Anatomy of spin-orbit-torque-assisted magnetization dynamics in Co/Pt bilayers: Importance of the orbital torque

TL;DR

This work tackles the complex origins of spin-orbit-torque–driven magnetization switching by developing a layer-resolved Pt/Co model that includes proximity-induced Pt moments and ab initio magneto-electric responses. It integrates a renormalized Co–Co spin Hamiltonian with electrically induced spin and orbital moments computed from first principles and couples them to atomistic spin-dynamics simulations. The key finding is that interfacial orbital moments generate a dominant field-like torque that lowers the switching field and enables sub-nanosecond, in-plane switching, while magnetization-dependent torques (M-even and M-odd components) shape the dynamics and potential anti-damping effects. This microscopic, layer-resolved approach clarifies the pivotal role of orbital torque at interfaces and provides design guidance for achieving fast, energy-efficient switching in NM/FM bilayers at room temperature.

Abstract

Understanding the mechanism driving magnetization switching in spin-orbit-torque-assisted devices remains a subject of debate. While originally attributed to the spin Hall effect and spin Rashba-Edelstein effect, recent discoveries related to orbital moments induced by the orbital Hall effect and the orbital Rashba-Edelstein effect have added complexity to the comprehension of the switching process in non-magnet/ferromagnet bilayers. Addressing this challenge, we present a quantitative investigation of a Pt/Co bilayer by employing atomistic spin dynamics simulations, incorporating the proximity-induced moments of Pt, as well as electrically induced spin and orbital moments obtained from first-principles calculations. Our layer-resolved model elucidates the damping-like and field-like nature of the induced moments by separating them according to their even and odd magnetization dependence. In addition to demonstrating that a larger field-like spin-orbit torque contribution comes from previously disregarded induced orbital moments, our work highlights the necessity of considering interactions with Pt induced moments at the interface, as they contribute significantly to the switching dynamics.

Figures (6)

• Figure 1: Illustration of the various spin-orbit torque phenomena. (a) SHE and OHE generated spin (red) and orbital (green) moments in the non-magnet (Pt) diffuse into the ferromagnetic (Co) layers. (b) SREE and OREE generated spin and orbital moments induced at the Pt-Co interface. (c) All of the effects cause in addition intermixed $M$-even and $M$-odd induced moments. The direction of $M$-even induced moments is perpendicular to $\bm{E}$ and $\hat{\bm{z}}$, whereas $M$-odd induced moments vary with magnetization direction as calculated from a Kubo linear-response formalism.
• Figure 2: Ab initio calculated expansion coefficients $P(A), P(A'), P(A"), P(A"')$ and $P(B)$, $P(B')$ of the induced spin (left) and orbital (right) moments according to Eqs. \ref{['eq:M-even_directions']} and \ref{['eq:M-odd-directions']} in a Pt/Co bilayer. The layer-resolved moments are plotted for 8 Pt layers (indices $1-8$) and 8 Co layers (indices $9-16$).
• Figure 3: Electric-field-induced magnetization switching of the Co magnetization in a Pt/Co bilayer. The figure compares simulations with ($\delta \mu_L \neq 0$) and without ($\delta \mu_L =0$) induced orbital moments for electric field values as indicated at room temperature.
• Figure 4: Simulated switching of the Co magnetization in the Pt/Co bilayer, when only $M$-even (left), and $M$-odd (right) induced moments are taken into account.
• Figure 5: Magnitude of the layer-resolved initial field-like and damping-like SOT components for $E =0.8$ mV/nm, separating the contributions from magnetization-independent, magnetization-dependent, $M$-even and $M$-odd induced moments $\delta \mu_{S,L}$, respectively. Layer 1 is the interface layer to the Pt, layer 8 is the surface layer of the Co film. The colored symbols depict different contributions to the total SOT ($T_{\text{total}}^{\text{SOT}}$), including the torques due to the interaction of local moments with induced spin moments in Co via exchange $(T^{S}_{\text{Co}})$, via intra-atomic exchange $(T^{S}_{\text{intra}})$, with induced spin moments at the interfacial Pt via renormalized exchange $(T_{\text{Pt}}^{S})$, with the induced orbital moments in Co via spin-orbit coupling $(T_{\text{Co}}^{L})$, and with induced orbital moments at the Pt interface via renormalized spin-orbit interaction $(T_{\text{Pt}}^{L})$, respectively.