Crystal facet orientation and temperature dependence of charge and spin Hall effects in noncollinear antiferromagnets: A first-principles investigation

Noncollinear antiferromagnets (nc-AFMs) have attracted increasing research attention in spintronics due to their unique spin structures and fascinating charge and spin transport properties. By using first-principles calculations, we comprehensively investigate the charge and spin Hall effects in representative noncollinear antiferromagnet $\mathrm{M}{\mathrm{n}}_{3}\mathrm{Pt}$. Our study reveals that the Hall effects in nc-AFMs are critically dependent on the crystal facet orientation and temperature. For (001)-oriented $\mathrm{M}{\mathrm{n}}_{3}\mathrm{Pt}$, each charge and spin Hall conductivity element comprises time-reversal odd ($T$-odd) and even ($T$-even) contribution, associated with longitudinal conductivity, which leads to sizable and highly anisotropic Hall conductivity. The temperature dependence of charge and spin Hall conductivity has been elucidated by considering both phonon and spin disorder scattering. The scaling relations between Hall conductivity and longitudinal conductivity have also been investigated. The existence of prominent spin Hall effect in nc-AFMs may generate spin current with ${S}_{z}$ spin polarization, which is advantageous for field-free switching of perpendicular magnetization. Our work may provide unambiguous understanding of the charge and spin transport in noncollinear antiferromagnets and pave the way for applications in antiferromagnetic spintronics.