Band alignment and charge transfer in complex oxide interfaces

The synthesis of transition metal heterostructures is currently one of the most vivid fields in the design of novel functional materials. In this paper we propose a simple scheme to predict \emph{band alignment }and \emph{charge transfer} in complex oxide interfaces. For semiconductor heterostructures band alignment rules like the well known Anderson or Schottky-Mott rule are based on comparison of the work function or electron affinity of the bulk components. This scheme breaks down for oxides due to the invalidity of a single workfunction approximation as recently shown (Phys. Rev. B 93, 235116; Adv. Funct. Mater. 26, 5471). Here we propose a new scheme which is built on a continuity condition of valence states originating in the compounds' shared network of oxygen. It allows for the prediction of sign and relative amplitude of the intrinsic charge transfer, taking as input only information about the bulk properties of the components. We support our claims by numerical density functional theory simulations as well as (where available) experimental evidence. Specific applications include i) controlled doping of SrTiO$_3$ layers with the use of 4$d$ and 5$d$ transition metal oxides and ii) the control of magnetic ordering in manganites through tuned charge transfer.


I. INTRODUCTION
Until today semiconductors present the most important class of functional materials for electronic applications. Their usage in electronic components and the continuous development of new devices keeps on pushing the limits of technology. In almost all such devices the key functionality originates not in the physics of the bulk, but in the peculiarities of interfaces [1]. Yet, semiconductor devices have intrinsic limitations: i) the characteristic length scales are relatively large so that further downscaling (current state of the art is 7nm technology) becomes very unlikely and Moore's law is bound to end; ii) solely charge degrees of freedom are exploited. Transition metal oxides (TMO) on the other hand provide spin, orbital, charge and lattice degrees of freedom [2,3] and are therefore viewed as one of the best candidates to replace semiconductors in future electronic device. Thanks to an immense progress of epitaxial growth techniques, TM oxides heterostructures can now be controlled on atomic length scales. Several novel physical phenomena have been discovered in recent years and potential multifunctional devices seem to be realizable [4][5][6][7][8].
In oxide electronics, one of the cornerstone mechanisms in complex heterostructures (in analogy to semiconductors) is the alignment of bands at a hetero interface and, driven by the resulting potential gradient, a charge transfer across the interface [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. This mechanism can be seen as intrinsic doping without undesired disorder induced by chemical doping. Consequently, controlling heterostructures with a wide variety and range of experimentally tunable parameters (e.g. strain, thickness, substrate choice, etc.) allows to engineer new phases which do not exist in bulk. It is, hence, obvious that predictive power for the direction and amplitude of charge transfer with rules that are as simple as possible is highly desirable.
A natural first attempt would be the usage of well es-tablished semiconductor rules, such as Anderson's or the Schottky-Mott rule [26]. As schematically shown in Fig.  1(a) the vacuum energy levels of the two semiconductors on either side of the heterojunction should be aligned, which rely on the electron affinity (or work function) of semiconductors. However, those rules are not suitable for TM oxides, due to the fact that the reduction of the work function to a single value is an approximation that does not hold for TM oxides [27,28]. Moreover, the characteristic lengthscales in oxides are one or two orders of magnitude smaller than in semiconductors, and hence certain approximations are no longer justified so that non-trivial microscopic terms need to be taken into account explicitly.
In this paper we propose a rule that is based on the continuity of states in the TMO's oxygen matrix and which allows for qualitative prediction of band alignment and charge transfer in complex TMO heterostructures. The oxygen continuity boundary condition allows us to explain and predict the induced charge transfer between the constituents of the heterostructure starting only from energetics of the bulk compounds. In the first part of our report we sketch the underlying driving forces in TMO hetero compounds which are built from perovskites ABO 3 with A being the a cation (e.g. Sr or La) and B as a TM from strongly correlated 3d, 4d, or strongly spin-orbit coupled 5d shell. We claim that bulk data for the oxygen 2p energies ε p of the components can be used for predictions of ABO 3 /AB ′ O 3 interfaces, and prove it by showing quantitative data for a wide range of materials. In the second part of the paper we provide selected examples as a proof of principle, and predictions for possible devices yet to be synthesized.

