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Signatures of a Two-Dimensional Ferromagnetic Electron Gas at the La0.7Sr0.3MnO3/SrTiO3 Interface Arising From Orbital Reconstruction Norbert Marcel Nemes,* María José Calderón,* Juan Ignacio Beltrán, Flavio Yair Bruno, Javier García-Barriocanal, Zouhair Sefrioui, Carlos León, Mar García-Hernández, María Carmen Muñoz, Luis Brey, and Jacobo Santamaría The breakdown of translational symmetry at interfaces between complex oxides leads to qualitatively new behaviors compared to their bulk properties.[1] For example, the interfacial discontinuity is screened by the formation of a two dimensional electron gas (2DEG) at the interface between two band insulators, LaAlO3/SrTiO3 (LAO/STO).[2–5] Heterostructures involving strongly correlated oxides have also given rise to exotic properties.[6,7] The electronic reconstruction at interfaces involving manganite perovskites is especially rich due to the complex interplay between orbital, charge, spin and lattice degrees of freedom. Although extensive literature has focused on the orbital reconstruction[8–13] resulting from the modified bonding at manganite interfaces, evidence for a 2DEG has remained scarce.[14] In the case of ferromagnetic (FM) and metallic manganites, an interfacial magnetic reconstruction may be difficult to disentangle from the layer “bulk” magnetism. Moreover, characterization of the interfacial phases is difficult, as most experimental probes cannot directly spot signals from buried interfaces. Here we show that an LSMO 2DEG emerges at the interfaces of [(La0.3Sr0.7MnO3)n/(SrTiO3)m]8 (LSMO/STO) superlattices grown in the (001) direction. We have performed angular dependent magnetotransport measurements with the magnetic field rotating out of the interface plane (see sketch in Figure 1). Besides the standard resistivity maxima for a perpendicular
N. M. Nemes, J. I. Beltrán, F. Y. Bruno, J. García-Barriocanal, Z. Sefrioui, C. León, J. Santamaría GFMC, Departamento de Física Aplicada III Universidad Complutense de Madrid Campus Moncloa E-28040, Madrid, Spain E-mail: [email protected] N. M. Nemes, M. J. Calderón, F. Y. Bruno, J. García-Barriocanal, Z. Sefrioui, C. León, M. García-Hernández, L. Brey, J. Santamaría Laboratorio de Heteroestructuras con aplicación en Spintronica, Unidad Asociada Consejo Superior de Investigaciones Científicas/ Universidad Complutense Madrid Sor Juana Inés de la Cruz, 3, E-28049 Madrid, Spain E-mail: [email protected] M. J. Calderón, J. I. Beltrán, M. García-Hernández, M. C. Muñoz, L. Brey Instituto de Ciencia de Materiales de Madrid ICMM-CSIC, Cantoblanco E-28049, Madrid, Spain
DOI: 10.1002/adma.201402829
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magnetic field, occurring for bulk manganites and two-dimensional STO systems,[15,16] we find an unexpected in-plane magnetoresistance peak. This peak is nearly independent of the relative orientation between the in-plane magnetic field and the current and is more prominent for the thinner manganite films, indicating an interfacial origin. Calculations of resistivity in a model system including spin-orbit coupling reveal that the inplane peak is due to transport through a two-dimensional (2D) system at the manganite interface. Density Functional Theory (DFT+U) calculations confirm that the 2D system results from a FM and metallic interfacial manganite layer antiferromagnetically coupled (A-type) to (and hence electrically decoupled from) the rest of the LSMO. The magnetic reconstruction is accompanied by an in-plane orbital polarization, consistent with X-ray absorption spectroscopy. Magnetoresistance measurements thus expose the character of the electronic reconstruction occurring at the interface between the FM and metallic LSMO and the insulating STO: A 2D FM metallic interfacial layer AFcoupled to the rest of the manganite layer (3D system). The presence of this AF layer at the LSMO interface may provide important clues for the depolarization of spin currents in magnetic tunnel junctions reported for this system.[17,18] The conduction electrons in perovskites are usually provided by the transition metal d-orbitals. These orbitals are split by the cubic crystal field in a lower t2g triplet and a higher eg doublet. The remaining degeneracies can be lifted by broken lattice symmetries, as in interfaces and surfaces, leading to confined orbital reconstructions. In particular, at a (001) interface the dxy orbital is shifted down with respect to the dyz and dxz orbitals[19–23] and the dx2-y2 and d3z2-r2 are also split.[8,24] These modifications are produced by both crystal-field distortions and changes in the bandwidth. The orbital reconstruction can be
B
LSMO STO
Figure 1. In-plane transport measurements are realized under a magnetic field rotating with respect to the interface plane. θ = 0 is for a magnetic field perpendicular to the interface plane (left). Picture that emerges from our experimental/theoretical results: the LSMO interface is magnetically reconstructed leading to an electrically decoupled 2D system (right).
