Charge-spin interconversion in epitaxial Pt probed by spin-orbit torques in a magnetic insulator

Toward 100% Spin–Orbit Torque Efficiency with High Spin–Orbital Hall Conductivity Pt–Cr Alloys

“…Figure d shows an obvious positive correlation between longitudinal ρ xx and ξ DL within a relatively conductive regime, and the spin Hall conductivity (SHC) of pure Pt (σ SH Pt ) is 4.47 × 10 5 ( ℏ /2 e ) Ω –1 m –1 . The magnitude of this apparent SHC is quite consistent with recent consensus that the SHC of Pt ranges from 5.9 × 10 5 to 8 × 10 6 ( ℏ /2 e ) Ω –1 m –1 . ,, The average spin Hall conductivity (SHC) of alloys (σ SH Pt ‑ Cr(V) ) are 6.45 × 10 5 ( ℏ /2 e ) Ω –1 m –1 for Pt–Cr and 6.03 × 10 5 ( ℏ /2 e ) Ω –1 m –1 for Pt–V. Additionally, if we further consider the spin transmission degradation from spin-memory loss (SML), spin backflow (SBF), − and possible effects from magnetic dead layer at the Pt/Co interface, the actual SHC would be even higher.…”

“…The magnitude of this apparent SHC is quite consistent with recent consensus that the SHC of Pt ranges from 5.9 × 10 5 to 8 × 10 6 (ℏ/2e) Ω −1 m −1 . 14,38,39 The average spin Hall conductivity (SHC) of alloys (σ SH Pt -Cr(V) ) are 6.45 × 10 5 (ℏ/2e) Ω −1 m −1 for Pt−Cr and 6.03 × 10 5 (ℏ/2e) Ω −1 m −1 for Pt−V. Additionally, if we further consider the spin transmission degradation from spin-memory loss (SML), 40 spin backflow (SBF), 41−43 and possible effects from magnetic dead layer at the Pt/Co interface, 17 the actual SHC would be even higher.…”

High Spin Hall Conductivity Induced by Ferromagnet and Interface

“…According to TMS theory and spin mixing conductivity theory, [ 16,47,54 ] it could be obtained by: $$\[ \begin{array}{*{20}{c}}{{\alpha _{{\rm{Pt/FePt}}}} = {\mathop{\rm Re}\nolimits} [{G^{{\rm{eff}}}}]\frac{{{\hbar ^2}\left| \gamma \right|}}{{2{{\rm{e}}^2}{M_{\rm{s}}}}}t_{\rm{F}}^{ - 1} + {\alpha _{{\rm{TMS}}}} + {\alpha _{{\rm{FePt}}}}}\end{array} \]$$ $$\[ \begin{array}{*{20}{c}}{{\theta _{{\rm{DL,Pt}}}} = \frac{{2{\mathop{\rm Re}\nolimits} [{G^{{\rm{eff}}}}]}}{{{\sigma _{{\rm{Pt}}}}{\rm{/}}{\lambda _{{\rm{Pt}}}}}}{\theta _{{\rm{Pt,intrinsic}}}} = T \times {\theta _{{\rm{Pt,intrinsic}}}}}\end{array} \]$$ $$\[ \begin{array}{*{20}{c}}{{\alpha _{{\rm{TMS}}}} = {\beta _{{\rm{TMS}}}}t_{\rm{F}}^{ - 2}}\end{array} \]$$where Re [ G eff ] is the real part of effective spin mixing conductivity, here we assume the spin memory loss (SML) is small enough because our samples have not been processed annealing and the Pt/FePt interface is very well as shown in Figure 1b, α TMS is the damping contributed by TMS, β TMS is the coefficient of TMS, θ Pt,intrinsic is the intrinsic SHA of Pt, σ Pt the conductivity, λ Pt the spin diffusion length of Pt, and T the interfacial spin transmittance of spin pumping theory. θ Pt,intrinsic and λ Pt used in this article are 0.8 and 1.4 nm respectively, [ 16,56 ] these two values are in range of most Pt/FM systems. To obtain Re [ G eff ], it is necessary to calculate α TMS by fitting α Pt / FePt ‐ 1 / t curve with Equation (7).…”

“…where the θ DL(FL), Pt equivalent is the Pt-equivalent SOT efficiency calculated by total ΔW(H FL ) and J Pt in Equation ( 3) and ( 4 [16,47,54] it could be obtained by: where Re[G eff ] is the real part of effective spin mixing conductivity, here we assume the spin memory loss (SML) is small enough because our samples have not been processed annealing and the Pt/FePt interface is very well as shown in Figure 1b, α TMS is the damping contributed by TMS, β TMS is the coefficient of TMS, θ Pt,intrinsic is the intrinsic SHA of Pt, σ Pt the conductivity, λ Pt the spin diffusion length of Pt, and T the interfacial spin transmittance of spin pumping theory. θ Pt,intrinsic and λ Pt used in this article are 0.8 and 1.4 nm respectively, [16,56] these two values are in range of most Pt/FM systems. To obtain Re[G eff ], it is necessary to calculate α TMS by fitting α Pt/FePt -1/t curve with Equation (7).…”

“…The calculated θ DL,Pt is similar to 0.26 DL torque efficiency in Pt/L1 0 -FePt [57] and higher than the interfaces between Pt and most ferromagnetic metals or insulators. [15,16,47,56,58] High lattice match and high-quality of Pt/ FePt interface may be the key reasons for near 40% transmittance in this kind of interface. As for the damping constants of Cu/FePt, it keeps near 0.33 in thick samples and increases very quickly as well when t F drops toward the cutoff thickness of 1.2 nm.…”