Hartree-Fock study on the5forbital magnetic moment of US

The U $5f$ spin ${(M}_{\mathrm{spin}})$ and orbital ${(M}_{\mathrm{orb}})$ magnetic moments in the ferromagnetic compound US are calculated on the basis of the Hartree-Fock approximation for an extended Hubbard model. Our tight-binding model includes the U $6p,5f,6d,$ and $7s$ orbitals and the S $3s,3p,$ and $3d$ ones, and the intra-atomic $5f-5f$ multipole interaction and the spin-orbit interaction in the $5f$ state are taken into account. Most of the parameters involved in the model are determined by fitting with the energy of Bloch electrons in the paramagnetic state obtained by a first-principles calculation based on the local density approximation (LDA). The calculated ratio of the moments $M_{\mathrm{orb}}{/M}_{\mathrm{spin}}$ of $-2.1$ and $M_{\mathrm{orb}}$ of $-3.2{\mu }_{\mathrm{B}}$ are in good agreement with available experimental results. The calculated magnetic circular dichroism spectrum at the U $3\overrightarrow{d}5f$ x-ray absorption also agrees with the recent experiment. An inclusion of the expectation values of the spin-off-diagonal operators in addition to the number operators in the $5f$ state is found to be crucially important in describing its proper magnetic state and problems of LDA in the estimation of $M_{\mathrm{orb}}$ are discussed in this context.