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reflected in the magnetic and electronic properties of the interface. This is the case of cuprate/manganite heterostructures, where the suppression of the superconductivity close to the interface has been ascribed to the partial emptying of the d3z2-r2 orbital.[25] Different magnetic reconstructions have also been reported in all-manganite[26] and manganite/insulator[9,10,24] superlattices and thin films. Anisotropic magnetoresistance (AMR) is a common feature of metallic ferromagnets and is defined as the difference in the system resistivity when an in-plane magnetization vector is parallel or perpendicular to the current.[27,28] In manganites, the AMR is small compared to the one shown by FM alloys[29] and the maximum resistance corresponds to a magnetic field applied perpendicularly to the current.[28,30–32] More complicated angular dependences (with extra peaks for a magnetic field parallel to the current) have been found under particular circumstances in Fe3O4,[33] LAO/STO,[34,35] and La0.3Ca0.7MnO3.[31] Epitaxial superlattices of LSMO (a FM metal) and STO (a Figure 2. Angular MR for different superlattices and thin films at 5 K and diamagnetic insulator) were grown on (001) oriented STO sub14 T with I[010] geometry. Resistances are normalized with respect to the strates using high pressure (3.2 mbar) oxygen plasma sputout-of-plane value, ie. R/R(θ = 0). The height of the pMR-peak increases tering at high temperature (900 °C), starting with LSMO and as the thickness of the LSMO film decreases. Inset: pMR-peak vs. low terminating with STO, with a total of eight bilayers. The LSMO temperature residual resistivity (ρ) for the various samples (superlattices and thin films). is fully strained with an in-plane lattice parameter fixed by the STO substrate. Examining the interface chemistry by scanning LSMO films a new resistivity peak emerges for in-plane B, transmission electron microscopy with Electron Energy Loss which we call in-plane angular magnetoresistance (pMR) peak. Spectroscopy (EELS) analysis all interfaces are observed to be The height of the pMR-peak increases with decreasing manLa0.7Sr0.3O/TiO2.[11] X-ray magnetic circular dichroism and ganite film thickness, as illustrated by the inset of Figure 2. The EELS measurements have revealed a small charge transfer to peak is suppressed by increasing temperature, disappearing Ti giving rise to a magnetic moment which is antiparallel to around 20 K, and is enhanced by the magnetic field at low that on the Mn sites.[11] The 5*5 mm2 square samples were contemperatures (Figure 3) (see also Supporting Information). We tacted at the corners in the van der Pauw geometry, and were demonstrate here that the pMR-peak is produced by a 2DEG then cooled and rotated in an applied magnetic field (B). For forming at the LSMO interface. A 2DEG may also arise at the in-plane rotations, the typical maximum resistivity of AMR for STO interface, however our calculations show that it is not B perpendicular to the current is recovered. For out-of-plane responsible for the observed pMR. rotations, the symmetry we are focusing on here, the rotation axis was parallel to a sample edge, coinciding with the [100] The pMR is largest for the thinnest LSMO with thick STO crystal axis of the substrate. We employed two possible current separation. This can be understood in terms of two different directions, I[100] and I[010], along the rotation axis and perpendicular to it, respectively. θ = 0 corresponds to B perpendicular to the interface plane, and θ = π/2 to an in-plane field. Contrary to what would be expected of AMR, no qualitative difference between the two in-plane current orientations was found, although the magnetization always stays perpendicular to the I[100] current whereas the angle it makes with the I[010] current varies as the sample rotates in the applied field (see Supporting Information). The angular magnetoresistance displays two qualitatively distinct behaviours, with maxima for the magnetic field either along the surface normal or in-plane. The former is the typical AMR behavior of ferromagnetic manganite films. This is precisely what we observe in a 24 nm (65 unit cells) thick LSMO film on STO: a resistance maximum Figure 3. (a) Temperature and (b) magnetic field dependence of the pMR-peak (I[010] geomfor perpendicular B and a minimum for in- etry) at different B-fields and temperatures as indicated in the legends for a [LSMO8/STO2]8 plane B (Figure 2). In contrast, for thinner superlattice.
