We present large-scale ab initio phonon calculations for the molecular quantum spin liquid XPd (dmit) 22. 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 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.
Fujiyama et al. (Thu,) studied this question.