The Parallel Susceptibility of an Antiferromagnet at Low Temperatures

Abstract

The spin wave method of Heller and Kramers is applied to a cubic antiferromagnetic crystal, oriented so that the direction of alignment of the sublattice spins is parallel to an external magnetic field. Taking into account exchange interactions and an anisotropy term, then the parallel susceptibility ${\ensuremath{\chi}}_{\mathrm{II}}$ is zero at $T=0$\ifmmode^\circ\else\textdegree\fi{}K, in agreement with the result of the molecular field treatment of the problem by Van Vleck. If nearest neighbor magnetic dipole interactions are included, ${\ensuremath{\chi}}_{\mathrm{II}}$ is nonzero but negligibly small: ${\ensuremath{\chi}}_{\mathrm{II}}\ensuremath{\sim}{10}^{\ensuremath{-}11}$ at $T=0$\ifmmode^\circ\else\textdegree\fi{}K. For $Tg0$ but much less than the antiferromagnetic Curie temperature, if the dipole interactions are neglected and the anisotropy is small, such that $\ensuremath{\zeta}=\frac{S{(24JK)}^{\frac{1}{2}}}{\mathrm{k}T}\ensuremath{\ll}1$, where $K$ is an anisotropy constant, then ${\ensuremath{\chi}}_{\mathrm{II}}\ensuremath{\propto}{T}^{2}$. If $\ensuremath{\zeta}\ensuremath{\gg}1$, then ${\ensuremath{\chi}}_{\mathrm{II}}\ensuremath{\propto}{T}^{\frac{1}{2}}\mathrm{exp}[\ensuremath{-}\frac{S{(24JK)}^{\frac{1}{2}}}{\mathrm{k}T}]$.