Statistical Mechanics and Field-Induced Phase Transitions of the Heisenberg Antiferromagnet

The spin-flop and flop-para phase transitions of a simple uniaxial antiferromagnet are analyzed by a Green-function analysis. The temperature dependence of the field for antiferromagnetic resonance, the parallel and perpendicular susceptibilities, and the sublattice magnetizations are also computed. It is shown that these effects are sensitive to the temperature-dependent renormalization of spin-wave energies, and this effect is analyzed in some detail. Results are in good semiquantitative agreement with antiferromagnetic resonance in Mn${\mathrm{F}}_2$ and ${\mathrm{Cr}}_2$ ${\mathrm{O}}_3$, with the phase transition boundaries in Mn${\mathrm{Br}}_2$·4${\mathrm{H}}_2$O, and with the perpendicular susceptibility of Mn${\mathrm{F}}_2$.