Can we prevent the "dead layer" formation at manganite interfaces?
Ayşegül Begüm Koçak, Julien Varignon, Sébastien Lemal, Philippe Ghosez, Marie-Bernadette Lepetit
CCan we prevent the “dead layer” formation at manganite interfaces?
Ay¸seg¨ul Beg¨um Ko¸cak,
1, 2, 3, 4
Julien Varignon, S´ebastien Lemal, Philippe Ghosez, and Marie-Bernadette Lepetit
1, 4 Institut N´eel, CNRS UPR 2940, Grenoble, France Institut National Polytechnique de Grenoble, France Theoretical Materials Physics, Q-Mat, CESAM,Universit´e de Li`ege, 4000, Sart Tilman, Belgium Institut Laue Langevin, Grenoble, France
The present work theoretically studies the possibility to hinder the formation of a “dead” layerat the interfaces in manganite superlattices. We showed that this goal can be reached by usingalkaline-earth simple oxides as alternating layers in very thin superlattices. Indeed, such alternatinglayer promotes the contraction of manganite layers at the interfaces and d x − y preferred e g orbitaloccupancy, while Boltzman’s transport calculations show an increase in conductivity. This resulthold for different manganites, different alkaline-earth simple oxides as well as different thicknessesof the two layers. PACS numbers:
Interfaces between perovskite oxides have been thesubject of intense research over the last decade. Thefirst reason is the outstanding properties discovered insuch interfaces ; let us only cite the superconductivitydiscovered at the interface between two band insulatorssuch as SrTiO (STO) and LaAlO [1]. Another reason isthe potential applications of such properties. Manganite-based devices using tunnel junctions are actively stud-ied for the design of spin valves or spin injectors. Suchjunctions present a high degree of spin polarization androbust magnetic properties at the interface between themanganite and the barrier. The main problem that hashindered the development of the such devices is the for-mation of a so-called ”dead-layer” [2, 3], below a criticaldistance to the interface. In such layers the magneto-transport properties are strongly depressed. The presentpaper proposes a possible solution to this critical prob-lem with not only a set of criteria to design appropriatebarriers, but also a detailed study of a realistic example.Manganites are known to be ferromagnetic metals overa large range of their phase diagram, and to presentcolossal magneto-resistance effects. Indeed, the recordvalue is of over 14 orders of magnitude in resistivitychange under magnetic field [4]). Their transport andmagnetic properties are controlled by small atomic dis-placements, allowing potential pathways to tune theirproperties using interfaces in very thin films and hetero-structures (see for instance Ref. 5–8, and Ref. 9 fora recent review). Unfortunately, a loss of magnetiza-tion and metalicity, also called “dead layer”, is observedover a thickness of few unit cells (u.c.) at the interfaceof ferromagnetic manganites, such as La / Sr / MnO (LSMO) or La / Ca / MnO (LCMO), and most per-ovskite substrates or combined layers [2, 3]. This “deadlayer” phenomenon has been the subject of many inter-pretations such as (i) homogeneous substrate strain [10],(ii) electronic and/or chemical phase separation [11] re-lated to structural inhomogeneities at the interface [12] or uncontrolled stoichiometry [13], (iii) manganese e g or-bital reconstruction that may induce C-type antiferro-magnetism [14, 15] and can be attributed to a weak de-localization at the interfaces [16]. The first hypothesisis incoherent with the relaxation rate of the substratestrain, shown to be larger than 1000 ˚A [11], while a dras-tic change in the transport properties [3, 13, 14] is ob-served at the STO interface, for films thinner then a fewu.c. In this work we would like to work with perfectinterfaces, we will thus not consider the consequences ofinperfectly grown interfaces and focus on the last hypoth-esis of enhanced d z occupancy at the interface. Such abehavior was attributed to an energetic lowering of the d z orbital over the d x − y