Anisotropic spin-density distribution and magnetic anisotropy of strained La$_{1-x}$Sr$_x$MnO$_3$ thin films: Angle-dependent x-ray magnetic circular dichroism

Magnetic anisotropies of ferromagnetic thin films are induced by epitaxial strain from the substrate via strain-induced anisotropy in the orbital magnetic moment and that in the spatial distribution of spin-polarized electrons. However, the preferential orbital occupation in ferromagnetic metallic La$_{1-x}$Sr$_x$MnO$_3$ (LSMO) thin films studied by x-ray linear dichroism (XLD) has always been found out-of-plane for both tensile and compressive epitaxial strain and hence irrespective of the magnetic anisotropy. In order to resolve this mystery, we directly probed the preferential orbital occupation of spin-polarized electrons in LSMO thin films under strain by angle-dependent x-ray magnetic circular dichroism (XMCD). Anisotropy of the spin-density distribution was found to be in-plane for the tensile strain and out-of-plane for the compressive strain, consistent with the observed magnetic anisotropy. The ubiquitous out-of-plane preferential orbital occupation seen by XLD is attributed to the occupation of both spin-up and spin-down out-of-plane orbitals in the surface magnetic dead layer.


INTRODUCTION
Magnetic anisotropy is one of the most important properties of ferromagnets and its external control has been a major challenge both from the fundamental and applied science points of view 1 . From the application point of view, enhancement of the magnetic anisotropy is necessary to realize magnets with high coercive fields, which can be utilized as high-density energy-storage magnets. From the scientific point of view, elucidating the microscopic origin of magnetic anisotropy has been an important issue because it is generally governed by the complex interplay between spin-orbit interaction and microscopic electronic states such as spin and orbital magnetic moments, band structures, and anisotropy of charge/spin densities. Especially, the magnetic anisotropy of ferromagnetic thin films is of great interest and importance because it can be controlled, e.g., by changing epitaxial strain and film thickness.
As for oxide materials, the perovskite-type manganese oxide La 1−x Sr x MnO 3 (LSMO) has been the most extensively studied ferromagnet due to its intriguing physical properties such as colossal magnetoresistance (CMR) and half-metallicity. The physical properties of LSMO can be controlled in various ways, e.g., by changing hole concentration x, substrate and the C-type AFM insulating phase under compressive strain from a LaAlO 3 (LAO) (001) substrate. The magnetic anisotropy of the LSMO thin films also depends on the epitaxial strain: the magnetic easy axes are in-plane when grown on the STO substrate and out-of-plane when grown on the LAO substrate 4,5 . First-principles calculations have predicted that the d x 2 −y 2 orbital is preferentially occupied under the tensile strain and that the d 3z 2 −r 2 orbital is preferentially occupied under the compressive strain 3 . However, previous x-ray linear dichroism (XLD) experiments have shown that the d 3z 2 −r 2 orbital is preferentially occupied for both STO and LAO substrates 6-8 . This apparent discrepancy with theory has been ascribed to the different orbital occupation between the surface and the bulk, that is, the spatial symmetry breaking at the surface leads to the preferential occupation of the d 3z 2 −r 2 orbital 6-8 . Thus, the microscopic electronic and magnetic states of LSMO thin films and their relationship with the macroscopic magnetic properties have remained elusive so far.
In the present work, we have employed a method which directly probes the orbital occupation of spin-polarized electrons using angle-dependent x-ray magnetic circular dichroism (XMCD) in core-level x-ray absorption spectroscopy (XAS). In the XMCD spin sum rule 9 , in addition to the well-known term which represents the spin magnetic moment M spin , there is an additional term called 'magnetic dipole term' M T which represents the spatial anisotropy of spin-density distribution, namely, the orbital shapes of the spin-polarized electrons. While XLD is sensitive to the orbital polarization of all the valence electrons, XMCD is sensitive to the orbital polarization of only spin-polarized electrons and, therefore, one can directly probe the orbital states of electrons which contribute to the ferromagnetism. In general, it is difficult to deduce M spin and M T separately from a single XMCD spectrum by using the sum rule. However, as we shall see below, one can separate the magnetic moment into the M spin and M T components from the angular dependence of the XMCD spectra, because they have different angular dependencies [10][11][12][13] . Hence, the spatial anisotropy of the spin-polarized electrons in the ferromagnetic materials can be deduced in addition to the total spin magnetic moment.
