An Anisotropic Enhancement of Spin Orbit Coupling in the Underscreened Anderson Lattice Model

The underscreened Anderson Lattice Model describes the uranium monochalcogenides, US, USe and UTe which at high temperatures, the Curie susceptibility show large magnetic moments, and the resistivities show lograithmic temperature variations indicative of a Kondo Effect. At lower temperatures, the magnetic moments are only partially compensated and the residual moments undergo transitions to ferromagnetic states. We examine the effect that the Coulomb and Hund's Rule exchange interaction have on the enhancement of the spin-orbit coupling in the Underscreened Anderson Lattice Model. We assume invariance under time-reversal and inversion. Within a rotationally invariant framework, we consider spin and orbital rotationally invariant interactions and an anisotropic crystal structure, and show that the spin-orbit coupling is enhanced and becomes anisotropic. The results are related to the unsual magnetic anisotropy observed in the ferromagnetic states of the cubic uranium monochalcogenides,