II. METHODS
To reveal general material trends, we first study bulk complex transition metal oxides ABO 3 with a cubic perovskite structure (in the majority of cases A is taken as Sr but we also discuss other cases like Ca and La) with B being a 3d (Ti-Co), 4d(Zr-Rh) or 5d (Hf-Ir) transition metal element. The lattice constant is fixed at the optimized value of SrTiO 3 , a=3.945Å [69]. We then use SrRuO 3 as an example for effects of strain, cation A substitution, structural distortion, and magnetism. Most calculations were carried out for superlattices of (ABO 3 ) n /(AB ′ O 3 ) n with n=5 and n=1, in order to estimate possible quantum confinement effects for the latter. Moreover, in order to validate the assumption of clean interfaces we performed simulations of a rough interface with a 25% cation mixture (for details see appendix). It turns out that the observed changes are indeed small and will not affect our conclusions. For the study of magnetism in SrMnO 3 heterostructures, we take into account an on-site Coulomb interaction U Mn =2eV and a realistic GdFeO 3 -type structural distortion which are considered to be important for a realistic description of the magnetism. In all calculations the atomic positions are fully relaxed.
Density functional theory (DFT) calculations were performed with the VASP (Vienna ab initio simulation package) code [29] using the generalized gradient approximation GGA -PBE functional [30] for electronic exchange and correlation. We consider that energy separation between transition metal d states and oxygen 2p states is usually underestimated in the PBE potential, and use the MBJ potential [31], which is implemented in wien2k [32]. We perform Wannier projection [33,34] of the oxygen p Bloch states and TM t 2g d states to obtain an accurate value of the local energy levels ε p and ε d [35] as shown in Fig. 4 and Table I. Be aware that ε p and ε d indicate the local energy terms of t 2g and oxygen p states respectively and not to the center of gravity for valence or conduction bands (ε v and ε c ) [36]. They coincide only in the ionic limit, but for finite covalence (i.e. oxygen-TM hybridization) ε v and ε c are split apart and the bands have no pure oxygen or TM character anymore. The values in Fig. 4 correspond to ε d and ε p . It turns out that covalence yields an energy drop of approximately 0.4eV of ε p for all materials listed in the Fig. 4. We have also carefully checked that the projection details such as including e g orbitals will not change our conclusion.
In order to obtain quantitative estimates for the charge transfer we integrate the electron density below the Fermi level (down to the energy gap between d and oxygen p states) projected inside atomic spheres. The radius of the atomic spheres (and here is the mentioned ambiguity in the definition) were chosen to the default values of PAW potential in VASP, e.g. 1.2 Angstrom for a Vanadium atom in SrVO 3 . In this way, the integrated electron density of Vanadium atom in bulk SrVO 3 is 0.75. Considering the formal valence of vanadium to be one d electron, we then take 0.75 as renormalizing factor which we also apply to the interface case in order to obtain a quantitative value for the charge transfer. Moreover, in order to estimate the sensitivity of such values with respect to the choice of the radius of atomic spheres, we have checked that a 10% increase of the radius only induces approximately a 3% change of the charge transfer estimated in this way. Hence, the numbers for the charge transfer given in Tab. I have to be taken with some care. We stress that our conclusions do not rely on specific quantitative values, but on overall trends. We plot the DOS for the two BO2 layers directly at the interface as well as for the TiO2 two unit cell further away. The alignment of oxygen states in this band insulator heterostructure is practically perfect.

III. INTRINSIC CHARGE TRANSFER IN COMPLEX OXIDE INTERFACES
Let us start the discussion with the idea that motivated the study. For the sake of simplicity we restrict ourselves to perovskite ABO 3 heterostructures along the (001) direction. As common in such TM oxide compounds the most relevant states are i) the empty or partially filled TM d states at the Fermi energy [70] which are split into t 2g and e g states in cubic perovskites and ii) the oxygen 2p states residing at an energy ε p a few eV below the Fermi energy and forming more or less covalent bonds with the TM d states. At an interface of two materials with different lattice constants or distortion patterns of an ideal cubic case we typically find a smooth transition where such structural features mutually propagate between the components of the heterostructure [37,38]. A rather natural observation is that such smooth structural transitions in the shared oxygen lattice necessarily demand a continuity of the oxygen states across the interface layers as a boundary condition.
