Convert Widespread Paraelectric Perovskite to Ferroelectrics

While nature provides a plethora of perovskite materials, only a few exhibit large ferroelectricity and possibly multiferroicity. The majority of perovskite materials have the nonpolar ${\mathrm{CaTiO}}_3(\mathrm{CTO})$ structure, limiting the scope of their applications. Based on the effective Hamiltonian model as well as first-principles calculations, we propose a general thin-film design method to stabilize the functional ${\mathrm{BiFeO}}_3(\mathrm{BFO})$-type structure, which is a common metastable structure in widespread CTO-type perovskite oxides. It is found that the improper antiferroelectricity in CTO-type perovskite and ferroelectricity in BFO-type perovskite have distinct dependences on mechanical and electric boundary conditions, both of which involve oxygen octahedral rotation and tilt. The above difference can be used to stabilize the highly polar BFO-type structure in many CTO-type perovskite materials.

Figure 1

In ${\mathrm{CdHfO}}_3$, the free energy of CTO-type and BFO-type structures as a function of (a) epitaxial (in-plane) strain only and zero external electric field; (b) constrained electric displacement field along the $z$ axis and zero stress in both in-plane and out-of-plane directions; (c) Phase stabilities in ${\mathrm{CdHfO}}_3$ as functions of both epitaxial (in-plane) strain and constrained electric displacement field along the $z$ axis; blue (orange) denotes the CTO (BFO)-type is energetically stable. (d) Oxygen octahedral rotations and $A$-cation coordination environment in the CTO-type and BFO-type structures. The vectors represent atom displacements in the AFE and FE modes. The oxygen atoms involved in the optimization of $A$-site cation coordination are labeled with 1, 2, and 3.

Figure 2

The change of free energy $\mathrm{\Delta }F(\overline{\eta })/\mathrm{unit}$ cell (20-atom) as a function of epitaxial strain is decomposed into contributions from (a) oxygen rotation and tilt, (b) elastic energy, and (c) polar ordering energies of AFE or FE, in which the energy terms of trilinear and four-linear couplings are plotted as solid lines. The energy of the unstrained CTO-type structure is set as the reference.

Figure 3

The change of free energy $\mathrm{\Delta }F(D)/\mathrm{unit}$ cell (20-atom) as a function of the electric displacement field is decomposed into contributions from (a) oxygen rotation and tilt, (b) elastic energy, and (c) polar ordering energies of AFE or FE, in which the energy terms of trilinear and four-linear couplings are plotted as solid lines. The energy of CTO-type structure without electric field is set as the reference.