# Layer-dependent spin-orbit torques generated by the centrosymmetric transition metal dichalcogenide $\beta$-MoTe$_2$

## TL;DR

This study demonstrates that centrosymmetric $eta$-MoTe$_2$ can generate significant out-of-plane antidamping spin-orbit torques, with a unique thickness dependence, challenging the notion that inversion symmetry breaking is necessary for such effects.

## Contribution

It reveals that bulk inversion symmetry breaking is not essential for out-of-plane antidamping torque generation, and explores the layer-dependent behavior of spin-orbit torques in $eta$-MoTe$_2$.

## Key findings

- Out-of-plane antidamping torque observed in $eta$-MoTe$_2$/Permalloy heterostructures.
- Torque strength is comparable to one-third of WTe$_2$.
- The torque depends on the number of layers, disappearing in bilayer $eta$-MoTe$_2$.

## Abstract

Single-crystal materials with sufficiently low crystal symmetry and strong spin-orbit interactions can be used to generate novel forms of spin-orbit torques on adjacent ferromagnets, such as the out-of-plane antidamping torque previously observed in WTe$_2$/ferromagnet heterostructures. Here, we present measurements of spin-orbit torques produced by the low-symmetry material $\beta$-MoTe$_2$, which unlike WTe$_2$ retains bulk inversion symmetry. We measure spin-orbit torques on $\beta$-MoTe$_2$/Permalloy heterostructures using spin-torque ferromagnetic resonance as a function of crystallographic alignment and MoTe$_2$ thickness down to the monolayer limit. We observe an out-of-plane antidamping torque with a spin torque conductivity as strong as 1/3 of that of WTe$_2$, demonstrating that the breaking of bulk inversion symmetry in the spin-generation material is not a necessary requirement for producing an out-of-plane antidamping torque. We also measure an unexpected dependence on the thickness of the $\beta$-MoTe$_2$ -- the out-of-plane antidamping torque is present in MoTe$_2$/Permalloy heterostructures when the $\beta$-MoTe$_2$ is a monolayer or trilayer thick, but goes to zero for devices with bilayer $\beta$-MoTe$_2$.