Confinement of magnetism in atomically-thin $La_{0.7}Sr_{0.3}CrO_3$/$La_{0.7}Sr_{0.3}MnO_3$ heterostructures

At crystalline interfaces where a valence mismatch exists, electronic and structural interactions may occur to relieve the polar mismatch leading to the stabilization of non-bulklike phases. We show that spontaneous reconstructions at polar $La_{0.7}Sr_{0.3}MnO_3$ interfaces are correlated with suppressed ferromagnetism for film thicknesses on the order of a unit cell. We investigate the structural and magnetic properties of valence-matched $La_{0.7}Sr_{0.3}CrO_3$ - $La_{0.7}Sr_{0.3}MnO_3$ interfaces using a combination of high-resolution electron microscopy, first principles theory, synchrotron X-ray scattering and magnetic spectroscopy and temperature-dependent magnetometry. A combination of an antiferromagnetic coupling between the $La_{0.7}Sr_{0.3}CrO_3$ and $La_{0.7}Sr_{0.3}MnO_3$ layers and a suppression of interfacial polar distortions are found to result in robust long range ferromagnetic ordering for ultra-thin $La_{0.7}Sr_{0.3}MnO_3$. These results underscore the critical importance of interfacial structural and magnetic interactions in the design of devices based on two-dimensional oxide magnetic systems.


MAIN TEXT Introduction
Structural, electronic and magnetic interactions at the interfaces between thin films of crystalline polar transition metal perovskites have led to the realization of a wide range of physical phenomena not found in the bulk constituent materials. These exotic phenomena, which include, twodimensional electronic gases, interfacial magnetism and superconductivity and orbital ordering are driven by interfacial chemical, structural, electronic and orbital reconstructions which serve to alleviate the polar mismatch at these interfaces. [1,2] A consequence of these reconstructions is that significant deviations in the atomic scale structural and electronic properties of atomic layers adjacent to the polar interfaces arise. Due to the strong coupling of the structural, electronic and magnetic properties in these materials, detrimental effects may be induced in layers close the interface leading to strong thickness-dependent physical properties. [3][4][5] To confine the functional properties of transition metal perovskites to two-dimensions in order to realize novel phenomena associated with quantum confinement and engineer novel device architectures including spin-tunnel junctions, understanding and controlling these interfacial interactions is crucial. Additionally, in multiferrroic heterostructures where the magnetoelectric coupling effect is confined to interfacial layers, [6] reducing the thicknesses of the component layers to the order of a unit cell will lead to an enhanced coupling of ferroic order parameters.
An important system which displays thickness-dependent transitions related to interfacial interactions is the LaSrMnO3 (LSMO)/SrTiO3 (STO) interface. LSMO films have been explored for their half-metallic properties and colossal magnetoresistance effects with applications in spintronic devices. [6] The magnetic and electronic properties are related to the Mn-O bond properties in neighboring unit cells through double exchange interactions and Jahn-Teller effects. [7] Distortions to the Mn-O bond angle achieved by chemical substitution and strain results in a modulation of the magnetic and electronic phases. [8] When grown as epitaxial thin films, properties of LSMO can be coupled to other functional oxides including ferroelectric and superconducting perovskite transition metal oxides. [6,9,10] LSMO films have been reported to undergo a ferromagnetic to paramagnetic transition for film thicknesses below 4-10 unit cells (uc) when grown on lattice-matched STO substrates. [3,11] The thickness-dependent phase transition has been attributed to interfacial interactions driven by the polar mismatch between the two materials. These interactions include interfacial ionic intermixing which leads to deviations in the composition of interfacial LSMO layers, [12,13] interfacial charge transfer evidenced by X-ray absorption spectroscopy and electron microscopy measurements, and ferro-distortive ionic displacements. [14][15][16] To eliminate the interfacial interactions which lead to suppressed magnetism, we show that the insertion of La1-xSrxCrO3 (LSCO) spacer layers at LSMO interfaces removes polar structural distortions observed at LSMO interfaces [14] and couples to the lattice symmetry of LSMO leading to robust ferromagnetism down to 2 uc in LSCO (M uc)/LSMO (N uc)/LSCO (M uc) (M/N/M) heterostructures grown on (001)-oriented STO substrates by molecular beam epitaxy. The role of the LSCO spacer is two-fold: (1) By matching the La/Sr ratio of the LSCO to the LSMO film, the polar mismatch at the LSMO interface is effectively removed and (2) LSCO which has a R3c symmetry with aaarotations (160 o Cr-O-Cr bond angle, 3.88 Å pseudocubic lattice constant) [17] couples to the oxygen octahedral rotations in LSMO alleviating the oxygen-octahedral mismatch. [18,19] Additionally, we observe an antiferromagnetic exchange interaction between the Cr and Mn ions at the LSMO/LSCO interface. Using a combination of temperature-dependent magnetometry, picometer-scale synchrotron X-ray based /structural characterization and elementspecific magnetic spectroscopy, we demonstrate the enhancement of ferromagnetic ordering in ultra-thin LSMO films, and the stabilization of bulklike ferromagnetism in LSMO layers as thin as 2 uc (0.8 nm). The results are confirmed by first principles theory.

