Low-Temperature Behavior of a Planar Ferromagnet

Abstract

We have examined the low-temperature properties of a simple cubic planar Heisenberg ferromagnet with nearest-neighbor interactions H=− ∑ ij JijSi·Sj− ∑ ij (Kij−Jij)SixSjxwhere −J≤K≤J. At zero temperature the spin deviation per spin increases from zero in the isotropic limit to 0.022 when K=0 and to 0.078 when K=−J. The ground state energy E0=−6N JS(S+β/6) is depressed by the anisotropy from β=0 in the isotropic limit to β=0.16 when K=0 and β=0.58 when K=−J. The lowest-order correction to the harmonic spin-wave frequency in the long-wave-length limit scales approximately as [U(T)-U(0)], where U(T) is the internal energy. The renormalization shifts the zero-temperature spin-wave frequency by less than 4S−1% (at K=0). We also calculate the spin-wave damping using a relaxation function formalism and find that in the hydrodynamic limit the decay rate is proportional to k2 in agreement with the predictions of macroscopic hydrodynamics.