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transport channels: one in the “bulk” of the LSMO layers and the other at the LSMO/STO interfaces, connected in parallel. The relative weight of the interfacial scattering is strongest with thin LSMO layers. Note that Figure 2 mixes together superlattices and thin films, showing also the angular MR of a thin (5 nm) and a thick (24 nm) LSMO film, with only the former displaying weak pMR. The largest pMR, in a [LSMO7/STO6]8 superlattice, is approximately 1% of the corresponding resistivity. The resistivity in Figure 2 for superlattices with different LSMO and STO thicknesses shows the expected trend: with thicker LSMO or thinner STO barrier the resistivity is lower.[11] The inset of Figure 2 shows the pMR of the various thin films and superlattices as a function of the low temperature (residual) resistivity. The additional residual resistivity is a measure of the interface-contribution, and the pMR grows linearly with it. This supports the picture of a two-fluid model, where the additional LSMO layers simply decrease resistivity while the pMR originates at the interface. Magnetoresistance anisotropies arise due to spin-orbit coupling (SOC). This interaction, albeit generally small for the materials at hand, produces shifts and anticrossings in the bands, which are dependent on the external magnetic field intensity and its orientation with respect to the crystalline axes. Using a semiclassical formula based on the Boltzmann transport equation and assuming a constant (non-k dependent) scattering time τ, the conductivity tensor σij (inverse of the resistivity ρij) can be calculated as
σ ij = e 2τ ∑ ∫ d k n
∂ f (ε ) i v n ( k )v nj ( k ) ∂ε n ( k )
(1)
ρ (arb. units)
with n the band index, ε(k) the band dispersion, f(ε) the Fermi distribution function, and vi the velocity (∂ε(k)/∂ki) in the i direction. It is clear from this formula that modifications of the band structure close to the Fermi level (such as those produced by spin-orbit coupling and exchange or magnetic fields) are to be reflected on the transport properties. We calculate the angular dependence of the resistance of three different systems: a 3D manganite, a 2D STO, and a 2D manganite (see Figure 4), and compare them to the experimental results. We show that the pMR peak can only arise from a 2D manganite. Manganites are modeled here by a double exchange Hamiltonian in which the itinerant electron spins in the eg orbitals are strictly parallel to the localized t2g electrons[28,36] (see Supporting Information). The local magnetic moments follow the external magnetic field in such a way that
STO
3D manganite
2D manganite
(b)
(a)
0
the magnetization of the system is fully saturated (infinite B approximation). The SOC between the eg orbitals occurs only as a second order process through the t2g ones.[28] Figure 4(a) shows the resulting in-plane resistivity for a 3D manganite as a function of the angle θ between the applied magnetic field and the interface plane. Consistent with the experimental observation for the thicker films, this resistivity is found to be larger for an out-of-plane (θ = 0) magnetic field. The pMR peak can neither be attributed to the STO interface. X-ray circular dichroism measurements render a finite charge and magnetic moment on the Ti at the STO interface.[11] Therefore, we may have a 2DEG at the STO interface. The Ti t2g orbitals are split due to the broken translational symmetry in the z-direction, and the carriers only occupy dxy. However, this 2D system does not give rise to a larger in-plane resistivity either, as revealed by calculating the effect of a Rashba SOC[37,38] on its conductivity (see Figure 4(b)). Our theoretical results are consistent with the experimental measurement reported for LAO/STO.[15,16] Charge redistribution and broken translational symmetries in heterostructures are known to modify the properties of manganite interfaces: orbital polarization and different magnetic orders may arise.[10,12–14,24,26,39–42] In particular, the suppression of the hopping in the growth direction (z-direction here) can lead to the reduction of the d3z2-r2 orbital bandwidth and a preferential occupation of dx2-y2. This planar-like orbital order at the interface can favor an A-type magnetic ordering,[24,43–45] coupling the interface layer antiferromagnetically to the rest of the manganite. Such a 2D system would be electrically decoupled as hopping between sites with antiparallel spins is suppressed in half-metals by virtue of the double exchange mechanism.[36] We would then have two differentiated manganite systems, as illustrated in Figure 1: one constituted by the “bulk” of the thin film (3D manganite in the following) and a 2D one at the interface. The 3D manganite shows the expected maximum of the resistivity with an out-of-plane magnetic field. However, removing the hopping in the z-direction (in order to simulate a 2D system) produces an orbital polarization with a much larger occupation density of the d3z2-r2 orbital at the Fermi level EF (see Figure 10 in the Supporting Information). The d3z2-r2 band gets flatter at EF with an in-plane magnetic field, leading to a larger resistivity compared to the perpendicular field, as shown in Figure 4(c). Hence, the transport through a 2D system at the manganite interface leads to the observed in-plane magnetoresistance peak (pMR). Note that the large Hund coupling
π/4
π/2
θ
3 π/4
0
π/4
π/2
θ
3 π/4
(c)
0
π/4
π/2
θ
3 π/4
π
Figure 4. Resistivity calculated as the inverse of σ in Equation 1 (a) for a 3D manganite, (b) for a dxy orbital system and (c) for a 2D manganite. θ is the magnetic field orientation with respect to the normal to the interface plane: θ = π/2 corresponds to an in-plane magnetic field. A maximum resistivity in the in-plane direction, consistent with the experimental observation of an additional peak for θ = π/2 in Figure 2, is found for a 2D manganite which may be forming at the interface with the STO layer.
