Anisotropic magnetism and spin fluctuations in the triangular-lattice spin-liquid candidate NaYbSe$_2$: a single-crystal $^{23}$Na and $^{77}$Se NMR study

The ytterbium-based delafossite NaYbSe$_2$ is discussed as a prototype for a spin-orbit entangled, effective spin-1/2 triangular spin lattice with emerging antiferromagnetic correlations and a quantum-spin-liquid (QSL) ground state. We report on a comprehensive study of the static and dynamic anisotropic magnetism in single-crystalline samples of NaYbSe$_2$, using NMR spectroscopy as a local-probe technique. We performed $^{23}$Na and $^{77}$Se NMR measurements in magnetic fields up to 16 T, applied along the in-plane and out-of-plane crystallographic directions and at temperatures from 300 down to 0.3 K. We could determine the anisotropic hyperfine contributions from the angular dependence of the $^{23}$Na and $^{77}$Se NMR spectra. In the paramagnetic regime, we probed the temperature dependence of the $^{23}$Na and $^{77}$Se spectral shift and the hyperfine coupling constants for fields applied along the principal crystal axes. The spin-lattice relaxation-rate data indicate critical spin fluctuations and the absence of long-range magnetic order at low magnetic fields and temperatures down to 0.3 K, evidenced by a monotonic increase of $1/T_1$ and associated spectral broadening. This is a clear proof of the evolution of a critical QSL ground state with residual fluctuations down to lowest temperatures. At elevated fields, we observe the emergence of long-range order, as the temperature-dependent $1/T_1$ rate passes through a pronounced maximum at $T_N$ at given field, followed by a decrease at lower temperatures. Further, we find an inhomogeneous broadening of the $^{23}$Na spectra below $T_N$, probing the histogram of the local-field distribution in the presence of the field-induced order.