Spin-flux phase in the Kondo lattice model with classical localized spins

We provide numerical evidence that a spin-flux phase exists as a ground state of the Kondo lattice model with classical local spins on a square lattice. This state manifests itself as a double-Q magnetic order in the classical spins with spin density at both (0,π) and (π,0) and further exhibits fermionic spin currents around an elementary plaquette of the square lattice. We examine the spin-wave spectrum of this phase. We further discuss an extension to a face-centered-cubic (fcc) lattice where a spin-flux phase may also exist. On the fcc lattice the spin-flux phase manifests itself as a triple-Q magnetically ordered state and may exist in γ-Mn alloys.