Edge states and the integer quantum Hall effect of spin-chiral ferromagnetic kagome lattice with a general spin coupling

The chiral edge states and the quantized Hall conductance (QHC) in the two-dimensional kagom\'{e} lattice with spin anisotropies included in a general Hund's coupling region are studied. This kagom\'{e} lattice system is periodic in the $x$ direction but has two edges in the $y$ direction. Numerical results show that the strength of the Hund's coupling, as well as the spin chirality, affects the edge states and the corresponding QHC. Within the topological edge theory, we give the expression of the QHC with the winding number of the chiral edge states on the Riemman surface. This expression is also compaired with that within the topological bulk theory and they are found to keep consistent with each other.