Effect of Dipolar Interactions on the Spin-Wave Spectrum of a Cubic Antiferromagnet

The effect of dipolar interactions on the spin-wave spectrum of a cubic antiferromagnet is studied. The spin-wave spectrum is found to consist of two branches whose frequencies are ${\left(\hslash \omega \right)}^2={\left(g\beta \right)}^2[H_A+H_E{a}^2{k}^2][H_A+H_E(2-a^2{k}^2)-\frac{8\pi M}{3}+8\mathrm{}\pi M{sin}^2{\partial }_k]$ and ${\left(\hslash \omega \right)}^2={\left(g\beta \right)}^2[H_A+H_E{a}^2{k}^2][H_A+H_E(2-a^2{k}^2)-\frac{8\pi M}{3}].\mathrm{}$ Here $a$ is the lattice constant, $M$ the magnetic moment per unit volume, $k$ the wave vector, ${\theta }_k$ the angle between the magnetization and the wave vector, and $H_A$ and $H_E$ the anisotropy and exchange fields. The reasons for discrepancies between these formulas and those given previously by other authors are discussed.