The formation of a novel spin-polarized 2D electron gas at the LaMnO$_3$
monolayer embedded in SrMnO$_3$ is predicted from the first-principles
density-functional calculations. The La (d) electrons become confined in the
direction normal to the interface in the potential well of the La layer,
serving as a positively-charged layer of electron donors. These electrons
mediate a ferromagnetic alignment of the Mn t$_{2g}$ spins near the interface
via the Anderson-Hasegawa double exchange and become, in turn, spin-polarized
due to the internal magnetic fields of the Mn moments.Comment: 5 pages, 6 figure

Nanda, B. R. K.

Satpathy, S.

Physical Review Letters

English

arXiv

B. R. K. Nanda

S. Satpathy

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Spin-Polarized Two-Dimensional Electron Gas at Oxide Interfaces

The possibility of formation of a fully spin-polarized 2D electron gas at the SrMnO3/(LaMnO3)1/  SrMnO3  heterostructure is predicted from density-functional calculations. The La(d)  electrons become confined in the direction normal to the interface in the electrostatic potential well of the positively charged layer of La atoms, acting as electron donors. These electrons mediate a ferromagnetic alignment of the Mn t2g  spins near the interface via Zener double exchange and become, in turn, spin-polarized due to the internal magnetic fields of the Mn moments.We acknowledge support of this work by the U.S.
Department of Energy through Grant No. DE-FG02-
00ER45818

