Thickness-Dependent Orbital-to-Spin Torque Signatures in Cr/Gd/Co Thin Films

Abstract

We studied orbital-torque generation in Cr(10nm)/Gd($t_{\mathrm{Gd}}$)/Co(3nm)/TaO$_x$ and the inverted stack Co(3nm)/Gd($t_{\mathrm{Gd}}$)/Cr(10nm) with $t_{\mathrm{Gd}}$ from 0 to $5\,\mathrm{nm}$ by combining electrical harmonic Hall measurements with magnetometry. A detailed understanding of the magnetometric data is obtained by cross-sectional chemical composition mapping. The data show temperature-dependent magnetic compensation points, while elemental analysis provides evidence of pronounced intermixing, in particular of Gd and Co layers. From the harmonic Hall dataset we extract the damping-like (DL) and field-like (FL) torque efficiencies normalized to the applied electric field, $ξ_{\mathrm{DL}}^{E}$ and $ξ_{\mathrm{FL}}^{E}$, and interpret their dependence on the Gd interlayer thickness using two different descriptions: (i) a naive-layer model and (ii) an alloy model that accounts for interfacial mixing. Notably, upon reversing the stack order, the FL contribution changes sign, whereas the DL contribution does not change sign within the harmonic Hall measurements.