Thickness dependence of spin–orbit torques in Pt/Co structures on epitaxial substrates

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 layer^27–31 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 (t_Pt nm)/Co (0.8 nm)/AlO_x (2 nm) layers, where the Pt thickness t_Pt 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 ρ_Pt of the samples according to the substrates. Figure 1(c) shows the results that ρ_Pt’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 t_Pt’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 ρ_Pt increases with decreasing t_Pt for all Pt films regardless of the substrate, demonstrating that interfacial scattering becomes dominant when t_Pt 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.

To investigate the Pt thickness dependence of SOTs in the Pt (t_Pt nm)/Co (0.8 nm)/AlO_x (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/AlO_x layers are identical. As schematically illustrated in Fig. 2(a), we measure the first and second harmonic Hall resistances (R_1w and R_2w) as a function of the in-plane magnetic field B_x along the x-direction. Here, we use an AC current J_c with a frequency of 19 Hz applied in the x-direction. Figures 2(b)–2(d) and 2(e)–2(g) show the R_1w and R_2w curves normalized by the anomalous Hall resistance R_A of each sample as a function of B_x for representative Pt/SrTiO₃, Pt/LaAlO₃, and Pt/SiO₂ samples. R_1w indicates the equilibrium magnetization direction, while R_2w represents the magnetization oscillation caused by the SOTs. The SOT-induced damping-like effective field B_DL can be calculated using R_1w and R_2w 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 t_Pt’s and extract the B_DL values using a J_c of 1 × 10¹¹ A/m². Figures 2(h)–2(j) show B_DL as a function of t_Pt for all three substrates. We find that the Pt thickness dependence of the B_DL 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). B_DL of the former samples gradually increases with t_Pt up to 3.5 nm, whereas that of the latter sample increases initially and decreases when t_Pt 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, as^51,52

where ℏ and e are the reduced Planck constant and the electron charge, respectively; M_s and t_Co 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. θ_bulk (θ_int) 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 B_DL vs t_Pt curve is well described by the conventional bulk spin Hall effect without considering the interfacial spin–orbit coupling effect, i.e., θ_int = 0. From the fitting, we extract θ_bulk = 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 B_DL 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 θ_int (red dotted line). In particular, the interface contribution is non-negligible for a small t_Pt, which is distinct from the SiO₂ sample. The extracted spin Hall angles are given in Table I. θ_bulk 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 θ_bulk, 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, θ_int 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 θ_int is estimated to be 15% and 22% of θ_bulk in the Pt/SrTiO₃ and Pt/LaAlO₃ samples, respectively, and its contribution becomes dominant in the thin t_Pt (<1 nm) region.

We next examine the spin Hall magnetoresistance (SMR) of the samples.^61–64 In this setup [Fig. 3(a)], we measure the longitudinal resistance R_xx while rotating the sample in the y–z 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. R_xx 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, R_xx 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 t_Pt of the SrTiO_3, LaAlO₃, and SiO₂ samples, where $ΔRxxSMR$ and $Rxx0$ are defined as R_xx(θ = 0°) − R_xx(θ = 90°) and R_xx(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 t_Pt. t_Pt 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 B_DL shown in Fig. 2. We analyze the SMR vs t_Pt results using the following equation, in which the interfacial spin–orbit coupling effect (θ_int) is taken into account similar to Eq. (1):

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 t_Pt, but it is absent in the SiO₂ samples. These results are consistent with the thickness-dependent SOT shown in Fig. 2. We extract the θ_bulk and θ_int values from the SMR measurements, which are summarized in Table I. θ_bulk is ∼0.24 ± 0.05 for all samples regardless of the substrates, whereas θ_int depends on the substrate: θ_int is ∼0.027 (∼0.045) for the SrTiO₃ (LaAlO₃) sample. The ratio of θ_int/θ_bulk 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 θ_bulk and θ_int 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.

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 θ_int value, which is about 12%–22% of θ_bulk. 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.