Low-energy spin dynamics of the quantum spin liquid candidate ${\mathrm{NaYbSe}}_2$

The family of rare-earth chalcogenides $A{\mathrm{RECh}}_2$ ($A$ = alkali or monovalent ions, RE = rare earth, and Ch = O, S, Se, and Te) appears as an inspiring playground for studying quantum spin liquids (QSLs). The crucial low-energy spin dynamics remain to be uncovered. By employing muon spin relaxation ($\mu \mathrm{SR}$) and zero-field (ZF) AC susceptibility down to 50 mK, we are able to identify the gapless QSL in ${\mathrm{NaYbSe}}_2$, a representative member with an effective spin-1/2, and explore its unusual spin dynamics. The ZF $\mu \mathrm{SR}$ experiments unambiguously rule out spin ordering or freezing in ${\mathrm{NaYbSe}}_2$ down to 50 mK, which is two orders of magnitude smaller than the exchange coupling energies. The spin relaxation rate $\lambda$ approaches a constant below 0.3 K, indicating that finite spin excitations are featured by a gapless QSL ground state. This is consistently supported by our AC susceptibility measurements. The careful analysis of the longitudinal field (LF) $\mu \mathrm{SR}$ spectra reveals a strong spatial correlation and a temporal correlation in the spin-disordered ground state, highlighting the unique feature of spin entanglement in the QSL state. The observations allow us to establish an experimental H-T phase diagram. The study offers insight into the rich and exotic magnetism of the rare-earth family.

Figure 1

Crystal structure of ${\mathrm{NaYbSe}}_2$ and schematic diagram of muon stopping site in ${\mathrm{NaYbSe}}_2$. The implanted ${\mu }^{+}$ mainly stops near ${\mathrm{Se}}^{2-}$ and probes the local magnetic environment and spin dynamics.

Figure 2

ZF $\mu \mathrm{SR}$ spectra of ${\mathrm{NaYbSe}}_2$. (a) ZF-$\mu \mathrm{SR}$ asymmetry spectra with the fitting curves using formula (1). (b) The contribution of the stretching exponential (SE) term and Kubo-Toyabe (KT) term obtained from (a) at the selected temperatures. The shaded areas accompanying the fitting curves in (b) are actually the fitting error bars.

Figure 3

LF-$\mu \mathrm{SR}$ spectra of ${\mathrm{NaYbSe}}_2$. (a)–(c) LF-$\mu \mathrm{SR}$ asymmetry spectra at 10, 1, and 0.1 K, respectively, with the fittings by formula (1). (d)–(f) The contribution of the stretching exponential (SE) term and the Kubo-Toyabe (KT) term corresponding to (a)–(c) at the selected magnetic fields. The shaded areas accompanying the fitting curves in (d)–(f) are actually the fitting error bars.

Figure 4

Temperature evolution of spin dynamics parameters. (a) ZF-$\mu \mathrm{SR}$ spin relaxation rate $\lambda$. (b) ZF-$\mu \mathrm{SR}$ stretching exponent $\beta$. (c) Decay rate $\sigma$ in the Kubo-Toyabe term. The three parameters describing the spin dynamics are defined in formula (1). (d) ZF AC susceptibility at various frequencies. Magnetic field dependence of spin dynamics.

Figure 5

(a) LF-$\mu \mathrm{SR}$ spin relaxation rate $\lambda$. The red solid circles are obtained from LF-$\mu \mathrm{SR}$ spectra, and the red solid line is produced by the expression (3). (b) LF-$\mu \mathrm{SR}$ stretching exponent $\beta$.

Figure 6

Experimental H-T phase diagram of ${\mathrm{NaYbSe}}_2$ based on the data in this paper and neutron and thermodynamics data from Refs. [7] and [19]. “CEF” refers to the phase in which CEF excitations play a dominant role. “Spin-ordered state” refers to the magnetically ordered state induced by magnetic fields.