Density-Functional Prediction of a Surface Magnetic Phase in ${\mathrm{SrTiO}}_3/{\mathrm{LaAlO}}_3$ Heterostructures Induced by Al Vacancies

Based on first-principles density functional calculations we propose a novel Al vacancy induced ferromagnetism occurring at the ${\mathrm{LaAlO}}_3$ surface of ${\mathrm{SrTiO}}_3/{\mathrm{LaAlO}}_3$ bilayers. Magnetism at cation vacancies away from the surface is quenched due to charge compensation. Magnetic surface Al vacancies are stabilized due to the built-in electric field inside the ${\mathrm{LaAlO}}_3$ region that raises the energy of the defect level, making charge compensation unfavorable. Surface Al vacancies prefer to form clusters and exhibit two-dimensional ferromagnetic alignment mediated by a long-range magnetic interaction. These results are discussed in light of recent experimental observations.

Figure 1

(a) The supercell used in the calculations consists of a 4 unit cell thick ${\mathrm{SrTiO}}_3$ substrate and a 4 unit cell thick ${\mathrm{LaAlO}}_3$ overlayer. Along the [001] direction the supercell contains alternating planes of $A_8{\mathrm{O}}_8$ (b) and $B_8{\mathrm{O}}_{16}$ (c) where $AB{\mathrm{O}}_3$ is the general perovskite formula. Sr atoms are represented as green spheres, Ti are light blue, La are pink, Al are dark blue, and oxygen atoms are red.

Figure 2

The layer resolved density of states (DOS) is plotted for the defect-free ${\mathrm{SrTiO}}_3/{\mathrm{LaAlO}}_3$ interface. The lowest DOS represents the ${\mathrm{TiO}}_2$ layer at the interface; plots above this are for the alternating $\mathrm{LaO}/{\mathrm{AlO}}_2$ planes of the ${\mathrm{LaAlO}}_3$ overlayer. The topmost DOS plot represents the ${\mathrm{AlO}}_2$ layer at the ${\mathrm{LaAlO}}_3$ surface. The red and blue lines represent O $2p$ and Ti $3d$ states, respectively; the dotted line is the Fermi level.

Figure 3

(a) Side view of the spin-density isosurface of the ${\mathrm{SrTiO}}_3/{\mathrm{LaAlO}}_3$ interface system with an Al vacancy in the surface layer. The layer in which the vacancy is located is indicated by a dotted red line; the interface is represented by a dotted black line. (b) Top view: the surface unit cell is viewed down the [$00\overline{1}$] direction with a surface Al vacancy at the center. The spin-density is highly delocalized in the $a\text{−}b$ plane suggesting long-range magnetic order. Sr atoms are represented as green spheres, Ti are light blue, La are pink, Al are dark blue, and oxygen atoms are red. The spin-density isosurface is represented in yellow; an isovalue of 0.003 has been used.

Figure 4

Layer resolved density of states for the ${\mathrm{SrTiO}}_3/{\mathrm{LaAlO}}_3$ bilayer with Al vacancies in the interface (a) and surface (b) layers. The layer in which the vacancy is present is indicated. The red and blue lines represent O $2p$ and Ti $3d$ states respectively; the dotted line is the Fermi level.

Figure 5

The total energies of Al vacancies (blue circles) and La vacancies (red circles) are calculated in each layer of the ${\mathrm{LaAlO}}_3$ film. The total energies are referenced to the ground state site.