Coexistence of superconductivity and magnetism in spin-fermion model of ferrimagnetic spinel in an external magnetic field

Abstract

A two-sublattice spin-fermion model of ferrimagnetic spinel, with spin- itinerant electrons at the sublattice A site and spin-s localized electrons at the sublattice B site is considered. The exchange between itinerant and localized electrons is antiferromagnetic. As a result, the external magnetic field, applied along the magnetization of the localized electrons, compensates the Zeeman splitting due to the spin-fermion exchange and magnon-fermion interaction induces spin antiparallel p-wave superconductivity which coexists with magnetism. We have obtained five characteristic values of the applied field (in units of energy) Hcr1 < H3 < H0 < H4 < Hcr2. At H0 the external magnetic field compensates the Zeeman splitting. When Hcr1 < H < Hcr2 the spin antiparallel p-wave superconductivity with T1u configuration coexists with magnetism. The superconductor-to-normal magnet transition at finite temperature is second order when H runs the interval . It is an abrupt transition when Hcr1 < H < H3 or H4 < H < Hcr2. This is proved calculating the temperature dependence of the gap for three different values of the external magnetic field Hcr1 < H < H3, H4 < H < Hcr2 and . In the first two cases the abrupt fall to zero of the gap at superconducting critical temperature shows that the superconductor-to-normal magnet transition is first order. The Hubbard term (Coulomb repulsion), in a weak-coupling regime, does not significantly affect the magnon-induced superconductivity. Relying on the above results one can formulate a recipe for preparing a superconductor from ferrimagnetic spinel: i) hydrostatic pressure above the critical value of insulator-metal transition; ii) external magnetic field along the sublattice magnetization with higher amplitude.