Crystallographic direction related spin current transmission in $\mathrm{MgO}\left(001\right)/{\mathrm{Fe}}_{0.79}{\mathrm{Si}}_{0.21}\left(001\right)/\mathrm{Pt}\left(111\right)$ epitaxial bilayers

Spin-pumping and spin-orbit torque efficiencies in ferromagnetic/heavy metal bilayers, which usually consist of the polycrystalline grains, are related to the spin current transmission from ferromagnets to heavy metals and vice versa, respectively. In this work, epitaxial ${\mathrm{Fe}}_{0.79}{\mathrm{Si}}_{0.21}\left(001\right)/\mathrm{Pt}\left(111\right)$ films were fabricated to investigate the spin-pumping efficiency and spin-orbit torque efficiency by ferromagnetic resonance and harmonic Hall resistance measurement techniques, respectively. Ferromagnetic resonance results show that the incremental magnetic damping constants in epitaxial ${\mathrm{Fe}}_{0.79}{\mathrm{Si}}_{0.21}\left(001\right)/\mathrm{Pt}\left(111\right)$, compared with those of the epitaxial ${\mathrm{Fe}}_{0.79}{\mathrm{Si}}_{0.21}\left(001\right)/\mathrm{Al}{\mathrm{O}}_x$ reference sample, depend on whether the external magnetic field is applied along the in-plane easy or hard axes of ${\mathrm{Fe}}_{0.79}{\mathrm{Si}}_{0.21}$. The Pt thickness-dependent anisotropic damping constant was ascribed to the anisotropic spin current absorption in epitaxial Pt(111) layer. When electric currents were applied along the easy and hard axes of ${\mathrm{Fe}}_{0.79}{\mathrm{Si}}_{0.21}$ in epitaxial ${\mathrm{Fe}}_{0.79}{\mathrm{Si}}_{0.21}\left(001\right)/\mathrm{Pt}\left(111\right)$ bilayers, a large difference between spin-orbit torques generated from Pt(111) was observed by a harmonic Hall resistance measurement method. Both of the results suggest that spin current transmission efficiency is related to the anisotropic spin Hall effect of epitaxial Pt(111) layer due to the different spin-orbit interaction energies along the different crystallographic directions of Pt.

Figure 1

High-resolution XRD patterns for samples grown on (001)MgO: $\mathrm{FeSi}\left(001\right)/\mathrm{Al}{\mathrm{O}}_x$ (a), FeSi(001)/Pt(001) (b), FeSi(001)/Pt(111) (c), and the Φ-scan patterns of FeSi(202), MgO(202), and Pt(202) lattice planes for $\mathrm{FeSi}\left(001\right)/\mathrm{Al}{\mathrm{O}}_x$ (d), FeSi(001)/Pt(001) (e), and Pt(002) lattice plane for FeSi(001)/Pt(111) (f).

Figure 2

X-ray reflectivity spectra of $\mathrm{FeSi}\left(001\right)/\mathrm{Al}{\mathrm{O}}_x$ (a), FeSi(001)/Pt(111) (b), and FeSi(001)/Pt(001) (c) (black circles represents the experimental data and the red lines represent the fitting curves) and x-ray scattering-length density (SLD) vs depth profile for $\mathrm{FeSi}\left(001\right)/\mathrm{Al}{\mathrm{O}}_x$ (d), FeSi(001)/Pt(111) (e), and FeSi(001)/Pt(001) (f) films. Labels in the map give the simulated parameters of the thickness ($t$), interface/surface roughness (σ), and density (ρ) of each layer.

Figure 3

Cross-sectional TEM image of MgO/FeSi/Pt sample (a), the high-resolution TEM image in MgO and FeSi layers (b), as well as in FeSi and Pt layers (c). The insets in (b) and (c) shows the fast Fourier transform plots of the corresponding layers.

Figure 4

Magnetic hysteresis loops of $\mathrm{FeSi}\left(001\right)/\mathrm{Al}{\mathrm{O}}_x$ (a), FeSi(001)/Pt(111) (b), and FeSi(001)/Pt(001) (c) with magnetic field $H$ applied parallel to the crystallographic axes of [110], [010], $\left[\overline{1}10\right]$, and $\left[\overline{1}00\right]$ of MgO. The in-plane angular dependence of resonance field $H_{\mathrm{r}}$ with respect to one of the substrate edges for three samples (d). The inset in (a) shows the exemplary angular-dependent remanence curves for $\mathrm{FeSi}\left(001\right)/\mathrm{Al}{\mathrm{O}}_x$ sample.

Figure 5

Typical FMR spectra recorded at various frequencies for FeSi(001)/Pt(111) sample with external field applied along easy axis (MgO[110]) (a) and hard axis (MgO[100]) (d). (b) and (c) represent $H_{\mathrm{r}}$ vs $f$ and △$H$ vs $f$ at easy axis for three samples, respectively. (e) and (f) represent $H_{\mathrm{r}}$ vs $f$ and △$H$ vs $f$ at hard axis for three samples, respectively. The fitting curves in (b) and (e) are based on Eq. (1). The linear fitting curves in (c) and (f) are based on Eq. (2). Here the nominal thickness of Pt is 7 nm for FeSi(001)/Pt samples.

Figure 6

Pt thickness-dependent resonance field $H_{\mathrm{r}}$ at various frequencies for FeSi/Pt(111) along easy (a) or hard axis (b) of FeSi, damping constant α (c), and the $\mathrm{\Delta }a$ for all samples (d).

Figure 7

The optical graph of the patterned Hall bar with measurement configurations (a), an exemplary first- (b) and second- (c) order harmonic Hall resistance vs angle ϕ and cosϕ with fixed external field $H_{x\text{−}\mathrm{ext}}=1245$ Oe along $\pm x$ axis. The external field $H_{y\text{−}\mathrm{ext}}$ is swept from −2500 to 2500 Oe and the magnitude of alternative current density $J_e=9.6\mathrm{MA}/\mathrm{c}{\mathrm{m}}^2$ along the [100] direction of FeSi (easy axis). The fitting curves are based on Eq. (4). The scale bar in (a) is 100 μm. The inset in (c) shows the second-order Hall resistance vs $H_{y\text{−}\mathrm{ext}}$.

Figure 8

The second-order harmonic Hall resistance vs cosϕ with the variation of magnitude of the alternative current density from $6.4–12.8\mathrm{MA}/\mathrm{c}{\mathrm{m}}^2$ for FeSi(001)/Pt(111) and current direction along FeSi[100] (a) and FeSi[110] (b), the dampinglike and fieldlike fields vs current density with current direction along FeSi[100] (c) and FeSi[110] (d).