Spin dynamics in the frustrated three-dimensional hyperkagom{\'e} compound $Gd_3 Ga_5 O_{12}$

We present the first neutron inelastic scattering results on the low temperature magnetic state of the three dimensional hyperkagom\'e compound Gd$_{3}$Ga$_{5}$O$_{12}$ (GGG). GGG is often classified as a strongly frustrated system with a manifold of continuously connected states. However, in contrast to the expectation of a continuum of gap-less excitations above a spin liquid-like ground state our results reveal three distinct inelastic modes found at 0.04(1), 0.12(2) an 0.58(3) meV at 0.06 K. The inelastic modes can be attributed to the magnetic ground state with the lowest and highest energy excitations showing spatial dependencies indicative of dimerized short range antiferromagnetic correlations. Short range correlations, reminiscent of spin liquid-like order, are static within the instrumental resolution (50 $\mu$eV) and represent 82% of the spectral weight. Longer range correlations, first observed by Petrenko, et al.\cite{Petrenko1998, develop below 0.14 ~K within the elastic cross section. The short range static correlations and dynamic components survive to high temperatures, comparable to the nearest neighbor exchange interactions. Our results suggest that the ground state of a three dimensional hyperkagom\'e compound differs distinctly from its frustrated counterparts on a pyrochlore lattice and reveals a juxtaposition of spin liquid order and strong dimerised coupling.