NMR study of supersolid phases in the triangular-lattice antiferromagnet Na2BaCo(PO4)2

Abstract

We report ultra-low-temperature $^{23}$Na NMR measurements on the Ising triangular lattice antiferromagnet Na$_2$BaCo(PO$_4$)$_2$, which precisely resolve the phase diagram under magnetic field applied along the crystalline $c$ axis. With increasing field, the NMR spectra resolve three ordered phases with distinct spin configurations: the Y, up-up-down (UUD), and V phases. The spin-lattice relaxation rate $1/T_1$ data demonstrate gapless excitations in the Y and V phases, strongly supporting their supersolid nature. However, the phase transitions from the UUD phase to the two supersolid phases exhibit dramatically different behaviors upon cooling. Prior to entering the Y phase, $1/T_1$ identifies a gapless regime within the UUD phase, suggesting a Berezinskii-Kosterlitz-Thouless phase above a second-order phase transition. In contrast, the coexistence of the UUD and V phases observed in our experiments provides direct evidence of a first-order phase transition between these phases.

Figures (4)

• Figure 1: $^{23}$Na Spectra at 0.035 K. (a) Spectra taken with decreasing fields. Data are shifted vertically for clarity. Near the transition fields, spectra are scaled by factors as marked. C and S label the central and satellite peaks, respectively. (b) Peak frequencies as functions of fields, where blue, green and red symbols represent the central (C) and satellite peaks (S), respectively, as labeled in (a). C1, C2 and C3 correspond to three central lines split due to magnetic ordering. (c) The resonance frequencies of simulated central NMR lines in the Y, UUD, V$_1$, V$_2$, and FP phases (see text) are plotted, with their respective magnetic configurations in each Co$^{2+}$ triangle, as illustrated by the arrows. Vertical lines mark the phase boundaries between different phases.
• Figure 2: NMR spectra at low fields. (a) High-frequency satellite spectra measured over a range of temperatures at 0.3 T, with the PM, UUD and Y phases and phase transition temperatures as labeled. (b) Full spectra measured at typical temperatures at 1 T, exhibiting a single PM-UUD phase transition. (c) $1/T_1$ as functions of temperatures at typical fields. $T_{\rm N}$ and $T_{\rm Y}$ denote the phase transitions into the UUD phase and Y phase, respectively. The gap function fits in the UUD phase are represented by the red solid lines, and the power-law function fits are depicted by straight lines.
• Figure 3: Spectra at high fields. (a) Spectra of the central peak measured at 1.15 T. The peak positions are marked by arrows. (b) Full spectra measured at 1.4 T. The blue arrows mark the central peaks, and the red and green arrows mark the satellite peaks. (c) Resonance frequencies of peaks extracted from (a), plotted as functions of field. The shaded blue areas mark the range of phase coexistence. (d) $1/T_1$ data at typical fields in the V phase and the FP phase.
• Figure 4: Magnetic phase diagram. The color map depicts a contour plot of the $1/T_1T$ data. The PM, UUD, Y, V, and FP phases and the phase transition lines among them are also determined. V$_{\rm 1}$ and V$_{\rm 2}$ are V phases with different configurations. Phase boundaries were determined using different methods as indicated. Thick (thin) solid lines represent the first (second)-order phase transitions, while dashed lines above the BKT phase and on the right side of the V$_{\rm 1}$ phase represent phase crossover lines with no obvious phase transition.