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Mn. All the Mn ions have partially filled eg states and all MnO2 planes are half-metals. The Density-of-States (DOS) at the Fermi level in the interface is very small because there is only one spin down band crossing the Fermi level (see Supporting Information). The Mn magnetic moments are –3.2, 3.4 and 3.5 µB moving away from the interface. Bulk behavior is already recovered in the central LSMO. These magnetic moments are consistent with the calculated small decrease of the Mn eg occupancy as one approaches the interface. In addition, there is a preferential occupation of the dx2-y2 orbital, which is slightly larger than the corresponding d3z2-r2. This orbital reconstruction is essentially confined to the interface. The orbital reconstruction at the interface is supported by X-ray linear dichroism Figure 5. Schematic half unit cell of the [LSMO14.5/STO2.5] superlattice as obtained from the results which show a tendency to increasing DFT calculation, showing the two different layers in the LSMO slab (left). Spin-resolved density of states projected on the atomic planes around the interface (right). The labeling corresponds occupation of dx2-y2 with respect to d3z2-r2 as the LSMO layer in a superlattice gets thinner to that of the unit cell, and upper (blue) and lower (red) lines within each plane represent, (see Supporting Information). respectively, the majority and minority spin densities. LSMO is a half-metal with inverse spinpolarization at the interface MnO2 layer. In summary, we have shown that in LSMO/STO superlattices there is a sharp magnetoresistance peak arising at low temperatures as the magnetic field is rotated towards the interapproximation used to describe manganites does not allow us face. Calculations of the resistivity taking into account the to study the dependence of the pMR on the magnetic field magspin-orbit coupling show that this in-plane peak signals the nitude and temperature. formation of a 2D manganite at the interface, decoupled from The coexistence of two decoupled 3D and 2D systems in the rest of the manganite layer, which could arise from a magthe LSMO slab is supported by DFT+U calculations. Several netic reconstruction. The 2D interfacial manganite would be ideal defect free [LSMOm/STOn] (001) superlattices have been ferromagnetic but antiparallel to the overall magnetization of studied. We use the plane-wave based Vienna ab initio simuthe layer. This reconstruction is supported by DFT+U calculation package (VASP) within the PBE+U approximation to lations. The X-ray absorption experiments clearly indicate an the exchange-correlation energy.[46,47] The superlattices have a in-plane orbital polarization of the interfacial eg Mn electrons. tetragonal structure and contain m and n unit cells of LSMO and STO, respectively. As observed experimentally for different Such magnetic modification could be related to the spin depomaterial systems, samples grown in high oxygen pressure by larization revealed by tunneling magnetoresistance measuresputtering are characterized by symmetric interfaces in most ments in manganite based tunneling devices. The anisotropic cases[10,11] (see Supporting Information). This corresponds magnetoresistance is hence giving away clues on the nature of the electronic reconstruction at oxide interfaces. nominally to consider half integer m and n values resulting in symmetric La0.7Sr0.3O/TiO2 interfaces. The calculations were spin-polarized: We considered parallel and antiparallel (FM and A-type AF) configurations at the interface with a collinear alignSupporting Information ment of the magnetization (see Supporting Information). Supporting Information is available from the Wiley Online Library or A two-layer model for the LSMO slab is considered, with from the author. a different stoichiometry at the interfaces, in order to take account of differences that may arise between the central part of the manganite layer and the interfaces. We have found that for a Sr-rich interface, an AF coupling between the interface Acknowledgements and the rest of the manganite layer is the most favored. This is We acknowledge funding from MINECO-Spain through grants FIS2012– consistent with the fact that the LSMO bulk phase diagram[36] 33521, MAT2011–27470-C02–01, MAT2011–27470-C02–02, MAT2012– shows an A-type AF phase for x > 0.5. The AF configuration is 38045-C04–04 and CSD2009–00013. JGB acknowledges funding by the lower in energy (EAF-EFM ∼ –30meV/Mn), independent of the ’Ramon y Cajal’ programme. values of m and n. Figure 5 shows the spin-resolved layer-projected density of Received: June 25, 2014 states for the [LSMO14.5/STO2.5] superlattice with a Sr-rich interRevised: August 29, 2014 face. Crucially, the spin polarization is inverted on the interface Published online: October 18, 2014