Satpathy, Sashi Sekhar, 1956-

University of Missouri: MOspace

Spin-Polarized Two-Dimensional Electron Gas at Oxide InterfacesB.R.K. Nanda and S. SatpathyDepartment of Physics and Astronomy, University of Missouri, Columbia, Missouri 65211, USA(Received 19 April 2008; published 18 September 2008)The possibility of formation of a fully spin-polarized 2D electron gas at the SrMnO3=ðLaMnO3Þ1=SrMnO3 heterostructure is predicted from density-functional calculations. The LaðdÞ electrons becomeconfined in the direction normal to the interface in the electrostatic potential well of the positively chargedlayer of La atoms, acting as electron donors. These electrons mediate a ferromagnetic alignment of the Mnt2g spins near the interface via Zener double exchange and become, in turn, spin-polarized due to theinternal magnetic fields of the Mn moments.DOI: 10.1103/PhysRevLett.101.127201 PACS numbers: 75.70.Cn, 71.10.Ca, 71.20.b, 73.20.rRecent advances in the fabrication of high-quality epi-taxial interfaces between perovskite oxides have led to arapid surge of interest in the study of new interface elec-tronic states. A number of oxide interfaces have beenshown to possess electrons confined to the interface regionforming a two-dimensional electron gas (2DEG). A clearexample is an isolated [100] monolayer of LaTiO3 grownin a SrTiO3 host [1–4]. The trivalent La substituting for thedivalent Sr in essence behaves as a positively charged layerof electron-donor dopants producing a wedge-shaped po-tential at the interface, where the electrons become con-fined. A similar type of electron gas has been observed atthe much-studied LaAlO3=SrTiO3 interface [5], althoughthe exact origin of the electron gas there remains contro-versial. A somewhat different physics resulting from theinterface polarization charges produces the 2DEG at thenitride and the oxide interfaces such as GaN=AlxGa1xN[6] and ZnO=MgxZn1xO [7]. These electron gases oftenshow clear Shubnikov–de Haas oscillations, and evensuperconductivity has been observed in one of the systems[8].Since many of these oxides contain magnetic atoms aswell, the question arises as to whether one may be able toget a spin-polarized electron gas at the interface, using theinternal magnetic fields of the magnetic atoms. In thisLetter, we predict from calculations based on the density-functional theory (DFT) the existence of just such a phaseat the manganite heterostructure consisting of a LaMnO3(LMO) monolayer embedded in the SrMnO3 (SMO) bulk,sketched in Fig. 1.The results presented here are obtained from the DFTstudies of the ðLMOÞ1=ðSMOÞ7 layered superlattice usingthe linear augmented plane wave (LAPW) [9] and thelinear muffin-tin orbitals (LMTO) methods [10] with thegeneralized gradient approximation (GGA) [11] or theCoulomb-corrected local spin density approximation(LSDAþU). The supercell consisted of twice this for-mula unit because of the magnetic structures considered inthe Letter. The structural relaxation was performed usingthe LAPW-GGA method for the magnetic structure. Thecalculated cubic lattice constant for the La compound is3.915 A˚ and for the Sr compound is 3.802 A˚, which areclose to the experimental values of 3.935 and 3.805 A˚,respectively. For the relaxed structure, we fixed the in-plane lattice parameter of the superlattice to be 3.802 A˚corresponding to the bulk lattice constant of the Sr com-pound. This was also the lattice constant for the SMO partin the direction normal to the superlattice, while the samefor the LMO monolayer was taken to be 4.15 A˚, whichpreserves the volume of the LMO unit cell in the bulk. Theatomic positions were then relaxed along the c axis.The results, presented in Fig. 2, indicate the movementof the cations away from the interface, while the anionsmove towards the interface due to the electrostatic attrac-tion of the La layer. This is similar to the cation-anionpolarization obtained for the ðSrTiO3Þn=ðLaTiO3Þ1 hetero-structure, where there also exists at the interface a posi-tively charged La layer [3,4,12]. The electronic structurefor the relaxed lattice was obtained using the LMTOmethod with the LSDAþU approximation, using theCoulomb and exchange parameters of U ¼ 5 eV and J ¼1 eV, respectively.MnO2LaMnO3 SrMnO3SrMnO3MnO2FM AFMAFMLaOSrOSrO2DEGSrLaMnFIG. 