Parametrization of LSDA+U for noncollinear magnetic configurations: Multipolar magnetism in UO2

Abstract

To explore the formation of noncollinear magnetic configurations in materials with strongly correlated electrons, we derive a noncollinear LSDA+U model involving only one parameter U, as opposed to the difference between the Hubbard and Stoner parameters U-J. Computing U in the constrained random phase approximation, we investigate noncollinear magnetism of uranium dioxide UO2 and find that the spin-orbit coupling (SOC) stabilizes the 3k ordered magnetic ground state. The estimated SOC strength in UO2 is as large as 0.73 eV per uranium atom, making spin and orbital degrees of freedom virtually inseparable. Using a multipolar pseudospin Hamiltonian, we show how octupolar and dipole-dipole exchange coupling help establish the 3k magnetic ground state with canted ordering of uranium f orbitals. The cooperative Jahn-Teller effect does not appear to play a significant part in stabilizing the noncollinear 3k state, which has the lowest energy even in an undistorted lattice. The choice of parameter U in the LSDA+U model has a notable quantitative effect on the predicted properties of UO2, in particular on the magnetic exchange interaction and, perhaps trivially, on the band gap: The value of U=3.46eV computed fully ab initio delivers the band gap of 2.11 eV in good agreement with experiment, and a balanced account of other pertinent energy scales.