Dynamics of ferroelectric thin films described by the transverse Ising model

The dynamic properties of thin films described by the Ising model in a transverse field (TIM) have been studied under the random-phase approximation. The frequencies of soft modes and surface modes have been obtained. For films with reduced surface interaction (compared to the bulk), the soft mode corresponds to a surface-like mode in the ferroelectric phase but to a bulk-like mode in the paraelectric phase. Conversely, for films with an enhanced surface interaction, the soft mode is a bulk-like mode in the ferroelectric phase and a surface-like mode in the paraelectric phase. The number of surface-like modes in the ferroelectric phase can be greater than one; the number increases as the temperature approaches the Curie temperature, and does not depend on the in-plane wavevector for a given temperature in the ferroelectric phase. However, there is only one surface-like mode in the paraelectric phase, and its character becomes bulk-like at large wavevector. The surface modes can be clearly seen from the frequency dependence of the dynamic susceptibility; the surface mode pole increases in strength with decreasing film thickness. The frequency dependences of optical reflectivity coefficients have also been obtained. The reflection peaks due to the surface modes lie below the bulk reststrahl band in the ferroelectric phase of films with reduced surface ferroelectricity, and also in the paraelectric phase of films with enhanced surface ferroelectricity; otherwise, they lie within the reststrahl band.