Coexistence of Ferromagnetism with Spin Triplet Superconductivity

Abstract

The experimental results for ZrZn$_{2}$, URhGe, and in some pressure ranges also for UGe$_{2}$, have shown that the ferromagnetic superconductors are weak itinerant ferromagnets. Guided by these results we describe the phenomenon of coexistence between equal spin triplet pairing superconductivity (SC) and ferromagnetism (F) using the extended Stoner model, which includes in Hamiltonian the on-site Coulomb interaction, $U$, and occupation dependent hopping integral. We use Hartree-Fock (H-F) approximation and the Green functions technique. In the H-F approximation the on-site Coulomb interaction plays the role of the on-site exchange (Hund's) field. All inter-site interactions will have included the inter-site kinetic correlation, $<c_{i\sigma}^{+}c_{j\sigma}>$, within the H-F approximation. We introduce the pressure-dependence to the hopping integral. Numerical results are compared with experimental data for ZrZn$_{2}$. The kinetic correlation creates the superconductivity without help of negative values of Coulomb interactions. The model can explain stimulation of triplet SC by the weak itinerant ferromagnetism. This effect was observed experimentally in ZrZn$_{2}$. Numerical analysis also confirms the experimental effect of decrease in critical temperatures (Curie and superconducting) with increasing external pressure.