Fully spin-polarized two-dimensional electron gas at the ${\mathrm{CoFe}}_2{\mathrm{O}}_4/{\mathrm{MgAl}}_2{\mathrm{O}}_4$(001) polar interface

We performed first-principles calculations to show that a fully spin-polarized two-dimensional electron gas can be created at the interface between the polar and insulating spinel oxides ${\mathrm{CoFe}}_2{\mathrm{O}}_4$ and ${\mathrm{MgAl}}_2{\mathrm{O}}_4$. We give a clear description of the physical parameters (in particular the atomic termination of the interfaces), which favor the formation of this electron gas that is due either to an electric field induced in stoichiometric oxide layers because of their polar character or to a charge reorganization that preserves the global electric neutrality in nonstoichiometric layers. We show that the electric field-induced spin-polarized two-dimensional electron gas can only exist if the thickness of the ${\mathrm{CoFe}}_2{\mathrm{O}}_4$ layer is large enough and that it may be destroyed by intermixing at the interfaces.

Figure 1

On the left, the ${\mathrm{CoFe}}_2{\mathrm{O}}_4/{\mathrm{MgAl}}_2{\mathrm{O}}_4$(001) 6/6 supercell with six atomic bilayers of ${\mathrm{CoFe}}_2{\mathrm{O}}_4$ and six bilayers of ${\mathrm{MgAl}}_2{\mathrm{O}}_4$, separated by one $p$-type ${[\mathrm{Mg}}_A$/(FeCo)${}_B{\mathrm{O}}_4$] and one $n$-type ${[\mathrm{Fe}}_A$/(${\mathrm{Al}}_2){}_B{\mathrm{O}}_4$] interface and the alternation of atomic planes corresponding to Table 1 and 1. On the right, the same superlattice with different cation distributions in ${\mathrm{CoFe}}_2{\mathrm{O}}_4$ [Table 1 to 1].

Figure 2

Total density of states projected on the successive atomic bilayers of the 6/6 supercell. The blue curves correspond to the ${\mathrm{CoFe}}_2{\mathrm{O}}_4$ layer, and the red curves to the ${\mathrm{MgAl}}_2{\mathrm{O}}_4$ layer, while the positive and negative curves correspond, respectively, to majority and minority spin electrons.

Figure 3

($x,y)$-averaged electrostatic Coulomb potential as a function of the $z$ coordinate, perpendicular to the interfaces (red curve) and its local $z$-averaged value (blue curve) for the 6/6 supercell.

Figure 4

Diagram of the IMT which corresponds to a transfer of electrons from the top of the valence band at the $p$ interface to the bottom of the conduction band at the $n$ interface. This transfer involves the minority spin channel electrons of ${\mathrm{CoFe}}_2{\mathrm{O}}_4$ (blue solid line), and not the majority spin (blue dashed line).

Figure 5

Minority spin band structures for the 6/6, 8/8, and 10/10 stoichiometric and asymmetric ${\mathrm{CoFe}}_2{\mathrm{O}}_4/{\mathrm{MgAl}}_2{\mathrm{O}}_4$(001) supercells. The contributions of the ${\mathrm{Fe}}_B$ atoms at the $n$ interface, and of the ${\mathrm{Co}}_B$ atoms at the $p$ interface are, respectively, represented by red and blue circles.

Figure 6

Layer-resolved densities of states for half of the nonstoichiometric supercells with (a) two $p$ interfaces and (b) two $n$ interfaces.

Figure 7

Density of states for majority spin (positive curves) and minority spin electron (negative curves) for (a) bulk ${\mathrm{MgAl}}_2{\mathrm{O}}_4$, (b) bulk cubic ${\mathrm{CoFe}}_2{\mathrm{O}}_4$, and (c) bulk tetragonal ${\mathrm{CoFe}}_2{\mathrm{O}}_4$.