Excitations of the ferroelectric order

We identify the bosonic excitations in ferroelectrics that carry electric dipoles from the phenomenological Landau-Ginzburg-Devonshire theory. The “ferron” quasiparticles emerge from the concerted action of anharmonicity and broken inversion symmetry. In contrast to magnons, the transverse excitations of the magnetic order, the ferrons in displacive ferroelectrics are longitudinal with respect to the ferroelectric order. Based on the ferron spectrum, we predict temperature-dependent pyroelectric and electrocaloric properties, electric-field-tunable heat and polarization transport, and ferron-photon hybridization.

Figure 1

Landau potential energy landscape for polarization fluctuations in ferroelectrics (green arrows). (a) Above the critical temperature $T_c$ in the paraelectric phase the potential is symmetric for the fluctuations around the minimum $P_0=0$ and the average of the fluctuations $\langle \delta P\rangle =\langle P-P_0\rangle =0$ even in the presence of anharmonicity [see Eq. (8)]. (b) Below $T_c$ the ferroelectric order breaks inversion symmetry and polarization fluctuates around finite $\pm P_0$ (e.g., the positive one in the figure) in an asymmetric potential, therefore carrying nonvanishing average electric dipoles, i.e., $\langle \delta P\rangle =\langle P-P_0\rangle <0$.

Figure 2

The dispersion relations and the corresponding electric dipoles (represented by color) of two ($\pm$) of ferron polaritons branches in the absence of damping. The electric dipoles are in units of $e\text{Å}$ with $\delta p_0=-0.15 e$Å. The parameters are for $\mathrm{Li}\mathrm{Nb}{\mathrm{O}}_3$ with $\varepsilon \left(\infty \right)=5.5$.