A Generalized Ginzburg-Landau Approach to Second Harmonic Generation

TL;DR

This paper introduces a generalized Ginzburg-Landau theory for second harmonic generation in magnetic materials, linking symmetry properties to SHG susceptibility and nonreciprocal optical effects.

Contribution

It develops a unified theoretical framework connecting magnetic order parameters and SHG susceptibility, extending Ginzburg-Landau theory to nonlinear optical phenomena in magnets.

Findings

Derived SHG susceptibility components from symmetry considerations.

Explained nonreciprocal optical properties in magnetic materials.

Applied theory to Cr₂O₃ and YMnO₃, demonstrating its relevance.

Abstract

We develop a generalized Ginzburg-Landau theory for second harmonic generation (SHG) in magnets by expanding the free energy in terms of the order parameter in the magnetic phase and the susceptibility tensor in the corresponding high-temperature phase. The non-zero components of the SHG susceptibility in the ordered phase are derived from the symmetries of the susceptibility tensor in the high-temperature phase and the symmetry of the order parameter. In this derivation, the dependence of the SHG susceptibility on the order parameter follows naturally, and therefore its nonreciprocal optical properties. We examine this phenomenology for the magnetoelectric compound Cr$_2$O$_3$ as well as for the ferroelectromagnet YMnO$_3$.