at the interface, due to a weakdelocalization of the former through the interface [16].Ferromagnetic manganites (and related hetero-structures) of general formula La − x A x MnO (A a diva-lent cation, x in the approximate range 0 . < x < . perovskite structure [22, 23], withthe Mn occupying the B site. The Mn atom is thus inan octahedron environment, which induces an energeticsplitting of the Mn 3 d orbitals into a t g — threefolddegenerated — low energy set, and a e g — twofolddegenerated — high energy one (ideal case). More-over, the Mn atoms are in a mixed valence ionic state(Mn ), with a 3 d − x high spin orbital occupancy. As aresult, the two e g orbitals, d z and d x − y , are partiallyoccupied by 1 − x electron which may delocalize (the d z electrons along the c direction and the d x − y onesin the ( a , b ) plane). This delocalization is energeticallyvery favorable, but will only occur when the spins ofneighboring Mn ions are ferromagnetically aligned. Insuch a case the delocalization energy gain overcomesthe antiferromagnetic exchange interaction betweenlocalized ions, and imposes a ferromagnetic ordering(double exchange mechanism) [17].In bulk materials the e g electrons are shared betweenthe two orbitals with equivalent occupancies. It results a r X i v : . [ c ond - m a t . m t r l - s c i ] J un in magnetic ordering and delocalization occurring in alldirections. In very thin films, however, the out-of-planedirection, c , spans only over a few u.c., and thus the ther-modynamic limit is only obtained in the in-plane, ( a , b ),directions. It is thus of crucial importance for the mag-netic and transport properties to maximize the d x − y orbital occupancy, responsible for the in-plane delocal-ization and thus magnetic and transport properties.When an interface “dead layer” is present, the d z electrons of the manganite delocalize in the empty d z orbitals of the substrate or of the alternating layer (typ-ically SrTiO , BaTiO or similar compounds). Even ifweak (about one or two tenth of an electron [16]), at theinterfaces this delocalization energetically favors the d z orbital occupancy over the d x − y one. It results in aJahn-Teller distortion of the MnO octahedron, with asplitting of the e g degeneracy [18] ( ε z < ε x − y ). Thein-plane delocalization is thus hindered (at least by car-rier density reduction). Consequently, the characteristicsof the “dead layer” phenomenon appear, (reduced fer-romagnetic spin arrangement and conductivity [3, 19]).Such a Jahn-Teller distortion induces a small increase ofthe c parameter [16, 20], that can be fully attributed tothe delocalization mechanism at the interfaces, as straineffects tend to reduce c . Indeed, on a STO substrate,manganites such as LSMO or LCMO are under ten-sile strain ( a STO = 3 . a LSMO = 3 . a LCMO = 3 . c . In orderto prevent the formation of a “dead layer”, one thus needsto interface the manganite with an alternating layer ma-terial hindering the delocalization between the differentlayers.The purpose of this work is thus to investigate, usingfirst-principle calculations, possible candidates for suchalternating layers. We will focus on LSMO-based hetero-structures over a SrTiO substrate.The first idea that may come to mind, is to use alter-nating layers with totally-filled d -shells, and a tetragonalstructure. Indeed, the latter was shown to be crucial inorder to prevent the rhombohedral distortion in the man-ganite layer, but rather favor a tetragonal one [18]. Let usremember that a tetragonal distortion, associated with a c parameter contraction, allows an enhancement of the d x − y orbital occupancy and thus of the desired proper-ties. One could therefore think of materials such as theBaSnO compound. Unfortunately, our test calculationson such hetero-structures exhibited a weak electron delo-calization, from the Sn filled d z orbitals towards the Mnpartially occupied ones, very similar to what we observedin our calculations on BTO/LSMO [18] or STO/LSMOheterostructures (that exhibit a JT distortion of ∼ .
