Anomalous Hall Conductivity of a Non-Collinear Magnetic Antiperovskite

The anomalous Hall effect (AHE) is a well-known fundamental property of ferromagnetic metals, commonly associated with the presence of a net magnetization. Recently, an AHE has been discovered in non-collinear antiferromagnetic (AFM) metals. Driven by non-vanishing Berry curvature of AFM materials with certain magnetic space group symmetry, anomalous Hall conductivity (AHC) is very sensitive to the specific type of magnetic ordering. Here, we investigate the appearance of AHC in antiperovskite GaNMn$_{3}$ as a representative of broader materials family ANMn$_{3}$ (A is a main group element), where different types of non-collinear magnetic ordering can emerge. Using symmetry analyses and first-principles density-functional theory calculations, we show that with almost identical band structure, the nearly degenerate non-collinear AFM $\Gamma_{5g}$ and $\Gamma_{4g}$ phases of GaNMn$_{3}$ have zero and finite AHC, respectively. In a non-collinear ferrimagnetic $M$-1 phase, GaNMn$_{3}$ exhibits a large AHC due to the presence of a sizable net magnetic moment. In the non-collinear antiperovskite magnets, transitions between different magnetic phases, exhibiting different AHC states, can be produced by doping, strain, or spin transfer torque, which makes these materials promising for novel spintronic applications.