Quantum disorder in the spatially completely anisotropic triangular lattice I: Heisenberg $S=1/2$ antiferromagnet

TL;DR

This study investigates how complete spatial anisotropy in a triangular lattice influences quantum disordered phases and magnetic order, revealing that anisotropy can connect different non-magnetic phases and explain experimental observations.

Contribution

It introduces the analysis of the completely anisotropic triangular lattice (SCATL) using spin-wave theory and exact diagonalizations, highlighting the role of anisotropy in quantum disordered phases.

Findings

Disordered phases separate different types of magnetic order.

Additional anisotropy connects two distinct gapped non-magnetic phases.

Anisotropy explains experimental observations of magnetic order in materials.

Abstract

Spin liquids occuring in 2D frustrated spin systems were initially assumed to appear at strongest frustration, but evidence grows that they more likely intervene at transitions between two different types of order. To identify if this is more general, we here analyze a generalization of the spatially anisotropic triangular lattice (SATL) with antiferromagnetic Heisenberg interactions, the spatially \emph{completely} anisotropic triangular lattice (SCATL). Using Takahashi's modified spin-wave theory, complemented by exact diagonalizations, we find indications that indeed different kinds of order are always separated by disordered phases. Our results further suggest that two gapped non-magnetic phases, identified as distinct in the SATL, are actually continuously connected via the additional anisotropy of the SCATL. Finally, measurements on several materials found magnetic long-range order where calculations on the SATL predict disordered behavior. Our results suggest a simple explanation through the additional anisotropy of the SCATL, which locates the corresponding parameter values in ordered phases. The studied model might therefore not only yield fundamental insight into quantum disordered phases, but should also be relevant for experiments on the quest for spin liquids.