Spinons and triplons in spatially anisotropic frustrated antiferromagnets:

Quantum antiferromagnetism is one of the richest subjects in condensed matter physics. It provides textbook examples of most of the collective phenomena known in the field, and for most of the analytical techniques known to theorists. Perhaps most intriguing are spin-1/2 systems on frustrated lattices, in which quantum effects are expected to be very strong and conventional techniques of analysis are of questionable reliability.

Perhaps the simplest example of such a problem is a spin-1/2 triangular quantum antiferromagnet. A few examples of such materials have emerged in recent years, with probably the most celebrated one being Cs₂CuCl₄, which should be understood as a spatially anisotropic triangular antiferromagnet, whose exchange J along one direction of "strong" bonds is approximately 3 times stronger than the exchange J' along the other two nearest-neighbor bonds. This material received particular attention because, alone amongst the new materials, it was extensively studied with inelastic neutron scattering (by Radu Coldea and co-workers). A surprising observation from the neutron scattering experiments was that the usually prominant sharp "magnon peak" in the structure factor was uncharacteristically small. Instead, the structure factor is dominated by a broad continuum contribution, containing the majority of the spectral weight.

This work prompted a deluge of theoretical proposals, attributing this behavior to proximity to an exotic two dimensional spin liquid state and/or quantum critical point. Perhaps as a backlash, more recently there have been a number of theoretical studies using very conventional semi-classical large-$S$ expansion methods. These actually make more connection to the experimental data, but to fit even the dispersion of the main peak in the neutron data require large renormalizations of the exchange parameters to be put in by hand in an ad hoc fashion. The quantitative failure of these methods for the most quantum case of spin-1/2 should not be too surprising.

Our work:

In this paper, we demonstrate that the neutron scattering results can be quantitatively understood, without fitting parameters, from a microscopic approach based on the anisotropy of the material. This striking agreement clearly indicates the irrelevance of any exotic scenario for this material. Instead, the scattering corresponds to contributions from descendents of the one-dimensional spinons of decoupled Heisenberg chains (which would be present were J' neglected). A qualitative result of our theory is that the J' coupling leads to formation of spin-1 "triplons", bound states of two spinons, in some regions of momentum space. These lead to sharp peaks (with small weight) in some but not all parts of the spectrum. This prediction is clearly born out in the experiments by Coldea and collaborators.

Read the paper.