We report neutron scattering, magnetic susceptibility and Monte Carlo theoretical analysis to verify the short-range nature of the magnetic structure and spin-spin correlations in a ${\mathrm{Yb}}_3{\mathrm{Ga}}_5{\mathrm{O}}_{12}$ single crystal. The quantum spin state of ${\mathrm{Yb}}^{3+}$ in ${\mathrm{Yb}}_3{\mathrm{Ga}}_5{\mathrm{O}}_{12}$ is verified. The quantum spins organize into a short-ranged emergent director state for $T<0.6$ K derived from anisotropy and near-neighbor exchange. We derive the magnitude of the near-neighbor exchange interactions $0.6<J_1<0.7\mathrm{K},J_2=0.12$ K and the magnitude of the dipolar exchange interaction, $D$, in the range $0.18<D<0.21$ K. Certain aspects of the broad experimental dataset can be modeled using a $J_{1}D$ model with ferromagnetic near-neighbor spin-spin correlations while other aspects of the data can be accurately reproduced using a $J_1{J}_{2}D$ model with antiferromagnetic near-neighbor spin-spin correlation. As such, although we do not quantify all the relevant exchange interactions, we nevertheless provide a strong basis for the understanding of the complex Hamiltonian required to fully describe the magnetic state of ${\mathrm{Yb}}_3{\mathrm{Ga}}_5{\mathrm{O}}_{12}$.

• Received 25 May 2020
• Revised 30 April 2021
• Accepted 13 July 2021

DOI:https://doi.org/10.1103/PhysRevB.104.064425