LSMO films and LSCO (M)/LSMO (N)/LSCO (M) (M/N/M) heterostructures and [LSCO (M)/
LSMO (N)] superlattices were synthesized by plasma-assisted oxide molecular beam epitaxy at a growth temperature of 800 o C. The LSMO thickness, N, was varied from 2 to 10 uc while the LSCO thickness, M, was fixed at either 2 or 3 uc to be above the decay length for surface polar distortions observed for LSMO [14] and LaNiO3 [20] films. A schematic of the heterostructures is shown in Figure 1(a). As shown in Figure 1(b), the LSCO layers possess the same +0.7/-0.7 net charge stacking along the growth direction. Hence, no polar discontinuity exists at the LSMO top and bottom interfaces. RHEED oscillations are observed for all the layers indicative of layer-by-layer growth as shown in Figure 1(c). The surface morphology of the films were characterized by atomic force microscopy. A representative atomic force microscope image is shown in Figure 1(d) for the 3/3/3 sample with a surface roughness of less than 1 unit cell.

High-resolution electron microscopy measurements
The aberration-corrected high angle annular dark field-scanning transmission electron microscopy (HAADF-STEM) (Z-contrast) image in Figure 1(e) shows the 2/6/2 heterostructure. Energydispersive x-ray spectroscopy (EDS) chemical maps reveal some chemical intermixing within a unit cell between Mn and Cr layers and Ti migration across the LSCO/STO interface. [21] In contrast, the La signal drops abruptly at the interface. Electron energy-loss spectroscopy (EELS) was also performed in the STEM to track relative variations in Mn and Cr oxidation state across the film with the L3/L2 white line ratio according to the method described by Tan, et al. [22]

Magnetization Measurements
The magnetic properties of the LSMO thin films and M/N/M heterostructures and [M/N] superlattices were characterized using a Quantum Design SQUID system. The magnetization curves normalized to the Mn are shown as a function of field and temperature at 10 K for M=3 and N=2,3,4,6 and 10 in Figure 2(a) and 2(b), respectively. Temperature-dependent curves were recorded after field cooling the samples in a 1 Tesla field applied in-plane. As will be discussed later, the magnetization in the LSMO sublattice is determined to be closed to bulk, and the reduced net SQUID magnetization as the LSMO thickness decreases is related to the contribution of antiparallel spins in the LSCO layers resulting from antiferromagnetic interactions between the LSMO and LSCO layers.
In contrast to the single layer LSMO films, the 3/N/3 heterostructures remain ferromagnetic down to N=2. Inserting 3 uc LSCO at the LSMO top and bottom interfaces results in ferromagnetic ordering below~150 K compared with the 2 uc LSMO films grown directly on STO which remains paramagnetic down to 2 K. To verify that the magnetism in the heterostructures is not within the LSCO layers alone, the magnetization for a 6 uc LSCO layer was measured and found to be similar to the STO substrate down to 2 K as shown in Figure S1 of the supplementary materials. [23] The results for the LSCO film are consistent with bulk LSCO which is a G-type antiferromagnet. [17] We further elucidate the magnetic coupling at LSCO/LSMO interface by measuring the magnetization hysteresis loops after cooling down the sample in ±0.5 T applied in-plane field. superlattice. There is a negative (positive) shift in the hysteresis loop when a positive (negative) field has been applied, indicating reversible switching of exchange bias. The exchange bias field is 332 Oe for both positive and negative field-cooled hysteresis loops. [24,25]

