattice through spin–orbit coupling, and so the charge-to-spin conversion efficiency, or effective spin Hall angle, can be largely enhanced through materials engineering.17–26 

There are two mechanisms for generating spin current in FM/HM bilayer structures: the bulk spin Hall effect (SHE) in the HM layer27–31 and the interfacial spin–orbit coupling effect.32–38 For the SHE, an in-plane charge current along the x-direction creates a spin current that flows in the z-direction carrying spin polarization in the y-direction. Since the SHE is of bulk origin, the magnitude of the SHE-based SOT depends on the HM thickness; it initially increases with the HM thickness and reaches a saturated value.5,39–42 This thickness dependence is determined by a characteristic length of the HM layer, i.e., spin diffusion length.39,41 When the HM is much thinner than the spin diffusion length, the SOT is reduced by the backflow of the spin current from the interface. On the other hand, the interfacial spin–orbit coupling effect creates a spin density at an interface with structural inversion asymmetry, which can considerably contribute to the SOT in FM/HM bilayers.7,12,37,43,44 Furthermore, recent theoretical and experimental results show that the FM/HM interface generates spin currents itself and their spin polarizations can be controlled by the magnetization direction.45–48 The SOT caused by the interfacial spin–orbit coupling effect decreases with increasing HM thickness because less current flows near the FM/HM interface. To date, most research on the interfacial spin–orbit coupling effect has been focused on the FM/HM interface;1,3,5,17,20–24,26,37 however, there is another interface, namely, the HM/substrate interface, which, in principle, can also contribute to the SOT. Recent theoretical calculations have shown that Rashba-type interfacial spin–orbit coupling at HM/insulator interfaces significantly contributes to the SOTs, resulting in a noticeable modification of the HM thickness dependence of SOT for HM layers thinner than the spin diffusion length.49–52 

In this study, we demonstrate interfacial SOTs originating at the Pt/substrate interface by investigating the Pt thickness dependence of SOTs in Co/Pt bilayers grown on single crystalline SrTiO3 and LaAlO3 and amorphous SiO2 substrates. We find that the SOT-induced effective damping-like fields and spin Hall magnetoresistances (SMRs) of the samples with single crystalline substrates show weak dependences on the Pt thickness, revealing non-negligible interfacial spin–orbit coupling effects in the samples. Our results suggest that SOT efficiency can be further enhanced by exploiting interfacial spin–orbit coupling at the HM/substrate interface.

Figure 1(a) shows the sample structure of perpendicularly magnetized Pt (tPt nm)/Co (0.8 nm)/AlOx (2 nm) layers, where the Pt thickness tPt ranges from 0.2 to 5.5 nm. The samples were deposited on three different substrates: single crystalline SrTiO3 (111) and LaAlO3 (111) and amorphous SiO2, which allows for the investigation of the interfacial spin–orbit coupling effect at the Pt/substrate interface. Figure 1(b) shows high-resolution x-ray diffraction (XRD) spectra of the samples, demonstrating that Pt (111) layers were epitaxially grown on SrTiO3 (111) and LaAlO3 (111) substrates, where the Pt layers were deposited at 200 °C. On the other hand, the Pt layer grown on the amorphous SiO2 substrate at room temperature forms a polycrystalline structure. The deposited films were patterned into 4 μm wide Hall cross-devices using photolithography and Ar ion milling. All measurements were carried out at room temperature. We first measured the Pt resistivity ρPt of the samples according to the substrates. Figure 1(c) shows the results that ρPt’s of the epitaxial Pt films grown on SrTiO3 and LaAlO3 substrates are about half that of the polycrystalline Pt film on the SiO2 substrate at all tPt’s used in this study. This indicates that bulk scatterings are suppressed in the epitaxial Pt layers due to their highly ordered crystal structures.53–56 Note that we confirm that the thin Pt layer forms a continuous film by performing x-ray reflectivity (supplementary material). Moreover, it is found that ρPt increases with decreasing tPt for all Pt films regardless of the substrate, demonstrating that interfacial scattering becomes dominant when tPt is reduced. Thus, it is expected that the interfacial spin–orbit coupling effect would play a critical role in the SOT of samples with a thin Pt layer.

FIG. 1.