1 (color online). The manganite heterostructure with amonolayer of LaMnO3 embedded in the SrMnO3 bulk, with theshadowed region indicating the spin-polarized 2DEG confined tothe interface region. Oxygen atoms occur at the intersections ofthe checkered lines forming the MnO6 octahedra.PRL 101, 127201 (2008) P HY S I CA L R EV I EW LE T T E R Sweek ending19 SEPTEMBER 20080031-9007=08=101(12)=127201(4) 127201-1  2008 The American Physical SocietyThe magnetic ground states of the two bulk compoundsare very different. While SMO with its Mn4þ (t32ge0g)configuration is a G-type antiferromagnet (AFM) withthe magnetic interaction between the Mn core spins drivenby superexchange [13], LMO is an A-type antiferromagnetwith a Mn3þ (t32ge1g) electronic configuration, with thepartially filled eg electrons mediating a ferromagneticdouble exchange between the t2g core spins on the MnO2planes [14,15]. For the present interface, there is just oneextra electron per La atom, which is localized near theinterface, occupying the Mn eg orbitals (see Fig. 3). Theseelectrons serving as the itinerant electrons in the standarddouble-exchange picture [16] modify the magnetism of theMn t2g core spins.In order to study the ground state, we have computed thetotal energies for several magnetic configurations. We findthe lowest-energy structure to be the one shown in Fig. 1,where the two MnO2 layers on either side of the La layerare ferromagnetic, while the remaining Mn atoms retainthe Ne´el G-type AFM of the SMO bulk. The remainingthree structures that we examined all have higher energies,viz., (i) the structure with a complete G-type magnetism,(ii) the structure where the layer ferromagnetism is ex-tended up to the second MnO2 layer on either side of theinterface, and (iii) the structure similar to the one in Fig. 1,except that the two MnO2 layers across the interface arealigned antiferromagnetically. The ferromagnetism at theinterface is explained by the fact that the itinerant egelectrons mediating the Zener double exchange residemainly in the two layers at the interface, even though asmall eg charge spreads to layers beyond the first layer.We note that the magnetic structure of the interface isvery much dependent on the strain condition [17,18], sothat the spin-polarized 2DEG may not exist for differentstrain conditions than the one studied here, where the in-plane lattice constant corresponds to the SMO bulk.The potential seen by the electron at the interface may becalculated from the variation of the cell-averaged point-charge Coulomb potential V, which was calculated by firstaveraging the potential over the volume of the ith Wigner-Seitz atomic sphere [2,19]:Vi ¼ 3qi2si þXjqjjri  rjj (1)and then by averaging over all spheres with a weight factorproportional to their volumes i: V ¼ PiiVi=Pii,where si is the sphere radius, ri its position, and qi is thetotal charge, nuclear plus electronic. In Eq. (1), the firstterm is the sphere average of the potential of the pointcharge located at the center of the muffin-tin sphere, andthe second term is the Madelung potential due to all otherspheres in the solid. The results plotted in Fig. 3 show thescreening of the bare linear potential due to the electro-static field of the charged La plane caused by the electronicas well as the lattice polarization. The screened potential isdeep enough to localize the donor electron within just afew layers of the interface. In fact, we find that about 0:7eis located on the first MnO2 layers and 0:14e on thesecond layers, and the remaining 0:16e is spread betweenthe remaining atoms.The presence of a substantial amount of the eg charge onthe firstMnO2 layer is consistent with the double-exchangemechanism for the layer ferromagnetism (Fig. 1) foundfrom the DFT calculations. However, although in the DFTresults, the structure, where the secondMnO2 layer is alsoferromagnetic in addition to the first, was not energeticallyfavorable, the leaked eg electrons into the second layercould result in a canted ferromagnetic state for this layer,depending on the amount of charge leakage and thestrength of the double exchange.To address this issue, we have studied the Zener-Anderson-Hasegawa double-exchange model [16] on afour-layer lattice (Fig. 4, inset), each layer being a squarelattice, as appropriate for the MnO2 layers. The modelHamiltonian, restricted to the Mn sites up to secondMnO2 planes away from the interface, is given by00.20.4n(z) (electron) LSDALSDA+U-4 -2 0 2 4z00.1V(z) (Ry)(LaMnO3)1/(SrMnO3)7FIG. 3. The cell-averaged potential VðzÞ calculated fromEq. (1) with distance z from the La layer in units of SrMnO3monolayer thickness (bottom) and the layer occupancy nðzÞ ofthe donated electrons, one per La atom, occupying predomi-nantly the Mn (eg) orbitals (top).MnOSrLa1.885Å 1.887Å 1.884Å 1.961Å 2.142Å1.817Å 1.876Å0.172Å0.113Å0.077Å0.026Å0.008Å0.002Å3.802ÅFIG. 2 (color online). Relaxed atomic positions for theðLMOÞ1=ðSMOÞ7 superlattice with arrows showing the atomicdisplacements. The bottom numbers indicate