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Comparative study of LaNiO$_3$/LaAlO$_3$ heterostructures grown by pulsed laser deposition and oxide molecular beam epitaxy PDF

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Preview Comparative study of LaNiO$_3$/LaAlO$_3$ heterostructures grown by pulsed laser deposition and oxide molecular beam epitaxy

Comparative study of LaNiO /LaAlO heterostructures grown by pulsed laser 3 3 deposition and oxide molecular beam epitaxy F. Wrobel,1 A. F. Mark,1 G. Christiani,1 W. Sigle,1 H.-U. Habermeier,1 P. A. van Aken,1 G. Logvenov,1 B. Keimer,1 and E. Benckiser1,a) Max Planck Institute for Solid State Research, Heisenbergstr. 1, 70569 Stuttgart, Germany (Dated: 24 January 2017) Variations in growth conditions associated with different deposition techniques can greatly affect the phase stability and defect structure of complex oxide heterostructures. We synthesized superlattices of the para- magnetic metal LaNiO and the large band gap insulator LaAlO by atomic layer-by-layer molecular beam 3 3 epitaxy (MBE) and pulsed laser deposition (PLD) and compared their crystallinity, microstructure as re- 7 vealed by high-resolution transmission electron microscopy images and resistivity. The MBE samples show 1 a higher density of stacking faults, but smoother interfaces and generally higher electrical conductivity. Our 0 2 study identifies the opportunities and challenges of MBE and PLD growth and serves as a general guide for the choice of deposition technique for perovskite oxides. n a J Theprospectofrealizingnewfunctionaldevicesbased of SrTiO (STO), with larger mismatch. The bulk 9 3 on transition metal oxides relies on the possibility to (pseudo)cubic lattice constants of STO, LSAT, LNO 1 tune their electronic or magnetic properties by epitax- and LAO are 3.91, 3.87, 3.84 and 3.83 ˚A, respectively.13 ] ial strain, confinement, doping, or interface effects. For Growth parameters were optimized individually for l e precise control of these parameters, a high crystal qual- each growth technique. PLD samples were prepared as - ity, accurate stoichiometry, and atomically sharp inter- describedinRef.10. MBEsamplesweregrownat550◦C r t facesarerequired. Inthepastyears,thinfilmdeposition in a 2.5×10-5mbar ozone atmosphere and cooled down s techniques such as PLD, magnetron sputtering or MBE at the same pressure. The fluxes of the effusion cells . t a havebeenoptimizedforthegrowthofoxideheterostruc- were calibrated with a quartz crystal monitor before m tures.1–5Thegrowthconditionsdiffersubstantiallyinde- growth. Reflection high-energy electron diffraction was position temperature, pressure, energy of the impinging used for real-time monitoring, enabling atomic layer - d particlesandstoichiometrycontrol. Sofarlittleisknown control. A detailed description of the MBE system and n about how imperfections, such as interface roughness, the growth process can be found in the Supplementary o chemicalnon-stoichiometry,surfacedegradation,andthe Material and in Ref. 14. c [ intergrowth of different phases are connected to differ- High-resolution XRD and reflectivity measurements ent growth methods and how they influence the physical were performed using a four-circle diffractometer with 1 properties of the resulting thin-film structures. a Cu K source. Transport measurements (sheet re- v α1 Here we report on a comparative investigation of an sistance and Hall resistance) were conducted in van-der- 6 6 intensively studied model system, namely superlattices Pauw geometry in fields up to 9T. Where needed, the 3 (SLs) composed of perovskite-type LaNiO3 (LNO) and Hall resistance ρH was corrected for the magnetoresis- 5 LaAlO3 (LAO), a paramagnetic metal and a large band tance, i.e., ρH = (ρxy(+B)−ρxy(−B))/2. The Hall co- 0 gap insulator in bulk, respectively.1,6–12 Prior work has efficient was calculated by R = t·∂ρ /∂B where the H H 1. revealedatransitionfromabulk-likeparamagneticstate thickness t is the LNO c-axis parameter multiplied by 0 toaspin-density-wavephasewithreducedelectricalcon- the number of LNO layers. 