From frustrated magnetism to spontaneous Chern insulators

We study the behavior of electrons interacting with a classical magnetic background via a strong Hund coupling. The magnetic background results from a Hamiltonian which favors at low temperature the emergence of a phase with nonzero scalar chirality. The strong Hund's coupling combined with the total chirality of the classical spins induces in the electrons an effective flux which results in the realization of a band structure with nonzero Chern number. First, we consider as a magnetic background a classical spin system with spontaneous net chirality. We study the density of states and Hall conductance in order to analyze the topological transitions as a function of the Fermi energy and the temperature of the classical spins. We also study a similar model in which the Chern number of the filled bands can be “tuned” with the external magnetic field, resulting in a topological insulator in which the direction of the chiral edge mode can be reverted by reversing the orientation of the magnetic field applied to the classical magnetic system.