the positions of theO planes, while the numbers on top indicate the cation-anionpolarizations (positions of Mn=Sr with respect to the O planes),which diminish quickly away from the interface.PRL 101, 127201 (2008) P HY S I CA L R EV I EW LE T T E R Sweek ending19 SEPTEMBER 2008127201-2H ¼Xiini þ tXhijicyicj þ H:c:þ JXhijiS^i  S^j 2JHXi~Si  ~si; (2)and it describes the double-exchange interaction of theitinerant electrons in a lattice of localized spins. Here cyiand ci are the field operators for the eg carriers, treatedwithin a one-band model, with i and  being the site andspin indices, respectively, ~Si is the localized t2g spin, and ~siis the spin density of the itinerant electrons. The on-siteenergy i (Vp on the second layer and zero on the first)describes the electric field at the interface and is theparameter that controls the leakage of the itinerant electroninto the second layer. J is the superexchange between thelocalized spins, while JH is the Hund’s coupling betweenthe itinerant and the localized electrons. From the earlierDFT studies of the bulk manganites [14,20,21], typicalvalues of the parameters are t0:15 eV, J  7 meV,and JH  1 eV. Note that, unlike our earlier work [22],here we neglect the on-site Coulomb energy between theitinerant carriers, since their number is small.The Hamiltonian (2) is solved by diagonalizing a 1616 Hamiltonian matrix (eight Mn atoms per unit cell andtwo spin types) for a number of ~k points in the two-dimensional Brillouin zone, and the total energy is calcu-lated by summing over the occupied states (two electronsper cell). The results summarized in Fig. 4 show that anantiferromagnetic second layer (canting angle  ¼ ) isoverwhelmingly favored over a canted state for a parame-ter of Vp  0:5 eV, which yields roughly the same amountof electron leakage into the secondMnO2 layer as obtainedfrom the DFT calculations. This indicates the absence of acanted state.The electronic structure corresponding to the lowest-energy magnetic structure (Fig. 1) is shown in Fig. 5. Thet2g states of one spin are occupied for each Mn atom and liefar below the Fermi energy EF because of the octahedralcrystal field produced by the MnO6 octahedron and thestrong Coulomb repulsion U. The vicinity of EF is occu-pied by the Mn-eg states. In the spin-majority channel, wesee extended eg states crossing the Fermi level, while in thespin-minority channel, they are unoccupied and open up agap at the Fermi energy, so that we have the equivalent of ahalf-metallic system in two dimensions.While there are a number of half-metallic systemsknown in 3D, the classic one being Fe3O4 [23], the presentcase is quite unique in the sense that the electrons at theFermi energy are confined to the interface region, produc-ing a fully spin-polarized 2DEG. This is in fact a key pointof this Letter.The bands crossing the Fermi energy are the majority-spin Mn1-eg (x2  y2 and 3z2  1) states belonging to thefirst-layer manganese atoms with bonding interactionacross the interface. The corresponding antibonding statesas well as all minority-spin Mn1-eg states occur higher inCanting angle (θ)/2πVp = 0.70 eVVp = 0.35 eVVp = 0.10 eVπEnergy (meV)−60−50−400θθinterfaceMn1Mn1Mn2Mn2FIG. 4. Total energy obtained from Eq. (2) as a function of thecanting angle between the nearest neighbor Mn spins in thesecond MnO2 layer for different values of the potential Vp.EFLa−d, fLa−d, fLSDA+UMn−t2gMn−t2gMn−egMn−egMn−t2gMn−t2gMn−egMn−egEnergy (eV)−8 −4 0 4−40400Spin−DownSpin−UpO−pSpin−Polarized 2DEGDOS (states/eV cell)X Γ M1.00−1.0X X Γ M X RREnergy (eV)Mn2−egMn1−egMn2−egx2−y2 x2−y23z2−13z2−1Spin−Up Spin−DownFIG. 5. Total densities of states for the ðLMOÞ1=ðSMOÞ7 superlattice for the majority and the minority spins (top) and the bandstructure in the vicinity of the Fermi energy (bottom). The symmetry points are  ð0; 0; 0Þ, X ð1;1; 0Þ, M ð0; 2; 0Þ, and Rð1;1;2a=cÞ in units of =2a, a being the in-plane lattice constant. The symbols Mn1 and Mn2 indicate the first and the secondlayer atoms, respectively, next to the interface.PRL 101, 127201 (2008) P HY S I CA L R EV I EW LE T T E R Sweek ending19 SEPTEMBER 2008127201-3energy and outside the energy range of Fig. 5. In contrast tothis, since the second layer manganese moments are anti-ferromagnetically organized, the Mn2-eg states occur inboth the minority- and the majority-spin channels as seenfrom the figure.As discussed earlier, the partially occupied eg statesmediate a ferromagnetic double exchange between thet2g core spins, which competes with the antiferromagneticsuperexchange. This double exchange is directional innature in the sense that its strength in the xy plane or