Classical Heisenberg antiferromagnet on a garnet lattice: A Monte Carlo simulation

Abstract

We have studied a classical antiferromagnet on a garnet lattice by means of Monte Carlo simulations in an attempt to examine the role of geometrical frustration in gadolinium gallium garnet ${\mathrm{Gd}}_{3}{\mathrm{Ga}}_{5}{\mathrm{O}}_{12}$ (GGG). Low-temperature specific heat, magnetization, susceptibility, the autocorrelation function $A(t),$ and the neutron scattering function $S(Q)$ have been calculated for several models including different types of magnetic interactions and with the presence of an external magnetic field applied along the principal symmetry axes. A model, which includes only nearest-neighbor exchange ${J}_{1},$ neither orders down to the lowest temperature nor does it show any tendency towards forming a short-range coplanar spin structure. This model, however, does demonstrate a magnetic field induced ordering below $T\ensuremath{\sim}{0.01J}_{1}.$ In order to reproduce the experimentally observed properties of GGG, the simulated model must include nearest-neighbor exchange interactions and also dipolar forces. The presence of weak next-to-nearest exchange interactions is found to be insignificant. In zero field $S(Q)$ exhibits diffuse magnetic scattering around positions in reciprocal space where antiferromagnetic Bragg peaks appear in an applied magnetic field.