Sequence of superconducting states in field cooled $FeCr_2S_4$

In the present article we discuss theoretically the emergence of superconductivity in field cooled $FeCr_2S_4$. The chromium electrons form a triplet $t_{2g}$ states and due to antiferromagnetic exchange with the iron spins have Zeeman splitting. Applied, during preparation, magnetic field along the moment of iron ions, successively compensates the Zeeman splittings. The chromium electrons with zero Zeeman energy form Cooper pairs induced by iron magnons. In that way, we predict theoretically the existence of sequence of superconducting states in field cooled $FeCr_2S_4$. Actually there are three different superconductors prepared applying, during preparation, different magnetic fields. In these compounds superconductivity coexist with the saturated magnetism of iron ions.