Magnetism, Spin-Orbit Coupling, and Superconducting Pairing in UGe$_2$

A consistent picture on the mean-field level of the magnetic properties and electronic structure of the superconducting itinerant ferromagnet UGe$_2$ is shown to require inclusion of correlation effects beyond the local density approximation (LDA). The "LDA+U" approach reproduces both the magnitude of the observed moment, composed of strongly opposing spin and orbital parts, and the magnetocrystalline anisotropy. The largest Fermi surface sheet is comprised primarily of spin majority states with orbital projection $m_{\ell}$=0, suggesting a much simpler picture of the pairing than is possible for general strong spin-orbit coupled materials. This occurrence, and the quasi-two-dimensional geometry of the Fermi surface, support the likelihood of magnetically mediated p-wave triplet pairing.