Magneto-optic dynamics in a ferromagnetic nematic liquid crystal

TL;DR

This paper explores the dynamic magneto-optic effects in ferromagnetic nematic liquid crystals through experiments and theoretical modeling, highlighting the role of cross-coupling between magnetization and director fields.

Contribution

It introduces a coupled dynamic model of magnetization and director fields, experimentally measures cross-coupling effects, and predicts methods to detect reversible coupling terms.

Findings

Identification of a dissipative cross-coupling coefficient.

Demonstration of dynamic cross-coupling importance.

Prediction of experimental signatures for reversible coupling.

Abstract

We investigate dynamic magneto-optic effects in a ferromagnetic nematic liquid crystal experimentally and theoretically. Experimentally we measure the magnetization and the phase difference of the transmitted light when an external magnetic field is applied. As a model we study the coupled dynamics of the magnetization, M, and the director field, n, associated with the liquid crystalline orientational order. We demonstrate that the experimentally studied macroscopic dynamic behavior reveals the importance of a dynamic cross-coupling between M and n. The experimental data are used to extract the value of the dissipative cross-coupling coefficient. We also make concrete predictions about how reversible cross-coupling terms between the magnetization and the director could be detected experimentally by measurements of the transmitted light intensity as well as by analyzing the azimuthal angle of the magnetization and the director out of the plane spanned by the anchoring axis and the external magnetic field. We derive the eigenmodes of the coupled system and study their relaxation rates. We show that in the usual experimental set-up used for measuring the relaxation rates of the splay-bend or twist-bend eigenmodes of a nematic liquid crystal one expects for a ferromagnetic nematic liquid crystal a mixture of at least two eigenmodes.