Spectrum and low-temperature bulk properties of triangular quantum spin liquid candidate NaYbSe$_2$

We report neutron scattering, pressure-dependent AC calorimetry, and AC magnetic susceptibility measurements of triangular lattice NaYbSe$_2$. We observe a continuum of scattering, which is reproduced by matrix product simulations, and no phase transition is detected in any bulk measurements. Comparison to heat capacity simulations suggest the material is within the Heisenberg spin liquid phase. AC Susceptibility shows a frequency-dependent peak at 40 mK, as has been observed in several triangular magnets.

💡 Research Summary

The authors present a comprehensive experimental investigation of the triangular‑lattice Yb‑based compound NaYbSe₂, a promising candidate for a quantum spin liquid (QSL). Using high‑quality single crystals, they combine inelastic neutron scattering (INS), pressure‑dependent AC calorimetry, and AC magnetic susceptibility measurements to probe the magnetic ground state down to temperatures well below 100 mK.

The INS data reveal a highly dispersive continuum of magnetic excitations with a well‑defined lower bound, most intense near the (1/3, 1/3, 0) wave‑vector that corresponds to the 120° order of related compounds. No magnetic Bragg peaks are observed down to 100 mK, indicating the absence of static order. The measured spectra are reproduced by matrix‑product‑state (MPS) calculations for a J₁‑J₂ Heisenberg model with J₂/J₁ ≈ 0.07 and a modest easy‑plane anisotropy (Δ ≈ 0.9). This parameter set places NaYbSe₂ just inside the theoretically predicted QSL region (the isotropic model’s QSL boundary lies at J₂/J₁ ≲ 0.063), consistent with recent neural‑quantum‑state (NQS) simulations. Finite‑size effects in the simulations produce a small artificial gap, but the overall agreement supports the relevance of the J₁‑J₂ model.

Specific‑heat measurements show no sharp anomalies from 100 mK down to the lowest temperatures, both at ambient pressure and under hydrostatic pressure up to 2 GPa. The heat‑capacity curve exhibits a modest C/T maximum near 800 mK and a relatively large low‑temperature C/T, both of which match the trends expected for larger J₂/J₁ ratios. When the data are rescaled by the fitted J₁, NaYbSe₂ displays a suppressed k_B T/J₁ ≈ 0.2 peak and enhanced low‑temperature entropy compared with the more ordered sibling KYbSe₂. Thermal‑pure‑quantum (TPQ) simulations of a 27‑site triangular cluster reproduce these trends, further confirming that NaYbSe₂ lies closer to the QSL side of the phase diagram.

AC susceptibility measured down to 20 mK uncovers a frequency‑dependent peak at ≈ 40 mK. The peak position T_f follows an Arrhenius law ν = ν₀ exp(−E_a/k_B T_f) with attempt frequencies ν₀ ≈ 3 × 10⁸ Hz and activation energies E_a/k_B ≈ 345 mK (in‑plane) and ≈ 463 mK (out‑of‑plane). Vogel‑Fulcher fits do not yield a meaningful freezing temperature, indicating that the dynamics are not characteristic of a conventional spin glass. The peak persists even with an ultra‑small excitation field (0.01 Oe), suggesting it is intrinsic rather than field‑induced. This low‑temperature slow dynamics coexists with the fast, continuum excitations seen in INS, a hallmark of a “spin‑liquid‑proximate” regime where quantum fluctuations dominate but rare‑region effects from disorder produce glassy‑like signatures at the longest time scales.

Quantum Fisher information (nQFI) analysis shows a reduced value (nQFI ≈ 2.3) compared with KYbSe₂ (nQFI ≈ 3.4), implying that NaYbSe₂ is beyond the quantum critical point separating the 120° ordered phase from the QSL and resides within the QSL region where spectral weight is more broadly distributed.

Overall, the study provides converging evidence that NaYbSe₂ realizes a Heisenberg‑type triangular QSL above ≈ 40 mK: (i) a continuum of magnetic excitations matching QSL simulations, (ii) absence of any thermodynamic phase transition in heat capacity under both ambient and applied pressure, and (iii) a low‑temperature regime where slow dynamics appear only in ultra‑low‑frequency susceptibility, consistent with disorder‑induced random‑singlet or rare‑region effects rather than bulk ordering. The authors conclude that NaYbSe₂ is a clean platform for exploring triangular‑lattice QSL physics, while highlighting the need for further probes (e.g., μSR, high‑resolution neutron spectroscopy, controlled disorder studies) to disentangle intrinsic quantum critical behavior from impurity‑driven glassiness at the lowest temperatures.