7 ductivitywithdecreasingthicknessoftheLNOlayers.1,9 Transmissionelectronmicroscopy(TEM)wasdoneus- 1 While the properties of both sets of SLs are generally ing scanning mode and the annular dark field (ADF) de- v: in good agreement, our systematic study revealed quan- tector in an abberation corrected JEOL ARM200F op- i titative differences in the value of resistivity and in the erated at 200 kV. Each thin foil was prepared by first X microstructure which can be attributed to lower inter- cutting a cross section through the layers, then thinning ar facial roughness in MBE samples and a more accurate the section using mechanical grinding and polishing on lanthanum-to-nickel ratio in PLD samples. both sides to create a wedge-shaped slice (wedge angle We compare SLs with the composition 2◦). The slice was thinned to electron transparency by [(LNO)n/(LAO)m]l, abbreviated by [n/m] × l in ion-milling with LN2 cooling. thefollowing. Theyweredepositedonthe(001)surfaces ThinSLswiththecomposition[4/4]×3grownbyMBE of cubic (LaAlO ) -(Sr AlTaO ) (LSAT), with 3 0.3 2 6 0.7 and PLD on LSAT show only minor differences in their a small lattice mismatch, and on the (001) surfaces XRD patterns, both in scans through the (0 0 1) and (0 1 3) reflection (in pseudo-cubic notation) and in reflec- tivity measurements (Fig. 1). The LNO/LAO-averaged pseudo-cubic in- and out-of-plane lattice parameters are a)[email protected] identicalwithintheexperimentalerror. Fromthedamp- 2 d -1 (Å -1 ) (a) ((bb)) 0 .0 0 0 .0 2 0 .0 4 0 .0 6 0 .0 8 .) .u (a M B E ity P L D s n te In ( a ) ity (a.u.) ( b ) Int. (a.u.)01 LAO s -0 .0 3 0 .0 0 0 .0 3 n q LNO te (°), n o rm . In 2 nm STO 0 .2 2 0 .2 4 0 .2 6 0 .2 8 0 .3 0 0 .3 2 (c) d -1 (Å -1 ) M B E ( c ) P L D FIG.2. (Coloronline)Annulardark-field(ADF)imageofan 3 .1 0 3 .1 0 MBE-grown[4/4]×8SLonSTOwherethedashedbluelines 1 2 .0 mark the edges of a 3D-Ruddlesden-Popper (3D-RP) fault. .)3 .0 5 3 .0 5 .) (a) Full image and (b) enlarged view of the boxed area in (r.l.u 6 .0 (r.l.u (Tah).e 3(Dc)-RAP3fa-duilmteanrissieosnafrlormeparenseandtdaittiioonnaolfLaaO3Dla-RyePr afatuiltts. L L 3 .0 0 0 .0 3 .0 0 bottom such that all layers above are shifted by half a unit cell. In a TEM image, a projection of several atoms on top of each other is measured and thus, the faulted area appears 2 .9 5 2 .9 5 as an overlay of the ideal structure – represented by big dots 0 .9 5 1 .0 0 1 .0 5 0 .9 5 1 .0 0 1 .0 5 in(b)–andtheshiftedstructure–representedbysmalldots K (r.l.u .) K (r.l.u .) in(b). White,blueandorangedotsrepresentLa,Ni,andAl, respectively. Note that the 3D-RP faults start in the LNO FIG.1. (Coloronline)Hardx-raydataoftwonominallyiden- layers. tical [4/4]×3 samples on LSAT substrates grown by MBE (green, solid line) and PLD (red, dashed line). (a) Reflectiv- ity. (b) Scans through the (001) reflections of substrate and SL. The average c-axis parameter is 3.768(8)˚A for the MBE simultaneously on the substrate. The electric potential sample and 3.773(5) ˚A for the PLD sample. The inset shows at the polar interface is not screened such that the for- the corresponding rocking curves measured at the (001) re- mation of NiO is favorable, and NiO precipitates form flectionofthefilmwheretheintensitieswerenormalizedsuch irreversibly. In MBE growth first a complete La layer is that the maximum intensity of each scan is 1. (c) Reciprocal thermally evaporated and oxidized. The resulting LaO space maps around the (103) reflections of substrate and SL layer acts as a buffer that prevents the