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Signatures of a Two-Dimensional Ferromagnetic Electron Gas at the La0.7Sr0.3MnO3/SrTiO3 Interface Arising From Orbital Reconstruction Norbert Marcel Nemes,* María José Calderón,* Juan Ignacio Beltrán, Flavio Yair Bruno, Javier García-Barriocanal, Zouhair Sefrioui, Carlos León, Mar García-Hernández, María Carmen Muñoz, Luis Brey, and Jacobo Santamaría The breakdown of translational symmetry at interfaces between complex oxides leads to qualitatively new behaviors compared to their bulk properties.[1] For example, the interfacial discontinuity is screened by the formation of a two dimensional electron gas (2DEG) at the interface between two band insulators, LaAlO3/SrTiO3 (LAO/STO).[2–5] Heterostructures involving strongly correlated oxides have also given rise to exotic properties.[6,7] The electronic reconstruction at interfaces involving manganite perovskites is especially rich due to the complex interplay between orbital, charge, spin and lattice degrees of freedom. Although extensive literature has focused on the orbital reconstruction[8–13] resulting from the modified bonding at manganite interfaces, evidence for a 2DEG has remained scarce.[14] In the case of ferromagnetic (FM) and metallic manganites, an interfacial magnetic reconstruction may be difficult to disentangle from the layer “bulk” magnetism. Moreover, characterization of the interfacial phases is difficult, as most experimental probes cannot directly spot signals from buried interfaces. Here we show that an LSMO 2DEG emerges at the interfaces of [(La0.3Sr0.7MnO3)n/(SrTiO3)m]8 (LSMO/STO) superlattices grown in the (001) direction. We have performed angular dependent magnetotransport measurements with the magnetic field rotating out of the interface plane (see sketch in Figure 1). Besides the standard resistivity maxima for a perpendicular
N. M. Nemes, J. I. Beltrán, F. Y. Bruno, J. García-Barriocanal, Z. Sefrioui, C. León, J. Santamaría GFMC, Departamento de Física Aplicada III Universidad Complutense de Madrid Campus Moncloa E-28040, Madrid, Spain E-mail: [email protected] N. M. Nemes, M. J. Calderón, F. Y. Bruno, J. García-Barriocanal, Z. Sefrioui, C. León, M. García-Hernández, L. Brey, J. Santamaría Laboratorio de Heteroestructuras con aplicación en Spintronica, Unidad Asociada Consejo Superior de Investigaciones Científicas/ Universidad Complutense Madrid Sor Juana Inés de la Cruz, 3, E-28049 Madrid, Spain E-mail: [email protected] M. J. Calderón, J. I. Beltrán, M. García-Hernández, M. C. Muñoz, L. Brey Instituto de Ciencia de Materiales de Madrid ICMM-CSIC, Cantoblanco E-28049, Madrid, Spain
DOI: 10.1002/adma.201402829
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magnetic field, occurring for bulk manganites and two-dimensional STO systems,[15,16] we find an unexpected in-plane magnetoresistance peak. This peak is nearly independent of the relative orientation between the in-plane magnetic field and the current and is more prominent for the thinner manganite films, indicating an interfacial origin. Calculations of resistivity in a model system including spin-orbit coupling reveal that the inplane peak is due to transport through a two-dimensional (2D) system at the manganite interface. Density Functional Theory (DFT+U) calculations confirm that the 2D system results from a FM and metallic interfacial manganite layer antiferromagnetically coupled (A-type) to (and hence electrically decoupled from) the rest of the LSMO. The magnetic reconstruction is accompanied by an in-plane orbital polarization, consistent with X-ray absorption spectroscopy. Magnetoresistance measurements thus expose the character of the electronic reconstruction occurring at the interface between the FM and metallic LSMO and the insulating STO: A 2D FM metallic interfacial layer AFcoupled to the rest of the manganite layer (3D system). The presence of this AF layer at the LSMO interface may provide important clues for the depolarization of spin currents in magnetic tunnel junctions reported for this system.[17,18] The conduction electrons in perovskites are usually provided by the transition metal d-orbitals. These orbitals are split by the cubic crystal field in a lower t2g triplet and a higher eg doublet. The remaining degeneracies can be lifted by broken lattice symmetries, as in interfaces and surfaces, leading to confined orbital reconstructions. In particular, at a (001) interface the dxy orbital is shifted down with respect to the dyz and dxz orbitals[19–23] and the dx2-y2 and d3z2-r2 are also split.[8,24] These modifications are produced by both crystal-field distortions and changes in the bandwidth. The orbital reconstruction can be
B
LSMO STO
Figure 1. In-plane transport measurements are realized under a magnetic field rotating with respect to the interface plane. θ = 0 is for a magnetic field perpendicular to the interface plane (left). Picture that emerges from our experimental/theoretical results: the LSMO interface is magnetically reconstructed leading to an electrically decoupled 2D system (right).
