Emergent magnetic behavior in the frustrated Yb₃Ga₅O₁₂ garnet

We report neutron scattering, magnetic susceptibility and Monte Carlo theoretical analysis to verify the shortrange nature of the magnetic structure and spin-spin correlations in a Yb₃Ga₅O₁₂ single crystal. The quantum spin state of Yb3+ in Yb₃Ga₅O₁₂ 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 nearneighbor exchange interactions 0.6 < J₁ < 0.7 K, J₂ = 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 J₁D model with ferromagnetic near-neighbor spin-spin correlations while other aspects of the data can be accurately reproduced using a J₁J₂D 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 Yb₃Ga₅O₁₂.