NMR evidence of spin supersolid and Pomeranchuk effect behaviors in the triangular-lattice antiferromagnet Rb$_2$Ni$_2$(SeO$_3$)$_3$

Abstract

We performed $^{85}$Rb nuclear magnetic resonance (NMR) measurements on the $S$ = 1 bilayer triangular-lattice antiferromagnet Rb$_2$Ni$_2$(SeO$_3$)$_3$ in magnetic fields up to 26 T. In the field range from 3 T to 26 T, the NMR spectral lines split and their respective spectral weight ratios reveal the existence of the magnetic up-up-down (UUD) phase, although the 1/3-plateau phase is only reached at fields above 16 T. Two distinct gapless regimes are further identified: one at low fields and low temperatures, and the other at high fields and high temperatures, consistent with the spin supersolid Y and V phases. Notably, the UUD-V phase boundary exhibits a negative slope in $dT/dH$, where the supersolid phase is located at temperatures above the solid phase due to strong low-energy spin fluctuations.

Figures (4)

• Figure 1: Phase diagram of Rb$_2$Ni$_2$(SeO$_3$)$_3$. Heat map represents the contour plot of $1/T_1T$ data. $T_{\rm N}$, $T_{\rm Y}$, and $T_{\rm U}$ represent the phase boundaries among the PM, UUD, Y, and V phases, which are determined from the spectral and the spin-lattice relaxation rate data as specified. Solid and dotted lines are guides to the eyes.
• Figure 2: Low-field NMR spectra. (a) $^{85}$Rb center lines measured at 11.5 T with decreasing temperatures. Vertical data offsets are applied for clarity. A$_1$ and A$_2$ are two peaks observed at and above 7.5 K, and B$_1$, B$_{2,3}$, and B$_4$ represent peaks resolved at lower temperatures. A three-Lorentzian fit is applied to the data at 5 K, with the relative spectral weight fixed at a ratio of 1:3:2. The simulated spectrum of the Y phase is plotted at 1.8 K (see text). (b) Frequencies of all resolved peaks as functions of temperatures. $T_{\rm {N}}$ and $T_{\rm Y}$ denote transition temperatures determined from the change of the frequency in the peaked spectra. Dashed lines are guides to the eyes. Inset: High-temperature $K_{\rm n}$ of A$_1$ and A$_2$ plotted against magnetic susceptibility. The solid straight lines are linear function fits to the data to obtain the hyperfine coupling constant (see text).
• Figure 3: High-field NMR spectra. (a) Spectra at 24 T measured with decreasing temperatures. Data are shifted vertically for clarity. B$_1$ to B$_4$ label the peaks resolved at low temperatures. Dashed lines are three-Lorentzian function fit applied to data at 6 K with fixed spectral weight ratio of 1:3:2 from left to the right, and four-Lorentzian function fit to data at 1.59 K with fixed ratio of 1:1:2:2. (b) Resonance frequencies of the respective spectral peaks measured at 24 T as functions of temperatures. Dash lines are guides to the eyes.
• Figure 4: Spin-lattice relaxation rates. (a) Low-field $1/T_1$ data as functions of temperatures. The blue and red arrows mark the peak positions labeled by $T_{\rm N}$ and $T_{\rm Y}$, respectively. Solid straight lines are guides to the power-law scaling 1/$T_1{\sim}T^3$. (b) High-field $1/T_1$ as functions of temperatures. Blue and green arrows mark the peak and the hump positions, labeled by $T_{\rm N}$ and $T_{\rm U}$ respectively. The solid lines are empirical function fits to $1/T_1{\sim}e^{-{\Delta}/{k_{\rm{B}}T}}$ with an energy gap $\Delta$. Inset: The determined $\Delta$ as a function of field.