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reflected in the magnetic and electronic properties of the interface. This is the case of cuprate/manganite heterostructures, where the suppression of the superconductivity close to the interface has been ascribed to the partial emptying of the d3z2-r2 orbital.[25] Different magnetic reconstructions have also been reported in all-manganite[26] and manganite/insulator[9,10,24] superlattices and thin films. Anisotropic magnetoresistance (AMR) is a common feature of metallic ferromagnets and is defined as the difference in the system resistivity when an in-plane magnetization vector is parallel or perpendicular to the current.[27,28] In manganites, the AMR is small compared to the one shown by FM alloys[29] and the maximum resistance corresponds to a magnetic field applied perpendicularly to the current.[28,30–32] More complicated angular dependences (with extra peaks for a magnetic field parallel to the current) have been found under particular circumstances in Fe3O4,[33] LAO/STO,[34,35] and La0.3Ca0.7MnO3.[31] Epitaxial superlattices of LSMO (a FM metal) and STO (a Figure 2. Angular MR for different superlattices and thin films at 5 K and diamagnetic insulator) were grown on (001) oriented STO sub14 T with I[010] geometry. Resistances are normalized with respect to the strates using high pressure (3.2 mbar) oxygen plasma sputout-of-plane value, ie. R/R(θ = 0). The height of the pMR-peak increases tering at high temperature (900 °C), starting with LSMO and as the thickness of the LSMO film decreases. Inset: pMR-peak vs. low terminating with STO, with a total of eight bilayers. The LSMO temperature residual resistivity (ρ) for the various samples (superlattices and thin films). is fully strained with an in-plane lattice parameter fixed by the STO substrate. Examining the interface chemistry by scanning LSMO films a new resistivity peak emerges for in-plane B, transmission electron microscopy with Electron Energy Loss which we call in-plane angular magnetoresistance (pMR) peak. Spectroscopy (EELS) analysis all interfaces are observed to be The height of the pMR-peak increases with decreasing manLa0.7Sr0.3O/TiO2.[11] X-ray magnetic circular dichroism and ganite film thickness, as illustrated by the inset of Figure 2. The EELS measurements have revealed a small charge transfer to peak is suppressed by increasing temperature, disappearing Ti giving rise to a magnetic moment which is antiparallel to around 20 K, and is enhanced by the magnetic field at low that on the Mn sites.[11] The 5*5 mm2 square samples were contemperatures (Figure 3) (see also Supporting Information). We tacted at the corners in the van der Pauw geometry, and were demonstrate here that the pMR-peak is produced by a 2DEG then cooled and rotated in an applied magnetic field (B). For forming at the LSMO interface. A 2DEG may also arise at the in-plane rotations, the typical maximum resistivity of AMR for STO interface, however our calculations show that it is not B perpendicular to the current is recovered. For out-of-plane responsible for the observed pMR. rotations, the symmetry we are focusing on here, the rotation axis was parallel to a sample edge, coinciding with the [100] The pMR is largest for the thinnest LSMO with thick STO crystal axis of the substrate. We employed two possible current separation. This can be understood in terms of two different directions, I[100] and I[010], along the rotation axis and perpendicular to it, respectively. θ = 0 corresponds to B perpendicular to the interface plane, and θ = π/2 to an in-plane field. Contrary to what would be expected of AMR, no qualitative difference between the two in-plane current orientations was found, although the magnetization always stays perpendicular to the I[100] current whereas the angle it makes with the I[010] current varies as the sample rotates in the applied field (see Supporting Information). The angular magnetoresistance displays two qualitatively distinct behaviours, with maxima for the magnetic field either along the surface normal or in-plane. The former is the typical AMR behavior of ferromagnetic manganite films. This is precisely what we observe in a 24 nm (65 unit cells) thick LSMO film on STO: a resistance maximum Figure 3. (a) Temperature and (b) magnetic field dependence of the pMR-peak (I[010] geomfor perpendicular B and a minimum for in- etry) at different B-fields and temperatures as indicated in the legends for a [LSMO8/STO2]8 plane B (Figure 2). In contrast, for thinner superlattice.