One might start by visualizing the oxygen continuity condition with a very simple sketch we show in Fig. 1 for an ABO 3 /AB ′ O 3 interface; later on we will extend our discussion to more general cases with different cations. In a hypothetical two step procedure the continuity condition would demand that at the interface the oxygen states need to be lined up which, for two materials with different ε p , would result in a mismatch of the Fermi energy E F equivalent to , see Fig. 1(c). Since E F must, however, be constant all through the heterostructure in equilibrium, a charge transfer occurs between the layers which itself creates i) an electrostatic potential drop ∆φ across the interface, ii) rigid band shifts we indicate by ∆ε DOS , and iii) a local electrostatic potential drop ∆ε dp yielding relative shifts between TM d and oxygen p. These three terms counter the original driving potential -see Fig. 1(d). As indicated in this last sketch we end up with a balance of potentials that has to be calculated self consistently. Before further formalization, let us support this hypothesis by numerical calculations starting with the easiest case of interfacing two band insulators which, in fact, has a one to one correspondence to the band alignment mechanism in semiconductor heterostructures.
In Fig. 2 we show the layer dependent density of states for the interface of SrTiO 3 and SrZrO 3 simulated in a 5/5 superlattice. The chemical potential, which is basically free to move inside the gap, is indicated by the dashed black line while the center of mass (i.e. the onsite energy) of the oxygen 2p states (dark gray DOS) is shown as a black solid line. In the plots, we show ZrO 2 and TiO 2 layers directly at the interface as well as the TiO 2 bulk-like layer two unit cells further away from the interface. As can be seen, the alignment of oxygen states across the interface and even in the next TiO 2 layer is practically perfect due to the absence of any charge transfer between the insulating layers. This observation is a first indication of the validity of the backbone hypothesis of the oxygen states continuity. We note in passing that we have an advantage compared to semiconductor heterostructures where obvious structural and electronic continuity is absent [39]. In such semiconducting heterojunctions one might try to employ the Anderson's (or Schottky-Mott) rules in order to estimate the band mismatch by the difference of the components electron affinity (or work function) [26]. It turns out, however, that in realistic cases this rules often fails to predict band offsets. Furthermore, a direct extrapolation of this rule to oxides is rather questionable due to the fact that the concept of a compounds work function is invalid as we have shown in a recent study of oxide heterostructure workfunctions [27,28] which strongly depend on details of the surface orientation and termination. In contrast, the oxygen state continuity rule is a much stronger boundary condition and, as we point out in several occasions, its predictions seem to agree well with experimental observation. Now we take one step further and consider SrNbO 3 instead of SrZrO 3 in the same geometry, i.e. a metal with one valence electron in the Nb 4d shell [40], which we show in Fig. 3 -here we see that an initial alignment of oxygen states has lead to electron transfer from Nb 4dto Ti 3d-states across the interface. The self consistently determined final position of oxygen states with respect to the Fermi level is in agreement with the expectations from our sketch in Fig. 1(d). I.e., the transferred electron has lead to an additional potential ∆φ in the interface region and changes in the local potentials (discussed in more detail below) which eventually leads to a balanced monotonous evolution of the layer dependent energy of oxygen 2p states. Let us stress, that in our picture the directions and relative strength of the charge transfer seem to be predictable just by comparison of ∆ε p of the bulk ABO 3 .
