${\mathrm{ErMgGaO}}_4$ is a quantum antiferromagnet wherein the pseudospin-1/2 degrees of freedom of ${\mathrm{Er}}^{3+}$ decorate two-dimensional triangular planes separated by disordered nonmagnetic bilayers of ${\mathrm{Mg}}^{2+}$ and ${\mathrm{Ga}}^{3+}$. Its sister compound, ${\mathrm{YbMgGaO}}_4$, has attracted much interest as a quantum spin liquid ground state candidate, although the presence of the disordered Mg-Ga bilayers adds complexity to this description. In contrast, our powder ${\mathrm{ErMgGaO}}_4$ sample shows a clear spin glass transition near $T_g\sim 2.5\mathrm{K}$, about 1/6 of its Curie-Weiss temperature. We have carried out new inelastic neutron scattering measurements on these powder ${\mathrm{ErMgGaO}}_4$ samples. At high energies, these show the expected crystalline electric field (CEF) transitions within the $J=15/2$ multiplet of ${\mathrm{Er}}^{3+}$, but with the first excited CEF level sufficiently low in energy ($\sim 3$ meV) so as to allow the possibility that virtual CEF transitions influence the exchange couplings. At zero energy transfer, we observe diffuse elastic scattering which is analyzed using Warren line shapes appropriate for two- dimensional (2D) correlations. This reveals dominant 2D stripy correlations below $T_g$, coexisting with 2D ${120}^{\circ }$-type correlations that persist above $T_g$. At low temperatures, the low energy inelastic component of the scattering shows a continuum with bandwidth of $\sim 0.8$ meV. This dynamic magnetic spectral weight can be modeled at all $Q$, energies, and temperatures as the sum of high energy and low energy damped harmonic oscillators (DHO), with the high energy DHO defining the bandwidth of $\sim 0.8$ meV. We use linear spin wave theory to model this inelastic scattering and to estimate its spin Hamiltonian parameters in terms of a $J_1-J_2-\mathrm{\Delta }$ model on the triangular lattice. This gives a good description of the low lying spectral weight for ErMgGaO4, and allows us to place it on the theoretical $J_1-J_2-\mathrm{\Delta }$ phase diagram with $\frac{J_2}{J_1}=0.13\pm 0.03$ and $\mathrm{\Delta }=0.4\pm 0.1$, which is close to the expected quantum phase boundary between the spin liquid and the stripy ordered phases.

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• Frustrated magnetism
• Quantum spin liquid
• Rare-earth magnetic materials
• Triangular lattice
• Neutron scattering