Emergent magnetic behaviour in the frustrated Yb${}_3$Ga${}_5$O${}_{12}$ garnet

Abstract

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 Yb${}_3$Ga${}_5$O${}_{12}$ single crystal. The quantum spin state of Yb${}^{3+}$ in Yb${}_3$Ga${}_5$O${}_{12}$ is verified. The quantum spins organise into a short ranged emergent director state for T $<$ 0.4 K derived from anisotropy and near neighbour exchange. We derive the magnitude of the near neighbour exchange interactions $0.6\mathrm{K}<J_1<0.7\mathrm{K},J_2=0.12$~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 modelled using a $J_{1}D$ model with ferromagnetic near neighbour spin-spin correlations while other aspects of the data can be accurately reproduced using a $J_1{J}_{2}D$ model with antiferromagnetic near neighbour 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 Yb${}_3$Ga${}_5$O${}_{12}$.

Main paper 10 pages, appendix 6 pages