Power-Law Suppression of Phonon Thermal Transport by Magnetic Excitations in a Molecular Quantum Spin Liquid

Abstract

We present large-scale ab initio phonon calculations for the molecular quantum spin liquid X[Pd(dmit)2]2. An unusually low average phonon velocity ( 700 {m/s}) and optical modes below 10 cm^{-1} confine the Debye T^{3} regime to T < 2 K. As the transfer-integral anisotropy approaches the maximally frustrated regime (t'/t \to 1), the lattice stiffens, ruling out lattice softening as the origin of the spin-liquid state. By quantifying the additional suppression of the thermal conductivity from experimental data, we observe a power-law behavior consistent with two-dimensional magnetic excitations with a nodal, approximately linear (Dirac-like) spectrum.

Figures (4)

• Figure 1: Crystal structure of X[Pd(dmit)$_2$]$_2$ (X = Et$_2$Me$_2$Sb). The blue-shaded region highlights the two-dimensional magnetic layer composed of [Pd(dmit)$_2$]$_2$ dimers hosting $S = 1/2$ spins. These magnetic layers are separated by closed-shell cation layers, giving rise to a quasi-two-dimensional structure.
• Figure 2: Phonon dispersions for X = EtMe$_3$Sb (a) and Et$_2$Me$_2$Sb (b), calculated without assuming a charge-order transition. The high-symmetry directions are $X=a^{*}-b^{*}$ and $Y=2a^{*}$ for (a), and $X(Y)=-a^{*}\pm b^{*}$ for (b), defined using the reciprocal vectors of the conventional cell. (c),(d) Phonon densities of states (DOS) for the two salts, with the total DOS in green and the [Pd(dmit)2]2$^{-}$ anion contribution in blue. Low-energy modes below 10 cm$^{-1}$ arise predominantly from vibrations within the anion layers.
• Figure 3: Calculated $C_{\mathrm{ph}}/T$ as a function of $T^2$ for (a) $0 < T^2 < 40$ K$^2$ and (b) $0 < T^2 < 4$ K$^2$. Experimental data for X = EtMe$_3$As (AF), EtMe$_3$Sb (QSL), and Et$_2$Me$_2$Sb (CO, below the structural phase transition) are replotted from Reference Nomoto2022. The calculated values are about twice as large as the experimental data, indicating that the phonon contribution alone overestimates the total specific heat, though the origin of this discrepancy remains to be understood.
• Figure 4: (a) Calculated thermal conductivity $\kappa/T$ for infinite and finite domain sizes $L$, compared with experimental data from Ref. Bourgeois-Hope2019. The data reported in Refs. Ni2019Nomoto2022 nearly overlap with the Sherbrooke-C1 dataset. A broad maximum around $T \approx 2$ K observed experimentally is reproduced for a characteristic domain size of $L \approx 100~\mu$m. (b) The ratio $R=\kappa_{\mathrm{exp}}/\kappa_{\mathrm{calc}}(L=\infty)$ (left axis), together with the experimentally inferred phonon scattering rate $1/\tau_{\mathrm{exp}}$ (right axis), where $\tau_{\mathrm{exp}}$ is defined in Eq. (\ref{['eq:tauexp_def']}). The quadratic power-law behavior is most clearly observed in $R(T)$.