X-ray Circular Dichroism Measurements
To further confirm that the observed ferromagnetism in the 3/N/3 heterostructures occurs in the LSMO layers, we performed element specific X-ray magnetic circular dichroism (XMCD) measurements at the Mn and Cr L2,3 absorption edges at 4.0.2 beamline at the Advanced Light Source using total electron yield. The absorption spectra at the Cr and Mn edges are consistent with previous measurements for La1-xSrxCrO3 [21] and La1-xSrxMnO3 for x=0.3. The difference between the X-ray absorption spectra measured with right (+) and left (-) circular-polarized light yields element-specific magnetic information for the Mn and Cr ions. The XMCD measurements were confirmed by switching the magnetic field direction. XMCD with a 0.5 Tesla in-plane field at 15 K are shown in Figure 3(a) and 3(b) at the Mn and Cr L-edges, respectively for a 3/3/3 sample.
Dichroic signals were observed at the Mn and Cr edges indicating magnetic ordering on both the Mn and Cr sublattices. The XMCD hysteresis loop measured at the Mn L-edge in Figure 3(c) confirms that the LSMO layer is ferromagnetic. The dichroic signal at the Cr L-edge, while weak, exhibits an identical field dependence to the results at the Mn edge but in the opposite direction as shown in Figure 3 The temperature dependence of the XMCD signal for a 3/6/3 heterostructure is shown in Figure   3(e) at the Mn L-edge. A reduction in the XMCD signal is observed as the temperature is increased from 80 K to 300 K. The magnitude of the XMCD intensities at the Cr and Mn L-edges are compared as a function of temperature in Figure 3(f) for the 3/6/3 sample. At both edges, a transition to a paramagnetic state is observed at ~ 200 K in agreement with the SQUID measurements in

