Coupled Electronic Spins, Nuclear Spins, and Phonons in a Cubic Antiferromagnet

The spin response functions for the electronic and nuclear spins in a cubic antiferromagnet are obtained in the random-phase approximation. These response functions are then used to investigate the coupled electronic-spin-nuclear-spin-phonon system. Predicted changes in phonon velocity and attenuation in RbMn${\mathrm{F}}_3$ due to interaction with electronic and nuclear spin waves are obtained. Some of these predictions agree with previous experiments and theory, and others can be checked by further experiments.