Soft Modes

Abstract

Soft modes were once regarded as direct evidence for binary structural changes, as implied by their frequencies diminishing toward the critical temperature to destabilize structure. In dielectric crystals, the condensate can be studied by applying time-dependent electric fields at the Brillouin-zone center. In contrast, neutron inelastic scatterings can be analyzed for soft modes at zone boundaries for cell-doubling transitions. Although the spatially distribution at ${{T}_{{\rm c}}}$ is implicit, soft modes can be studied for symmetry changes in crystals with varying temperature. Driven by the adiabatic potential, the soft mode exhibits a thermal response of condensates in crystals near ${{T}_{{\rm c}}}$, as implied by the Born–Huang principle. In this chapter, soft modes are discussed as related to symmetry changes in the lattice.