Spin-wave analysis to the spatially anisotropic Heisenberg antiferromagnet on a triangular lattice

Abstract

We study the phase diagram at T = 0 of the antiferromagnetic Heisenberg model on the triangular lattice with spatially-anisotropic interactions. For values of the anisotropy very close to Jα/J β = 0.5, conventional spin wave theory predicts that quantum fluctuations melt the classical structures, for S = 1/2. For the regime J β < Jα, it is shown that the incommensurate spiral phases survive until J β /Jα = 0.27, leaving a wide region where the ground state is disordered. The existence of such nonmagnetic states suggests the possibility of spin liquid behavior for intermediate values of the anisotropy.For a long time frustrated quantum antiferromagnets have been intensively studied. In this context, the antiferromagnetic Heisenberg model on a triangular lattice is a prototype for such systems. From the proposition of Anderson and Fazekas that this model is a candidate to exhibit spin liquid behavior 1 , a lot of work was done to understand the nature of its ground state. Although there is a general conviction that the ground state is ordered with a magnetic vector Q = (4π/3, 0) 2,3 , some authors found a situation very close to a critical one or no magnetic order at all, leaving the answer still controversial 4,5 . A systematic way to study the role of frustration is to vary the strength of the exchange interaction along the bonds. Recently Bhaumik et al. 6 explored the existence of collinear phases on triangular and pentagonal lattices and proposed that the critical value of the anisotropy, below which the ground state has collinear order, can be taken as a measure of frustration.From the experimental point of view, the unconventional properties of the organic superconductors κ − (BEDT − T T F ) 2 X and their similarities with the cuprates 8 renewed the interest in the triangular topology. In particular, it was argued 7,9 that the Hubbard model on a triangular lattice with anisotropic interactions at half filling could be a good candidate to explain such properties. In the limit of strong coupling this model can be mapped to the Heisenberg model with anisotropic interactions J α = t 2 α /U , J β = t 2 β /U where t α and t β are the anisotropic hoppings. Furthermore, experiments suggest that the relevant values of J α /J β are about 0.3−1 (see for details Ref. 9 ), so the combined effect of anisotropy and frustration will take an important role in these materials.In this paper we address the phase diagram of the Heisenberg model on the triangular lattice with spatiallyanisotropic interactions by mean of conventional spin wave theory. Our approach provides the values of anisotropy where nonmagnetic states appear signaling the possible existence of spin liquid behavior.The Hamiltonian is:where J α and J β are positive and correspond to interactions along directions δ α and δ β respectively (see figure 1). In order to develop a linear spin wave theory, we need to know previously the classical phase diagram. Basically, we replace the spin operators by classical vectors on the x − y plane and minimize the energy whic...

Spin-liquid phase due to competing classical orders in the semiclassical theory of the Heisenberg model with ring exchange on an anisotropic triangular lattice

“…2, we plot the classical phase diagrams obtained for the three models. For K = 0, we observe a transition from Néel to spiral order with q = cos −1 (−J /2J ) for J /J = 0.5, consistent with previous studies of the Heisenberg model [53,54]. With increasing ring exchange the Néel and collinear phases are stabilized, while the spiral order is destabilized in the full and extended Heisenberg models.…”

“…All three models are equivalent for K/J = K /J = 0.0. This model has been studied via LSWT previously [53,54]. As in these studies, we find a quantum critical point driven by the vanishing of the spin-wave velocity at J /J = 0.5 and a quantum disordered phase for J /J 3.75.…”

“…However, later numerical work [52] has shown that the ground state has "120 • order"-a special case of spiral order, discussed below, with an ordering wave vector Q = (2π/3,2π/3). A range of other methods have been used to study the Heisenberg model on the anisotropic triangular lattice including linear spin-wave theory [53,54], modified spin-wave theory [55], series expansions [12,56], the coupled cluster method [57], large-N expansions [58], variational Monte Carlo [59], resonating valence bond theory [15,19,[60][61][62], pseudofermion functional renormalization group [63], slave rotor theory [64], renormalization group [65], and the density matrix renormalization group [66]. These calculations show that for small J /J , Néel (π,π) order is realised and spiral (q,q) long-range AFM order is realized for J /J ∼ 1.…”

Large-Nsolutions of the Heisenberg and Hubbard-Heisenberg models on the anisotropic triangular lattice: application to Cs2CuCl4and to the layered organic superconductors κ-(BEDT-TTF)2X (BEDT-TTF≡bis(ethylene-dithio)tetrathiafulvalene); X≡anion)

“…Much is known about these two limiting cases. Additional insight [16,17] comes by considering different values of the ratio J 2 /J 1 . At J 2 = 0, the square lattice limit, there is long-range Néel order with a magnetic moment of approximately 0.6µ B ; see reference [12].…”

Magnetism in BEDT-TTF materials

“…The anisotropic triangular lattice has been studied by many authors, both within the Heisenberg spin Hamiltonian [8,9], and the half-filled Hubbard Hamiltonian [3,10]. Within the Heisenberg Hamiltonian the antiferromagnetic phase can correspond to either the three-sublattice spiral phase or the two-sublattice collinear phase [1].…”