Before providing numerical data and materials calculations to confirm this, let us give more formal arguments. Indeed, the concept of band alignments at interfaces is well known and understood in semiconducting pn-junctions [41], where one observes charge modulations in the so called "space charge" region of the typical order of ≈ 100Å. In the pn-junctions two identical semiconductors are interfaced which, however have a Fermi level mismatch due to different, either p-or n-type, kind of doping that is resolved by charge transfer. Yet, in our case there are some crucial differences specific to oxide interfaces: First of all our length-scales are at least one order of magnitude smaller and the variation of the induced potential on the order of a fewÅ prohibits clearly a semiclassical model commonly used for semiconductors. Secondly, we have to consider more microscopic details for the energy balance equation which finally determines ∆n e . Namely, in addition to ∆φ (the only term of relevance for semiconductor pn-junctions) the charge transfer in oxides induces shifts in the local potentials of the different TM sites which might be disentangled into contributions (i) from mutual change of the valence of B and B ′ site ∆ε dp yielding relative shifts between TM d-and oxygen 2p-states with a sign equal to that of ∆n e and ii) from the specific structure of density of states ∆ε DOS . In summary we can write − ∆ε p = ∆φ + ∆ε DOS + ∆ε dp The terms on the right hand side depend on the transferred charge ∆n e and we may try to linearize them. For the first term ∆φ we can assume a plate capacitor model which would yield a potential drop per unit cell of ∆φ = ∆n e · d/ǫ with d being the effective distance of charge transfer cross the interface and ǫ the dielectric permitivity [42,43]. The second term can be simplified by assuming an approximately constant density of states around Fermi level , D B and D B ′ the local density of states for B and B ′ sites. This contribution D can be seen from Fig. 3 to be of the order of up to 1eV. The last term indicates the change of ε dp induced by the charge transfer that modifies the valence of transition metal.The argument for the linearity in ∆n e of the last term is easily understood by considering a Hartree type self energy (∝ n e ) so we can assume ∆ε dp ≈ ∆n e · U H . U H reflects the change of the energy due to the static single particle mean-field energy that comes from electronic Coulomb interaction. Using virtual crystal approximation for SrVO 3 allows us to roughly estimate this contribution to be also of the order of 1eV. Hence, assuming the charge transfer of the order of ∆n e =1 will lead, different to semiconductors, to non-negligible contributions of D and U H , since the first term d/ǫ, i.e. the typical length scale, is much smaller in our oxide heterostructures than in semiconductors. We arrive eventually at a simplified linear relation between ∆n e and ε bulk p : While also the simplified equation is hardly solvable in a closed form it allows for a remarkable insight and confirmation of our initial idea: The sign and strength of the charge transfer at an interface between two materials, which turns out to be much larger than in semiconductor devices, should be determined by the difference of the respective bulk oxygen 2p energies with respect to their Fermi level ε p . [71]. With this insight we generate DFT reference data for a variety of bulk compounds. The results are summarized in Fig. 4 where we plot the average energy of oxygen 2p states (filled symbols) and the average energy of partially filled d-orbitals (empty symbols) with respect to the Fermi level [72] for SrBO 3 (solid lines) with B being a 3d (black), 4d (red), or 5d (blue) element. For the 3d series we additionally show oxygen p energies for LaBO 3 (dashed line). The figure nicely shows clear trends in the series of materials considered: • Within the intra 3d, 4d, and 5d series we observe a monotonous and almost linear increase of ε p of about 2 − 3eV within each period.
• Within one group we have a monotonous drop in ε p for a given configuration of about ≥ 3 eV from 3d to 5d compounds.
• Changing Sr to La, i.e. decreasing the oxidation number of the transition metal leads to a decrease of ε p up to two eV. This change is actually closely related to ∆ε valence in Eq. 2 and represents in some way the extreme case where we have changed the nominal charge by 1. We note, moreover, that a change of the cation with identical oxidation state ({Sr, Ca, Ba} or { La, Y}) leaves the results for ε p basically unchanged, see table Tab. IV in the appendix.
Before we turn to the discussion of how these numbers can be used for predictions we need to address the fact that the results shown in Fig. 4 are all obtained for undistorted cubic unit cells. The energy scale of the listed material trends is of the order of a few eV and it should be emphasized that certain effects beyond idealized structures will lead to modifications of ε p on energy scales that are non-negligible compared to our reference data. Therefore we have performed calculations for specific cases studying the influence of strain, orthorhombic distortions, and magnetism (in Tab. IV in the appendix we provide the numerical data for these benchmark cases).
