  Magnetic competition in topological kagome magnets is studied by
incorporating the spin-orbit coupling, the anisotropic Hund coupling and spin
exchange into 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 (FM) to the in-plane antiferromagnetism (AFM) is
achieved by a universal property of the critical in-plane Hund coupling. At
two-thirds filling the phase transition from the out-of-plane FM to the
in-plane AFM is accompanied by a topological transition from quantum anomalous
Hall (QAH) to quantum anomalous spin Hall (QASH) effect. Nearby half filling a
large anomalous Hall conductance is observed at the magnetic phase transition.
At finite temperature the out-of-plane FM is stable until a crossing
temperature, above which the in-plane AFM is stable, but the out-of-plane FM
magnetization is still finite. This suggests a coexistence of these magnetic
phases in a finite temperature range.
