Emergent magnetic behavior in the frustrated Yb 3 Ga 5 O 12 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 $Tl0.6$ K derived from anisotropy and near-neighbor exchange. We derive the magnitude of the near-neighbor exchange interactions $0.6l{J}_{1}l0.7\phantom{\rule{4pt}{0ex}}\mathrm{K},\phantom{\rule{4pt}{0ex}}{J}_{2}=0.12$ K and the magnitude of the dipolar exchange interaction, $D$, in the range $0.18lDl0.21$ 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 ${\mathrm{Yb}}_{3}{\mathrm{Ga}}_{5}{\mathrm{O}}_{12}$.