Angular dependence of spin-orbit torque in monolayer $Fe_3GeTe_2$

TL;DR

This paper investigates how spin-orbit torque in monolayer Fe3GeTe2 depends on the angle of magnetization, revealing higher order effects that enable electric switching without external magnetic fields.

Contribution

It introduces a first-principles analysis of angular dependence of spin-orbit torque in monolayer Fe3GeTe2, highlighting the importance of higher order terms in magnetic dynamics.

Findings

Higher order spherical harmonic terms significantly influence torque behavior.

Deterministic magnetic switching achieved without external magnetic fields.

Angular dependence crucial for designing spintronic devices.

Abstract

In ferromagnetic systems lacking inversion symmetry, an applied electric field can control the ferromagnetic order parameters through the spin-orbit torque. The prototypical example is a bilayer heterostructure composed of a ferromagnet and a heavy metal that acts as a spin current source. In addition to such bilayers, spin-orbit coupling can mediate spin-orbit torques in ferromagnets that lack bulk inversion symmetry. A recently discovered example is the two-dimensional monolayer ferromagnet $Fe_3GeTe_2$. In this work, we use first-principles calculations to study the spin-orbit torque and ensuing magnetic dynamics in this material. By expanding the torque versus magnetization direction as a series of vector spherical harmonics, we find that higher order terms (up to $\ell=4$) are significant and play important roles in the magnetic dynamics. They give rise to deterministic, magnetic field-free electrical switching of perpendicular magnetization.