Role of Structural Coupling at the LSMO/LSCO Interface
To determine the contribution of the atomic-scale structure to the enhanced magnetization, synchrotron surface diffraction experiments were performed at the 33ID beamline at the Advanced Photon Source to image the atomic-scale structures of the interface-engineered heterostructures.
Crystal truncation rods (CTRs) and superstructure rods were measured to determine the atomic scale structures and octahedral rotations profiles. The crystalline quality of the 3/N/3 heterostructures is confirmed by the observance of clear Laue oscillations along the off-specular CTRs ( Figure S3 in the Supplementary Materials) [23]. The CTRs were converted to real-space 3D electron density maps using the coherent Bragg rod analysis (COBRA) [20] phase retrieval technique from which the layer resolved atomic positions were extracted and refined using the GenX X-ray fitting algorithm [26]. From this analysis, the atomic positions were determined with sub-picometer resolution. The rotation of the oxygen octahedra in the LSMO and LSCO layers leads to a doubling of the perovskite unit cell and half order rods in reciprocal space. The amplitude of the octahedral rotations are determined from fits to the integer-order crystal truncation rods and the half-order rods measured ( Figure S4 of the Supplementary Materials) [23] for the samples.
The converged structure for the 3/3/3 sample is shown in Figure 4(a). Out-of-phase (aacin the To confirm that the suppressed distortions in the LSMO layers encapsulated with LSCO are related to the absence of polar discontinuities at the LSMO interfaces, we compare the layer-resolved lattice cation-anion displacements along the growth direction for a 4 uc LSMO film and a 3/4/3 heterostructure grown on (001) oriented SrTiO3 are shown in Figure 5(a) and Figure 5(b), respectively. The measured crystal truncation rods and half-order Bragg peaks for the 3/4/3 sample are shown in Figure S5 and S6 respectively, of the Supplementary Materials. At the surface of the 4uc LSMO film and the LSCO cap layer of the 3/4/3 sample, the O anions are displaced toward the substrate relative to the cations. The ionic rumpling decays 3 uc below the film surface in agreement with previous results for a 10 uc LSMO film [14] and uncapped LaNiO3 films. [20]. While polar distortions are observed in the 4 uc LSMO film, the distortions are suppressed in the encapsulated LSMO layers in the 3/3/3 and 3/4/3 samples.
The ionic displacements at the uncapped LSMO film surface are related to a surface electric field which arises due to the polar MnO2 -terminated surface with a net -0.7e charge. The decay length for the surface distortions are found to be on the order of 3 uc (~12 Å) which is consistent with the enhanced screening length observed for the rare-earth nickelates [20] and theoretical predictions for the manganites [15,16]. For the uncapped LSMO film, the surface ionic rumpling leads to an elongation in the Mn-O bond-length which is correlated with reduced double exchange interactions and a suppression of ferromagnetic ordering in the uncapped LSMO film. [14,16,28] On the other hand, the polar distortions are suppressed in the LSMO layers encapsulated with LSCO spacers leading to ferromagnetism in the LSCO/LSMO heterostructures. The measured layer resolved polar displacements for the 3/4/3 heterostructure shown in Figure 5(b) show that the polar distortions are confined to the top LSCO layer. The absence of polar distortions at the LSCO/STO substrate interface may be related to a reduction in the interface polar discontinuity driven by chemical intermixing observed in Figure 1(e). While the surface distortions may arise due to incomplete surface layers and atomic vacancies, the direction of the distortions point to the surface field as a significant driver for the observed distortions. [14,20,29] The structural measurements and XMCD results confirm that the insertion of LSCO spacer layers leads to bulk-like Mn-O bonding and stoichiometric LSMO layers which are correlated with the stabilization of ferromagnetization in the encapsulated LSMO layers. The elimination of magnetic dead layers in the LSCO/LSMO/LSCO heterostructures is in contrast to the analogous nominally valence-matched La0.6Sr0.4FeO3(LSFO)/La0.6Sr0.4MnO3 interface where dead layers still exist. [30] At the LSFO/LSMO interface, an inherent charge transfer between Fe and Mn occurs which hole dopes the LSMO layers leading to antiferromagnetic interfacial LSMO layers. [30] This transfer, is reduced at the LSCO/LSMO interface, as evidenced by the ferromagnetic ground state of the 3/N/3 heterostructures.
The magnetization measured by SQUID normalized to the LSMO thickness in Figure 2  is consistent with this assumption. Additionally, we find that the Mn XMCD signal for a 3/2/3 and 3/3/3 heterostructure ( Figure S2(b)) are identical, in agreement with the assumption above.

Determination of Mn and Cr moments in [LSCO/LSMO] superlattices
To further validate the model described above  The theoretical Cr magnetic moment is overestimated compared to the experiment: this is likely because our calculations are done by treating the spins in the approximation that they are collinear (rather than non-collinear) [37]. For the experimental results discussed above, it is likely the spins on the Cr atoms suffer from frustration due to a competition between two magnetic interactions.

First Principles Theory
The first coupling is across the interface with the Mn where the interfacial Cr atoms are anti-aligned with the FM Mn atoms at the interface. The second effect is the coupling within LSCO itself which in the bulk is of AFM-G type [17].

