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

TL;DR

This study combines neutron scattering, magnetic susceptibility, and Monte Carlo simulations to reveal short-range magnetic order and emergent quantum spin states in Yb$_3$Ga$_5$O$_{12}$ garnet at very low temperatures.

Contribution

It provides detailed experimental and theoretical analysis of the magnetic interactions and emergent states in Yb$_3$Ga$_5$O$_{12}$, advancing understanding of frustrated quantum magnets.

Findings

Identification of short-range magnetic order below 0.4 K.

Quantification of exchange interactions: J1, J2, and dipolar D.

Observation of an emergent director state from quantum spins.

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 $0.6\; {\rm K} < J_1 < 0.7\; {\rm K}, J_2 = 0.12$~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 $J_1D$ model with ferromagnetic near neighbour spin-spin correlations while other aspects of the data can be accurately reproduced using a $J_1J_2D$ 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$_{12}$.