formation of NiO show that both samples are fully strained to the substrate. precipitates. Instead,asmoothlayerformsandthepolar discontinuity can be alleviated through, e.g., the forma- tion of oxygen vacancies. ingofthereflectivitycurves, wealsoextractnearlyiden- tical surface roughnesses of 4˚A (about one perovskite Common features observed in ADF images of all sam- unit cell) for both samples. Differences between MBE ples (Fig. 2 and 3) are 3D-Ruddlesden-Popper (3D- and PLD grown samples become more apparent in x-ray RP) faults caused by an additional layer of LaO over a diffraction/reflectivity data of thicker SLs with a larger smallarea-fractionofalayer.15 Allsubsequentlayersare number of interfaces (e.g. [2/2]x20; see the Supplemen- shifted by half a unit cell, and the shifted volume is sur- tary Material). roundedbyanadditionallayerofLaOateachsideofthe WhiletheaveragestructurefromXRDofthetwosam- fault as can be seen in the enlarged view of Fig. 2b and ples is nearly identical, there are differences at the local inthethree-dimensionalrepresentationofsuchafaultin level as revealed by TEM. Fig. 2 shows an ADF image Fig.2c. Theedgesofthis3D-RParemarkedwith(blue) taken of an MBE-grown [4/4]×8 SL on STO. As a first dashed lines in Fig. 2a & b and Fig. 3a & c. observationwenotethattheinterfacewiththesubstrate Withintheshiftedvolumeofa3D-RPfault,theSLfol- is atomically sharp. It was previously reported that lows the ideal structure. Therefore, in order to estimate nanometer-sizedNiOprecipitatesformattheLNO/STO the volume of the defect itself, the edges of this shifted interface due to the difference in polarity.8 These precip- volume should be measured. Based on an evaluation of itateswerenotobservedinMBE-grownsamples(Fig.2). the edges of the faults (marked with (blue) dashed lines A possible explanation is the difference in deposition se- in Fig. 2a & b and Fig. 3a & c), the faulted volume is quence. During a laser pulse La, Ni and O are deposited estimated to be less than 9 % and 2 % in the MBE and 3 (a) (b) (c) (d) Layer count001...050 1 2 3 4 5 6 Layer count001...050 1 2 3 4 5 6 Layer count001...050 1 2 3 4 5 6 Layer count001...050 1 2 3 4 5 6 Number of consecutive Ni/Al layers Number of consecutive Ni/Al layers Number of consecutive Ni/Al layers Number of consecutive Ni/Al layers FIG.3. (Coloronline)Annulardarkfield(ADF)imagesoffourSLsgrownonLSAT.Theedgesofthe3D-RPfaultsaremarked with(blue)dashedlines. (a)[4/4]×8(MBE),(b)[4/4]×8(PLD),(c)[2/2]×20(MBE)and(d)[2/2]×20(PLD).Theintensity inside the white boxes was integrated in the lateral direction and the resulting profile is shown as red lines inside the boxes. From these plots, we extracted the normalized Ni and Al intensities by dividing each minimum of the plot, which corresponds tooneNiorAllayer,bythemaximumoftheLalayerunderneath(labeledbyI andI inthefollowing). Subsequently,the Ni Al mean intensity value (I) iscalculated fromthe averageof all normalizedNi andAl intensities alongthe SL stacking direction. Finally, we counted the number of consecutive Ni (I > I) and Al (I < I) layers. Layers with an intensity that was equal Ni Al to the average intensity were not counted. We conducted this kind of analysis for several images of the same sample and the resulting fractions of layers with their corresponding thicknesses are shown in the bottom panels below each ADF image. The solid lines serve as a guide to the eye. PLD samples, respectively. These numbers are obtained distributed vacancies are filled with lanthanum or nickel bymeasuringthecontourlengthsoftheRPfaultedareas appears very likely. LSAT is a solid solution with statis- inallavailableimagesandnormalizingthemtothetotal tical occupation of Sr and La cations at A sites and Al image area. and Ta on B cation sites of the perovskite ABO struc- 3 The LaO