Spin-supersolidity induced quantum criticality and magnetocaloric effect in the triangular-lattice antiferromagnet Rb$_2$Co(SeO$_3$)$_2$

Abstract

We performed high-field magnetization, magnetocaloric effect (MCE), and NMR measurements on the Ising triangular-lattice antiferromagnet Rb$_2$Co(SeO$_3$)$_2$. The observations of the 1/3-magnetization plateau, the split NMR lines, and the thermal activation behaviors of the spin-lattice relaxation rate $1/T_1$ between 2 T and 15.8 T provide unambiguous evidence of a gapped up-up-down (UUD) magnetic ordered phase. For fields between 15.8 T and 18.5 T, the anomaly in the magnetic susceptibility, the slow saturation of the NMR line spectral ratio with temperature, and the power-law temperature dependence of $1/T_1$ suggest the ground state to be a spin supersolid with gapless spin excitations. With further increasing the field, the Grüneisen ratio, extracted from the MCE data, reveals a continuous quantum phase transition at $H_{\rm C}\approx$ 19.5 T and a universal quantum critical scaling with the exponents $νz~\approx~$1. Near $H_{\rm C}$, the large high-temperature MCE signal and the broad peaks in the NMR Knight shift and $1/T_1$, manifest the strong spin fluctuations driven by both magnetic frustration and quantum criticality. These results establish Rb$_2$Co(SeO$_3$)$_2$ as a candidate platform for cryogenic magnetocaloric cooling.

Figures (5)

• Figure 1: DC and pulsed-field magnetization.a$M(T)$ measured under DC field. b$dM/dT$ as functions of temperatures. $T_{\rm N}$ is determined at the dip and peak position at each field as marked. c Pulsed-field $M(H)$ measured at selected temperatures with field-up (solid lines) and field-down (dotted lines) sweeps. The 1/3 magnetization plateau is resolved below 4 K. d$dM/dH$ as functions of fields. All peak features are indicated by down-arrows and marked as $H_{\rm V}$, $H_{\rm N}$ and $H^*_{\rm M}$, respectively. Data are shifted vertically for clarity.
• Figure 2: $^{85}$Rb NMR spectra.a Center spectral lines measured at 1.8 K under typical fields. P$_0$ (above $T_{\rm N}$), P$_1$, and P$_2$ (below $T_{\rm N}$) mark different resonant. b Relative spectra weight ratio $I_1/I_2$ (left axis) and FWHM of P$_0$ and P$_2$ (right axis) as a functions of field taken at 1.8 K. c$K_{\rm n}(T)$ at fields close to $H_{\rm C}$. d-g Center spectral lines measured at typical fields and temperatures, which characterize the UUD phase in d, the SS phase in e, and the critical regime in f and g at low temperatures. Spectra are shifted vertically for clarity.
• Figure 3: Spin-lattice relaxation rates.a$1/T_1$ as a function of temperature, measured under fields from 6 T to 22 T. Peaks marked by red arrows denote AFM transition temperatures $T_{\rm N}$. Solid straight lines represent power-law fits $1/T_1 \propto T^5$ at 17 T and 18 T. b Spin gap $\Delta$ as a function of field extracted by $1/T_1 \propto e^{-\Delta/K_{\rm B}T}$. c Enlarged view plot of $1/T_1$ at 18.74 T and 19 T. $T_R^*$ mark the temperature location of broad peaks above $T_{\rm N}$.
• Figure 4: Pulsed-field magnetocaloric data and the Grüneisen ratio.a Adiabatic $T(H)$ data measured with different initial temperatures, by field-up (dotted lines) and field-down (solid lines) sweeps. $H^*_{\rm S}$ denotes the location of the minimum at each sweep. b Grüneisen ratio $\Gamma_H$ calculated from the $T(H)$ by down sweeps with varying temperatures (see text). c$\Gamma_H$ plotted as a function of field at selected sample temperatures as listed. The dotted line is a function fit $\Gamma_H~=~G_{\rm r}(H-H_{\rm C})^{-1}$ to the envelope of the data, where $H_{\rm C}~\approx~$19.5 T is obtained. d Data collapse of $\Gamma_H$ in the quantum critical regime which yields critical exponents ${\nu}z\approx1$.
• Figure 5: Phase diagram. Solid lines represent the adiabatic $T(H)$ data with field by down sweeps. $H^*_{\rm S}$ denotes the high-temperature dip position in the $T(H)$ curve. Open symbols represent phase transition or crossovers boundaries from different probes, including $T_{\rm N}$ determined in $dM/dT$ and $1/T_1$, $H_{\rm N}$ in $dM/dH$ and FWHM, $H_{\rm V}$ (UUD-V boundary) in $dM/dH$ and FWHM, and high-temperature crossovers $H^*_{\rm M}$ in $dM/dH$, $H^*_{\rm S}$ in adiabatic $T(H)$ data, $T^*_{\rm R}$ in $1/T_1$, and $T^*_{\rm f}$ in $K_{\rm n}$.