Finite field regime for a quantum spin liquid in $\alpha \text{−}{\mathrm{RuCl}}_3$

An external magnetic field can induce a transition in $\alpha \text{−}{\mathrm{RuCl}}_3$ from an ordered zigzag state to a disordered state that is possibly related to the Kitaev quantum spin liquid. Here, we present field-dependent inelastic neutron scattering and magnetocaloric effect measurements implying the existence of an additional transition out of the quantum spin-liquid phase at an upper field limit $B_u$. The neutron scattering shows three distinct regimes of magnetic response. In the low-field ordered state the response shows magnon peaks; the intermediate-field regime shows only continuum scattering, and above $B_u$ the response shows sharp magnon peaks at the lower bound of a strong continuum. Measurable dispersion of magnon modes along the $(0,0,L)$ direction implies non-negligible interplane interactions. Combining the magnetocaloric effect measurements with other data, a $T\text{−}B$ phase diagram is constructed. The results constrain the range where one might expect to observe quantum spin-liquid behavior in $\alpha \text{−}{\mathrm{RuCl}}_3$.

Figure 1

Field dependence of the inelastic neutron scattering at the 2D $\mathrm{\Gamma }$ point for two values of the out-of-plane wave-vector transfer. Data obtained at 1.5 K on a 2 g single crystal of $\alpha \text{−}{\mathrm{RuCl}}_3$ using the FLEXX triple-axis spectrometer. (a) Zero-field data. A field of (b) 8 T and (c) 13.5 T was applied in the honeycomb plane perpendicular to a Ru-Ru bond [see inset of (b)]. The solid lines are fits and the dashed lines show the model free background for (0,0,3.3) as described in the text. Error bars represent one standard deviation assuming Poisson statistics.

Figure 2

(a) The $L$ dependence of the spin-wave energy observed at the 2D $\mathrm{\Gamma }$ point at 0 and 13.5 T. Dashed and dotted lines are fits to the dispersion as described in the text. (b) The magnetic field dependence of the 2D $\mathrm{\Gamma }$-point spin-wave energy measured at wave-vector transfers (0,0,3.3) and (0,0,4.3), close to the minimum and maximum of the $L$ dispersion. The colors indicate three regions of the inelastic response as described in the text. The hatched region marks the low-energy range not resolved in this data. In region II no magnon peaks were identified in the neutron scattering data. The region between $B_c$ and $B_u$ determined by MCE is shown by the vertical dashed lines. In both panels the error bars represent one standard deviation of the fitted peak positions.

Figure 3

(a) MCE difference curve at 2.3 K. The black arrows show the locations of transitions (see text). Inset: Temperature difference between sample and heat bath due to MCE. The red and blue arrows indicate the field-sweep directions. (b) The $T\text{−}B$ phase diagram of $\alpha \text{−}{\mathrm{RuCl}}_3$ as determined in this work. The phase boundaries were deduced from the magnetocaloric effect (MCE), neutron diffraction (ND), inelastic neutron scattering (INS), specific heat ($c_p$), and magnetic susceptibility (${\chi }_{\text{DC}}$) obtained previously [27]. Four potential phases are indicated by the colors. Inset: Magnetic Bragg peak intensity at 2.2 K as a function of magnetic field, measured using the CORELLI instrument at SNS. The solid line is a guide to the eye.