Evidence for Goldstone-like and Higgs-like structural modes in the model PbMg1/3Nb2/3O3 relaxor ferroelectric

Abstract

Effective Hamiltonian simulations are conducted to unveil the nature of the low-frequency polar modes in the prototype relaxor ferroelectric, $\mathrm{Pb}({\mathrm{Mg}}_{1/3}{\mathrm{Nb}}_{2/3}){\mathrm{O}}_{3}$. Above the so-called ${T}^{*}$ temperature, only a single soft-mode exists, with its frequency increasing under heating. On the other hand, for temperatures lower than the freezing temperature, this single soft-mode splits into two modes, with one mode slightly changing its low resonant frequency while the other exhibiting a resonant frequency sharply increasing under cooling, in agreement with previous measurements. More importantly, we present evidences that these two modes can be regarded as Goldstone-like and Higgs-like modes, inherent to the Mexican-hat-form of the atomic displacement potential we also reveal here, therefore extending the types of systems exhibiting Higgs-boson characteristics to relaxor ferroelectrics.