Trends in (LaMnO3)n/(SrTiO3)m superlattices with varying layer thicknesses

We investigate the thickness dependence of the structural, electronic, and magnetic properties of (LaMnO3)n/(SrTiO3)m (n, m = 2, 4, 6, 8) superlattices using density functional theory. The electronic structure turns out to be highly sensitive to the onsite Coulomb interaction. In contrast to bulk SrTiO3, strongly distorted O octahedra are observed in the SrTiO3 layers with a systematic off centering of the Ti atoms. The systems favour ferromagnetic spin ordering rather than the antiferromagnetic spin ordering of bulk LaMnO3 and all show half-metallicity, while a systematic reduction of the minority spin band gaps as a function of the LaMnO3 and SrTiO3 layer thicknesses originates from modifications of the Ti dxy states.

Simulation Package 24 with projector augmented wave pseudopotentials and employ the generalized gradient approximation in the parametrization of Perdew, Burke, and Ernzerhof (including spin polarization). The density of states is calculated by the tetrahedron method (smearing 0.01 eV) with Blöchl corrections 25 . Because of the correlated nature of the transition metal d orbitals, we add an onsite Coulomb interaction using the Lichtenstein scheme 26 . The values for the U and J parameters are taken from Refs 27-29 as 4 eV and 1 eV for the Mn d states, 5 eV and 0.5 eV for the Ti d states, and 9 eV and 1 eV for the La f states. We have tested for the bulk compounds that these values are transferable to the parametrization of Perdew, Burke, and Ernzerhof by comparing the densities of states, which show no qualitative difference. The optimized lattice constant of SrTiO 3 is 3.97 Å, with a band gap of 2.6 eV, and the optimized in-plane and out-of-plane lattice constants of LaMnO 3 are 3.95 Å and 4.01 Å. The total densities of states obtained for bulk SrTiO 3 and strained bulk LaMnO 3 (half-metallic) are shown in Fig. 1. Structural optimization of the superlattices with and without onsite interaction is found to yield substantial differences in the electronic structure, especially near the Fermi level. More specifically, the minority channel shows a metallic character without onsite interaction for n:m = 2:2 (2 unit cells of LaMnO 3 alternate with 2 unit cells of SrTiO 3 ), whereas with onsite interaction we obtain a half-metallic character. The supercells have C 2h point group symmetry (tetragonal perovskite structure). An optimized in-plane lattice constant of 5.56 Å is obtained for the 2:2 system and is used for the larger superlattices. The out-of-plane lattice constant is optimized individually in each case. Starting from the 2:2 system, we fix the LaMnO 3 thickness and increase the SrTiO 3 thickness (2:4, 2:6, 2:8) or fix the SrTiO 3 thickness and increase the LaMnO 3 thickness (4:2, 6:2, 8:2). The 4:4 system is also considered for comparison. Figure 2(left) illustrates the 2:4 system as an example. There are two types of interfaces, the n-type LaO/ TiO 2 interface and the p-type SrO/MnO 2 interface, denoted in the following as n-IF and p-IF, respectively. The nomenclature refers to the compensating charges formed at the ( ) / ( )    Table 1. A schematic view of the Mn-O and Ti-O bonds is given in Fig. 2(right). For increasing n the Mn-O bond length at the p-IF maintains a value of 2.10 Å, while the Ti-O bond length decreases (bulk value 1.95 Å) from 1.91 Å in the 2:2 system to 1.87 Å in the 8:2 system. At the n-IF the Mn-O bond length shows no clear trend, while the Ti-O bond length grows significantly from 2.04 Å in the 2:2 system to 2.08 Å in the 8:2 system. It is found that all Ti atoms shift systematically off the center of their O octahedron towards the p-IF by up to 0.1 Å (in all cases more at the p-IF than at the n-IF), implying that a permanent dipole is created, while bulk SrTiO 3 is not ferroelectric. The off-centering is generally enhanced at the interfaces when n increases and reduced when m increases. It is known that the properties of SrTiO 3 are very sensitive to dopants and external perturbations 30 so that it cannot surprise that the superlattices react similarly 31 . We also note that we obtain for bulk SrTiO 3 a ferroelectric distortion of 0.03 Å, which is a known artefact of the employed methodology 32 . However, this effect is significantly smaller than the off-centerings described above and therefore does not affect our conclusions.
Bulk LaMnO 3 is an A-type antiferromagnetic (AFM) Mott insulator, due to a combination of superexchange and Zener double exchange 33 , whereas SrTiO 3 is a non-magnetic insulator (d 0 configuration of Ti). Figure 3 shows the total densities of states obtained for the 2:2, 2:8, and 8:2 systems. The general  Figure 4 demonstrates systematic changes for varying n and m. The density of states at the Fermi energy remains similar for growing m but increases significantly for growing n due to the fact that these states mainly belong to the LaMnO 3 layer. Importantly, for increasing n as well as m, the minority spin band gap is reduced substantially. Indeed, the band onsets in the 2:8 and 8:2 systems are close to the Fermi energy so that the half-metallicity will most likely vanish for n, m > 8. The reduction of the minority spin band gap is explained by the projected densities of states of the Ti atoms at the n-IF in Fig. 5. The Ti 3d orbitals, being split into d xy , d yz , d xz (t 2g ) and − d x y 2 2 , − d z r 3 2 2 (e g ) states due to the octahedral crystal field, systematically shift to lower energy for increasing n and m, which is consistent with previous experimental observations for LaAlO 3 /SrTiO 3 interfaces 34 . The energetic lowering is strongest for the d xy states, which thus govern the reduction of the minority spin band gap. The orbital ordering seen in Fig. 5 decreases for increasing m, while it remains similar for increasing n. In addition, it is always more pronounced at the n-IF than at the p-IF, and almost lost at the p-IF and in the bulk-like regions of the 2:8 system. Figure 6 gives projected densities of states of Ti atoms in layers with increasing distance from the 2:8 n-IF. As to be expected, away from the n-IF the states shift to higher energy. Projected densities of states of the Mn atoms at the p-IF are shown in Fig. 7. Note that the Mn Mn states are a result of the in-plane strain. The metallicity at the p-IF is substantially reduced for increasing n, especially in the 8:2 system, as the LaMnO 3 layer becomes more bulk-like. Figure 8 gives projected densities of states of the Mn atoms in layers with increasing distance from the 8:2 p-IF. The distinct difference between the − d x y 2 2 and − d z r 3 2 2 states is reduced when the distance increases. In order to assess the magnetic ground state, we study the total energies for FM and A-type AFM spin ordering for strained bulk LaMnO 3 and the superlattices. Other spin orderings (such as C-type and G-type AFM) have much higher energies, as we have checked for the 2:2 system. FM spin ordering is found to be favorable, in agreement with previous experiments 20, 23,34 and calculations 35 as well as reports on related perovskite oxide interfaces [36][37][38] . The energy difference (per formula unit) between FM and A-type AFM spin ordering is 0.75 eV for strained bulk LaMnO 3 , whereas in the case of the superlattices it slightly decreases from 0.27 eV to 0.20 eV for increasing m and remarkably increases from 0.27 eV to 0.85 eV for increasing n, which shows that it can be attributed to the LaMnO 3 layer (the Ti magnetic moments are very small). Because of this, we normalize our results in the following with respect to the number of Mn atoms. The energy difference steadily decreases for increasing n as well as m though the FM ordering, which is due to Zener double exchange between partially filled Mn e g states 39  Interestingly, induced Ti magnetic moments of 0.02 to 0.04 μ B are observed at both interfaces in our systems, see Table 2, whereas far from the interfaces they are negligible (< 0.01 μ B ). For increasing m they increase (decrease) at the n-IF (p-IF), while for increasing n we obtain higher magnetic moments at the p-IF (~0.04 μ B ) than at the n-IF (~0.02 μ B ). We note that even small Ti magnetic moments at perovskite oxide interfaces can have important consequences for the magnetism 34,41 . We find Mn magnetic moments of 3.72 to 4.03 μ B , with larger values at the n-IF than at the p-IF in all cases. When m increases they increase (decrease) at the n-IF (p-IF), while the changes are not systematic under variation of n. The highest value appears in the 4:4 system at the n-IF. Concerning the charges in the atomic orbitals, we find small but finite differences from the corresponding bulk values at both interfaces, see Table 2. A detailed analysis shows that for increasing n (m) the Mn atoms lose more (less) charge at the p-IF. Moreover, the Ti (Mn) atoms gain (lose) charge at the n-IF (p-IF) in all cases, while there is no clear trend at the p-IF (n-IF) because of the larger distances of the atoms from to the interface plane. The observed small charge transfers give rise to the mentioned Ti magnetic moments but cannot explain the ferroelectric distortions in the SrTiO 3 layer, which thus are likely direct consequences of the interface interaction.

