Numerical estimation of the ground states of frustrated antiferromagnet gadolinium gallium garnet

The classical ground states of the frustrated antiferromagnet gadolinium gallium garnet are studied in three distinct phases in a range of external magnetic fields. It is found that a simple optimization strategy based around Monte–Carlo simulated annealing is insufficient to correctly describe the disordered phases in reasonable time scales, and a rapid and reliable optimization scheme which is able to locate states of significantly lower energy is devised. In the zero-field phase the optimization scheme reproduces the long-range multipole order describing antiferromagnetic spin correlations around ten site rings, which has previously been inferred at finite temperatures from experimental neutron scattering data. In the intermediate field phase the simulated ground states are found to agree well with experimental neutron scattering data at the lowest temperatures, and it is shown that the multipole directors are also useful in understanding the spin structure in this phase.