Modified transverse Ising model for the dielectric properties of SrTiO₃ films and interfaces

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. arXiv:1905.07430v1 [cond-mat.mes-hall]

Mechanism for Switchability in Electron-Doped Ferroelectric Interfaces

“…This model, described in detail below, was developed in Ref. [47] where it was applied to LaAlO 3 /SrTiO 3 interfaces.…”

“…The lattice polarization is modeled with a modified transverse Ising model, [47] which for the layered geometry takes the form…”

“…Of the remaining parameters in Eq. ( 7), Ω and J 0 determine the bulk transition temperature and low-T polarization, while J 1 is proportional to the square of the dipole-dipole correlation length [47]. E iz is the electric field in layer i z .…”

“…The self-consistent polarization and electron density are calculated for the model parameters shown in Table I. Except for J 0 and µ, these parameters were obtained by fitting to SrTiO 3 [47] and are presumed to apply to lightly doped SrTiO 3 as well. Relative to their values in SrTiO 3 [47], we have reduced the parameter µ slightly to give polarization values similar to those found in Sr 1−x Ca x TiO 3−δ thin films [42], while we have increased J 0 to obtain a FE transition at T c = 30 K, which is comparable to what is measured in insulating Sr 0.98 Ca 0.02 TiO 3 [42].…”

“…In regions where depolarizing fields are screened, the characteristic length scale for spatial gradients of the polarization is the Landau-Ginzburg-Devonshire (LGD) correlation length, ξ. We can obtain an estimate for ξ by using the relationship between the transverse Ising model and the simplest LGD functional, [47]…”