alongthe z axis depends on the occupancy of the individual egorbitals (x2  y2 and 3z2  1) [17,18]. Since we have bothorbitals significantly occupied, as seen from the band plotof Fig. 5, this leads to a strong double exchange both in thefirst MnO2 layers and between these layers across theinterface, resulting in the layer ferromagnetic structure asshown in Fig. 1.The interface Fermi surface, shown in Fig. 6, is con-stituted out of the Mn1-eg (x2  y2 and 3z2  1) states, andtheir orbital characters may be inferred from the bandstructure shown in Fig. 5. The Fermi surface consists ofelectronlike pockets at the  and M points and holelikepockets centered at the X points. The holes have relativelyhigher mass, so that the transport along the interface maybe expected to be electronlike.Although the interface suggested in this Letter has notbeen grown to our knowledge (but is certainly possible togrow), it is encouraging that there are several experimentalworks on the LMO/SMO superlattices which seem to sup-port the existence of a ferromagnetic state at the interface[17,24,25]. It would be gratifying if the spin-polarized2DEG can be established experimentally in these oxidesystems.In summary, our density-functional studies suggest theformation of a fully spin-polarized 2DEG at the LaMnO3layer embedded in a thick SrMnO3 bulk. This occurs due tothe confinement of the La electrons near the interfacebecause of the electrostatic potential of the positivelycharged La layer. These electrons occupy the Mn-eg statesnear the interface, mediating a Zener double exchange,which stabilizes a ferromagnetic structure of the Mn spinsand the electrons become, in turn, completely spin-polarized due to the magnetic fields of the Mn atoms.The Ne´el G-type antiferromagnetism of the bulk SrMnO3is retained in the secondMnO2 layer from the interface andbeyond. We note that earlier experiments have observed afully spin-polarized 2DEG but with an external magneticfield present, e.g., in the modulation-doped CdMnTe quan-tum structures and for the lowest Landau level in theGaAs=AlGaAs quantum wells [26]. The complete spinpolarization of the 2DEG without any external magneticfield promises to be a novel feature for the perovskite oxideinterfaces.We acknowledge support of this work by the U.S.Department of Energy through Grant No. DE-FG02-00ER45818.[1] A. Ohtomo et al., Nature (London) 419, 378 (2002).[2] Z. S. Popovic´ and S. Satpathy, Phys. Rev. Lett. 94, 176805(2005).[3] D. R. Hamann et al., Phys. Rev. B 73, 195403 (2006).[4] S. Okamoto et al., Phys. Rev. Lett. 97, 056802 (2006).[5] M. Hujiben et al., Nature Mater. 5, 556 (2006); A. Ohtomoand H.Y. Hwang, Nature (London) 427, 423 (2004).[6] D. R. Hang et al., Appl. Phys. Lett. 89, 092116 (2006).[7] A. Tsukazaki et al., Science 315, 1388 (2007).[8] N. Reyren et al., Science 317, 1196 (2007).[9] P. Blaha et al., WIEN2K, ‘‘An Augmented Plane Wave þLocal Orbitals Program for Calculating CrystalProperties’’ (Karlheinz Schwarz, Technische UniversitatWien, Austria, 2001), ISBN 3-9501031-1-2.[10] O. K. Andersen and O. Jepsen, Phys. Rev. Lett. 53, 2571(1984).[11] J. P. Perdew and Y. Wang, Phys. Rev. B 45, 13 244 (1992);J. P. Perdew et al., Phys. Rev. Lett. 77, 3865 (1996).[12] P. Larson, Z. Popovic, and S. Satpathy, Phys. Rev. B 77,245122 (2008).[13] A. J. Millis, Phys. Rev. B 55, 6405 (1997).[14] S. Satpathy, Z. S. Popovic´, and F. R. Vukajlovic, Phys.Rev. Lett. 76, 960 (1996).[15] D. Feinberg et al., Phys. Rev. B 57, R5583 (1998).[16] P.W. Andersen and H. Hasegawa, Phys. Rev. 100, 675(1955); C. Zener, Phys. Rev. 82, 403 (1951); P.-G. deGennes, Phys. Rev. 118, 141 (1960).[17] H. Yamada et al., Appl. Phys. Lett. 89, 052506 (2006).[18] B. R. K. Nanda and S. Satpathy, Phys. Rev. B 78, 054427(2008).[19] W.R. L. Lambrecht et al., Phys. Rev. B 41, 2813 (1990).[20] W. E. Pickett and D. J. Singh, Phys. Rev. B 53, 1146(1996).[21] H. Meskine, H. Ko¨nig, and S. Satpathy, Phys. Rev. B 64,094433 (2001).[22] S. K. Mishra et al., Phys. Rev. B 55, 2725 (1997).[23] Z. Zhang and S. Satpathy, Phys. Rev. B 44, 13 319 (1991).[24] S. J. May et al., Phys. Rev. B 77, 174409 (2008).[25] S¸. Smadici et al., Phys. Rev. Lett. 99, 196404 (2007).[26] A. Lemaitre et al., Phys. Rev. B 62, 5059 (2000); S.Melinte et al., Phys. Rev. Lett. 84, 354 (2000).ΓXXMFIG. 6. The Fermi surface of ðLMOÞ1=ðSMOÞ7 shown in theinterface Brillouin zone.PRL 101, 127201 (2008) P HY S I CA L R EV I EW LE T T E R Sweek ending19 SEPTEMBER 2008127201-4

Two Dimensional Spin-Polarized Electron Gas at the Oxide Interfaces

Two Dimensional Spin-Polarized Electron Gas at the Oxide Interfaces

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