Starting with strain, we see for the example of SrRuO 3 , that 1% compressive strain will decrease the ε p of clearly non-negligible 0.2eV and realize that this effect can actually be additionally exploited to tune the energetics for the desired effect [44,45]. Next, we turn to orthorhombic distortions [22] in the same material for which we also observe a change of ε p of the order of 0.3eV compared to the cubic case which is less but still important for a reliable prediction. Finally, let us address the influence of magnetic order for ferromagnetic SrRuO 3 . Here we see a split between up and down states not only in the Ru 4d states but also in the associated oxygen states of 0.7eV. We remark that this issue does not occur in antiferromagnetic ordered structures and also for temperatures higher than the Curie temperature. In the FM ordered phase a prediction of the charge transfer by our simplified scheme is not straight forward and becomes questionable if the corresponding energy scales are equal or larger than the ∆ε p in question.
After these remarks, however, we will now show that for many cases the numerical data for the bulk materials shown in Fig. 4 can be exploited in order to predict the charge transfer in layered heterostructures composed of the listed materials. Starting with the compounds shown in Figures 2 and 3 does not result in any electron transfer after equalizing the Fermi levels in line with Eq. 3 due to the diverging D contribution in the right hand side denominator. For the second case, however, we observe that for SrNbO 3 the oxygen states are much lower in energy than those of SrTiO 3 , i.e. ∆ε p = 2.03eV ≫ 0. Hence, an alignment of oxygen states would lead to a mismatch of the Fermi energy such that electron needs to be transferred from Nb 4d-states to the Ti 3d-states for a constant equilibrium chemical potential across the interface. We can exploit the above reported trends in order to make general predictions: • Given the monotonous trends within early materials of the same period in the SrBO 3 series we conclude that electron transfer will be only possible from lighter to heavier B compounds. This is somewhat counter intuitive: For instance, d 1 SrVO 3 will transfer its electron to d 2 SrCrO 3 but not to the empty Ti 3d states of SrTiO 3 . As it turns out, this is in agreement with experiment and other numerical simulations for a variety of interfaces including LaMnO 3 /LaNiO 3 [17,[46][47][48], LaTiO 3 /LaFeO 3 [19,49,50], LaTiO 3 /LaNiO 3 [18,23], and SrVO 3 /SrMnO 3 [44,45].
• Given the monotonous behaviour of ε p within one group over different periods we can state that also here electron will be transferred from the heavier to the lighter B element. e.g. SrNbO 3 will electron dope SrVO 3 .
• For the more general case of ABO 3 /AB ′ O 3 one has to consider precise values to make predictions. For instance, SrIrO 3 should be able to intrinsically dope SrMnO 3 at an interface, while SrRuO 3 cannot dope SrTiO 3 .
In order to strengthen the first claim of this list we extend our simulations with a calculation of a SrTiO 3 /SrVO 3 interface for which we have a ∆ε p = −0.37eV. Indeed, consistent with our arguments we see from Fig. 5 that practically no charge transfer occurs. The layer resolved partial density of states shows that basically all d electron remains in the SrVO 3 slab and the oxygen 2p states are rather well aligned. [73] At this point it might be asked if our analysis can be applied also to periodic stacks which are further away from the limit of a single interface than the so far considered 5/5 stacks. In order to answer this question we performed several simulations of (SrBO 3 ) 1 /(SrB ′ O 3 ) 1 heterostructures and summarize the results in Tab. I. Remarkably, we find that in all cases the charge transfer can been anticipated in direction and relative amplitude with the data from Fig. 4. This is remarkable since it is not a prior clear that a qualitative argument made for the interface between two bulk materials still holds for a periodic stack with strong quantum confinement effects [51] and lattice relaxations at the interfaces. They are fully taken into account in the heterostructure calculations but do not spoil the predictive capabilities from bulk calculations neither. Looking closer at the values in Tab. I reveals a remarkable consistency between ∆ε p and ∆n e . We have already seen in the example of the SrTiO 3 /SrVO 3 interface that in order to dope electron into Ti or V 3d states, 4d or 5d TM components have  I: Sign and trends of electron transfer in (SrBO3)1/(SrB ′ O3)1 heterostructures. We list the energies of oxygen 2p states resolved by BO2 (ε i p (BO2)), AO (ε i p (AO)) and B ′ O2 layers (ε i p (B ′ O2)) with respect to the Fermi energy as well as the induced electron transfer ∆ne from B to B ′ sites. ∆εp taken from Fig. 4 is also listed. to be considered since a positive ∆ε p is needed and, as we can see from the stacks in the first four rows ∆n e grows monotonously with ∆ε p . The same is true for the opposite case (reported in the lower four rows) where an increased negative ∆ε p drives an increased transfer from the vanadium 3d states to heavier elements like Cr, Mn, Fe, and Co in the 3d series. Moreover, we can learn from the observation ∆ε p > ε i p (B) − ε i p (B ′ ), that for the energy balance (Eq. 2) besides ∆φ, ∆ε DOS and ∆ε valence contribute significantly.
