Elastic constants and ultrasonic attenuation in the cone state of the frustrated antiferromagnet Cs_2CuCl_4

TL;DR

This study combines theoretical modeling and experimental measurements to analyze how elastic constants and ultrasonic attenuation in Cs_2CuCl_4 vary with magnetic field in its cone magnetic state, revealing magnon behavior as quasiparticles.

Contribution

It provides a combined theoretical and experimental analysis of elastic and ultrasonic properties in the cone state of Cs_2CuCl_4, highlighting magnon-phonon interactions and their field dependence.

Findings

Reasonable agreement between theory and experiment away from critical field.

Ultrasonic attenuation rate scales with the fourth power of phonon momentum.

Magnons behave as well-defined quasiparticles in the studied regime.

Abstract

In an external magnetic field perpendicular to the plane of the layers, the quasi two-dimensional frustrated antiferromagnet Cs_2CuCl_4 exhibits a magnetically ordered "cone state" at low temperatures. In this state the component of the magnetic moments in field direction is finite, while their projection onto the plane of the layers forms a spiral. We present both theoretical and experimental results for the magnetic field dependence of the elastic constants and the ultrasonic attenuation rate in the cone state. Our theoretical analysis is based on the usual spin-wave expansion around the classical ground state of a Heisenberg model on an anisotropic triangular lattice with Dzyaloshinskii-Moriya interactions. Magnon-phonon interactions are modeled by expanding the exchange interactions up to second order in powers of the phonon coordinates. As long as the external magnetic field is not too close to the critical field where the cone state becomes unstable, we obtain reasonable agreement between theory and experiment, suggesting that at least in this regime magnons behave as well-defined quasiparticles. We also show that the assumption of well-defined magnons implies that at long wavelengths the ultrasonic attenuation rate in the cone state of Cs_2CuCl_4 is proportional to the fourth power of the phonon momentum.