04 inthe interface layer, a dominant d z occupancy and a weak d z delocalization in the Ti orbitals.). This delocaliza-tion is associated with an increase of the Mn d z orbitaloccupancy, and a Jahn-Teller distortion. One can thus expect such hetero-structures to exhibit a “dead layer”phenomenon.Another way to prevent the inter-layers delocalizationof the LSMO Mn d z orbitals is to totally avoid d or-bitals, in the alternating layer material. The requirementfor the alternating layer should thus be i) no d orbitals,ii) a tetragonal or cubic structure, and iii) a compoundallowing perfect epitaxy with the manganite layer. Ful-filling all those requirements are the simple alkaline-earthoxides, and more specifically the BaO compound. In-deed, the mismatch between BaO and LSMO is only of0.7%, and between BaO and the STO substrate 0.3%.Of course the epitaxy imposes a BaO unit cell ( F m ¯3 m cubic group [24]) rotated in-plane by an angle of 45 ◦ [25],compared to the manganite unit cell (see figure 1).We thus studied, using first-principles calculations,[La / Sr / MnO ] n [BaO] p superlattices on a STO sub-strate, alternating a few u.c. of manganite and of simpleBarium oxide. Superlattices with other alkaline-earth ox-ides were also investigated to see whether the results areresilient to a change in the alternating layer, despite theirunrealistic strain values [26].We performed geometry optimizations for the differentsuperlattices, using periodic density functional calcula-tions. Since epitaxial films normally follow the structureof the substrate, we imposed to our optimizations to keepthe substrate in-plane lattice constants (optimized usingthe same computational parameters). The alkaline-earthoxides are strong insulators, while the manganite layersare expected to be metallic, one thus needs to choose afunctional that properly positions the metal Fermi levelwith respect to the insulator gap. We used the B1WChybrid functional [27], that was specifically designed toproperly treat both gaps and weak distortions, two keycomponents in the present systems. The calculationswere done using the CRYSTAL package [28], with thebasis sets and effective core pseudopotentials (ECP) ofref. 29. As the LSMO A-site cations disorder is difficultto treat within periodic calculations, we run a set of cal-culations with different orderings, using true atoms oraverage ones. The average ions were modeled as in ref-erence 18, that is using ordered cations ECPs but withaveraged effective nuclear charges. The effect of these av-erage charges is to hinder possible electronic localizationinduced by the cation orders. Unless specified, we willonly present results that are independent of the cationorder or model. Finally we used a √ a × √ a × c unitcell in order to allow octahedra rotations and in-planeantiferromagnetic (AFM) ordering (see figure 1).We first studied the [La / Sr / MnO ] [BaO] super-lattice, using all 6 cations models and different magneticorders ; that is ferromagnetic (FM), A-type AFM (in-plane FM and out-of-plane AFM), C-type AFM (in-planeAFM and out-of-plane FM) and G-type AFM (in-planeand out-of-plane AFM).Notice that in what follows we consider superlattices FIG. 1: (color online) Schematic representation of the[La / Sr / MnO ] [AO] and [La / Sr / MnO ] [AO] super-lattices. with stoichiometric layers yielding, in most cases, asym-metric interfaces as it would be in real heterostructures.As it will be discussed in the last Section, this has how-ever no direct impact on our conclusions.Our calculations showed that the magnetic groundstate always imposes a FM in-plane order and a to-tal net magnetic moment. The two out-of-plane mag-netic arrangements are quasi-degenerate within DFT er-ror bars. Indeed, the energy difference per LSMO u.c.(or equivalently per Mn), between FM and A-type AFMorders, is in average 8 meV/u.c., with a mean devia-tion of 16 meV. This is smaller than the room tempera-ture ( k B T ∼