Before the end of this section where we have focused mostly on interfaces of the form SrBO 3 /SrB ′ O 3 let us make some remarks about the generalization to ABO 3 /A ′ BO 3 and the most general ABO 3 /A ′ B ′ O 3 interfaces. In Fig. 4 we have already shown data for LaBO 3 in comparison to the SrBO 3 series. If we consider the same element on the B site our scheme is directly applicable as before. More specifically, ε p of a LaBO 3 perovskite is always lower than in the corresponding SrBO 3 so that at a LaBO 3 /SrBO 3 interface the electron is always transferred from LaBO 3 to SrBO 3 which is consistent with experiments, e.g. for the case of LaTiO 3 /SrTiO 3 [9,52] or LaMnO 3 /SrMnO 3 [13,16].
Additional complications arise in the most general ABO 3 /A ′ B ′ O 3 setup where we have two qualitatively different interface configurations which might be either AO- We might actually consider the realistic case of a SrTiO 3 /LaMnO 3 interface [14,15,24,53]. Starting with the interface TiO 2 -LaO we assume to have a unit of LaTiO 3 linked with SrTiO 3 on the one side and LaMnO 3 on the other -so we have broken the problem down to a SrTiO 3 /LaTiO 3 and a LaTiO 3 /LaMnO 3 interface which we know how to handle. As a result, by considering our reference data, we would arrive at a prediction of charge transfer at the interface from the Ti states of the central LaTiO 3 part to its neighbors. The opposite is true for the other possible interface SrO-MnO 2 , and in this case a decomposition as before would yield the conclusion that no charge transfer will occur. This line of argument is in agreement with experiments on SrTiO 3 /LaMnO 3 where electron transferred has been observed for the LaO-TiO 2 terminated interface [15]. According to our claim, the other interface structure, SrO-MnO 2 , which experimentally can be realized by inserting a monolayer of SrMnO 3 , should not allow for such charge transfer. Please note we did not consider the contribution from polar discontinuity [42,54], which might induce complexity such as oxygen vacancies and other defects.
We conclude our first main section with the claim that charge transfer at the interfaces of perovskite heterostructures can be qualitatively predicted by comparison of bulk qualities. It is not even necessary to perform a numerical simulation of the interface in order to anticipate the direction and relative magnitudes of charge transfer.

IV. APPLICATIONS AND PREDICTIONS
In the second part of our paper we highlight two applications of our prediction scheme starting with the controlled doping of SrTiO 3 (see IV A) drawing also a parallel to heterogeneous semiconductor devices. We then turn to magnetic transitions in manganite heterostructures triggered by controlled charge transfer (see IV B) explaining past theoretical and experimental results in the context of our unifying concept which we then complement by predictions on how to improve external control of such transitions.  Fig. 3 but now including an additional buffer layer between SrTiO3 and SrNbO3. The unit cell of this three-component symmetric heterostructure has the form (SrTiO3)5/(SrZrO3)2/(SrNbO3)1/(SrZrO3)2. As can be seen the electron transfer from Nb to Ti remains intact even after inclusion of the buffer layer excluding a pivotal role of microscopic details in the orbital degrees of freedom at the SrTiO3/SrNbO3 interface.