Discussion
Based on the Goodenough-Kanamori rules, a FM superexchange interaction is expected between Mn 3+ (d 4 , t2g 3 eg 1 ) and Cr 3+ (d 3 , t2g 3 eg 0 ) due to eg 0 -eg 1 interactions as has been observed in LaMn-xCr1-xO3 [38]. Confinement and the tensile epitaxial strain imposed by the STO substrate will lead

Sample Preparation
The LSCO layers and the LSMO films were grown at 800 o C in 3x10 -6 Torr atomic oxygen from an oxygen plasma source on TiO2-terminated SrTiO3 (Crystec) substrates by molecular beam epitaxy. The films were grown by co-deposition from effusion cells at a growth rate of approximately 1 unit cell per minute. After growth, the samples were slowly cooled down at 5 o C/min in 5x10 -6 Torr oxygen in the growth chamber to ensure complete oxidation. The film thickness and surface crystallinity were monitored in-situ by reflection high energy electron diffraction (RHEED).

Electron Microscopy
Electron microscopy samples were prepared by conventional cross-section mechanical polishing and argon ion milling. Aberration-corrected high angle annular dark field-scanning transmission electron microscopy (HAADF-STEM) imaging and energy-dispersive x-ray spectroscopy (EDS) were performed using a FEI Titan G2 60-300 kV operated at 200 kV with a convergence semiangle of 19.6 mrad. The electron beam was monochromated to achieve 0.4 eV energy resolution and a dispersion of 0.05 eV/channel was used. Electron energy loss spectroscopy (EELS) was performed to determine the variation of Cr and Mn valence by tracking three spectral features across the LSCO/LSMO heterostructure: the energy-loss near edge fine structure (ELNES), the energy shift of the L-edges, and the L3/L2 integrated white line ratio (WLR) [22,43]. EELS data were collected by acquiring 2-D spectrum images of the film at a sampling rate of approximately 1Å/pixel.

SQUID Magnetization Measurements
The magnetic properties of the LSMO thin films and M/N/M heterostructures and [M/N] superlattices were characterized using a Quantum Design SQUID system. The temperature dependent magnetization curves were measured on warming in an applied in-plane field of 1 KOe.

Synchrotron Diffraction Measurements
Synchrotron to a 5% increase in the optimal crystallographic R1 factor.

Soft X-ray XAS and XMCD Measurements
Soft X-ray magnetic circular dichroism (XMCD) measurements at the Mn and Cr L2,3 absorption edges at were performed at the 4.0.2 beamline at the Advanced Light Source using total electron yield. A magnetic field of 0.5 Tesla was applied parallel to the sample surface.

Density Functional Theory Methodology
The DFT calculations have been performed using the Quantum Espresso code [35] using the PBE exchange correlation functional [34] and ultrasoft pseudopotentials [36] using a k-mesh of 7x7x5 for the bulk 20 atom unit cell and 7x7x3 for the 40 atom superlattices. For a c(2x2)x2 20 atom unit cell for LSMO we obtain an in-plane lattice constant of 3.90 Å and simulate the strain to the STO lattice constant by imposing an in-plane lattice constant of 3.905 Å on the superlattices.
For bulk LSMO we correctly obtain a ferromagnetic ground state. However, for the LSCO we obtain AFM-C instead of AFM-G as the ground state. For a 20 atom unit cell we find that the AFM-G state is 24 meV higher than AFM-C; while the AFM-A state is 86meV and FM state is 213 meV higher than AFM-C. It is likely that the issues in LSCO calculations are due to the fact that we are using a collinear spin calculation, as applying a U did not stabilize the AFM-G ground state and previous studies have used a non-collinear spin calculation to correctly predict the AFM-G ground state. Finally, we need a correct way to estimate the local magnetic moment of the atoms, as we notice that in bulk STO-strained LSMO, the magnetic moment calculated on the Mn site using Competing interests: There are no competing financial interests of the authors. Data and materials availability: Additional data related to this paper may be requested from the authors.