25 meV). Whether the DFT ground stateis the FM or the A-type AFM configuration dependson the specific cation ordering. The in-plane AFM or-dered states are much higher in energy, ranging between130 meV and 210 meV above the ground states.Figure 2 pictures the statistics of both the Jahn-Tellerdistortion (JTd) (measured as d OO /a −
1, with d OO the out-of-plane O-(Mn)-O distance) and c/a ( c beingthe perovskite A-sites distances) as a function of the e g orbitals-occupancies ratio. Results are given for eachmono-layer and the two possible ground states. Beforeanalyzing the results let us keep in mind that the two in-terface layers are non equivalent, since one corresponds toa (La/Sr,O)–(BaO) interface and the other to a (MnO )–(BaO) interface.One sees immediately that all three layers are com-pressed along the c direction, except for the central layerin two AFM calculations. Similarly, the Mn-octahedraof the interface mono-layers are compressed along c anddisplay a dominant d x − y orbital occupancy, favorableto the searched magnetic semi-metal behavior. Onlythe central monolayer exhibits sometimes an elongationof the Mn-octahedra, with a dominant d z occupancy.This behavior is the exact opposite of what is found in -0.06 -0.03 0 0.03 0.06 0.09 c/a-1 d x - y d z -0.06 -0.03 0 0.03 0.06 0.09 Jahn-Teller distortion d x - y d z FIG. 2: (color online) η ( d x − y ) /η ( d z ) ratio of the d x − y and d z orbitals M¨ulliken occupancies in each mono-layer asa function of the Jahn-Teller distortion (JTd) (measured as d OO /a −
1, with d OO the out-of-plane O-(Mn)-O distance) andof c/a ( c being measured as the perovskite A-sites distance).Red and pink symbols refer to the interfacial mono-layers,blue symbols to the central ones. Diamonds are for the FMorder and stars for the A-type AFM one. The green dashedsquares show the experimental values of LSMO over STO for6 m.l. thin films exhibiting a dead layer. The Jahn-Tellerdistortion and c/a ratios are extracted from the cumulativedisplacements in Ref. 20 and the η ( d x − y ) /η ( d z ) ratio isextracted from linear dichroism experiments of Ref. 14. BulkLSMO corresponds to the cross point between the dashedlines. [LSMO] [BTO] superlattices [18, 30], in which the inter-face layers are elongated with a dominant d z occupancy,responsible for the dead layer behavior. One should alsopoint out that octahedra rotations are essentially negli-gible in these hetero-structures (rotation values less than1 ◦ ).The fact that the FM and A-type AFM orders arefound so close in energy tells us that, in real systemssuch superlattices may present one or the other spin ar-rangement as the ground state, according to the spe-cific cation disorder. In any way at room temperatureboth state can be expected to be occupied with similarprobabilities. Our results thus show that such super-lattices should display a net total magnetization (even-though reduced compared to the FM state), and moreimportantly a large magnetic moment for the interfacelayers. Concerning the transport properties we com-puted the conductivity tensor for the [LSMO] [BaO] and the [LSMO] [BaTiO ] systems using the Boltz-trap [31] code. Figure 3 clearly shows a strong increasein the in-plane conductivity for the system with BaOalternating layers. The dominant d x − y orbital occu-pancy at the interfaces, supported by the conductivitycalculations, lead us to think that using simple oxides asalternating layers is indeed a promising way to preventthe “dead layer” phenomenon. FIG. 3: Transport calculations on [LSMO] [BaO] and[LSMO] [BaTiO ] systems. The dotted line represent theFermi level. One can however wonder if this conclusion