(a) Illustration of a perpendicularly magnetized Pt (tPt nm)/Co (0.8 nm)/AlOx (2 nm) layered structure on three different substrates: single crystalline SrTiO3 (111) and LaAlO3 (111) substrates and amorphous SiO2 substrate. (b) High-resolution x-ray diffraction spectra for the Pt (4 nm)/SrTiO3, Pt (4 nm)/LaAlO3, and Pt (5 nm)/SiO2 samples. (c) Pt resistivities ρ as a function of tPt for the Pt/SrTiO3, Pt/LaAlO3, and Pt/SiO2 samples.

FIG. 1.

(a) Illustration of a perpendicularly magnetized Pt (tPt nm)/Co (0.8 nm)/AlOx (2 nm) layered structure on three different substrates: single crystalline SrTiO3 (111) and LaAlO3 (111) substrates and amorphous SiO2 substrate. (b) High-resolution x-ray diffraction spectra for the Pt (4 nm)/SrTiO3, Pt (4 nm)/LaAlO3, and Pt (5 nm)/SiO2 samples. (c) Pt resistivities ρ as a function of tPt for the Pt/SrTiO3, Pt/LaAlO3, and Pt/SiO2 samples.

Close modal

To investigate the Pt thickness dependence of SOTs in the Pt (tPt nm)/Co (0.8 nm)/AlOx (2 nm) samples, we first performed harmonic Hall voltage measurements.5–7 Note that these samples are referred to as Pt/SrTiO3, Pt/LaAlO3, and Pt/SiO2 because the Co/AlOx layers are identical. As schematically illustrated in Fig. 2(a), we measure the first and second harmonic Hall resistances (R1w and R2w) as a function of the in-plane magnetic field Bx along the x-direction. Here, we use an AC current Jc with a frequency of 19 Hz applied in the x-direction. Figures 2(b)2(d) and 2(e)2(g) show the R1w and R2w curves normalized by the anomalous Hall resistance RA of each sample as a function of Bx for representative Pt/SrTiO3, Pt/LaAlO3, and Pt/SiO2 samples. R1w indicates the equilibrium magnetization direction, while R2w represents the magnetization oscillation caused by the SOTs. The SOT-induced damping-like effective field BDL can be calculated using R1w and R2w in a low magnetic field regime (from −200 to 200 mT), as given by BDL=2dR2wdBext/d2R1wdBext2.6 Note that the planar Hall effect, which is ∼20% of the anomalous Hall effect, and thermal contribution have been taken into account (supplementary material). We repeat the harmonic Hall voltage measurements for different tPt’s and extract the BDL values using a Jc of 1 × 1011 A/m2. Figures 2(h)2(j) show BDL as a function of tPt for all three substrates. We find that the Pt thickness dependence of the BDL of the SrTiO3 and LaAlO3 samples [Figs. 2(h) and 2(i)] is dissimilar to that of the polycrystalline SiO2 sample in Fig. 2(j). BDL of the former samples gradually increases with tPt up to 3.5 nm, whereas that of the latter sample increases initially and decreases when tPt is greater than 2.5 nm. This indicates that SOT is considerably modified by the substrate, which we attribute to the interfacial spin–orbit coupling effect of the Pt/single crystalline substrate. For quantitative analysis, we employ a recently proposed analytical model, including both the bulk and interfacial spin–orbit coupling effects, as51,52

BDL=jc2eMstCoθbulk+θint2csch2tPt2λGtanhtPt2λGcothtPtλ+12λρPt,
(1)

