# Magnetic and Crystal Symmetry Control on Spin Hall Conductivity in Altermagnets

## TL;DR

This paper explores how magnetic and crystal symmetry affect spin Hall conductivity in altermagnets, which could lead to new spintronic devices.

## Contribution

The study reveals how structural tilting and magnetic ordering influence unconventional spin Hall conductivity in zero-net-magnetization materials.

## Key findings

- RuO2 shows trivial unconventional spin Hall conductivity under tilted geometry.
- CrSb and MnTe exhibit robust intrinsic unconventional spin Hall conductivity due to reduced magnetic symmetry.
- The interplay of crystal and magnetic symmetry can be controlled via structural tilting and magnetic axis orientation.

## Abstract

Altermagnets combine zero net magnetization with spin splitting, opening new opportunities for next‐generation spintronic devices. In this work, the unconventional spin Hall conductivity (USHC) in three representative materials—RuO2, CrSb, and MnTe is explored. It is clarified how distinct magnetic and crystal symmetries modulate their spin Hall responses. RuO2 exhibits only trivial USHC under a tilted geometry, demonstrating that symmetry projections alone can induce apparent unconventional elements. In contrast, CrSb and MnTe manifest robust intrinsic USHC driven by symmetry reduction through easy‐axis magnetic ordering without structural tilts. Through extensive first‐principles calculations, the complementary roles of the time‐reversal (T)‐even and T‐odd components in determining the overall spin Hall conductivity are demonstrated. The findings indicate that the interplay between crystal and magnetic symmetry can be controlled through structural tilting and magnetic axis orientation. These results pave the way for the engineering of multifunctional spintronic devices. In particular, they highlight zero‐net‐moment materials with tunable spin configurations as promising platforms for coherent and robust spin transport.

Crystal structures and schematic illustrations of the spin Hall effect (SHE) in altermagnets. High‐symmetry RuO2 exhibits conventional SHE, while tilted RuO2 shows trivial unconventional SHE (USHE) caused by structural tilting. CrSb and MnTe, with reduced magnetic symmetry, display intrinsic USHE arising from symmetry‐driven spin–momentum locking, leading to nonorthogonal spin‐current geometries.