layers surrounding the fault in growth direc- ture, hence the termination of the substrate surface is tion, i.e., perpendicular to the substrate-film interface, chemically not well defined. During the MBE growth of areaconsequenceofthefirstadditionalatomicLaOlayer thefirstatomicLalayerthevacanciesarefilledresulting at the bottom of the shifted volume. Therefore, we also in one bright atomic layer. The extended bright region compared R, defined as the lengths of the faults paral- inthePLD-grownsamplecanbeunderstoodifonetakes lel to the substrate normalized to the total length of the into account that the energy of impinging particles is image multiplied by the nominal, total number of LaO much higher, thus more atomic layers are affected. layers (64 in the [4/4] and 80 in the [2/2] SLs). In MBE The lower energy of the impinging particles and the samples, R is less than 1%. For PLD samples, R is at atomic layer-by-layer growth are assumed to also lead least a factor of three smaller. to sharper LNO-LAO interfaces, and indeed, the MBE TheobtainednumbersreflecttheLanon-stoichiometry samples appear to have flatter interfaces than the PLD necessarytocreatetheobserveddensityofRPfaults. De- samples. In order to visualize and quantify this obser- spite the large volume of the shifted areas in the image, vation, we extracted the Ni, Al, and La layer intensities the change in stoichiometry indicated by one RP fault through integrating over the area marked with a white is very small because the adjustments in the cation ra- box in Fig. 3a-d. The statistical analysis of the resulting tio occur only at the edges of the shifted region. In PLD intensity oscillations in stacking direction are shown in growththecationstoichiometryispredeterminedmacro- the panels below each ADF image of Fig. 3a-d. While in scopically by the composition of the target. In MBE theMBEsamplesabout75%ofthelayerstackshavethe growth stoichiometry control takes place on the level of intendedthickness,thisistrueforonlyabout50%inthe individual atomic layers and is therefore less accurate, PLD-grown SLs. The majority of the remaining layer hence a higher density of 3D-RP faults results. stacks have either one layer less (about 27% for PLD- At the substrate-film interface of samples grown on and 15% for MBE-grown SLs) or one layer extra (about LSAT (Fig. 3a-d), the images show a bright layer in- 12% for PLD- and 6% for MBE-grown SLs). Whereas in dicating the accumulation of heavier atoms in all sam- PLD-grown samples in average 18% of the layer stacks ples. In the MBE samples, only one atomic layer right deviate by more than one layer in thickness, such strong attheinterfaceisaffectedwhereasinthePLDsamples2 variations of thickness were not found in MBE-samples. –3layersappearbrighter. Ascenariowherestatistically These numbers indicate that the variation of the layer 4 1000 100 (b) (c) 5 [2/2]x6 [3/3]x4 4 [4/4]x3 m) 100 s)10 -3m) [12/3]x1 cW m²/V 22 c 3 [[225/2/0]x]6x1 (rm 10 MBE µ (c 1 n x10( 2 [[1265//33]]xx11 1 (a) 1000 100 (e) 5 [2/2]x6 [3/3]x4 4 [4/4]x3 m) 100 s)10 -3m) [12/3]x1 cW m²/V 22 c 3 [[625/2/3]x]6x1 (rm 10 PLD µ (c 1 n x10( 2 [3/3]x4 1 (d) (f) 0 50 100 150 200 250 300 0 50 100 150 200 250 300 0 50 100 150 200 250 300 T (K) T (K) T (K) FIG. 4. (Color online) Temperature dependent resistivity (a & d), Hall mobility (b & e), and carrier densities (c & f) of [(LNO) /(LAO) ] grown by MBE (upper panels, a-c) and PLD (lower panels, d-f) on LSAT with n, m and l as denoted in n m l the legend. Data for nominally identical, PLD- and MBE-grown samples are shown. Data for selected, additional samples are shown with open symbols to demonstrate sample-to-sample variations and systematic differences between PLD and MBE. thicknesses is clearly reduced for the MBE samples and of charge carriers determined for