where and e are the reduced Planck constant and the electron charge, respectively; Ms and tCo are the saturation magnetization and thickness of Co; and λ and G↑↓ are the spin diffusion length of Pt and the spin mixing conductance of the Pt/Co interface, respectively. θbulk (θint) represents the spin Hall angle caused by the bulk spin Hall effect in Pt (the interfacial spin–orbit coupling effect at the Pt/substrate interface). Here, we assume that the spin–orbit coupling effect at the Pt/Co interface is the same regardless of the Pt thickness and, therefore, does not contribute to the thickness-dependent SOT. We first analyze the SiO2 sample [Fig. 2(j)], where the BDL vs tPt curve is well described by the conventional bulk spin Hall effect without considering the interfacial spin–orbit coupling effect, i.e., θint = 0. From the fitting, we extract θbulk = 0.15, λ = 0.9 ± 0.2 nm, and G↑↓ = (7 ± 1) × 1014 Ω−1 m−2, which are consistent with literature values of similar structures.40,57–60 In contrast, the thickness dependence of BDL for the SrTiO3 and LaAlO3 samples [Figs. 2(h) and 2(i)] deviates from the bulk spin Hall effect (blue dotted line) but can be explained when introducing a non-zero θint (red dotted line). In particular, the interface contribution is non-negligible for a small tPt, which is distinct from the SiO2 sample. The extracted spin Hall angles are given in Table I. θbulk is obtained to be ∼0.22 for all samples regardless of the substrate, which is expected because it is primarily caused by the Pt layer. Note that the similar bulk θbulk, despite the very different resistivities, may indicate that there are other intrinsic contributions due to the crystal structure in addition to the extrinsic contribution.25,53–56 On the other hand, θint strongly depends on the substrate, indicating a significant contribution from the interfacial spin–orbit coupling effect at the epitaxial Pt/single crystalline substrate interface. The magnitude of θint is estimated to be 15% and 22% of θbulk in the Pt/SrTiO3 and Pt/LaAlO3 samples, respectively, and its contribution becomes dominant in the thin tPt (<1 nm) region.

FIG. 2.

(a) Schematic for the harmonic Hall voltage measurements, where Bx is the external magnetic field and Jc is the AC current applied in the x-direction. (b)–(g) Representative results of the first (b)–(d) and second (e)–(g) harmonic Hall resistance R1w and R2w curves normalized by the anomalous Hall resistance RA as a function of Bx. (b) and (e) Pt (1.4 nm)/Co (0.8 nm)/AlOx (2 nm) on SrTiO3, (c) and (f) Pt (1.4 nm)/Co (0.8 nm)/AlOx (2 nm) on LaAlO3, and (d) and (g) Pt (1.4 nm)/Co (0.8 nm)/AlOx (2 nm) on SiO2 samples. BDL vs tPt for Pt (tPt)/Co (0.8 nm)/AlOx (2 nm) on SrTiO3 (h), Pt(tPt)/Co (0.8 nm)/AlOx (2 nm) on LaAlO3 (i), and Pt(tPt)/Co (0.8 nm)/AlOx (2 nm) on the SiO2 (j) sample. The blue (red) dotted lines represent the fitted BDL when θbulk (θint) is only considered. The black solid lines represent the sum of the θbulk and θint contributions. Here, Jc is 1 × 1011A/m2 for all samples.

FIG. 2.

(a) Schematic for the harmonic Hall voltage measurements, where Bx is the external magnetic field and Jc is the AC current applied in the x-direction. (b)–(g) Representative results of the first (b)–(d) and second (e)–(g) harmonic Hall resistance R1w and R2w curves normalized by the anomalous Hall resistance RA as a function of Bx. (b) and (e) Pt (1.4 nm)/Co (0.8 nm)/AlOx (2 nm) on SrTiO3, (c) and (f) Pt (1.4 nm)/Co (0.8 nm)/AlOx (2 nm) on LaAlO3, and (d) and (g) Pt (1.4 nm)/Co (0.8 nm)/AlOx (2 nm) on SiO2 samples. BDL vs tPt for Pt (tPt)/Co (0.8 nm)/AlOx (2 nm) on SrTiO3 (h), Pt(tPt)/Co (0.8 nm)/AlOx (2 nm) on LaAlO3 (i), and Pt(tPt)/Co (0.8 nm)/AlOx (2 nm) on the SiO2 (j) sample. The blue (red) dotted lines represent the fitted BDL when θbulk (θint) is only considered. The black solid lines represent the sum of the θbulk and θint contributions. Here, Jc is 1 × 1011A/m2 for all samples.

Close modal
TABLE I.

The extracted θbulk and θint and the ratio θbulk/θint obtained from harmonic Hall and spin magnetoresistance results in the Pt/SrTiO3, Pt/LaAlO3, and Pt/SiO2 samples.

