Quantum corrections to the spin-wave spectrum of La$_2$CuO$_4$ in an external magnetic field

TL;DR

This paper calculates quantum fluctuation effects on the spin-wave spectrum of La$_2$CuO$_4$ under magnetic fields, incorporating interactions and comparing results with experiments to understand magnetic excitations.

Contribution

It provides a leading-order 1/S correction to the spin-wave spectrum considering exchange and Dzyaloshinskii-Moriya interactions, aligning theory with experimental data.

Findings

Quantum fluctuations modify the spin-wave gaps under magnetic fields.

Theoretical results agree with experimental measurements of gap dependence.

Estimated coupling constants are consistent with observed magnetic behavior.

Abstract

The effects of quantum fluctuations on the magnetic field dependence of the spin-wave gaps in the lamellar antiferromagnet La$_2$CuO$_4$ are considered. Nonlinear corrections to the spin-wave spectrum are calculated to leading order in 1/S, where $S$ is the localized spin. The nearest-neighbor exchange interactions between the Cu spins as well as the Dzyaloshinskii-Moriya interactions are taken into account. Using the experimental values of the components of the $g$-factor tensor, we get a satisfactory agreement with the experimental results for the field dependence of the gaps by Gozar {\it et al.} [Phys. Rev. Lett. {\bf 93}, 027001 (2004)], and obtain consistent values of the in-plane and inter-plane coupling constants. The field dependence of the dispersion of spin waves propagating perpendicular to the CuO$_2$ planes is also discussed.