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We provide numerical evidence that a spin-flux phase exists as a ground stateof the Kondo lattice model with classical local spins on a square lattice. Thisstate manifests itself as a double-Q magnetic order in the classical spins withspin density at both $(0,\pi)$ and $(\pi,0)$ and further exhibits fermionicspin currents around an elementary plaquette of the square lattice. We examinethe spin-wave spectrum of this phase. We further discus an extension to a facecentered cubic (FCC) lattice where a spin-flux phase may also exist. On the FCClattice the spin-flux phase manifests itself as a triple-Q magnetically orderedstate and may exist in $\gamma$-Mn alloys.Comment: 5 pages, 3 figure

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