Interface-induced ferroelectric domains and charged domain walls in $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_3/\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$ superlattices

Heterostructures comprising of polar and nonpolar perovskites, such as $\mathrm{LaAl}{\mathrm{O}}_3/\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$, have been extensively studied because of the discovery of a two-dimensional electron (or hole) gas [2DEG (or 2DHG)] at the interface. $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_3/\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$ is chemically similar to $\mathrm{LaAl}{\mathrm{O}}_3/\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$ with polar/nonpolar interfaces. However, $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_3$ exhibits spontaneous ferroelectric polarization, which leads to interesting effects in $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_3/\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$. Our theoretical simulations exhibit some different physical phenomena in this system, including interface-induced ferroelectric domains, monodirectional polarization, and 2DEGs (or 2DHGs) at the domain walls. Furthermore, it was identified that the observed 2DEGs (or 2DHGs) were spin polarized and exhibited ferromagnetism. The origin of the ferromagnetic 2DEGs (or 2DHGs) is discussed. These spin-polarized 2DEGs (or 2DHGs) observed in our $\mathrm{Bi}\mathrm{Fe}{\mathrm{O}}_3/\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$ model would be important for fundamental research and applications.

Figure 1

Charged/neutral $\mathrm{Bi}{\mathrm{O}}^{+}/\mathrm{Ti}{{\mathrm{O}}_2}^0$ interface (a) and $\mathrm{Fe}{{\mathrm{O}}_2}^{+}/\mathrm{Sr}{\mathrm{O}}^0$ interface (b) in BFO/STO superlattice. In such a structure, the polar block consists of alternating positively and negatively charged atomic layers along the growth direction, and the nonpolar block is composed of electrically neutral atomic layers.

Figure 2

Optimized BFO/STO superlattice models in which (a) both the upper and lower interfaces are type $N$, denoted as type N-N, (b) both interfaces are type $P$, denoted as type P-P, and (c) the upper and lower interfaces are type $N$ and $P$, respectively, denoted as type P-N. Here and in the following figures, purple, brown, and red spheres represent the Bi, Fe, and O atoms, respectively; green and sky-blue spheres represent the Sr and Ti atoms, respectively.

Figure 3

Effects of charged/neutral interfaces on the directions of the polarization displacement of the Bi ions at type $P$ (a) and type $N$ (b) interfaces, where $n$ is the interface unit normal. ${\mathrm{Bi}}^{3+}$ ions are denoted by purple circles. The circles of dash line correspond to paraelectric phase in initial state, and the circles of solid line correspond to the preferred direction of displacement.

Figure 4

In-plane components of polar displacement of Bi ions in type N-N system (a) without structural strain and (b) with structural strain along the $z$ axis ($\frac{c-c_0}{c_0}=-3.76\%$, where $c$ and $c_0$ are the lattice constants along $z$ axis with and without strain).

Figure 5

Layer-resolved densities of states (LRDOSs) of BFO blocks in superlattices with type (a) N-N, (b) P-P, and (c) P-N interfaces. In these plots, only the projected densities of states of the $\mathrm{Fe}\_3d$ orbitals are shown.

Figure 6

(a) Partial charges of the conduction band edges in the BFO/STO superlattice with type N-N interfaces. (b) Partial charges of the valence band edges in the BFO/STO superlattice with type P-P interfaces. The yellow and light blue represent the electron and hole cloud. The upper inset shows a side view of the $\mathrm{Fe}{\mathrm{O}}_2$ layer outlined by the dotted line in the main panel image; the middle and lower insets show the total DOS of the band edges of type N-N and P-P systems, respectively. (c) The magnetic structure of $\mathrm{Fe}\_3d$ in type N-N system. The white and black arrows represent the spin of localized and itinerant $\mathrm{Fe}\_3d$ electrons, respectively. The insets show the spin density distributions of $\mathrm{Fe}{\mathrm{O}}_2$ layers at and away from the domain wall respectively, in which the green and gray colors represent the net spin-up (↑) and spin-down (↓) electron density, respectively.