will remainvalid if one increases the size of the manganite layer. Inorder to check this point we increased the size of theLSMO layer to 6 mono-layers, and performed the calcu-lations for one typical cation configuration. To keep thiscalculation to a reasonable size, we needed to simulta-neously decrease the BaO layer thickness. We thus firstchecked whether such a reduction would affect the re-sults. For this purpose we run test calculations on thepreceding superlattice with only two mono-layers of BaO( i.e. on [LSMO] [BaO] ). These calculations showed asimilar behavior to the calculations with 6 BaO mono-layers, and thus validate 2 BaO mono-layers model.Our calculations on the [LSMO] [BaO] superlatticesshowed that the ground state again imposes in-plane fer-romagnetism. The spin arrangement in the c directiondisplays a ↑↑↓↓↑↑ pattern (“ uudduu ”) with a total netmagnetization for the system. This ground state is againvery close in energy to the FM state and the A-type AFMstate. The latter does not however correspond to a fullAFM state, since it exhibits a non null net total magne-tization of about 1 /
10 of an electron per Mn atom.The dominant e g orbital occupancy in the differentLSMO mono-layers is found qualitatively independent ofthe out-of–plane spin ordering (see table I for an exam-ple). Indeed, as in the [LSMO] [BaO] calculations, themono-layers at the interfaces are contracted and stronglydominated by the d x − y orbital occupancy. In fact onlythe inner most mono-layer is still elongated and domi-nated by d z orbital occupancy. As it can be seen inTable I, the Mn magnetic moments and the amplitudeof the Jahn-Teller distortion exhibit a strong correlation.The Mn-octahedra in the inner most mono-layer exhibita strong elongation and the largest Mn magnetic mo-ment. This specificity of the inner most mono-layer isresponsible for the non-vanishing total magnetization in the A-type AFM state. These results show that, when in- LSMO e g orb. spin pop. c/a − µ Mn mono-layer d x − y d z -0.46 -0.25 -0.021 -0.038 -3.454 -0.30 -0.74 0.013 0.070 -3.895 e g orbitals, c/a ratio, JTd (Jahn-Teller distortion) and µ Mn (Mn magneticmoment) in the [La / Sr / MnO ] [BaO] ground state of onetypical cation order. Values for the two other low energystates (FM and A-type AFM) are qualitatively equivalent. creasing the thickness of the LSMO layer, one essentiallyincreases the thickness of the interface layers and not ofthe central one. The former being contracted along c anddominated by d x − y orbital occupancy, it confirms thatthe use of BaO alternating layers hinder the formation ofa “dead layer” at the LSMO interfaces.Finally we checked whether this result is resilient to achange in the simple oxide and manganite compounds.We thus performed a set of calculations using BaO, SrOand MgO as alternating layers, and LSMO or LBMO asmanganite layers ([La / A / MnO ] [BO] ), for a typi-cal cation disorder model [26]. Table II summarizes the e g orbital occupancies for those calculations. One may LAMO e g orb. spin pop.mono-layer d x − y d z P /mmm ) 2 0.24 P /mmm ) 2 0.40 e g orbitalsin the [La / A / MnO ] [BO] ground state (A=Sr, Ba ;B=Ba, Sr, Mg). The shown example was chosen as the cationordering associated with the lowest ground state energy. notice that the (LBMO) (BaO) and (LSMO) (SrO) su-perlattices have in theory equivalent interfaces, unlike allthe other superlattices we studied. One sees in table IIthat this symmetry is kept in the (LSMO) (SrO) su-perlattice. Indeed, the two calculations with and with-out imposed symmetry yield equivalent results withinerror bars. For the (LBMO) (BaO) superlattice how-ever, this is not the case. Indeed, a spontaneous sym-metry breaking occurs along the c axis, associated witha small energetic stabilization (37 meV (cid:39)
