Strong anisotropic anomalous Hall effect and spin Hall effect in the chiral antiferromagnetic compoundsMn3X(X=Ge, Sn, Ga, Ir, Rh, and Pt)

We have carried out a comprehensive study of the intrinsic anomalous Hall\neffect and spin Hall effect of several chiral antiferromagnetic compounds,\nMn$_3X$ ($X$ = Ge, Sn, Ga, Ir, Rh and Pt) by $ab~initio$ band structure and\nBerry phase calculations. These studies reveal large and anisotropic values of\nboth the intrinsic anomalous Hall effect and spin Hall effect. The Mn$_3X$\nmaterials exhibit a non-collinear antiferromagnetic order which, to avoid\ngeometrical frustration, forms planes of Mn moments that are arranged in a\nKagome-type lattice. With respect to these Kagome planes, we find that both the\nanomalous Hall conductivity (AHC) and the spin Hall conductivity (SHC) are\nquite anisotropic for any of these materials. Based on our calculations, we\npropose how to maximize AHC and SHC for different materials. The band\nstructures and corresponding electron filling, that we show are essential to\ndetermine the AHC and SHC, are compared for these different compounds. We point\nout that Mn$_3$Ga shows a large SHC of about 600 $(\\hbar/e)(\\Omega\\cdot\ncm)^{-1}$. Our work provides insights into the realization of strong anomalous\nHall effects and spin Hall effects in chiral antiferromagetic materials.\n