Frustration, ring exchange, and the absence of long-range order inEtMe3Sb[Pd(dmit)2]2: From first principles to many-body theory

Abstract

We parameterize Hubbard and thence spin models for EtMe3Sb[Pd(dmit)2]2 from broken symmetry density functional calculations. This gives a scalene triangular model where the largest net exchange interaction is three times larger than the mean interchain coupling. The chain random phase approximation shows that the difference in the interchain couplings is equivalent to a bipartite interchain coupling, favoring long-range magnetic order. This competes with ring exchange, which favors quantum disorder. Ring exchange wins.EtMe 3 Sb[Pd(dmit) 2 ] 2 (EtMe 3 Sb) is a quantum spin liquid (QSL) candidate shrouded in mystery. It lacks magnetic ordering down to the lowest temperatures measured [1-3], but the physics that results in a quantum disordered state remains under debate. EtMe 3 Sb shares important structural motifs with the quantum spin liquids κ-(BEDT-TTF) 2 Cu 2 (CN) 3 (κ-Cu) and κ-(BEDT-TTF) 2 Ag 2 (CN) 3 (κ-Ag). A crucial question is: how closely related are their ground states?EtMe 3 Sb, κ-Cu, and κ-Ag all form structures with alternating layers of organic molecules and counter-ions. In all three materials, the organic molecules dimerize with one unpaired electron found on each dimer in the insulating phase. The main structural difference between them is the spacial arrangement the dimers. Within κ-Cu and κ-Ag, neighboring dimers are almost perpendicular to one another, whereas in EtMe 3 Sb, the dimers (gray circles in Fig. 1a) form quasi-onedimensional stacks (along the horizontal in Fig. 1a).κ-Cu and κ-Ag are Mott insulators. In the strong coupling limit, where the Hubbard U is much greater than the largest interdimer hopping integral, t, their insulating phase is described by the isosceles triangular Heisenberg model (Fig. 1c). This model has two candidate QSL phases. Firstly, a QSL has been suggested in the region 0.6 J /J 0.9 [4-6], for which the ground state remains controversial. Secondly, the large J /J limit is adiabatically connected to the Tomonaga-Luttinger liquid (TLL) expected for uncoupled chains, J /J 1.4 [6][7][8][9][10][11]. Theories in this regime show an emergent 'one-dimensionalization' whereby the many-body state is more one-dimensional than the underlying Hamiltonian [12][13][14][15]. However, the validity of the strong coupling limit in these materials is uncertain because both materials undergo a Mott metal-insulator transition under moderate pressures. This motivates the inclusion of higher order terms, most importantly ring exchange, in the spin model. It has been shown that these can also cause QSL phases [16][17][18][19][20].Many early studies explored the possibility that the spin liquid in EtMe 3 Sb can be explained by one of the above theories. However, the lower symmetry of EtMe 3 Sb means that all three exchange interactions are different, i.e., it is described by a scalene triangular lattice, Fig. 1a,b. EtMe 3 Sb is also close to a Mott transition and so ring exchange is likely to be important.

$x$-[Pd(dmit)$_2$]$_2$ as a quasi-1D, scalene Heisenberg model

“…This 2D picture was reinforced by approximate fits of the 2D triangular Heisenberg model to the magnetic susceptibility data [16,17]. However, more recent ab inito investigations using more sophisticated methods like DFT have suggested that, for most compounds, t B > t S ≈ t r [18][19][20][21][22][23]. Our BS-DFT calculations confirm and strengthen this result as we find that J B J s ≈ J r .…”

“…In molecular crystals such as x-[Pd(dmit) 2 ] 2 , J SE ij is often the largest term [19,22,23]. It arises from virtual hopping processes and usually favors antiferromagnetism [32].…”

“…Estimates of J ij from Hückel and DFT band structure calculations typically neglect J DE ij . However, studies that have calculated J DE ij directly have found that its magnitude is significant in these compounds [3,22,23]. For this reason, studies that take direct exchange into account are bound to be more successful at accurately modeling experimental behaviors in x-[Pd(dmit) 2 ] 2 .…”

Interplay of dipoles and spins in κ−(BEDT−TTF)2X , where X=Hg(

“…The resulting spin model could range from a subtly anisotropic quasi-two-dimensional system (for weak charge disproportionation) to quasi-onedimensional spin systems (for large charge disproportionation). However, we note that the geometrical frustration of the magnetic interactions means that this quasi-one-dimensional limit is more stable than one might naively expect [33,35,36]. Therefore, the effective one-dimensionalization of the system when it is dipole ordered could be important for understanding the large "dipole-solid + spin-liquid" phase found by Hotta in her exact diagonalization studies of the NIH model [6].…”

Electronic correlation and geometrical frustration in molecular solids: A systematic ab initio study of β′−X[Pd(dmit)2]2Misawa1, Yoshimi2, Tsumuraya3 2020Phys. Rev. Research15280View full textAdd to dashboardCite

“…We note that both V i j and J i j reduce the magnetic ordered moment (see S. 5 in the SM [39]). The mechanism of the reduction can be attributed to the reduction of U and resultant enhancement of the higher-order interactions such as the ring-exchange interactions, which suppress the magnetic long-range orders [47][48][49].…”