Spin relaxation in cubic liquid crystals. The role of symmetry

Abstract

Cubic liquid-crystalline phases are usually regarded as isotropic systems. This view is justified for physical properties that transform as second rank tensors. However, the time correlation functions describing spin relaxation in cubic phases include components that transform as fourth rank tensors, which distinguish between cubic and spherical symmetry. In this work we explore the consequences of this fact for spin relaxation behaviour in cubic phases using group theoretical methods. We identify the two irreducible crystal frame time correlation functions of a cubic phase, derive the orientation dependence of the laboratory frame time correlation functions for single crystal samples, and discuss the relation of the cubic (fourth rank) order parameter to the microstructure of the phase. Finally, as an illustration of the general results, we derive the time correlation functions for a specific model of a micellar cubic phase.