The spontaneous electrical and spin Hall effect in a collinear antiferromagnet

In collinear antiferromagnets, since the combined operation of time reversal and a half-unit-cell translation is symmetric for the magnetic lattice, a spontaneous Hall effect is usually absent. Here, we show that in a collinear antiferromagnet, MnTe, the non-magnetic atomic structure breaks such symmetry, therefore allows a spontaneous Hall effect, which is known as planar Hall effect. Such spontaneous Hall effect does not result from the intrinsic Berry curvature. Instead, it comes from the extrinsic scattering centers with either positive or negative polarized spins along the easy axis of the Neel vector. This behavior is intriguing since it is by now the most convenient method to read-out (and potentially to write) the information encoded in antiferromagnets for high-speed device applications. Such zero-field planar Hall effect has already been observed in experiments. Our calculation shows that the spontaneous Hall effect and spin Hall effect can be up to 30%, suggesting a vast space to improve the performance for device applications.