Orbital magnetization and its effects in spin-chiral ferromagnetic Kagome lattice

Recently, Berry phase in the semiclassical dynamical of Bloch electrons has been found to make a correction to the phase-space density of states and a general multi-band formula for finite-temperature orbital magnetization has been given [Phys. Rev. Lett. \textbf{97}, 026603 (2006)], where the orbital magnetization $\mathcal{M}$ consists of two parts, i.e., the conventional part $M_{c}$ and the Berry-phase correction part $M_{\Omega}$. Using this general formula, we theoretically investigate the orbital magnetization and its effects on thermoelectric transport and magnetic susceptibility properties of the two-dimensional \textit{kagom\'{e}} lattice with spin anisotropies included. The study in this paper is highly interesting by the occurrence of nonzero Chern number in the lattice. The spin chirality parameter $\phi$ (see text) results in profound effects on the orbital magnetization properties. It is found that the two parts in orbital magnetization opposite each other. In particular, we show that $M_{c}$ and $M_{\Omega}$ yield the paramagnetic and diamagnetic responses, respectively. It is further shown that the orbital magnetization displays fully different behavior in the metallic and insulating regions, which is due to the different roles $M_{c}$ and $M_{\Omega}$ play in these two regions. The anomalous Nernst conductivity is also calculated, which displays a peak-valley structure as a function of the electron Fermi energy.