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transport channels: one in the “bulk” of the LSMO layers and the other at the LSMO/STO interfaces, connected in parallel. The relative weight of the interfacial scattering is strongest with thin LSMO layers. Note that Figure 2 mixes together superlattices and thin films, showing also the angular MR of a thin (5 nm) and a thick (24 nm) LSMO film, with only the former displaying weak pMR. The largest pMR, in a [LSMO7/STO6]8 superlattice, is approximately 1% of the corresponding resistivity. The resistivity in Figure 2 for superlattices with different LSMO and STO thicknesses shows the expected trend: with thicker LSMO or thinner STO barrier the resistivity is lower.[11] The inset of Figure 2 shows the pMR of the various thin films and superlattices as a function of the low temperature (residual) resistivity. The additional residual resistivity is a measure of the interface-contribution, and the pMR grows linearly with it. This supports the picture of a two-fluid model, where the additional LSMO layers simply decrease resistivity while the pMR originates at the interface. Magnetoresistance anisotropies arise due to spin-orbit coupling (SOC). This interaction, albeit generally small for the materials at hand, produces shifts and anticrossings in the bands, which are dependent on the external magnetic field intensity and its orientation with respect to the crystalline axes. Using a semiclassical formula based on the Boltzmann transport equation and assuming a constant (non-k dependent) scattering time τ, the conductivity tensor σij (inverse of the resistivity ρij) can be calculated as
σ ij = e 2τ ∑ ∫ d k n
∂ f (ε ) i v n ( k )v nj ( k ) ∂ε n ( k )
(1)
ρ (arb. units)
with n the band index, ε(k) the band dispersion, f(ε) the Fermi distribution function, and vi the velocity (∂ε(k)/∂ki) in the i direction. It is clear from this formula that modifications of the band structure close to the Fermi level (such as those produced by spin-orbit coupling and exchange or magnetic fields) are to be reflected on the transport properties. We calculate the angular dependence of the resistance of three different systems: a 3D manganite, a 2D STO, and a 2D manganite (see Figure 4), and compare them to the experimental results. We show that the pMR peak can only arise from a 2D manganite. Manganites are modeled here by a double exchange Hamiltonian in which the itinerant electron spins in the eg orbitals are strictly parallel to the localized t2g electrons[28,36] (see Supporting Information). The local magnetic moments follow the external magnetic field in such a way that
STO
3D manganite
2D manganite
(b)
(a)
0
the magnetization of the system is fully saturated (infinite B approximation). The SOC between the eg orbitals occurs only as a second order process through the t2g ones.[28] Figure 4(a) shows the resulting in-plane resistivity for a 3D manganite as a function of the angle θ between the applied magnetic field and the interface plane. Consistent with the experimental observation for the thicker films, this resistivity is found to be larger for an out-of-plane (θ = 0) magnetic field. The pMR peak can neither be attributed to the STO interface. X-ray circular dichroism measurements render a finite charge and magnetic moment on the Ti at the STO interface.[11] Therefore, we may have a 2DEG at the STO interface. The Ti t2g orbitals are split due to the broken translational symmetry in the z-direction, and the carriers only occupy dxy. However, this 2D system does not give rise to a larger in-plane resistivity either, as revealed by calculating the effect of a Rashba SOC[37,38] on its conductivity (see Figure 4(b)). Our theoretical results are consistent with the experimental measurement reported for LAO/STO.[15,16] Charge redistribution and broken translational symmetries in heterostructures are known to modify the properties of manganite interfaces: orbital polarization and different magnetic orders may arise.[10,12–14,24,26,39–42] In particular, the suppression of the hopping in the growth direction (z-direction here) can lead to the reduction of the d3z2-r2 orbital bandwidth and a preferential occupation of dx2-y2. This planar-like orbital order at the interface can favor an A-type magnetic ordering,[24,43–45] coupling the interface layer antiferromagnetically to the rest of the manganite. Such a 2D system would be electrically decoupled as hopping between sites with antiparallel spins is suppressed in half-metals by virtue of the double exchange mechanism.[36] We would then have two differentiated manganite systems, as illustrated in Figure 1: one constituted by the “bulk” of the thin film (3D manganite in the following) and a 2D one at the interface. The 3D manganite shows the expected maximum of the resistivity with an out-of-plane magnetic field. However, removing the hopping in the z-direction (in order to simulate a 2D system) produces an orbital polarization with a much larger occupation density of the d3z2-r2 orbital at the Fermi level EF (see Figure 10 in the Supporting Information). The d3z2-r2 band gets flatter at EF with an in-plane magnetic field, leading to a larger resistivity compared to the perpendicular field, as shown in Figure 4(c). Hence, the transport through a 2D system at the manganite interface leads to the observed in-plane magnetoresistance peak (pMR). Note that the large Hund coupling
π/4
π/2
θ
3 π/4
0
π/4
π/2
θ
3 π/4
(c)
0
π/4
π/2
θ
3 π/4
π
Figure 4. Resistivity calculated as the inverse of σ in Equation 1 (a) for a 3D manganite, (b) for a dxy orbital system and (c) for a 2D manganite. θ is the magnetic field orientation with respect to the normal to the interface plane: θ = π/2 corresponds to an in-plane magnetic field. A maximum resistivity in the in-plane direction, consistent with the experimental observation of an additional peak for θ = π/2 in Figure 2, is found for a 2D manganite which may be forming at the interface with the STO layer.
