Effective Hamiltonian simulations are conducted to unveil the nature of the low-frequency polar modes in the prototype relaxor ferroelectric, $\mathrm{Pb}\left({\mathrm{Mg}}_{1/3}{\mathrm{Nb}}_{2/3}\right){\mathrm{O}}_3$. 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.

中文翻译：

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PbMg1 / 3Nb2 / 3O3弛豫铁电体模型中类似金石和希格斯结构模式的证据

进行了有效的汉密尔顿模拟，以揭示原型弛豫铁电体中低频极性模式的性质， $\mathrm{铅含量}（{镁}_{\mathrm{1个}/3}{铌}_{2/3}）{\mathrm{Ø}}_3$。上面所谓${Ť}^{*}$温度，只有一个软模式存在，其频率随着加热而增加。另一方面，对于低于冰点温度的温度，该单一软模式分为两种模式，一种模式会略微改变其低共振频率，而另一种模式则在冷却后共振频率会急剧增加，这与之前的测量结果一致。更重要的是，我们提供的证据表明这两种模式可以看作是Goldstone类和Higgs类模式，这也是我们在此处揭示的原子位移势的墨西哥帽形式所固有的，因此扩展了展示Higgs-类系统的类型弛豫铁电体的玻色子特性。