Spin-Lattice Interaction in UO2. I. Ground-State and Spin-Wave Excitations

A microscopic theory of the effect of spin-lattice interaction on the ground-state and spin-wave excitations in U${\mathrm{O}}_2$ is presented. Three parameters required by a Jahn-Teller description of the local spin-lattice interactions and an exchange constant are introduced as basic variables to describe the system at $T=0\mathrm{}$°K. The spin-lattice ground state reveals a competition between the Jahn-Teller forces and the exchange energy that results in a reduction of the magnitude of the spin. It is also shown that the indirect quadrupole-quadrupole interaction caused by the virtual exchange of an optical phonon is as large as the exchange coupling (∼30°K), and significantly modifies the spin-wave energies and wave functions. Values for the interaction parameters are obtained by fitting the theory to the excitation spectra and to wave functions deduced from far-infrared absorption spectroscopy and from the inelastic scattering of neutrons. The theory is consistent with the upper limits placed on the lattice distortion and with the anomolous behavior of the elastic constant $C_{44}$.