Controlled confinement of half-metallic two-dimensional electron gas in ${\mathrm{BaTiO}}_3/{\mathrm{Ba}}_2{\mathrm{FeReO}}_6/{\mathrm{BaTiO}}_3$ heterostructures: A first-principles study

Using density functional theory calculations, we establish that the half-metallicity of bulk ${\mathrm{Ba}}_2{\mathrm{FeReO}}_6$ survives down to 1 nm thickness in ${\mathrm{BaTiO}}_3/{\mathrm{Ba}}_2{\mathrm{FeReO}}_6/{\mathrm{BaTiO}}_3$ heterostructures grown along the (001) and (111) directions. The confinement of the two-dimensional (2D) electron gas in this quantum well structure arises from the suppressed hybridization between Re/Fe $d$ states and unoccupied Ti $d$ states, and it is further strengthened by polar fields for the (111) direction. This mechanism, distinct from the polar catastrophe, leads to an order of magnitude stronger confinement of the 2D electron gas than that at the ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ interface. We further show low-energy bands of (111) heterostructure display nontrivial topological character. Our work opens up the possibility of realizing ultrathin spintronic devices.

Figure 1

Geometry of BTO/BFRO/BTO heterostructures with $c$ axis oriented along the growth directions, (111) [panels (a), (c)] and (001) [panels (b), (d)]. Layerwise nominal charges for the two heterostructures are shown in panels (a) and (b). The in-plane honeycomb lattice with two triangular sublattices on different layers in the case of the (111) heterostructure and the in-plane square lattice in the case of the (001) heterostructure are marked in panels (c) and (d), respectively.

Figure 2

Density of states, projected onto Fe $d$ (solid line) and Re $d$ states (shaded area), in bulk BFRO [panel (a)], and in heterostructures along (111) [panel (b)] and (001) [panel (c)]. The zero of the energy is set at $E_F$. Panel insets show the zoomed DOS close to $E_F$. Panel (d) depicts the energy levels of Fe $t_{2g}$ and Re $t_{2g}$ in absence of the Fe-Re hybridization, and the renormalized Re $t_{2g}$ energy positions after hybridization with Fe $t_{2g}$ states. See text for details.

Figure 3

(a) The GGA (left panels) and GGA+SO (right panels) band structures of (111) (top panels) and (001) (bottom panels) heterostructures plotted along the high symmetry directions. For the (111) heterostructure, the chosen high symmetry directions are $K=(0.3333,0.3333,0)$, to $\mathrm{\Gamma }=(0,0,0)$ to $M=(0.5,0.0,0)$ to K to $\mathrm{\Gamma }$. For the (001) heterostructure, the chosen high symmetry directions are $\mathrm{\Gamma }$ to $M=(0.5,0.5,0.0)$ to $X=(0.0,0.5,0.0)$ to $\mathrm{\Gamma }$. Zero of the energy is set at respective $E_F\text{"s}$. The blue rectangular area highlights the band topology at high symmetry $K$ point in the (111) heterostructure.

Figure 4

Out-of-plane and in-plane projection of the conducting charge density in (111) [(a) and (b), respectively] and (001) heterostructure geometries [(c) and (d), respectively]. The isosurface values are chosen as $0.023e^{-}/{\AA }^3$. The charge densities are calculated from contributions within an energy window $[E_F-0.5\text{eV},E_F]$. Various atomic distances have been marked. (e) Planar averaged conducting charge density versus distance along the growth direction for (111) and (001) heterostructures. The distances are measured from the center of the unit cell, which is at the midpoint of the bilayer.