A. Electron doping in SrTiO3 heterostructure
As a first application we chose to highlight how to control doping of one of the most widely spread and used TM oxide compounds SrTiO 3 . So far SrTiO 3 has been doped by various 3d TM oxides e.g. LaAlO 3 [10] and LaTiO 3 [9] to produce a two dimensional electron gas but there is no known SrBO 3 with B from the 3d series. With the data from Fig. 4 we have already given the reason why this is not surprising and, in fact, impossible. The very naive guess that electron from a more filled 3d element like, e.g. vanadium would spill into the empty Ti 3d states is prohibited by the energy balance that originates in the oxygen states continuity condition (see Fig. 5). So, SrVO 3 is identified as a bad candidate for doping SrTiO 3 . Instead we have seen in Fig. 3 that SrNbO 3 is a much more promising component for that purpose. In (SrTiO 3 ) 5 /(SrNbO 3 ) 5 the continuity of oxygen 2p states drives a sizable charge transfer. What we have not discussed yet, however, is the question if microscopic details of orbital degrees of freedom at the interface, which are not included in our scheme, are equally or even more important for the charge transfer than the considered energetics. In order to shed light on this issue we extend our calculations with the inclusion of an insulating buffer layer which will allow for a spatial separation of Ti and Nb d-states. The choice of a perovskite buffer layer is actually quite straight forward in the light of our reference data and we chose SrZrO 3 for this purpose which will remain band insulating in the three component heterostructure. In Fig. 5 we show the result for a symmetric (SrTiO 3 ) 5 /(SrZrO 3 ) 2 /(SrNbO 3 ) 1 /(SrZrO 3 ) 2 superlattice which is experimentally realizable [21,[55][56][57].
Here we see another confirmation of our simple argument: while the buffer layer remains band insulating we still observe a transfer of electron from Nb to Ti d-states even though they are spatially separated. At this point we might refer to an analogous technique in semiconductor setups where the doping impurities are spatially separated from the charge carriers. A concept which is commonly known as "modulation doping" and widely applied in so called MODFET setups [58,59]. Besides the shown results we have checked the dependence of the charge transfer amplitude as a function of the thickness of the buffer layer but were unable to find significant trends up to supercells that include buffers of 5 bulk unit cells. In fact modulation doped oxides recently started to attract some theoretical [43] and experimental [21,53,57] researchers.

B. AFM to FM transition in SrMnO3 heterostructures
After having exemplified how our oxygen energetics argument can be used to anticipate charge transfer in the case of SrTiO 3 based heterostructures we now take one step further by considering manganite heterostructures. Here the goal is similar yet more ambitious since a provoked charge transfer in SrMnO 3 setups should have a sensitive impact on magnetic transitions. Starting point for us is bulk SrMnO 3 which is found to have a G-type antiferromagnetic ground state. Our goal is to find an appropriate heterostructure in which doping into Mn dstates triggers a transition to a ferromagnetic ground state -see review papers [60][61][62][63] and references therein. From our reference data we see that it should actually be rather easy to provoke electron transfer into Mn dstates considering the comparatively large value of ε p for Mn. Indeed it turns out that by employing our predictive scheme we can confirm experimentally known routes to charge-transfer induced magnetic transition and classify possible heterostructure components to tune more or less charge transfer.
We carried out calculations for 1/1 and 2/2 layered superlattice (SrMnO 3 ) 1 /(SrBO 3 ) 1 (considering also a GdFeO 3 structural distortion since magnetism can be strongly coupled to the lattice) for four different species of B site elements. The results are summarized in Tab. II where we report the size of the magnetic moment on the B and the Mn site of the respective compound. We have sorted the table with ascending electron transfer. As anticipated choosing SrIrO 3 as interfacing partner will  [44,45]. We can further predict which components would yield a much more significant electron transfer: Candidates are easily nominated from Fig. 4 and to this end we select SrNbO 3 , which is recently grown experimentally [40], as well as SrTaO 3 -our most potent electron donor for oxide heterostructures. The selected components perform as predicted in the numerical simulations and we observe a large charge transfer pushing the (SrMnO 3 ) 1,2 /(SrNbO 3 ) 1,2 and (SrMnO 3 ) 1,2 /(SrTaO 3 ) 1,2 into a ferromagnetic metallic ground state with ordered Mn moments up to 3.74µ B . [74] In order to underline the data given in Tab. II we plot the resolved single particle density of states in Fig. 7 -this time, however, for magnetic DFT calculations. In the upper panels of the figure we start as a reference with the bulk results for the gapped antiferromagnetic DOS of SrMnO 3 and metallic and paramagnetic SrTaO 3 . In the lower two panels one can nicely observe how in the (SrMnO 3 ) 1 /(SrTaO 3 ) 1 heterostructure almost all Ta d electron is depleted in the MnO 2 layers yielding a metallic ferromagnetic ground state with significant filling of the Mn 3d-e g states.

