Low-Energy Excitations in Quantum Spin Liquids Identified by Optical Spectroscopy
Résumé
The electrodynamic response of organic spin liquids with highly-frustrated triangular lattices has been measured in a wide energy range. While the overall optical spectra of these Mott insulators are governed by transitions between the Hubbard bands, distinct in-gap excitations can be identified at low temperatures and frequencies, which we attribute to the quantum-spin-liquid state. For the strongly correlated β ′-EtMe3Sb[Pd(dmit)2]2, we discover enhanced conductivity below 175 cm −1 , comparable to the energy of the magnetic coupling J ≈ 250 K. For ω → 0 these low-frequency excitations vanish faster than the charge-carrier response subject to Mott-Hubbard correlations, resulting in a dome-shape band peaked at 100 cm −1. Possible relations to spinons, magnons and disorder are discussed. PACS numbers: 75.10.Kt 71.30.+h, 74.25.Gz 78.30.Jw Quantum spin liquids are an intriguing state of matter [1-4]: although the spins interact strongly, the combination of geometrical frustration and quantum fluctuations prevents long-range magnetic order even in two and three dimensions. It took decades before clear experimental realizations of this theoretical concept [5, 6] became available, first in the organic compound κ-(BE-DT-TTF) 2 Cu 2 (CN) 3 , which crystallizes in a triangular pattern [7], and later in the kagome lattice of ZnCu 3-(OH) 6 Cl 2 [8-10]. Despite this progress, a smoking-gun experiment identifying its essential features is still lacking , and even a reliable theoretical description of real spin-liquid systems remains a subject of much dispute. At present, the fundamental nature of the spin-liquid state is far from being understood. The intensely studied quantum-spin-liquid candidate Herbertsmithite (ZnCu 3 (OH) 6 Cl 2) shows no magnetic order and no indications of a spin gap down to 0.1 meV, inferring that the spin excitations form a continuum [2]. This important issue, however, is far from being settled neither from the experimental nor from the theoretical side [11, 12]; the discussion on the nature of the quantum-spin-liquid state is rather controversial [13-19]. In this Letter we investigate the electrodynamic response of three organic quantum spin liquids. While close to the Mott transition the charge degrees of freedom dominate the conductivity, our optical experiments reveal considerable low-frequency absorption deep inside the Mott-insulating state. The observed dome-like feature is confined by the exchange energy J, suggesting a relation to the spin degrees of freedom and exotic spin-charge coupling. We study the charge-transfer salts κ-(BEDT-TTF) 2-Cu 2 (CN) 3 (abbreviated CuCN, BEDT-TTF denotes bis(ethylenedithio)tetrathiafulvalene), κ-(BEDT-TTF) 2-Ag 2 (CN) 3 (called AgCN) and β ′-EtMe 3 Sb[Pd(dmit) 2 ] 2 (short EtMe, here EtMe 3 Sb stands for ethyltrimethylsti-bonium and dmit is 1,3-dithiole-2-thione-4,5-dithiolate), where the molecular dimers with spin-1 2 form a highly frustrated triangular lattice [7, 20-22]. At ambient pressure no indication of Néel order is observed at temperatures as low as 20 mK, despite the considerable antifer-romagnetic exchange of J ≈ 220 − 250 K. The origin of the spin-liquid phase is unresolved since the geometrical frustration introduced by a triangular lattice should not be sufficient to stabilize the quantum-spin-liquid state for ordinary Heisenberg exchange interactions [23-25]. Recently it was proposed that, alternatively, intrinsic disorder [26-28] or dynamical fluctuations [29] may play a crucial role for stabilizing the spin-liquid state in these molecular materials. In contrast to the completely insulating material Her-bertsmithite, where the on-site Coulomb repulsion U and bandwidth W are in the eV range (U = 8 eV [30]), the energy scales of these organic compounds are significantly smaller; here, k B T has a large effect on the Mott gap already for a few hundred Kelvins as evident in dc transport [22, 28, 31]. Moreover, the molecular conductors under study are closer to the metallic phase due to weaker correlations. With U/W ≈ 1.5, CuCN is almost at the metal-insulator transition; in fact it becomes supercon-ducting at T c = 3.6 K under hydrostatic pressure of only 4 kbar [7]. For AgCN the effective correlations are more pronounced, as U/W = 2, while EtMe is far on the Mott insulating side with U/W ≈ 2.4 [32]. Heat capacity measurements suggested gapless spin excitations for CuCN
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