Anomalous Hall effect in a compensated ferrimagnet: Symmetry analysis for Mn3Al

Abstract

It has long been believed that the anomalous Hall effect (AHE) can only be observed in ferromagnets. However, any magnetic material can exhibit AHE due to the broken time-reversal symmetry. In this work, we present a nontrivial AHE on the compensated ferrimagnet ${\mathrm{Mn}}_{3}\mathrm{Al}$ using symmetry arguments and first-principles calculations. Nonzero components of anomalous Hall conductivity ${\ensuremath{\sigma}}_{\ensuremath{\alpha}\ensuremath{\beta}}$ are determined based on the magnetic space group of ${\mathrm{Mn}}_{3}\mathrm{Al}$. The explicit first-principles calculation confirms ${\ensuremath{\sigma}}_{xy}=\ensuremath{-}320\phantom{\rule{4pt}{0ex}}{(\mathrm{\ensuremath{\Omega}}\phantom{\rule{0.16em}{0ex}}\mathrm{cm})}^{\ensuremath{-}1}$. The nature of Berry curvature responsible for the intrinsic origin of AHE is further identified using group theory: lifted degeneracies at $\frac{1}{2}K\mathrm{\ensuremath{\Gamma}}$, $L$, and $\frac{1}{2}{K}^{\ensuremath{'}}\mathrm{\ensuremath{\Gamma}}$ induced by spin-orbit interactions. Moreover, the global behaviors of Berry curvatures are shown over the whole Brillouin zone which reveal the overlooked contributions around ${X}^{\ensuremath{'}}$.