Ordering in ${\mathrm{Cs}}_2\mathrm{Cu}{\mathrm{Cl}}_4$: Possibility of a proximate spin liquid

The layered spiral magnet ${\mathrm{Cs}}_2\mathrm{Cu}{\mathrm{Cl}}_4$ displays several interesting properties that have been suggested as evidence of proximity to a two-dimensional quantum spin liquid. In this paper we study a concrete version of this proposal and suggest experiments that can potentially confirm it. We study universal critical properties of two-dimensional frustrated quantum magnets near the quantum phase transition between a spiral magnetic state and a spin liquid state with gapped bosonic spinons in the framework of an O(4)-invariant critical theory proposed earlier [A. Chubukov, T. Senthil, and S. Sachdev, Phys. Rev. Lett. 72, 2089 (1994)]. Direct numerical calculation of the anomalous exponent in spin correlations shows that the critical scattering has broad continua qualitatively similar to experiment. More remarkably we show that the enlarged O(4) symmetry leads to the same slow power-law decay for the vector spin chirality and the Néel correlations. We show how this may be observed through polarized-neutron scattering experiments. A number of other less dramatic consequences of the critical theory are outlined as well.

Figure 1

Schematic representation of the triangular lattice in the $b\text{−}c$ plane. The $a$ direction is perpendicular to the plane. There are two coupling constants: $J$ along the horizontal chains and $J^{\prime }$ along the zigzag bonds.

Figure 2

Dzyaloshinski-Moriya interaction is nonzero along oriented zigzag bonds that are denoted by vectors ${\delta }_1$ and ${\delta }_2$.