Sound velocity and attenuation measurements on the frustrated garnet material ${\mathrm{Gd}}_3{\mathrm{Ga}}_5{\mathrm{O}}_{12}$ (GGG) are presented as a function of field and temperature, with two different magnetic field orientations: $\left[100\right]$ and $\left[110\right]$. We demonstrate that the phase diagram is highly anisotropic, with two distinct field-induced ordered phases for $H\left|\right|\left[110\right]$ and only one for $H\left|\right|\left[100\right]$. Extensive lattice softening is found to occur at low fields, which can be associated with spin fluctuations. However, deep within the spin liquid phase a low-temperature stiffening of the lattice and reduced attenuation provide evidence for a spin gap which may be related to short-range antiferromagnetic correlations over minimal ten-spin loops.

• Received 7 July 2017

DOI:https://doi.org/10.1103/PhysRevB.96.060411