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 $(0,\pi)$ and $(\pi,0)$ 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 discus 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 $\gamma$-Mn alloys.