Especially, in the geometry where M spin is perpendicular to the incident x rays [so-called transverse XMCD (TXMCD) geometry] 11 , one can extract the pure M T component.
Although TXMCD has been theoretically studied since two decades ago [10][11][12][13][14] , there have been only few experimental reports [15][16][17][18] because the direction of the magnetic field is fixed parallel or nearly parallel to the incident x rays in conventional XMCD measurement systems. Recently, we have developed an apparatus for angle-dependent XMCD experiments using a vector-type magnet where the direction of the magnetic field can be rotated using two pairs of superconducting magnets 19 . In this paper, we report on the angle-dependent XMCD and TXMCD experiments on ferromagnetic LSMO (x = 0.3) thin films grown on STO and LAO substrates, and investigate the effect of epitaxial strain on the orbital states of spin-polarized electrons. We have revealed that the LSMO thin film under tensile (compressive) strain has d x 2 −y 2 -like (d 3z 2 −r 2 -like) spin-density distribution, which is different from the charge-density distribution deduced from the XLD measurements. The origin of the difference between the spin-and charge-density distributions is attributed to the preferential occupation of both the spin-up and spin-down d 3z 2 −r 2 orbitals at the surface, which suggests the formation of magnetic dead layers at the surface.

RESULTS
Angular dependence of XMCD spectra and TXMCD. Figure 1a shows a schematic drawing of the experimental setup for angle-dependent XMCD. One can change the direction of the external magnetic field using two sets of superconducting magnets orthogonally arranged. The experimental geometry is schematically drawn in Fig. 1b with the definition of the angles of incident x rays (θ inc ), applied magnetic field (θ H ), and magnetization (θ M ). Note that in general θ M is not equal to θ H unless the applied magnetic field is large enough to fully align all the electron spins along the magnetic field direction. According to the XMCD sum rules 9,20 , the 'effective' spin magnetic momentP · [M spin + (7/2)M spin ] is proportional to ∆I 3 + 2∆I 2 , whereP is a unit vector along the x-ray incident direction, and ∆I 3 and ∆I 2 are the integrals of the XMCD spectra over the Mn L 3 (2p 3/2 → 3d) and Mn L 2 (2p 1/2 → 3d) absorption edges, respectively. Under the assumption that the orbital magnetic moment M orb and the magnetic dipole moment M T are small enough compared to M spin , the projected spin magnetic momentP · M spin is approximately proportional to the XMCD integrals ∆I 3 or  directed nearly perpendicular to the incident x rays (P · M spin ∼P · M ∼ 0) around these θ H 's, namely, the TXMCD geometry is expected to exist around these angles.
The orange and green curves in Fig. 3a shows the expanded XMCD spectra for LSMO/STO at θ H = −20 • and for LSMO/LAO at θ H = −50 • , respectively. (We note that we have chosen these angles by the comparison with theoretical TXMCD spectra, as described below.) Finite XMCD signals, which is expected to originate from the magnetic dipole term M T , are clearly observed. One may suspect that M spin is not precisely aligned perpendicular to the x rays and yields this finite XMCD signals. This possibility, however, can be ruled out because the line shapes of the observed XMCD spectra are quite different from those of the conventional (longitudinal) XMCD (black curve in Fig. 3a).
Furthermore, the spectral line shapes of LSMO/STO and LSMO/LAO are nearly identical but only the sign of the spectra is reversed. This suggests that the sign of M T , namely the anisotropy of the spin-density distribution, is reversed reflecting the opposite epitaxial strain.
