Thermodynamic Stability of BiFeO₃ (0001) Surfaces from ab Initio Theory

Abstract

The relative stability of multiferroic BiFeO (0001) surfaces, which is the (111) facet in the pseudocubic notation, with different stoichiometry is systematically studied by using ab initio thermodynamic approach in order to obtain insights into the stable surface terminations. We predict that under most chemical potential conditions the thermodynamically favored terminations for the negative and positive surfaces are -Bi-O and -Fe-O-Bi, respectively. The predicted difference in oxygen content between the negative and positive surfaces is consistent with experimental observations at the BiFeO/metal interfaces ( Nat. Mater. , 2014 , 13 , 1019 , DOI: 10.1038/nmat4058 ; Adv. Mater. , 2015 , 27 , 6934 , DOI: 10.1002/adma.201502754 ). We determine the atomic geometries and electronic states as well as the magnetic properties for the negatively and positively polarized stable surfaces. Our results demonstrate that not only the stoichiometry and atomic geometries but also the electronic and magnetic properties of the BiFeO (0001) surfaces show strong dependence on the ferroelectric polarization direction. Therefore, we expect that the surface physical and chemical properties of the BiFeO (0001) surfaces can be easily tuned by an external electric field.

Magnetism and multiferroic properties at MnTiO3 surfaces: A DFT study

“…The purpose of this paper is to introduce in the simplest possible terms the apparent difficulties associated with defining polarization in bulk solids. Then, we use a theoretical procedure to explore the surface energies without surface reconstructions or chemical adsorptions commonly used to cancel the macroscopic dipole and stabilize the Type-3 Tasker's surface, as proposed by Dai and co-authors [16][17][18]. First, we introduce the unrelaxed cleavage energy ( ) of the complementary terminations (Z + and Z − ), as the required energy to cut the crystal into two unrelaxed complementary terminations, as follows: Here, and E bulk correspond to the total energies for the unrelaxed slab model and the bulk unit, whereas n and A represent the number of bulk units used in the slab construction and the surface area, respectively.…”

“…In the next step, the relaxation of the complementary terminations (Z + and Z − ) was performed, considering that only the outer MnTiO 3 layers were allowed to relax while the inner positions were clamped to reproduce the bulk [16][17][18]. The unrelaxed cleavage energy ( ) was then computed as:…”

“…Further, Dai et al performed systematic DFT+U calculations to study the nature, thermodynamic stability, and ferroelectric-induced Pd adsorption on the BiFeO 3 (0 0 0 1) polar surfaces. The main observations of these authors are focused on the different chemical natures of positive and negative surface terminations, which exhibit an enhanced relation between spontaneous polarization and weak ferromagnetism as well as distinct behavior as a substrate for metal adsorption, suggesting the intriguing catalytic properties of the metal/BiFeO 3 interface [16][17][18].…”

A broad theoretical investigation of R‐3, R3c, and R‐3c polymorphs of FeCrO3

“…The surface was obtained from a slab construction model according to ( hkl ) crystalline planes, which were obtained from the full optimized bulk structure. In particular, the ilmenite and corundum surfaces evaluated are nonpolar, while the LNO‐type structure presents a polar (001) surface, requiring a specific approach that not requires chemical absorption or surface reconstruction to cancel the macroscopic dipole 61,62 . First, unrelaxed cleavage energy ( ) of the complementary terminations ( T U and T D ) were evaluated from Equation , where and corresponds to the total energies for the unrelaxed optimized model and the bulk unit, the n and A represents the number of bulk units used in slab construction and the surface area, respectively.…”

“…First, unrelaxed cleavage energy ( ) of the complementary terminations ( T U and T D ) were evaluated from Equation , where and corresponds to the total energies for the unrelaxed optimized model and the bulk unit, the n and A represents the number of bulk units used in slab construction and the surface area, respectively. Then, the complementary terminations ( T U and T D ) were relaxed (optimized) considering that the only outer layers are representative to describe the surface properties and the core layer presents the bulk property 61,62 . Hence, the cleavage energy for relaxed surfaces ( ) was obtained from Equations and .…”