Magnetic Measurements
An important issue in measuring the magnetic signals of ultra-thin films is determining the contribution of the underlying substrate. Bulk SrTiO3 is expected to be diamagnetic however, the presence of magnetic impurities on the ppm level and high temperature annealing conditions can lead to finite ferromagnetism and paramagnetic effects. Figure S1 show the uncorrected magnetization versus temperature for a bare STO, a 2 uc LSMO film, a 6 uc LSCO film and a LSCO(3)/LSMO(2)/LSCO(3) (3/2/3) heterostructure grown on STO. It is evident from the raw data that a ferromagnetic signal sits atop a paramagnetic background only for the 3/2/3 heterostructure.
The ferromagnetic ordering in the 3/2/3 heterostructure is confirmed by the magnetization versus field measurements as shown in Figure 2 of the main text.

Structural refinement
The atomic coordinates, layer composition and Debye-Waller factors extracted from the COBRAderived electron densities are refined using the GenX fitting program. The layer resolved oxygenoctahedral tilts and rotations are determined by fitting the measured integer-order crystal truncation rods ( Figure S3) and the half-order rods ( Figure S4) for the 3/3/3 sample. The corresponding rods are shown in Figure S5 and Figure S6 for the 3/4/3 sample. For the fit, we assume equal fractions of 4 90 o rotation domains.

Effect of growth conditions on magnetization
Two growth procedures were compared for the synthesis of the LSCO (M)/LSMO (N) heterostructures by MBE. In the first approach, the LSCO (M)/LSMO (N) heterostructures were LSCO layers were grown in 10 -8 Torr molecular oxygen and the LSMO films were grown in 3x10 - 6 Torr atomic oxygen from a plasma source. The samples were cooled down in 1x10 -6 Torr oxygen in the growth chamber at a rate of 25 o C/minute. Film growth was followed by an ex-situ post anneal in high purity O2 at 700 o C for 12 hours to minimize the formation of Oxygen vacancies. The second approach involved the growth of both the LSCO and LSMO layers at in 3x10 -6 Torr atomic oxygen from a plasma source. The samples were cooled down at 5 o C/min in 5x10 -6 Torr oxygen in the growth chamber to ensure complete oxidation. We find that while both growth methods result in ferromagnetic ground states, the second approach leads to higher paramagnetic-ferromagnetic transition temperatures and higher net moments. The differences may be attributed to differences in oxygen stoichiometry of the LSMO layers. For the first method, the low oxygen pressure used for the LSCO growth may result in a slight reduction of the LSMO layers which is avoided by growing both layers in a high oxygen pressure.

Electron energy-loss spectroscopy (EELS)
EELS was performed to map the variation of Cr and Mn valence by tracking three spectral features across the LSCO/LSMO heterostructure: the energy-loss near edge fine structure (ELNES), the energy shift of the L-edges, and the L3/L2 integrated white line ratio (WLR) [22,43]. EELS data were collected by acquiring 2-D spectrum images of the film at a sampling rate of approximately 1Å/pixel (additional experimental parameters are given in the main text). Figure S10(a) shows an EELS elemental color map and a HAADF-RevSTEM [44] image overlaid, revealing the alternating LSCO and LSMO layers. Rows of the spectrum images were averaged to achieve the Cr and Mn L-edge intensity images shown in Figures S10 (b,c), with the distance from the interface corresponding directly to Figure S10 Figure S10 (d) also as a function of film depth) was determined following the process outlined by Tan, et al. [22] with a custom Matlab script including Fourier-ratio deconvolution to remove plural scattering effects, a two-step background correction, and integration of the peaks with a 4 eV integration window per peak. The WLR is related to valence by an exponential function, but the values are roughly inversely proportional.