SubstrateMeasurementθbulkθintθint/θbulk
SrTiO3 Harmonic Hall 0.21 ± 0.04 0.041 ± 0.008 0.19 
SMR 0.22 ± 0.04 0.027 ± 0.005 0.12 
LaAlO3 Harmonic Hall 0.22 ± 0.03 0.046 ± 0.007 0.21 
SMR 0.29 ± 0.06 0.045 ± 0.009 0.16 
SiO2 Harmonic Hall 0.23 ± 0.03 0.001 <0.01 
SMR 0.19 ± 0.04 0.001 <0.01 
SubstrateMeasurementθbulkθintθint/θbulk
SrTiO3 Harmonic Hall 0.21 ± 0.04 0.041 ± 0.008 0.19 
SMR 0.22 ± 0.04 0.027 ± 0.005 0.12 
LaAlO3 Harmonic Hall 0.22 ± 0.03 0.046 ± 0.007 0.21 
SMR 0.29 ± 0.06 0.045 ± 0.009 0.16 
SiO2 Harmonic Hall 0.23 ± 0.03 0.001 <0.01 
SMR 0.19 ± 0.04 0.001 <0.01 

We next examine the spin Hall magnetoresistance (SMR) of the samples.61–64 In this setup [Fig. 3(a)], we measure the longitudinal resistance Rxx while rotating the sample in the yz plane under a magnetic field of 6 T, large enough to saturate the magnetization of Co along the magnetic field direction. Figures 3(b)3(d) show representative SMR measurement data of the Pt/SrTiO3, Pt/LaAlO3, and Pt/SiO2 samples, respectively. Rxx is largest when the polar angle of the sample θ is 0° or 180°, i.e., when the magnetization is aligned perpendicular to the polarization of the accumulated spins due to the spin Hall and/or interfacial spin–orbit coupling effects. In this configuration, the spin current is mostly absorbed by the FM Co layer. On the other hand, Rxx is minimized when θ = 90° or 270°, where the polarization of the accumulated spins is parallel to the magnetization direction, and the spins are reflected back from the Pt/Co interface. Figures 3(e)3(g) show the SMR ratio, ΔRxxSMR/Rxx0, as a function of Pt thickness tPt of the SrTiO3, LaAlO3, and SiO2 samples, where ΔRxxSMR and Rxx0 are defined as Rxx(θ = 0°) − Rxx(θ = 90°) and Rxx(θ = 0°), respectively. Similar to the harmonic Hall voltage measurement results, the thickness dependences of the SMR of the Pt/SrTiO3 and Pt/LaAlO3 samples are different from that of the SiO2 sample, in particular, for a small tPt. tPt with the largest SMR in the single crystalline substrate sample is ∼1 nm, much smaller than that in the SiO2 sample of 2.5 nm. This implies that the interfacial spin–orbit coupling effect can influence the SMR, just as with BDL shown in Fig. 2. We analyze the SMR vs tPt results using the following equation, in which the interfacial spin–orbit coupling effect (θint) is taken into account similar to Eq. (1):

ΔRxxSMR/Rxx0=θbulkθbulk+θint2csch2tPt2λλdGtanh2tPt2λGcothtPtλ+σ2λ.
(2)

Here, σ is the conductivity of the Pt layer. Figures 3(e)3(g) show the fitting results, demonstrating that a non-negligible interfacial spin–orbit coupling effect contributes to the SMR in the SrTiO3 and LaAlO3 samples, especially for thin tPt, but it is absent in the SiO2 samples. These results are consistent with the thickness-dependent SOT shown in Fig. 2. We extract the θbulk and θint values from the SMR measurements, which are summarized in Table I. θbulk is ∼0.24 ± 0.05 for all samples regardless of the substrates, whereas θint depends on the substrate: θint is ∼0.027 (∼0.045) for the SrTiO3 (LaAlO3) sample. The ratio of θint/θbulk is 0.12 (0.16) for the Pt/SrTiO3 (Pt/LaAlO3) sample, similar to the results obtained from the harmonic Hall measurements. This corroborates that the interfacial spin–orbit coupling effect at the epitaxial Pt/substrate interface plays an important role in the generation of spin current and the associated SOTs. Note that the magnitudes of θbulk and θint extracted from the SMR are different from those from the harmonic measurement. This is possibly due to the spin currents generated in the FM layer, Co in our samples. For example, a charge current flowing in an FM layer creates a spin current through the spin anomalous Hall effect and its spin polarization is parallel to the magnetization direction.45,46,65–67 This effect is not considered in Eq. (2) of the SMR model and may result in the discrepancy. However, further experimental and theoretical investigations are required to verify this argument.

