Low-Temperature Behavior of a Planar Ferromagnet

• Published in: Journal of applied physics 1971-01, Vol.42 (4), p.1415-1416
• Main Authors: Semura, J. S., Huber, D. L.
• Format: Article
• Language: English
• ISSN: 0021-8979; 1089-7550
• DOI: 10.1063/1.1660270

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.