similar SLs.1 Finally, that more layers have the intended thickness. oxygenvacancies,whosedensityishardtodetermineex- perimentally in thin films, can lead to a further increase We now compare temperature dependent resistivity, of resistivity. HallcarrierdensitiesandHallmobilityofnominallyiden- tical samples grown on LSAT by the two different tech- A dimensional crossover from a paramagnetic metallic niques,whichweremeasuredbystandardfour-pointcon- state to a weakly insulating, antiferromagnetic state has tact experiments (Fig. 4). been observed in LNO-based SLs and thin films on var- ious substrates,1,9,17 and has been attributed to changes Overall,theresistivityvaluesofPLDsamplesgrownon at the Fermi level seen in photoemission.4,18,19 Although LSATishigherandthemobilitylowerthanthoseoftheir the critical thickness below which these changes occur is MBEcounterparts(seeFigure4a,b,d,e). Inparticular, under dispute, similar phenomena have been observed in thelow-temperaturebehaviorofthesampleswithhigher all experiments, on ultra-thin films and SLs alike. LNOthicknessdeviatessignificantlywhichisreflectedin ahigherresidualresistanceratio[ρ(300K)/ρ(2K)](RRR) Transport data shown in Fig. 4 confirm the dimen- for the MBE samples (e.g. 5.3 vs. 3.7 for a pair of two sionalcrossover. Inaccordancewithliteraturedata,1,4,20 [4/4]×3 samples). A 25 u.c. thick film grown by MBE we observe a clear change in resistivity between 2 and 4 shows an RRR as high as 18.4 and a room temperature unit cell thick LNO layers, while the variations are small resistivity as low as 78 µOhm·cm (Fig. 4a) which is an for thicker LNO layers. This observation is true for both improvement compared to previously reported data for PLD- and MBE-grown samples, but only in MBE-grown both ceramic and thin film samples.4,16 In contrast, the samples the carrier density is strongly reduced (Fig. 4c) highestRRRfoundinaPLDsampleofthepresentstudy simultaneously. AlthoughLNOpossessesalargeholeand is 4.9. These differences also become evident in the Hall smallelectronFermisurface,itisassumedthatthemain mobility of Fig. 4b & e and point to higher defect and/ contribution to conductivity arises from holes, in agree- orimpuritydensityinthePLDsamples. Thepresenceof ment with field-dependent Hall measurements showing a 3D-RP faults in the MBE samples has a smaller impact linear and positive slope. onelectricaltransport. Thiscanbeexplainedbythefact In MBE samples, the temperature and thickness de- thatthefaultsrarelystartatthesample-substrateinter- pendence of the carrier density is highly reproducible face but mostly after 16 unit cells. Moreover, the size and systematically changing with the LNO thickness, of the shifted volume is larger than the mean free path as shown with the additional data on similar or nomi- 5 nally identical samples (Fig. 4c, solid symbols compared 3I.Bozovic,G.Logvenov,I.Belca,B.Narimbetov, andI.Sveklo, with open symbols). This is, in general, not the case Phys.Rev.Lett.89,107001(2002). for PLD samples (Fig. 4f). PLD samples do not show 4P. D. C. King, H. I. Wei, Y. F. Nie, M. Uchida, C. Adamo, S.Zhu,X.He,I.Bozovic,D.G.Schlom, andK.M.Shen,Nat. a clear trend of the carrier density with respect to the Nanotechnol.9,443(2014). LNO layer thickness. Only the temperature dependence 5A.J.Hauser,E.Mikheev,N.E.Moreno,J.Hwang,J.Y.Zhang, ofathickLNOfilmresemblesitsMBEequivalent. Local andS.Stemmer,Appl.Phys.Lett.106,092104(2015). scale defects such as interface and surface roughness can 6E.Benckiser,M.W.Haverkort,S.Brueck,E.Goering,S.Macke, reduce the effectively conducting thickness and lateral A. Frano, X. Yang, O. K. Andersen, G. Cristiani, H.-U. Haber- meier, A. V. Boris, I. Zegkinoglou, P. Wochner, H.