  We investigate magnetic orderings on kagome lattice numerically from the
tight-binding Hamiltonian of electrons, governed by the filling factor and
spin-orbit coupling (SOC) of electrons. We find that even a simple kagome
lattice model can host both ferromagnetic and noncollinear antiferromagnetic
orderings depending on the electron filling, reflecting gap structures in the
Dirac and flat bands characteristic to the kagome lattice. Kane--Mele- or
Rashba-type SOC tends to stabilize noncollinear orderings, such as magnetic
spirals and 120-degree antiferromagnetic orderings, due to the effective
Dzyaloshinskii--Moriya interaction from SOC. The obtained phase structure helps
qualitative understanding of magnetic orderings in various kagome-layered
materials with Weyl or Dirac electrons.
