Emergent magnetic behavior in the frustrated Yb3Ga5O12 garnet

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 $0.6<{J}₁<0.7\phantom{\rule{4pt}{0ex}}\mathrm{K},\phantom{\rule{4pt}{0ex}}{J}₂=0.12$ 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 ${J}₁D$ model with ferromagnetic near-neighbor spin-spin correlations while other aspects of the data can be accurately reproduced using a ${J}₁{J}₂D$ 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 ${\mathrm{Yb}}₃{\mathrm{Ga}}₅{\mathrm{O}}₁₂$.