Discussion
The structural, electronic, and magnetic properties of (LaMnO 3 ) n /(SrTiO 3 ) m superlattices have been investigated and compared for various thicknesses n:m. Both n and m are found to strongly affect the material properties. In general, the SrTiO 3 layers show heavy distortions of the O octahedra, which are not present in bulk SrTiO 3 , consistent with recent experimental findings 42 . Since LaMnO 3 is polar along the [001] direction (with alternating (LaO) + and (MnO 2 ) − layers) and SrTiO 3 is non-polar, a compensation mechanism is required. As the strained LaMnO 3 is metallic, we could expect accumulation of charge carriers at the interfaces. However, this effect is much too small according to the charge deviations reported in Table 2 so that a second mechanism must play a role. The projected densities of states of the Ti atoms in layers of increasing distance from the 2:8 n-IF in Fig. 6 show an almost continuous shift of all curves to higher energy. This reflects the built up of an electric field, which in turn induces ferroelectric distortions in the SrTiO 3 region, as discussed before. The ferroelectric distortions constitute the main compensation mechanism in the present superlattice. Similar distortions of the TiO 6 octahedra have been reported in Ref. 28.
All studied systems exhibit half-metallicity, though our results indicate that this property will vanish for n, m > 8. FM spin ordering is always energetically favorable over AFM spin ordering but the preference becomes smaller for increasing n, since the A-type AFM ordering of bulk LaMnO 3 starts to dominate. The Ti magnetic moments observed at the interfaces are small. The authors of Ref. 43    the high electrical conductivity of the LaAlO 3 /SrTiO 3 interface is related to the formation of O vacancies during the deposition process due to the extra charges introduced into the system 44 . In addition, Sr/La intermixing leads to a metallic interface between the insulators LaTiO 3 and SrTiO 3 , because mixed valent Ti states are created 45 . We expect that these factors are less important for the LaMnO 3 /SrTiO 3 interface, as it was found to be rather sharp 42 . We find a systematic reduction of the minority spin band gaps with increasing n and m, which originates mainly from an energetic downshift of the Ti d xy states.

Methods
The atomic sphere radii are chosen such that overlap is avoided during the ionic relaxation, for which we set the energy tolerance to 10 −3 eV, employ a 4 × 4 × 1 k-mesh, a Gaussian smearing of 0.05 eV, and an energy cutoff of 500 eV. To obtain accurate electronic states, we set the energy tolerance to 10 −5 eV and adopt dense k-meshes of 8 × 8 × 3 for n + m = 4, 8 × 8 × 2 for n + m = 6, and 8 × 8 × 1 for n + m = 8 and 10.