Frequency renormalization and its effects in nonlinear phononics with $Q_RQ_{IR}^{2}$-type coupling

TL;DR

This paper analytically investigates the effects of frequency renormalization in nonlinear phononics systems with specific quadratic couplings, revealing saturation and splitting phenomena under strong and polarized IR pumping.

Contribution

It provides the first analytical results for phonon displacements and frequencies in a two-phonon system with $Q_RQ_{IR}^2$ coupling, extending understanding of nonlinear phononics effects.

Findings

Frequency renormalization causes saturation of Raman mode at high pump fields.

Degenerate IR modes split under elliptically or linearly polarized ultrashort pulses.

Results reveal nonlinear effects not captured by first-principles calculations.

Abstract

A two-phonon system with lowest-order coupling of form $Q_RQ_{IR}^2$ is studied by perturbation method, and analytic results for both phonon displacements and frequencies are obtained. The frequency renormalization of infrared (IR) active mode brings the rectification of Raman mode to saturate at high pump field. For degenerate IR mode with coupling of form $Q_R(Q_{IR,x}^2-Q_{IR,y}^2)$, the frequency of IR mode will split when resonantly pumped by elliptically or linearly polarized ultrashort mid-IR pulse, realizing Raman rectification and magnetization simultaneously. Our results reveal a dynamical effect of nonlinear phononics not captured by first-principles calculation, extend the dynamical multiferroicity to systems with coupling $Q_R(Q_{IR,x}^2-Q_{IR,y}^2)$, and the method can be readily applied to higher-order couplings. The amplitude saturation under strong pump field stimulates future researches to overcome this nonlinear effect.