Magnetic competition in topological kagome magnets

Magnetic competition in topological kagome magnets is studied by incorporating the spin-orbit coupling, anisotropic Hund coupling and spin exchange into a tight-binding electron dynamics in the kagome lattice. Using the Bogoliubov variational principle we find the stable phases at zero and finite temperatures. At zero temperature and in the strong Ising-Hund coupling regime, a magnetic tunability from the out-of-plane ferromagnetism to the in-plane antiferromagnetism is achieved through a universal property of the critical in-plane Hund coupling. At low temperature the out-of-plane ferromagnetism is stable until a finite crossing temperature. Above the crossing temperature the in-plane antiferromagnetism is stable, but the magnetization of the out-of-plane ferromagnetism still survives. This suggests a metastable coexistence of these magnetic phases in a finite temperature range. A large anomalous Hall conductance is observed in the Ising-Hund coupling limit.