Spin-phonon interactions in a Heisenberg antiferromagnet. I. The spin-wave spectrum

The effects of spin-phonon interactions in a uniaxial Heisenberg antiferromagnet are studied using a field-theoretical perturbation technique and an expansion in powers of the high-density parameter 1/z, where z is the number of spins interacting with any given spin. The renormalized energy and damping of the spin-wave excitations are evaluated to second order in the spin-phonon coupling, and the dependence of these quantities on temperature, wavevector and anisotropy factors is obtained. The calculations are valid over a wide range of temperature below the Neel temperature T N and detailed discussions are given for the cases of (i) low temperatures and (ii) temperatures close to T N . Some numerical estimates are made for MnF 2 .