Spin-Lattice Interaction in UO2. II. Theory of the First-Order Phase Transition

Abstract

A theory of the first-order phase transition in U${\mathrm{O}}_2$ is presented and discussed in the molecular-field approximation. An isotropic nearest-neighbor exchange and local quadrupole-lattice interaction are taken as the basic interactions in the model. Interesting behavior is obtained due to the two distinct ways in which the collective ground-state degeneracy can be removed at $T=0\mathrm{}°$K: a cooperative Jahn-Teller distortion or a polarization of the sublattice magnetization by the exchange field. Depending on the relative gain in free energy obtained by these two mechanisms, one obtains four different types of behavior near the critical point: (1) a second-order transition to a distorted state with no magnetic ordering; (2) a second-order transition to a distorted state followed by a second-order magnetic transition; (3) a first-order transition yielding a discontinuous change in lattice distortion and sublattice magnetization; (4) a second-order magnetic transition accompanied by a weak distortion. The temperature dependence of the elastic constant $C_{44}$ is also derived. The parameters required to give a first-order transition in agreement with the measured discontinuity in sublattice magnetization and the correct behavior for $C_{44}$ are found to be consistent with the parameters obtained from the measured spin-wave excitations.