Thermal conductivity of the quantum spin liquid candidate EtMe₃Sb[Pd(dmit)₂]₂: No evidence of mobile gapless excitations

The search for highly mobile gapless spin excitations in quantum spin liquids (QSL) is currently attracting considerable attention. We examined this specific issue via thermal conductivity measurements on one of the most promising QSL candidates, the organic insulator EtMe₃Sb[Pd(dmit)₂]₂ (dmit-131). We performed heat conduction experiments down to 0.07 K on a total of 8 high-quality single crystals of dmit-131. Contrary to previous reports, our body of data consistently and reproducibly shows the absence of a T-linear contribution to the thermal conductivity of dmit-131 at low temperatures, showing that no spin excitation contribute to the heat transport. Consequently, the spin excitations in dmit-131 are localized and not mobile. Our data further reveal a strongly suppressed phonon conductivity, evidence that the phonons are heavily scattered by those localized spin excitations. Comparison with published data on numerous spin-liquid materials shows, in fact, that this is a widespread phenomenon and that it should be considered in any future theory of QSLs.