In order to show that the obtained spectra arise from genuine TXMCD, we have calculated the TXMCD spectra under tensile or compressive strain using the Mn 3+ O 6 cluster model  Table 1. The K u values in Table 1 (K u > 0 corresponding to out-of-plane easy axis) clearly show that finite MCA is present in the LSMO/STO (LSMO/LAO) thin film which favors in-plane (out-of-plane) easy magnetization, consistent with the present (Supplementary Fig. 3) and previous 4,5 magnetic measurements. Table 1 also shows that the electric quadrupole moment Q zz = 1 − 3ẑ 2 is positive (negative) for the STO (LAO) substrate. Since (7/2) Q zz = +2 for the d x 2 −y 2 orbital and (7/2) Q zz = −2 for the d 3z 2 −r 2 orbital (as shown in the first column of Fig. 1  is more x 2 − y 2 -like for the STO (tensile) substrate and more 3z 2 − r 2 -like for the LAO (compressive) substrate. This supports the TXMCD result that the spin-density distribution in the strained LSMO thin films is anisotropic. The degrees of the preferential orbital polarization |(7/2) Q zz /2| are estimated to be ∼ 2.5% and ∼ 6% for LSMO/STO and LSMO/LAO, respectively.
The advantage of the present method in deducing the magnetic anisotropy from the angle-dependent XMCD is that one can eliminate the effect of extrinsic spectral changes due to the saturation effect 25 , because the incident angle of the x rays is fixed. In addition, this method can be used in principle for dilute magnetic systems such as ultrathin films and lightly-doped magnetic semiconductors, for which the conventional magnetometry is hardly applicable, offering the possibility of estimating the magnetic anisotropy of these systems more accurately.

DISCUSSION
The deduced anisotropic spin distribution in the LSMO thin films (x 2 − y 2 -like in the case of the STO substrate and 3z 2 − r 2 -like in the case of the LAO substrate) is consistent with the preferential orbital occupation expected from the strain from the substrate. It is also consistent with the preferential orbital occupation which has been suggested by the transport and magnetic measurements and the density-functional calculation 3 . On the other hand, the results of XLD measurements 6 show that the d 3z 2 −r 2 orbital is more preferentially occupied than the d x 2 −y 2 orbital even in the case of tensile strain (STO substrate), which has been attributed to the symmetry breaking at the surface and interface 8 . The reason why the preferential orbital occupation seen by XMCD is consistent with that expected from the strain, in spite of its surface sensitivity comparable to XLD, may become apparent if one notices that XMCD is sensitive only to the spin-polarized electrons while XLD is sensitive to all the d electrons. If the majority part of the surface Mn atoms occupies the d 3z 2 −r 2 orbital due to the symmetry-breaking effect but are not spin-polarized, the 3z 2 − r 2 -like charge-density distribution at the surface and interface should be observed in the XLD measurements, while the x 2 − y 2 -like spin-density distribution from underneath layers should be observed in the XMCD measurements.
Indeed, there have been several reports which suggest the presence of magnetic dead layers at the surface or the interface of the FM LSMO thin films 26,27 . The present angle-dependent XMCD and TXMCD studies, therefore, indicate close connection between the magnetic dead layer and the 3z 2 − r 2 -like preferential orbital occupation at the surface of LSMO thin films. Further experiment is needed in order to test this hypothesis, e.g., by XLD measurements in the fluorescence-yield mode, in which we expect similar orbital polarization as the present study due to the longer penetration depth of the fluorescence-yield mode than the electron-yield mode.

Sample preparation.
LSMO (x = 0.3) thin films were grown on Nb-doped STO (001) and undoped LAO (001) (in the pseudo-cubic notation) substrates by laser molecular beam epitaxy 28  The XAS and XMCD measurements were performed using a vector-magnet XMCD apparatus 19 with circularly polarized soft x rays at the helical undulator beam line BL-16A2 of KEK-PF. The measurement temperature T for the LSMO/LAO film was 30 K, while it was set to 270 K for the LSMO/STO film. A lower T was chosen for the LSMO/LAO film because the saturation magnetization at room temperature was low 3 , while a higher T was chosen for the LSMO/STO film because the magnetic anisotropy at low temperature was too large to saturate the magnetization along the magnetic hard axis (out-of-plane direction). The strength of the applied magnetic field was 0.7 T for the LSMO/STO film and 0.5 T for the LSMO/LAO film. The spectra were taken in the total electron-yield mode, which is a relatively surface-sensitive measurement mode (with a probing depth λ of ∼ 3 nm) 25 . When the magnetic field is applied nearly parallel to the film surface, photo-ejected electrons are absorbed back to the sample due to the Lorentz force and the photocurrent drops to almost zero. In order to avoid this, we applied a negative bias voltage of ∼ 200 V to the sample holder to help the photo-ejected electrons escape from the samples. The measurements were performed at a pressure of ∼ 1 × 10 −9 Torr. The intensity of the incident x rays was monitored by a photocurrent from the post-focusing mirror.