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Mn. All the Mn ions have partially filled eg states and all MnO2 planes are half-metals. The Density-of-States (DOS) at the Fermi level in the interface is very small because there is only one spin down band crossing the Fermi level (see Supporting Information). The Mn magnetic moments are –3.2, 3.4 and 3.5 µB moving away from the interface. Bulk behavior is already recovered in the central LSMO. These magnetic moments are consistent with the calculated small decrease of the Mn eg occupancy as one approaches the interface. In addition, there is a preferential occupation of the dx2-y2 orbital, which is slightly larger than the corresponding d3z2-r2. This orbital reconstruction is essentially confined to the interface. The orbital reconstruction at the interface is supported by X-ray linear dichroism Figure 5. Schematic half unit cell of the [LSMO14.5/STO2.5] superlattice as obtained from the results which show a tendency to increasing DFT calculation, showing the two different layers in the LSMO slab (left). Spin-resolved density of states projected on the atomic planes around the interface (right). The labeling corresponds occupation of dx2-y2 with respect to d3z2-r2 as the LSMO layer in a superlattice gets thinner to that of the unit cell, and upper (blue) and lower (red) lines within each plane represent, (see Supporting Information). respectively, the majority and minority spin densities. LSMO is a half-metal with inverse spinpolarization at the interface MnO2 layer. In summary, we have shown that in LSMO/STO superlattices there is a sharp magnetoresistance peak arising at low temperatures as the magnetic field is rotated towards the interapproximation used to describe manganites does not allow us face. Calculations of the resistivity taking into account the to study the dependence of the pMR on the magnetic field magspin-orbit coupling show that this in-plane peak signals the nitude and temperature. formation of a 2D manganite at the interface, decoupled from The coexistence of two decoupled 3D and 2D systems in the rest of the manganite layer, which could arise from a magthe LSMO slab is supported by DFT+U calculations. Several netic reconstruction. The 2D interfacial manganite would be ideal defect free [LSMOm/STOn] (001) superlattices have been ferromagnetic but antiparallel to the overall magnetization of studied. We use the plane-wave based Vienna ab initio simuthe layer. This reconstruction is supported by DFT+U calculation package (VASP) within the PBE+U approximation to lations. The X-ray absorption experiments clearly indicate an the exchange-correlation energy.[46,47] The superlattices have a in-plane orbital polarization of the interfacial eg Mn electrons. tetragonal structure and contain m and n unit cells of LSMO and STO, respectively. As observed experimentally for different Such magnetic modification could be related to the spin depomaterial systems, samples grown in high oxygen pressure by larization revealed by tunneling magnetoresistance measuresputtering are characterized by symmetric interfaces in most ments in manganite based tunneling devices. The anisotropic cases[10,11] (see Supporting Information). This corresponds magnetoresistance is hence giving away clues on the nature of the electronic reconstruction at oxide interfaces. nominally to consider half integer m and n values resulting in symmetric La0.7Sr0.3O/TiO2 interfaces. The calculations were spin-polarized: We considered parallel and antiparallel (FM and A-type AF) configurations at the interface with a collinear alignSupporting Information ment of the magnetization (see Supporting Information). Supporting Information is available from the Wiley Online Library or A two-layer model for the LSMO slab is considered, with from the author. a different stoichiometry at the interfaces, in order to take account of differences that may arise between the central part of the manganite layer and the interfaces. We have found that for a Sr-rich interface, an AF coupling between the interface Acknowledgements and the rest of the manganite layer is the most favored. This is We acknowledge funding from MINECO-Spain through grants FIS2012– consistent with the fact that the LSMO bulk phase diagram[36] 33521, MAT2011–27470-C02–01, MAT2011–27470-C02–02, MAT2012– shows an A-type AF phase for x > 0.5. The AF configuration is 38045-C04–04 and CSD2009–00013. JGB acknowledges funding by the lower in energy (EAF-EFM ∼ –30meV/Mn), independent of the ’Ramon y Cajal’ programme. values of m and n. Figure 5 shows the spin-resolved layer-projected density of Received: June 25, 2014 states for the [LSMO14.5/STO2.5] superlattice with a Sr-rich interRevised: August 29, 2014 face. Crucially, the spin polarization is inverted on the interface Published online: October 18, 2014
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