FIG. 3.

(a) Schematic for the spin Hall magnetoresistance measurements. Here, we use an AC current Jc of 1 × 1011A/m2 along the x-direction. Longitudinal resistance Rxx is measured as a function of the polar angle θ in the yz plane under an external magnetic field of 6 T. Representative results of the SMR ratio ΔRxxSMR/Rxx0 as a function of θ for Pt(0.8 nm)/Co (0.8 nm)/AlOx (2 nm) on SrTiO3 (b), Pt(0.8 nm)/Co (0.8 nm)/AlOx (2 nm) on LaAlO3 (c), and Pt(1.0 nm)/Co (0.8 nm)/AlOx (2 nm) on SiO2 (d) samples. ΔRxxSMR/Rxx0 depending on tPt in Pt(tPt)/Co (0.8 nm)/AlOx (2 nm) on SrTiO3 (e), Pt(tPt)/Co (0.8 nm)/AlOx (2 nm) on LaAlO3 (f), and Pt(tPt)/Co (0.8 nm)/AlOx (2 nm) on SiO2 (g) samples. The blue (red) dotted lines represent the fitted ΔRxxSMR/Rxx0, where θbulk (θint) is solely considered. The black solid lines represent the sum of θbulk and θint contributions.

FIG. 3.

(a) Schematic for the spin Hall magnetoresistance measurements. Here, we use an AC current Jc of 1 × 1011A/m2 along the x-direction. Longitudinal resistance Rxx is measured as a function of the polar angle θ in the yz plane under an external magnetic field of 6 T. Representative results of the SMR ratio ΔRxxSMR/Rxx0 as a function of θ for Pt(0.8 nm)/Co (0.8 nm)/AlOx (2 nm) on SrTiO3 (b), Pt(0.8 nm)/Co (0.8 nm)/AlOx (2 nm) on LaAlO3 (c), and Pt(1.0 nm)/Co (0.8 nm)/AlOx (2 nm) on SiO2 (d) samples. ΔRxxSMR/Rxx0 depending on tPt in Pt(tPt)/Co (0.8 nm)/AlOx (2 nm) on SrTiO3 (e), Pt(tPt)/Co (0.8 nm)/AlOx (2 nm) on LaAlO3 (f), and Pt(tPt)/Co (0.8 nm)/AlOx (2 nm) on SiO2 (g) samples. The blue (red) dotted lines represent the fitted ΔRxxSMR/Rxx0, where θbulk (θint) is solely considered. The black solid lines represent the sum of θbulk and θint contributions.

Close modal

In this article, we report a non-negligible interfacial spin–orbit coupling contribution to the SOTs in epitaxial Pt/single crystalline substrate (SrTiO3 and LaAlO3) samples. We investigate the Pt thickness dependence of the SOT-induced effective damping-like fields and SMR of the Pt/SrTiO3 and Pt/LaAlO3 samples and find that they are much weaker than those of the Pt/SiO2 control sample. This is attributed to the interfacial spin–orbit coupling effect in the Pt/SrTiO3 and Pt/LaAlO3 samples, which is dominant for thin Pt thicknesses (<1 nm). Based on a model including both the bulk and interfacial effects, we estimate the θint value, which is about 12%–22% of θbulk. These results suggest a way to enhance SOT efficiency for spintronic-based applications through the comprehensive materials engineering of bulk and interfacial SOTs.

See the supplementary material for information about x-ray reflectivity of the Pt/Co films grown on SrTiO3 and LaAlO3 substrates, planar Hall effect consideration in the harmonic analysis, and the thermoelectric contribution to the second harmonic resistance.

This work was supported by the National Research Foundation of Korea (Grant No. NRF-2020R1A2C2010309). R.T. was supported by the Graduate Program in Spintronics at Tohoku University. M.K. and J.N. acknowledge financial support from the Japanese Ministry of Education, Culture, Sports, Science, and Technology (MEXT) in the Grant-in-Aid for Scientific Research (Grant No. 15H05699). B.-G.P. acknowledges support from KAIST-funded Global Singularity Research Program for 2021.

We have no conflict of interest to declare.

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

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Supplementary Material