Quadrupolar superexchange interactions, multipolar order, and magnetic phase transition in UO2

The origin of noncollinear magnetic order in UO₂ is studied by an ab initio dynamical-mean-field-theory framework in conjunction with a linear-response approach for evaluating intersite superexchange interactions between U 5 f² shells. The calculated quadrupole-quadruple superexchange interactions are found to unambiguously resolve the frustration of face-centered-cubic U sublattice toward stabilization of the experimentally observed noncollinear 3k-magnetic order. Therefore, the exotic 3k-antiferromagnetic order in UO₂ can be accounted for by a purely electronic exchange mechanism acting in the undistorted cubic lattice structure. The quadrupolar short-range order above magnetic ordering temperature T_N is found to qualitatively differ from the long-range order below T_N.