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Terbium gallium garnet (TGG), Tb$_3$Ga$_5$O$_{12}$, is well known for itsapplications in laser optics, but also exhibits complex low-temperaturemagnetism that is not yet fully understood. Its low-temperature magnetic orderis determined by means of time-of-flight neutron powder diffraction. It isfound to be a multiaxial antiferromagnet with magnetic Tb$^{3+}$ ions formingsix sublattices of magnetic moments aligned parallel and anti-parallel to the$\langle100\rangle$ crystallographic directions of the cubic unit cell. Thestructure displays strong easy-axis anisotropy with respect to a two-fold axisof symmetry in the local orthorhombic environment of the Tb$^{3+}$ sites. Thecrystal-field splitting within the single-ion ground-state manifold isinvestigated by inelastic neutron scattering on powder samples. A strongtemperature dependence of the quasidoublet ground-state is observed and revisedparameters of the crystal-field Hamiltonian are given. The results of bulkmagnetic susceptibility and magnetisation measurements are in good agreementwith values based on the crystal-field model down to 20~K, where the onset ofmagnetic correlations is observed.

Magnetic order and single-ion anisotropy in Tb$_3$Ga$_5$O$_{12}$