430 K) perLBMO u.c. This induces a symmetry breaking in the e g orbitals occupancies as can be seen in table II. Never-theless, all manganite interface mono-layers are favoringa d x − y occupancy over a d z one, as was the case for the(LSMO) n (BaO) p compounds. This result thus seems toremain valid independently of the manganite compoundand of the simple oxide chosen for the alternating layer.As a conclusion one may recall that thin films andsuperlattices of [La / A / MnO ] (A=Sr, Ca) manganitecompounds, over an SrTiO substrate, have been exten-sively studied in the hope to find a good material for elec-tronic and spintronics applications. Indeed, on such anSTO, the LSMO is under tensile strain, so one is entitledto expect that the elastic energy will favor a contractionof the mono-layers along the c direction. Due to the de-generacy of the e g orbitals, such a contraction would haveenhanced the occupation of the d x − y over the d z andthus the ferromagnetic and metallic behavior through thedouble exchange mechanism. Unfortunately the forma-tion of a non-magnetic and insulating layer (called “deadlayer”) at the interface prevents to reach this goal. This“dead layer” originates in a weak delocalization of the Mn d z orbitals in the empty Ti ones. The energy gain in thisphenomenon overvalues the elastic energy loss [16]. As aconsequence a preferred occupancy of the Mn d z orbitalsassociated with an elongation (along the c direction) ofthe interface mono-layers takes place.In this paper, we theoretically studied different possi-bilities to hinder the interface delocalization using suit-able alternating layers in superlattices. Our first princi-ple calculations show that superlattices alternating man-ganite and alkaline-earth simple oxides efficiently preventinter-layer delocalization, promote mono-layers contrac-tion at the interfaces and a preferred d x − y occupancyover the d z one, and finally strongly increase the in-plane conductivity. Our studies show that this resultshould hold for different manganite and alternating layerthicknesses. One can thus reasonably expect that suchsuperlattices may present the long searched magnetic andelectric properties. Acknowledgments
We thank the IDRIS (project n ◦ ◦ ◦ [1] A. Ohtomo and H. Y. Hwang, Nature (London) ,423 (2004) ; A. Brinkman, M. Huijben, M. van Zalk, J.Huijben, U. Zeitler, J. C. Maan, W. G. van der Wiel,G. Rijnders, D. H. A. Blank, and H. Hilgenkamp, Nat.Mater. , 493 (2007) ; A. D. Caviglia, S. Gariglio, N.Reyren, D. Jaccard, T. Schneider, M. Gabay, S. Thiel,G. Hammerl, J. Mannhart and J.-M. Triscone, Nature , 624 (2008).[2] H. Yamada, Y. Ogawa, Y.H. Sato, M. Kawasaki, H.Akoh, Y. Tokura, Science, , 646 (2004).[3] M. Huijben, L. W. Martin, Y.-H. Chu, M. B. Holcomb,P. Yu, G. Rijnders, D. H. A. Blank, R. Ramesh, Phys.Rev B , 094413 (2008).[4] D. Saurel, C. Simon, A. Pautrat, C. Martin, C. Dewhurstand A. Brˆulet, Phys. Rev. B 82 , 054427 (2010).[5] Y. W. Yin, J. D. Burton , Y-M. Kim, A. Y. Borisevich,S. J. Pennycook, S. M. Yang, T. W. Noh, A. Gruverman,X. G. Li, E. Y. Tsymbal and Qi Li, Nature Materials ,397 (2013).[6] J. D. Burton and E. Y. Tsymbal, Phys. Rev. B 80 ,174406 (2009) ; ibid. Phys. Rev. Letters , 157203(2011).[7] H. Chen and S. Ismail-Beigi, Phys. Rev.
B 86 , 024433(2012).[8] See for instance : C. Thiele, K. Drr, O. Bilani, J. Rdeland L. Schultz, Phys. Rev.
B 75 , 054408 (2007) ; C. A.F. Vaz, J. Hoffman, Y. Segal, M. S. J. Marshall, J. W.Reiner, Z. Zhang, R. D. Grober, F. J. Walker, and C. H.Ahn, J. Appl. Phys. , 07D905 (2011).[9] C. A. F. Vaz, F. J. Walker, C. H. Ahn and S. Ismail-Beigi,J. Phys.: Condens. Matter B 68 , 134444 (2003).[11] I. C. Infante, F. S´anchez, J. Fontcuberta, M. Wojcik, E.Jedryka, S. Estrad´e, F. Peir´o, J. Arbiol, V. Laukhin andJ. P. Espin´os, Phys. Rev.
