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arXiv:1110.1406 · Physical Review B

Incommensurate correlations in the anisotropic triangular Heisenberg lattice

Andreas Weichselbaum, Steven R. White

Published Dec 27, 2011• 68 citations
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Abstract

We study the anisotropic spin-1/2 antiferromagnetic triangular Heisenberg lattice in two dimensions, seen as a set of chains with couplings $J$ (${J}^{\ensuremath{'}}$) along (in-between) chains, respectively. Our focus is on the incommensurate correlation that emerges in this system in a wide parameter range due to the intrinsic frustration of the spins. We study this system with traditional density matrix renormalization group using cylindrical boundary conditions to least constrain possible incommensurate order. Despite that the limit of essentially decoupled chains ${J}^{\ensuremath{'}}/J\ensuremath{\lesssim}0.5$ is not very accessible numerically, it appears that the spin-spin correlations remain incommensurate for any finite $0<{J}^{\ensuremath{'}}<{J}_{{}^{{}_{\mathrm{C}}}}^{\ensuremath{'}}$, where ${J}_{{}^{{}_{\mathrm{C}}}}^{\ensuremath{'}}/J>1$. The incommensurate wave vector ${q}_{J}$, however, approaches the commensurate value corresponding to the antiferromagnetic correlation of a single chain very rapidly with decreasing ${J}^{\ensuremath{'}}/J$, roughly as ${q}_{J}\ensuremath{\sim}\ensuremath{\pi}\ensuremath{-}{c}_{1}{({J}^{\ensuremath{'}}/J)}^{n}{e}^{\ensuremath{-}{c}_{2}J/{J}^{\ensuremath{'}}}$.

DOI
10.1103/physrevb.84.245130

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We investigate the anisotropic triangular lattice that interpolates from decoupled one-dimensional chains to the isotropic triangular lattice and has been suggested to be relevant for various quasi-two-dimensional materials such as Cs2CuCl4{\text{Cs}}_{2}{\text{CuCl}}_{4}Cs2​CuCl4​ or $\ensuremath{\kappa}\text{\ensuremath{-}}{(ET)}_{2}{\text{Cu}}_{2}{(\text{CN})}_{3}$. We obtain an excellent accuracy by means of a representation for the resonating valence-bond wave function with both singlet and triplet pairings. This approach allows us to establish that the magnetic order is rapidly destroyed away from the pure triangular lattice and incommensurate spin correlations are short range. A nonmagnetic spin liquid naturally emerges in a wide range of the phase diagram with strong one-dimensional character.
We study the ground-state properties of weakly frustrated Heisenberg ferrimagnetic chains with nearest- and next-nearest-neighbor antiferromagnetic exchange interactions and two types of alternating sublattice spins S1>S2,{S}_{1}>{S}_{2},S1​>S2​, using 1/S1/S1/S spin-wave expansions, density-matrix renormalization group, and exact diagonalization techniques. It is argued that the zero-point spin fluctuations completely destroy the classical commensurate-incommensurate continuous transition. Instead, the long-range ferrimagnetic state disappears through a discontinuous transition to a singlet state at a larger value of the frustration parameter. In the ferrimagnetic phase we find a disorder point marking the onset of incommensurate real-space short-range spin-spin correlations.
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