Proximate Spin Liquid Ground State Arising from Competing Stripy and 120$^{\circ}$ Spin Correlations in the Triangular Quantum Antiferromagnet ErMgGaO$_4$

Abstract

ErMgGaO$_4$ is a quantum antiferromagnet wherein the pseudospin-1/2 degrees of freedom of Er$^{3+}$ decorate two-dimensional triangular planes separated by disordered non-magnetic bilayers of Mg$^{2+}$ and Ga$^{3+}$. Unlike its sister compound, YbMgGaO$_4$, our powder ErMgGaO$_4$ sample shows a clear spin glass transition near $T_g \sim 2.5$~K, about 1/6 of its Curie-Weiss temperature. We have carried out new inelastic neutron scattering measurements on these powder ErMgGaO$_4$ samples. At high energies, we observed crystalline electric field (CEF) transitions within the $J=15/2$ multiplet of 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 E=0, we observe diffuse elastic scattering which is analysed using Warren lineshapes appropriate for two dimensional 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 $J_1-J_2-Δ$ 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 $J_1-J_2-Δ$ phase diagram with $\frac{J_1}{J_2}=0.13 \pm 0.03$ and $Δ=0.4 \pm 0.1$, which is close to the expected quantum phase boundary between the spin liquid and the stripy ordered phases.

Figures (19)

• Figure 1: (a) The crystal structure of ErMgGaO$_4$, showing the triangular planes of Er$^{3+}$ interleaved with disordered triangular bilayers of Mg$^{2+}$ and Ga$^{3+}$. (b) The x-ray diffraction data measured from our powder sample of ErMgGaO$_4$, along with our Rietveld refinement to this data. The sample is 97$\%$ phase pure with the main impurity being unreacted MgO at the $\sim$ 2$\%$ level.
• Figure 2: (a) The low-temperature magnetic susceptibility measured from our approximately phase-pure ErMgGaO$_4$ powder sample with a field strength of $H = 0.01$ T, for both FC (red) and ZFC (blue) protocol. The inset shows a close-up of the FC-ZFC bifurcation at $T_g = 2.5$ K. (b) The inverse magnetic susceptibility measured from our approximately phase-pure ErMgGaO$_4$ powder sample for a field strength of $H = 5$ T. The line shows the Curie-Weiss fit to the inverse susceptibility curve between $T = 50$ and 100 K, yielding $\Theta_{\mathrm{CW}} \approx -14$ K and $\mu_{\mathrm{eff}} \approx 9.4$$\mathrm{\mu_B}$.
• Figure 3: Powder-averaged inelastic neutron scattering spectra of ErMgGaO$_4$ at $T = 5$ K for incident neutrons of energy (a) $E_{\mathrm{i}} = 20$ meV and (b) $E_{\mathrm{i}} = 150$ meV, with a dataset measured from the empty sample can at $T = 5$ K subtracted for each incident energy. The CEF transitions used to extract the CEF parameters are highlighted by horizontal arrows.
• Figure 4: Constant $|Q|$ cuts of the (a) $\mathrm{E_i}=20~$meV and (b) $\mathrm{E_i}=150~$meV data. A $|Q|$ integration range of $|Q|=[1.75, 2.5]\AA^{-1}$, and $|Q|=[3.6, 3.85]\AA^{-1}$ are used in (a) and (b), respectively. The red solid lines are calculated CEF excitation spectra convolved with the instrumental resolution at each $\mathrm{E_i}$ by assuming all Er$^{3+}$ to occupy the center of the octahedra. The blue line is obtained by assuming a random occupancy of the centered ($z_{\mathrm{Er}^{3+}}$) and off-centered position ($z_{\mathrm{Er}^{3+}}=\pm d_0\approx\pm 0.1\AA$) with a probability of $0.7$ and $0.3$, respectively (see Appendix for further details). The $\mathrm{E_i}=150~$meV data is enlarged in the inset of (b) to highlight the CEF peak at 70 meV. The black solid line in the inset is fit by the sum of two Gaussian peaks on a linear background. Widths of the two peaks are fixed to the instrumental resolution of $\Delta=9~$meV at $\mathrm{E_i}=150~$meV.
• Figure 5: (a,b) Temperature-dependent magnetic susceptibilities, $\chi_\mathrm{exp}=\frac{M}{H}$, of a powder sample of ErMgGaO$_4$ measured with an external field of $H=0.01~$T (black circle) and $H=5~$T (cyan circle). Theoretically calculated magnetic susceptibilities at the same fields, $\chi_\mathrm{theo}$, are shown in solid lines. (b) is the same as (a) but zooms into the region with $\mathrm{T<50}~$K. (c) Theoretically predicted in-plane ($\chi_{\perp c}$) and out-of-plane ($\chi_{\parallel c}$) magnetic susceptibilities.