Higgs Mode and Magnon Interactions in 2D Quantum Antiferromagnets from Raman Scattering

TL;DR

This paper develops a theoretical model for Raman scattering in 2D quantum antiferromagnets, revealing how Higgs and magnon interactions shape the spectrum and providing evidence for the Higgs mode in experimental data.

Contribution

The study introduces a diagrammatic calculation of Raman spectra incorporating Higgs and magnon contributions, highlighting the Higgs mode's role in 2D antiferromagnets.

Findings

Higgs mode contributes a broad continuum above two-magnon peaks.

Two-magnon peak appears at approximately 2.44 J.

Experimental spectra align with theory only when Higgs contributions are included.

Abstract

We present a theory for Raman scattering on 2D quantum antiferromagnets. The microscopic Fleury-Loudon Hamiltonian is expressed in terms of an effective $O(3)$ - model. Well within the N\'eel ordered phase, the Raman spectrum contains a two-magnon and a two-Higgs contribution, which are calculated diagramatically. The vertex functions for both the Higgs and magnon contributions are determined from a numerical solution of the corresponding Bethe-Salpeter equation. Due to the momentum dependence of the Raman vertex in the relevant $B_{1g}+E_{2g}$ symmetry, the contribution from the Higgs mode is strongly suppressed. Except for intermediate values of the Higgs mass, it does not show up as separate peak in the spectrum but gives rise to a broad continuum above the dominant contribution from two-magnon excitations. The latter give rise to a broad, asymmetric peak at $\omega\simeq 2.44\, J$, which is a result of magnon-magnon interactions mediated by the Higgs mode. The full Raman spectrum is determined completely by the antiferromagnetic exchange coupling $J$ and a dimensionless Higgs mass. Experimental Raman spectra of undoped cuprates turn out to be in very good agreement with the theory only with inclusion of the Higgs contribution. They thus provide a clear signature of the presence of a Higgs mode in spin one-half 2D quantum antiferromagnets.