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The magnetic behaviour of gadolinium gallium garnet in an external magneticfield at zero temperature is considered. For high fields a classical spin modelof the gadolinium ions predicts a spin configuration that is periodic at thelevel of the smallest repeating unit cell. The quantum version of the model istreated via a truncated Holstein-Primakoff transformation with axes defined bythe classical spin configuration, and the magnon excitation bands arecalculated. 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 iscaused by one or more magnon modes becoming soft as the field is decreased. Ingeneral the soft modes occur at incommensurate wavevectors and therefore breakthe periodicity of the spin configuration below the transition. One exceptionoccurs when the field aligns with one of the principle crystal axes, in whichcase periodicity of the spin configuration is found to be maintained on alarger crystallographic cubic cell even below the transition. This simple caseis studied in more detail. Comparisons are drawn with existing experimentaldata, and further experimental tests of the model are suggested.

Model of the low temperature magnetic phases of gadolinium gallium garnet