B 76 , 224415 (2007).[12] M. Bibes, Ll. Balcells, S. Valencia, J. Fontcuberta, M.Wojcik, E. Jedryka, and S. Nadolski, Phys. Rev. Letters , 067210 (2001).[13] L. F. Kourkoutis, J. H. Song, H. Y. Hwang and D. A.Muller, PNAS , 11682 (2010) ; J. A. Mundy, Y.Hikita, T. Hidaka, T. Yajima, T. Higuchi, H. Y. Hwang,D. A. Muller and L. F. Kourkoutis, Nat. Commun. ,3464 (2014).[14] A. Tebano, C. Aruta, S. Sanna, P. G. Medaglia, G.Balestrino, A. A. Sidorenko, R. DE Renzi, G. Ghir-inghelli, L. Braicovich, V. Bisogni, N. B. Brookes, Phys.Rev. Letters , 137401 (2008).[15] A. Tebano, A. Orsini, P. G. Medaglia, D. Di Castro, G.Balestrino, B. Freelon, A. Bostwick, Young Jun Chang,G. Gaines, E. Rotenberg and N. L. Saini, Phys. Rev. B82 , 214407 (2010).[16] M.-B. Lepetit, B. Mercey and C. Simon, Phys. Rev. Let-ters , 087202 (2012). [17] C. Zener, Phys. Rev. , 403 (1951).[18] A. Sadoc, B. Mercey, C. Simon, D. Grebille, W. Prel-lier and M.-B. Lepetit, Phys. Rev. Letters , 046804(2010).[19] I. Pallecchi, L. Pellegrino, E. Bellingeri, A. S. Siri, D.Marr, A. Tebano and G. Balestrino, Phys. Rev. B 78 ,024411 (2008).[20] R. Herger, P. R. Willmott, C. M. Schlep¨uz, M. Bj¨ock, S.A. Pauli, D. Martoccia, B. D. Patterson, D. Kumah, R.Clarke, Y. Yacoby, M. D¨obeli, Phys. Rev. B , 085401(2008).[21] G.M. Meyer, R.J. Nelmes, J. Hutton, Ferroelectrics ,461 (1978).[22] L. Pinsard, J. Rodriguez Carvajal, A. Revcolevschi, J.Alloys & Compounds , 152 (1997) ; P.G. Radaelli,G. Iannone, M. Marezio, H.Y. Hwang, S.-W. Cheong,J.D. Jorgensen, D.N. Argyriou, Phys. Rev. B 56 , 8265(1997).[23] J. Blasco et al , J. Phys.: Cond. Matter , 7427 (1996).[24] R. J. Zollweg, Phys. Rev. , 671 (1955) ; D. Taylor,Trans. J. British Ceram. Soc. , 5 (1984).[25] J. Junquera, M. Zimmer, P. Ordejon and Ph. Ghosez,Phys. Rev. B, , 155327 (2003) ; E. Bousquet, J. Jun-quera and Ph. Ghosez, Phys. Rev. B, , 045426 (2010).[26] Although the lattice mismatch of the LSMO and LBMO with MgO (and even SrO) might be far too large for suchsuperlattices to be realized in practice, this constitues avaluable computer experiment to illustrate the generalityof our results.[27] D. I. Bilc, R. Orlando, R. Shaltaf, G. M. Rignanese, J.I˜niguez and P. Ghosez, Phys. Rev. B, , 165107 (2008).[28] R. Dovesi et al , V. R. Saunders, C. Roetti, R. Orlando, C.M. Zicovich-Wilson, F. Pascale, B. Civalleri, K. Doll, N.M. Harrison, I. J. Bush, P. DArco, M. Llunell, M. Causand Y. Nol CRYSTAL14 User’s Manual, University ofTorino, Torino (2014).[29] To be found on Crystal website. Mn : M. D. Towler, N. L. Allan, N. M. Harrison, V. R.Saunders, W. C. Mackrodt and E. Apra, Phys. Rev. B50 , 5041 (1994) ; O : T. Bredow, K. Jug and R. A. Evarestov, Phys. StatusSolidi B 243 , R10 (2006).
Mg, Ca, Sr & Ba : P.J. Hay and W.R. Wadt, J. Chem.Phys. 82, 284 (1985) ; S. Piskunov, E. Heifets, R.I. Egli-tis, G. Borstel, Comp. Mat. Science , 165 (2004) ; La : X. Cao, M. Dolg, J. Chem. Phys. 115, 7348 (2001).[30] H. Chen et al. Nano Letters , 4965, (2014).[31] G.K.H. Madsen and D.J. Singh, Comp. Phys. Com.175