# Modified transverse Ising model for the dielectric properties of SrTiO$_3$ films and interfaces

## TL;DR

This paper improves the transverse Ising model by adding pseudospin anisotropy to better describe the dielectric properties of SrTiO$_3$ films and interfaces, capturing inhomogeneity effects and quantized states.

## Contribution

The authors introduce a modified TIM with pseudospin anisotropy, providing a more accurate description of inhomogeneous ferroelectric systems like SrTiO$_3$ films and interfaces.

## Key findings

- Modified TIM predicts different polarization profiles.
- Quantized states at interfaces only appear in the modified model.
- Differences are significant at low temperatures.

## Abstract

The transverse Ising model (TIM), with pseudospins representing the lattice polarization, is often used as a simple description of ferroelectric materials. However, we demonstrate that the TIM, as it is usually formulated, provides an incorrect description of SrTiO$_{3}$ films and interfaces because of its inadequate treatment of spatial inhomogeneity. We correct this deficiency by adding a pseudospin anisotropy to the model. We demonstrate the physical need for this term by comparison of the TIM to a typical Landau-Ginzburg-Devonshire model. We then demonstrate the physical consequences of the modification for two model systems: a ferroelectric thin film, and a metallic LaAlO$_{3}$/SrTiO$_{3}$ interface. We show that, in both cases, the modified TIM has a substantially different polarization profile than the conventional TIM. In particular, at low temperatures the formation of quantized states at LaAlO$_{3}$/SrTiO$_{3}$ interfaces only occurs in the modified TIM.