Magneto-optic and transverse transport properties of non-collinear antiferromagnets

Previous studies on the anomalous Hall effect in coplanar noncollinear antiferromagnets are revisited and extended to magneto-optic properties, namely magneto-optic Kerr effect (MOKE) and x-ray magnetic dichroism (XMCD). Starting from group-theoretical considerations the shape of the frequency-dependent conductivity tensor for various actual and hypothetical spin configurations in cubic and hexagonal ${\mathrm{Mn}}_{3}X$ compounds is determined. Calculated MOKE and x-ray dichroism spectra are used to confirm these findings and to give estimates of the size of the effects. For ${\mathrm{Mn}}_{3}\mathrm{IrPt}$ and ${\mathrm{Mn}}_{3}\mathrm{PtRh}$ alloys the concentration dependence of the anomalous and spin Hall conductivity is studied in addition.