Importance of spin-orbit coupling in layered organic salts

Abstract

We investigate the spin-orbit coupling (SOC) effects in α-and κ-phase BEDT-TTF and BEDT-TSF organic salts. Contrary to the assumption that SOC in organics is negligible due to light C, S, H atoms, we show the relevance of such an interaction in a few representative cases. In the weakly correlated regime, SOC manifests primarily in the opening of energy gaps at degenerate band touching points. This effect becomes especially important for Dirac semimetals such as α-(ET)2I3. Furthermore, in the magnetic insulating phase, SOC results in additional anisotropic exchange interactions, which provide a compelling explanation for the controversial field-induced behaviour of the quantum spin-liquid candidate κ-(ET)2Cu2(CN)3. We conclude by discussing the importance of SOC for the description of low-energy properties in organics.Layered organic materials have long served as ideal systems for studying complex physical phenomena such as the interplay between charge and spin order, unconventional superconductivity, and, exotic phases emerging from strong electronic correlations [1][2][3][4]. In these systems, high compressibility and synthetic versatility allows fine tuning of the underlying interactions via physical and chemical pressure, thus providing access to many different ground states. For example, significant evidence has recently emerged for a quantum spin liquid (QSL) state in a number of triangular-lattice organics,However, the appearance of very small energy gaps, and field-induced anomalies in the former material remain essentially unexplained. Likewise, interest has recently grown in the α-phase materials α-(ET) 2 I 3 [10] and α-(BETS) 2 I 3 [11]. The former material has been argued to form, under pressure, a zero gap semimetal (ZGS) with the Fermi energy located at the intersection of a pair of tilted Dirac cones [10,12,13]. However, the low-energy electronic and magnetic response shows significant departure from theoretical expectations for simple Dirac systems [14,15]. An unexplored aspect is the effect of spin-orbit coupling (SOC) in these systems.For (inorganic) magnetic insulators, strong SOC may generate large anisotropic magnetic interactions, associated with exotic spin-liquid states discussed e.g. for the iridates and α-RuCl 3 [16][17][18][19][20][21][22]. In weakly correlated systems such as BiSb, Bi 2 Te 3 , etc. [23][24][25][26], SOC tends to open a gap in the bulk, and may lead to nontrivial band topology and associated exotic edge states. Such effects have rarely been considered for the organic ET salts, as the light C, S, H atoms provide only moderate SOC. Nonetheless, it is known that SOC plays a dominant role in the spin relaxation of graphene [27][28][29] and organic-based semiconductors [30], and may be relatively enhanced for orbitally degenerate systems [31]. Indeed, in this work, we argue, despite a weak relative magnitude, that SOC is relevant for the low-energy properties in selected (representative) organic salts. We discuss as primary examples, the α-phase Dirac semimetals, and κ-phase...

Thermal Expansion Studies on the Spin‐Liquid‐Candidate System κ‐(BEDT‐TTF)2Ag2(CN)3

“…Following the same entropy arguments as outlined above, this would imply that t < t′ for κ‐CuCN. Whereas extended Hückel calculations and exact diagonalization agree well with that conclusion, ab initio calculations suggest for κ‐CuCN that t′ / t < 1. The reason for this inconsistency in the theoretical results is unclear at present and calls for further investigations.…”

“…Our result of t′ / t < 1 is consistent with the value of t′ / t ≈0.9 obtained from extended Hückel calculations based on low‐temperature structural data. Also, exact diagonalization results suggest that t > t′ in κ‐AgCN . Interestingly, the thermal expansion coefficient of the sister compound κ‐CuCN (see ref.…”

Ab Initio Approaches for Low‐Energy Spin Hamiltonians

“…In contrast, “hybrid” cluster expansion methods have proved to be suitable . In this case, the intermediate electronic Hamiltonian was taken to be , including two orbitals per ET dimer (the highest lying bonding and antibonding orbitals) with an average filling of 3/4.…”

“…On the basis of these calculations, the authors of refs. derived several interesting observations related to the electronic and magnetic properties of some representative ET‐based compounds. Significant contributions from higher order terms beyond the typical 4 t 2 / U approximation were found by studying the size convergence of the cluster expansion.…”

Effects of anisotropy in spin molecular-orbital coupling on effective spin models of trinuclear organometallic complexes

“…There are several strongly correlated molecular materials in which spin-orbit coupling is relevant including, metalorganic frameworks [8], layered organic salts [9,10], and multinuclear coordinated organometallic complexes [11][12][13][14][15]. The elementary building blocks of multinuclear complexes are molecular clusters containing transition metal ions whose d orbitals are hybridized with molecular orbitals where each of the hybrids is typically described by a single Wannier orbital [16].…”