Deterministic Switching of Perpendicular Ferromagnets by Higher harmonics of Spin-orbit Torque in Noncentrosymmetric Weyl Semimetals

TL;DR

This paper demonstrates that higher-harmonic spin-orbit torques enable deterministic switching of perpendicular ferromagnets in Weyl semimetals without symmetry breaking, advancing spintronics control methods.

Contribution

It introduces a mechanism where higher-order spin-orbit torque components induce reliable magnetization switching in symmetric systems, supported by first-principles calculations.

Findings

Higher-harmonic torques create additional fixed points for magnetization.

First-principles calculations on PrAlGe show sizable higher-harmonic torques.

Deterministic switching occurs without explicit symmetry breaking.

Abstract

Field-free deterministic switching of perpendicular ferromagnets is a central challenge for spintronics applications, typically requiring explicit symmetry breaking. Here we show that deterministic switching can instead be achieved through higher angular harmonics of spin-orbit torques, even in systems that preserve in-plane mirror symmetries. Using a vector spherical harmonics expansion, we demonstrate that these higher-harmonic torque components naturally give rise to additional out-of-equator fixed points, enabling reliable magnetization reversal when their magnitude is comparable to conventional lowest-order torques. We illustrate this mechanism with first-principles calculations on the noncentrosymmetric Weyl ferromagnet PrAlGe, where the combination of Weyl-node band topology and strong spin-orbit coupling produces sizable higher-harmonic torque components. Because the Fermi surface is small, the conventional lowest-order torques are relatively weak, allowing the higher-order harmonics to compete on equal footing and strongly reshape the magnetization dynamics. The resulting spin dynamics confirm deterministic switching without additional symmetry breaking. Our results establish higher-harmonic spin-orbit torque as a key ingredient for understanding and controlling magnetization dynamics in topological and spintronic materials.