Cluster-model calculation. octahedral cluster with D 4h symmetry (elongated or shrunk along the [001] direction) was used (Fig. 3c). The energy levels of the Mn 3d orbitals under this symmetry are schematically drawn in Fig. 3d. The Mn 3d, Mn 2p core, and O 2p orbitals were taken as basis functions. Charge transfer from the ligand O 2p to the Mn 3d orbitals was taken into account, and we considered three electron configurations for both the initial and final states: 2p 6 3d 4 , 2p 6 3d 5 L, and 2p 6 3d 6 L 2 for the initial state, and 2p 5 3d 5 , 2p 5 3d 6 L, and 2p 5 3d 7 L 2 for the final state. We adjusted the following parameters to reproduce the experimental TXMCD spectra: U dd (Mn 3d-3d Coulomb energy), U pd (Mn 2p-3d Coulomb energy), ∆ (charge-transfer energy from O 2p to Mn 3d), (pdσ) (Slater-Koster parameter between Mn 3d and O 2p), and 10Dq (crystal-field splitting between the Mn e g and t 2g levels). The magnitude of the D 4h crystal-field splitting 8Cp (splitting between the x 2 − y 2 and 3z 2 − r 2 levels) 17 was fixed to 0.08 eV and only its sign was varied, because varying the magnitude of 8Cp only changed the magnitude of XMCD and did not change the spectral line shape. We neglected the anisotropy of transfer integrals due to the D 4h symmetry of the MnO 6 cluster and transfer integrals between the O 2p orbitals, in order to reduce the number of adjustable parameters. The x-ray incident angle was chosen to be in the [101] direction. In order to fully align the spins perpendicular to the incident x rays, a molecular field (an effective magnetic field corresponding to the exchange interaction) of 0.01 eV along the [101] direction was introduced. We note that this molecular field is strong enough to saturate the magnetization of the Mn ions.
Simulation of angular dependence ofP · M spin based on the Stoner-Wohlfarth model.
We have adopted the Stoner-Wohlfarth model 24 in order to simulate the angular dependence of the projected effective spin magnetic momentP · M eff spin (≃P · M spin ) in Figs. 4a and 4b. By assuming that the film has only a single magnetic domain and that the magnetic anisotropy has only the uniaxial component of the lowest order, the magnetic energy (per volume) E can be expressed as where H is the magnitude of the external magnetic field, M sat is the saturation magnetization, and K u is the uniaxial anisotropy constant for MCA (K u > 0 for out-of-plane easy axis). The three terms in Eq. (1) represent the Zeeman energy due to the applied magnetic field, the shape magnetic anisotropy which originates from the demagnetization field in the film, and the MCA which originates from a conbined effect of microscopic electron occupation and spin-orbit interaction. By minimizing E with respect to θ M , we deduced θ M as a function of θ H , H, K u , and M sat . Then, the projection of the effective spin magnetic momentP · M eff spin ≡P · [M spin + (7/2)M T ] was calculated using the deduced θ M by the following equation: where Q zz ≡ 1 − 3ẑ 2 is the electric quadrupole moment [For the derivation of Eq. (2), see Supplementary Note 1]. This gives the θ H dependence of the projected moment P · M eff spin for a set of parameters (K u , M sat , and Q zz ). The obtained θ H dependence was fitted to the experimental one (Fig. 4) to deduce K u , M sat , and Q zz using the least-square method.

Data availability
The data supporting the findings of this study are available from the corresponding authors on reasonable request.