Topological Hall effect in weakly canted antiferromagnets
Jotaro J. Nakane, Kazuki Nakazawa, Hiroshi Kohno
Abstract
Motivated by a recent experiment on manganese oxide thin films, we theoretically study the topological Hall effect in a weakly canted antiferromagnet with textured N\'eel ($\mathbit{n}$) and uniform ($\mathbit{l}$) components of magnetization. Treating the N\'eel texture by a spin gauge field and the uniform component perturbatively, we obtain an analytical expression for the topological Hall conductivity. The result is proportional to the emergent magnetic field, $\mathbf{\ensuremath{\nabla}}\ifmmode\times\else\texttimes\fi{}{\mathbit{A}}_{\mathrm{AF}}$, where ${A}_{\mathrm{AF},i}=\mathbit{l}\ifmmode\cdot\else\textperiodcentered\fi{}({\ensuremath{\partial}}_{i}\mathbit{n}\ifmmode\times\else\texttimes\fi{}\mathbit{n})$ is an emergent vector potential in antiferromagnets, which consists of the spin-chirality density, $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbit{l}}\ifmmode\cdot\else\textperiodcentered\fi{}({\ensuremath{\partial}}_{x}\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbit{l}}\ifmmode\times\else\texttimes\fi{}{\ensuremath{\partial}}_{y}\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbit{l}})$, formed by the normalized uniform moment $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbit{l}}=\mathbit{l}/|\mathbit{l}|$, and one formed by the N\'eel and uniform components in the presence of spatial variation of canting. The result is discussed in comparison with the previous study on ferromagnets in the weak-coupling regime.