Variational Treatment of the Heisenberg Antiferromagnet
Abstract
A form of the Peierls freeenergy variational theorem is applied to the Heisenberg Hamiltonian for a threedimensional system with nearestneighbor antiferromagnetic interaction. For a large magnetic field (h≡gμH4SJz~1) we find a phase boundary separating a region of antiferromagnetic order from one of ferromagnetic order. At low temperatures (θ≡kT2SJz<<1) the phase boundary has the leading behavior: h=1aθ^{32} with a=2ζ (32) (32π)^{32}S for a simple cubic antiferromagnetic lattice (e.g., RbMnF_{3}). At the phase boundary the magnetization is continuous; whereas a discontinuity in the susceptibility is suggested but not firmly established by this treatment. Lowtemperature expressions are given for the magnetization, susceptibility, and specific heat above the boundary. Numerical calculations show that, for the approximation used, the phase boundary extends to a maximum θ at which the magnetization is nonzero. For the limiting case of h=0 we obtain Keffer and Loudon's renormalized spectrum and magnetization for a ferromagnet and for an antiferromagnet from a single variational calculation. Attention is also given to a reduced Hamiltonian which, when treated by the variational method, exhibits the properties of an antiferromagnetic molecular field model previously proposed by Garrett for S=12.
 Publication:

Physical Review
 Pub Date:
 March 1964
 DOI:
 10.1103/PhysRev.133.A1382
 Bibcode:
 1964PhRv..133.1382F