Topological Hall effect in canted antiferromagnets

The topological Hall effect (THE) is a Hall effect caused by a noncoplanar spin texture, or its spin chirality, in ferromagnetic conductors. This effect is absent in antiferromagnets (AF) due to the cancellation of the two sublattice chiralities. However, if the AF spins are canted, the overall spin chirality, hence the THE, can be finite.

Motivated by a recent experiment [1], we study the THE in a canted AF with textured Néel and uniform moments. Treating the two textures by a spin gauge field, we derive an analytical expression for the topological Hall conductivity (THC). The emergent magnetic field is written as ▽×A, where A is an emergent vector potential in canted AF. With the obtained THC, we discuss various regimes such as the strong and weak coupling regimes, and large and small canting regimes. In particular, in the strong-coupling large-canting limit, the THC is given by the Berry phase formula ("Bruno formula") multiplied by a reduction factor because of the presence of the Néel moment.

[1] L. Vistoli et al., Nature Physics, Vol. 15, 67 (2019)