Magnetic Field‐Induced Instabilities in Liquid Crystals

Abstract

We use the Landau–de Gennes model to investigate the magnetic field‐induced instabilities in liquid crystals. In particular, we examine the change of weak and strong stabilities in the pure smectic states and in the pure nematic states. Motivated by de Gennes’ discovery on the analogies between liquid crystals and superconductors, we introduce critical magnetic fields $H_{\text{\rm s}}$ and $H_{\rm sh}$. The pure smectic states lose their global minimality (strong stability) at $H_{\text{\rm s}}$ and lose their local minimality (weak stability) at $H_{\rm sh}$. We also examine the change of stability in the pure nematic states. We show in the case of equal elastic coefficients that a liquid crystal in a sufficiently strong magnetic field will not be in a pure nematic state, which exhibits a significant difference between the Landau–de Gennes model for liquid crystals and the Ginzburg–Landau model for superconductivity.