-J. Kim, inhomogeneities render the current path more complex. V.Hinkov, andB.Keimer,Nat.Mater.10,189(2011). These are possible reasons for the discrepancies between 7J.W.Freeland,J.Liu,M.Kareev,B.Gray,J.W.Kim,P.Ryan, MBEandPLDSLs. Forthickfilmsinterfaceandsurface R. Pentcheva, and J. Chakhalian, Euro Phys. Lett. 96, 57004 roughnesses play a minor role and as a consequence, the (2011). carrier density of such a thick film (63 u.c.) agrees with 8E. Detemple, Q. M. Ramasse, W. Sigle, G. Cristiani, H.-U. Habermeier, E. Benckiser, A. V. Boris, A. Frano, P. Wochner, a corresponding MBE sample (25 u.c.). M. Wu, B. Keimer, and P. A. van Aken, Appl. Phys. Lett. 99, In conclusion, our comparative study of LNO-LAO 211903(2011). SLs grown by MBE and PLD shows the opportunities 9A.Frano,E.Schierle,M.W.Haverkort,Y.Lu,M.Wu,S.Blanco- and challenges of both methods and demonstrates the Canosa, U. Nwankwo, A. V. Boris, P. Wochner, G. Cristiani, successful growth of perovskite oxide heterostructures. H. U. Habermeier, G. Logvenov, V. Hinkov, E. Benckiser, E. Weschke, and B. Keimer, Phys. Rev. Lett. 111, 106804 Whiletheatomiclayer-by-layerdepositioninMBEyields (2013). onaveragesharperinterfaces,thecationstoichiometryis 10M. Wu, E. Benckiser, M. W. Haverkort, A. Frano, Y. Lu, more difficult to control. Depending on the chemistry of U. Nwankwo, S. Bru¨ck, P. Audehm, E. Goering, S. Macke, the material, the deviations from stoichiometry can give V. Hinkov, P. Wochner, G. Christiani, S. Heinze, G. Logvenov, risetoacomplexmicrostructure,asdemonstratedbythe H.-U. Habermeier, and B. Keimer, Phys. Rev. B 88, 125124 (2013). RP faults occurring in the LNO layers of the MBE film. 11M. K. Kinyanjui, Y. Lu, N. Gauquelin, M. Wu, A. Frano, Future work should focus on mitigating the stoichiomet- P. Wochner, M. Reehuis, G. Christiani, G. Logvenov, H.- ricvariationsinMBEgrowthandontransportmeasure- U. Habermeier, G. A. Botton, U. Kaiser, B. Keimer, and ments on samples with reduced lateral dimensions. E.Benckiser,Appl.Phys.Lett.104,221909(2014). 12Y. Lu, A. Frano, M. Bluschke, M. Hepting, S. Macke, J. Strempfer, P. Wochner, G. Cristiani, G. Logvenov, H.-U. Habermeier, M. W. Haverkort, B. Keimer, and E. Benckiser, SUPPLEMENTARY MATERIAL Phys.Rev.B93,165121(2016). 13A. Wold, B. Post, and E. Banks, J. Am. Chem. Soc. 79, 4911 SeeSupplementaryMaterialforadditionalinformation (1957). 14F. Baiutti, G. Christiani, and G. Logvenov, Beilstein J. Nan- on the sample growth as well as for further XRR and otechnol.5,596(2014). XRD data. 15E. Detemple, Q. M. Ramasse, W. Sigle, G. Cristiani, H.-U. Habermeier, B. Keimer, and P. A. van Aken, J. Appl. Phys. 112,013509(2012). ACKNOWLEDGMENTS 16J.-S. Zhou, L. G. Marshall, and J. B. Goodenough, Phys. Rev. B89,245138(2014). 17R.Scherwitzl,S.Gariglio,M.Gabay,P.Zubko,M.Gibert, and We acknowledge the financial support by the DFG J.-M.Triscone,Phys.Rev.Lett.106,246403(2011). via TRR80, project G1, and funding from the European 18H.K.Yoo,S.I.Hyun,Y.J.Chang,L.Moreschini,C.H.Sohn, H.-D.Kim, A.Bostwick, E.Rotenberg, J.H.Shim, andT.W. Union Seventh Framework Program [FP/2007-2013] un- Noh,Phys.Rev.B93,035141(2016). der grant agreement no 312483 (ESTEEM2). 19G.Berner,M.Sing,F.Pfaff,E.Benckiser,M.Wu,G.Christiani, G. Logvenov, H.-U. Habermeier, M. Kobayashi, V. N. Strocov, 1A. V. Boris, Y. Matiks, E. Benckiser, A. Frano, P. Popovich, T.Schmitt,H.Fujiwara,S.Suga,A.Sekiyama,B.Keimer, and V. Hinkov, P. Wochner, M. Castro-Colin, E. Detemple, V. K. R.Claessen,Phys.Rev.B92,125130(2015). Malik,C.Bernhard,T.Prokscha,A.Suter,Z.Salman,E.Moren- 20D.P.Kumah,A.S.Disa,J.H.Ngai,H.Chen,A.Malashevich, zoni, G. Cristiani, H.-U. Habermeier, and B. Keimer, Science J.W.Reiner,S.Ismail-Beigi,F.J.Walker, andC.H.Ahn,Adv. 332,937(2011). Mater.26,1935(2014). 2R.Scherwitzl, P.Zubko, C.Lichtensteiger, andJ.-M.Triscone, Appl.Phys.Lett.95,222114(2009).

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