V. SUMMARY AND OUTLOOK
In summary we have presented a simple prediction scheme for the tuning of charge transfer in oxide heterostructures. By employing arguments based on the requirement that the p states of the oxygen network in a heterostructure need to be continuous, we were able to utilize reference data from bulk calculations in Fig. 4 to predict the direction and relative amplitude of charge ! " # FIG. 7: Plot of the density of states with the usual color/marker convention (including now also 3d-eg states plotted in blue). We show results for magnetically ordered calculations starting with bulk results in the upper two panels. SrMnO3 is G-type antiferromagnetic ordered and SrTaO3 paramagnetic. In the lower two panels we plot the data for the two layers in a (SrMnO3)1/(SrTaO3)1 heterostructure including a GdFeO3 distortion. We see the dramatic influence of the electron transfer from Ta to Mn and the induction of ferromagnetic ordered metallic MnO2 layers.
transfer between layers in oxide heterostructures. Remarkably this scheme remains in tact even for layered compounds down to a 1/1 geometry. As a proof of principle we provided simulations for electron doping of SrTiO 3 in heterogeneous arrays simultaneously confirming experimentally known trends and offering suggestions to material growers which are the most promising components to control the low energy electronic structure. In a second application part we have exemplified, with the help of SrMnO 3 based heterostructures, how controlled charge transfer can be systematically exploited in order to trigger magnetic phase transitions. The shown examples are only a taste of what can be predicted with the unifying concepts we presented and we hope that experimental colleagues will be inspired by our work to create new materials and devices. This includes specifically also the possibility to couple/entangle -via charge transferphysics of 3d and 5d TM oxides [25,64] which, each on their own, are governed by very different energy scales. One might try, for instance, to induce spin-orbit coupling effects in 3d systems, e.g. in the case of SrMnO 3 /SrTaO 3 where one might find a large magnetic anisotropy energy and antisymmetric exchange on the magnetic Mn sites. One might even target the realization of yet more ex-otic skyrmion, spin-spiral, and topological phases. On the computational side we already started a hunt for the best possible candidates to be manipulated towards exciting new ground states.
In order to give an outlook for future theory and computational development we state once more that for certain cases the application of our scheme is not straight forward and needs to be extended. One of these cases is the interfacing of compounds that are ferromagnetic ordered in bulk. Another issue that should be mentioned is the change of ε p due to correlation effects: Given that the relevant effects we discussed have a characteristic energy scale of a few eV, shifts due to single particle self energies might have to be included instead of the simplified ∆ε dp contribution in Eq. 2. A very clear example where this will be the case is the usage of charge transfer insulators, typically found in late 3d TM oxides e.g.
cuprates. An extension to include such correlation effects is very desirable since the sensitivity of correlated electron systems would add even more possibilities to generate novel functionality like, e.g. the recently suggested Mott transistor [65]. Moreover, focusing more on material trends the presented initial study did not extensively discuss how to use the thickness of periodic stacks or buffer layers to quantitatively tune charge transfer and how to interface non-perovskite oxides. The oxygen continuity condition, or adaptations thereof, should be valid not only in the complex oxides with perovskite structures, but also in other lattice structures like anatase, pyrochlores, spinel, Ruddlesden-Popper and double perovskites [66][67][68] which are structurally equal to the 1/1 interfaces along a (111) direction. for benchmark calculations including effects of cation exchange, orthorhombic distortion, strain, and ferromagnetic ordering.