Model of the low temperature magnetic phases of gadolinium gallium garnet

TL;DR

This paper models the low temperature magnetic phases of gadolinium gallium garnet under external magnetic fields, predicting a field-sensitive transition involving magnon mode softening and changes in spin configuration periodicity.

Contribution

It introduces a combined classical and quantum spin model for gadolinium gallium garnet, predicting field-induced transitions and spin configuration changes at low temperatures.

Findings

Predicts a magnetic transition at 1.9-2.1 T sensitive to field direction.

Identifies magnon mode softening as the cause of the transition.

Shows that periodicity is maintained along principal axes even below the transition.

Abstract

The magnetic behaviour of gadolinium gallium garnet in an external magnetic field at zero temperature is considered. For high fields a classical spin model of the gadolinium ions predicts a spin configuration that is periodic at the level of the smallest repeating unit cell. The quantum version of the model is treated via a truncated Holstein-Primakoff transformation with axes defined by the classical spin configuration, and the magnon excitation bands are calculated. The model predicts a transition in the field range of $1.9$ -- $2.1\mathrm{T}$, sensitive to the direction of the applied field, which is caused by one or more magnon modes becoming soft as the field is decreased. In general the soft modes occur at incommensurate wavevectors and therefore break the periodicity of the spin configuration below the transition. One exception occurs when the field aligns with one of the principle crystal axes, in which case periodicity of the spin configuration is found to be maintained on a larger crystallographic cubic cell even below the transition. This simple case is studied in more detail. Comparisons are drawn with existing experimental data, and further experimental tests of the model are suggested.