Constraining the parameter space of a quantum spin liquid candidate in applied field with iterative optimization

The quantum spin liquid (QSL) state is an exotic state of matter featuring a high degree of entanglement and lack of long-range magnetic order in the zero-temperature limit. The triangular antiferromagnet ${\mathrm{YbMgGaO}}_4$ is a candidate QSL host, and precise determination of the Hamiltonian parameters is critical to understanding the nature of the possible ground states. However, the presence of chemical disorder has made directly measuring these parameters challenging. Here we report neutron scattering and magnetic susceptibility measurements covering a broad range of applied magnetic field at low temperature. Our data shows a field-induced crossover in ${\mathrm{YbMgGaO}}_4$, which we reproduce with complementary classical Monte Carlo and density matrix renormalization group simulations. Neutron scattering data above and below the crossover reveal a shift in scattering intensity from $M$ to $K$ points and, collectively, our measurements provide essential characteristics of the phase crossover that we employ to strictly constrain proposed magnetic Hamiltonian parameters despite the chemical disorder. Constrained exchange parameters further suggest the material's proximity to the QSL state in the clean limit. More broadly, our approach demonstrates a means of pursuing QSL candidates where Hamiltonian parameters might otherwise be obscured by disorder.

Figure 1

Tunnel diode oscillation (TDO) frequency and cantilever torque response versus applied field. (a),(b) TDO ($\mathrm{\Delta }f/f\propto \mathrm{\Delta }\mathbf{M}/\mathrm{\Delta }\mathbf{H}$) shows an anomaly for $\mathbf{H}\parallel c$ and $\mathbf{H}\perp \mathbf{c}$, respectively, which weakens as temperature increases [curves offset for clarity in (a),(b)]. (c) Anomaly's response to applied field shows anisotropy. (d) $d\mathbf{M}/d\mathbf{H}$ measured with SQUID corroborates TDO measurement. (e) integrating TDO $\mathrm{\Delta }$ frequency from 0 to the approximate saturation is further corroborated by dc susceptibility measurements (see Materials and Methods in Supplemental Material [18].

Figure 2

Diffuse neutron scattering from magnetic structure for a series of fields with $\mathbf{H}\parallel \mathbf{c}$. (a) Color maps of Brillouin zone integrated $(-0.5<\mathbf{l}<0.5)$. As field increases, spectral weight shifts from $M$ points to $K$ points, then $\mathrm{\Gamma }$ points, in agreement with (b) calculated $S\left(\mathbf{Q}\right)$ with ${\sigma }_{g_{\perp }}=0.3, {\sigma }_{g_{\parallel }}=1.2, {\sigma }_J=0.5$ at 130 mK. (c) Integrated neutron scattering intensity $(-0.5<\mathbf{l}<0.5)$ along $(\mathbf{h}+0.5,\mathbf{h}\text{−}0.5,0)$. (d) Calculated $S\left(\mathbf{Q}\right)$ along $(\mathbf{h}+0.5,\mathbf{h}\text{−}0.5,0)$.

Figure 3

Calculated magnetization curves and background-subtracted integrated TDO measurement for $\mathbf{H}\perp \mathbf{c}$ and magnetization curves obtained with Monte Carlo sampling and DMRG. (a) Classical Monte Carlo simulation of magnetization (featuring biquadratic terms and disorder) at $T=0.01$ K. (b) Derivative with respect to applied field of classical Monte Carlo simulation in (a). (c) Integration of the change in TDO frequency at $T=0.35$ K. (d) Change in TDO frequency at $T=0.35$ K. (e) Comparison of magnetization from DMRG calculations (blue) versus classical simulations with biquadratic interaction (${\lambda }_1=0.3, {\lambda }_2=0.03$) when $\mathbf{H}\parallel \mathbf{c}$ and (f) $\mathbf{H}\perp \mathbf{c}$. Addition of biquadratic terms mimics quantum mechanical plateau for applied field perpendicular to the sample $c$ axis.

Figure 4

Contour plots of projected hyper volumes that result from different sets of experimental observations. Each subpanel is a 2D projection of 7D hyper volumes. The uncertainties based on spin-wave dispersion (black solid line), field induce transition (blue solid line), and field evolution of integrated intensity of the $K$ peak $I_k\left(\mathbf{Q}\right)$ (red solid line), are shown by multicolor contours. The contour red lines reveal the shape of the cost function ${\chi }_{\text{combined}}^2$ because they correspond to different values of the cutoff $c^k$. Solid, dashed, and dotted red lines correspond to the largest, intermediate, and smallest value of $c^k$, respectively.

Figure 5

Comparison of field dependence of $S\left(\mathbf{Q}\right)$ calculated for parameters from four unique models, including those found in this study and as suggested by constraints determined in Ref. [17]. $S\left(\mathbf{Q}\right)$ calculated for integer fields 0–5 T at 130 mK. Note that the field-induced transition visible in the diffuse scattering data is absent for the parameters other than those used for this study, suggesting stringent constraints on the possible models for the system.