Polar catastrophe, electron leakage, and magnetic ordering at the ${\text{LaMnO}}_3/{\text{SrMnO}}_3$ interface

Electronic reconstruction at the polar interface ${\text{LaMnO}}_3/{\text{SrMnO}}_3$ (LMO/SMO) (100) resulting from the polar catastrophe is studied from a model Hamiltonian that includes the double and superexchange interactions, the Madelung potential, and the Jahn-Teller coupling terms relevant for the manganites. We show that the polar catastrophe, originating from the alternately charged LMO layers and neutral SMO layers, is quenched by the accumulation of an extra half electron per cell in the interface region as in the case of the ${\text{LaAlO}}_3/{\text{SrTiO}}_3$ interface. In addition, the $\text{Mn}{e}_g$ electrons leak out from the LMO side to the SMO side, the extent of the leakage being controlled by the interfacial potential barrier and the substrate induced epitaxial strain. The leaked electrons mediate a Zener double exchange, making the layers adjacent to the interface ferromagnetic, while the two bulk materials away from the interface retain their original type A or G antiferromagnetic structures. A half-metallic conduction band results at the interface, sandwiched by the two insulating bulks. We have also studied how the electron leakage and consequently the magnetic ordering are affected by the substrate-induced epitaxial strain. Comparisons are made with the results of the density-functional calculations for the ${\left(\text{LMO}\right)}_6/{\left(\text{SMO}\right)}_4$ superlattice.

Figure 1

Illustration of the polar catastrophe for the LMO/SMO (100) interface. The layers are neutral on the SMO side, but are charged $\pm 1$ on the LMO side leading to the unrestricted growth of the Coulomb potential (dashed line) and the scenario where it is healed by accumulating 0.5 electrons per cell on the interfacial ${\text{MnO}}_2$ layer (solid line). The layer numbers indicated in this figure are used throughout the paper.

Figure 2

Layer-projected $\text{Mn}{e}_g$ occupancy across the interface, as obtained from the model Hamiltonian with dielectric constant $ϵ=10$. About half an electron per Mn atom accumulate at the interface to remove the polar catastrophe and, furthermore, a small number of electrons leak from the LMO to the SMO side. Electrons at the interface form a spin-polarized 2D electron gas, sandwiched between the two insulating bulks.

Figure 3

(Color online) Minimum-energy magnetic configuration at the LMO/SMO interface for typical parameters and unstrained condition as obtained from both the density-functional and model calculations. The first ${\text{MnO}}_2$ layer on the SMO side can be tuned FM or AFM by changing the strain condition as discussed in the text.

Figure 4

Madelung potential seen by the Mn ions in various layers without and with the charge reconstruction as obtained from the self-consistent calculation using the model Hamiltonian [Eq. (1)]. Without the charge reconstruction, the potential grows unrestricted away from the interface (polar catastrophe), which is healed by accumulation of half an electron per cell at the interface. The reconstructed charge at the interface has a dipole moment that leads to a potential step (bottom figure).

Figure 5

(Color online) $\text{Mn}{e}_g$ occupancy across the LMO/SMO interface for different values of the dielectric constant $ϵ$ (symbols connected by lines) compared with the density-functional results for the ${\left(\text{LMO}\right)}_6/{\left(\text{SMO}\right)}_4$ superlattice (filled squares). An increased $ϵ$ results in a diminished Madelung potential and, consequently, electrons leak deeper into the bulk.

Figure 6

(Color online) Layer-projected $\text{Mn}{e}_g$ densities of states obtained from the model Hamiltonian indicating extra electrons or holes accumulated at the interfacial layers, while away from the interface, the $e_g$ states are either half filled (LMO) or unoccupied (SMO). The electrons are effectively spinless with only the spin state aligned parallel to the Mn core spin at a particular Mn site allowed to be occupied $\left(J_H=\infty \right)$, so that we have a single spin channel in this figure. Within this single spin $e_g$ bands, the interfacial Mn atoms, on layer #0, are roughly quarter-filled, so that there are approximately $0.5e^{-}$ per Mn atom.

Figure 7

Variation in the energy of the lowest $\text{Mn}{e}_g$ state of each ${\text{MnO}}_2$ layer, obtained using DFT-LMTO from the layer-projected wave-function characters for the ${\left(\text{LMO}\right)}_6/{\left(\text{SMO}\right)}_4$ superlattice. This variation in energy is indicative of the potential experienced by the $\text{Mn}{e}_g$ electrons across the interface.

Figure 8

Density-functional results for majority and minority spin $\text{Mn}d$ densities of states for SMO and LMO layers away from the interface indicating the bulklike insulating behavior. Results are for the innermost ${\text{MnO}}_2$ layers in the ${\left(\text{LMO}\right)}_6/{\left(\text{SMO}\right)}_4$ superlattice.

Figure 9

Same as Fig. 8 for interfacial layers, indicating the presence of carriers at the interface, which are also spin polarized. Spin-minority states are unoccupied indicating half metallicity.

Figure 10

Energy splitting of the $\text{Mn}{e}_g$ orbitals due to in-plane compressive and tensile strain conditions used in our model Hamiltonian.

Figure 11

Electron leakage to the individual ${\text{MnO}}_2$ layers on the SMO side as a function of strain.

Figure 12

The total energy as a function of the canting angle $\theta$ and strain $\Delta$. The parameter $\theta$ is the angle between the neighboring Mn core spins in the first ${\text{MnO}}_2$ layer on the SMO side. The figure shows that the considered ${\text{MnO}}_2$ plane either stabilizes with FM order or AFM order depending on the strain condition. No canted magnetism is found.

Figure 13

Magnetic phase diagram for the first ${\text{MnO}}_2$ layer on the SMO side as a function of the dielectric constant $ϵ$ and strain $\Delta$. Rest of the layers maintain the magnetic behavior of the corresponding bulk materials, either AFM or FM within each layer, throughout the range of parameters considered.