Anomalous orbital structure in a spinel-perovskite interface $\gamma$-Al$_2$O$_3$/SrTiO$_3$

In all archetypical reported (001)-oriented perovskite heterostructures, it has been deduced that the preferential occupation of two-dimensional electron gases is in-plane $d_\textrm{xy}$ state. In sharp contrast to this, the investigated electronic structure of a spinel-perovskite heterostructure $\gamma$-Al$_2$O$_3$/SrTiO$_3$ by resonant soft X-ray linear dichroism, demonstrates that the preferential occupation is out-of-plane $d_\textrm{xz}$/$d_\textrm{yz}$ states for interfacial electrons. Moreover, the impact of strain further corroborates that this anomalous orbital structure can be linked to the altered crystal field at the interface and symmetry breaking of the interfacial structural units. Our findings provide another interesting route to engineer emergent quantum states with deterministic orbital symmetry.

Very recently with the observation of interface enhanced high-temperature superconductivity (60 -100 K) 30,31 and high mobility conduction electrons (∼ 1.4 × 10 5 cm 2 V −1 s −1 ) 10 in SrTiO 3 (STO)-based interfaces, probing the interactions between charge, spin, orbital, and structural degrees of freedom at the interfaces became fundamentally important to understand interface enhanced emergent electronic states. Specifically, the orbital symmetry of conduction carriers is primarily linked to the symmetry of the superconducting gap 4 and the mobility of electrons [10][11][12] . To this end, the orbital configuration, responsible for the high mobility of electrons in a spinel-perovskite interface (for example γ-Al 2 O 3 /SrTiO 3 , AlO/STO) 10,11,32 is still an open question. From the experimental point of view, surface sensitive angle resolved photoemission spectroscopy (ARPES) with polarized photons is a suitable probe of symmetry of the surface electronic structure 19 , but it has limited applicability for the electronically active buried interfaces. In contrast to ARPES, interface sensitive linearly polarized x-ray absorption spectroscopy (XAS) has proven to be a powerful tool to resolve the orbital symmetry 6,9,[13][14][15][16][17][18]33,34 .
In this work, using the AlO/STO heterostructure as a model system, we report on unique orbital symmetry and orbital occupancy, which is reversed compared to other well-known 2DEGs based on perovskite titanates. Resonant soft X-ray linear dichroism (XLD) studies combined with d.c. transport measurements have confirmed the orbital symmetry inversion driven by the altered crystal field at the interface and symmetry breaking of the TiO 6 octahedral units.

Results
High quality AlO/STO heterostructures were synthesized by pulsed laser deposition (see Supplementary Fig. 1 and Methods for details). With its spinel structure, bulk γ-Al 2 O 3 is cubic (space group F d3m) with a lattice parameter a = 7.911 A 35,36 , which is close to twice of the lattice parameter of bulk SrTiO 3 a = 3.905Å. It is interesting to note that γ-Al 2 O 3 is generally regarded as a defect spinel Al 8/3 O 4 (32 oxygen ions, 64/3 Al cations, and 8/3 vacancies for one unit cell γ-   and LaTiO3/SrTiO3, red arrow) show negative sign for the first feature (at ∼ 457.85 eV), whereas spinel-perovskite heterostructure (AlO/STO, blue arrow) displays positive sign indicating dxz/dyz is the preferential state of interfacial electrons for the later structure. The spectra of LaAlO3/SrTiO3 was adapted with permission from reference 16. Theoretically, to show the reversed lineshape of XLD for different orbital configurations, the calculation data were adapted with permission from reference 17. b, Strain effects for AlO/STO/NGO and AlO/STO/TSO to XLD signal (compressive strain ∼ −1.16 % on NdGaO3 (NGO) and tensile strain ∼ + 1.29 % on TbScO3 (TSO) substrates, respectively; thickness of STO layer is ∼ 10 unit cells or 3.9 nm) and effects of oxygen vacancies in annealed STO single crystal to XLD signal. Comparing with the contributions from oxygen vacancies (annealed STO substrate) and bare STO substrate itself, the XLD signal at AlO/STO is robust. (Copyrighted by the American Physical Society.) with a crystal field gap as large as ∼ 2 eV in the octahedral symmetry 9,13-18 . Additionally, the strong spin-orbit interaction induces the splitting of the Ti 2p core level into 2p 1/2 and 2p 3/2 states. Therefore, four main features are commonly observed in Ti L-edge XAS spectra (see Fig. 1b,c and Supplementary  Fig. 3). With lower crystal symmetry (e. g. tetragonal or orthorhombic symmetry as compared to octahedral symmetry) 19 , the degeneracy of t 2g and e g states can be further lifted, leading to an in-plane d xy subband with possibly lower energy than the out-of-plane d xz /d yz subband and available as the lowest energy state at the interface 9,13-17 . To investigate the orbital configuration, XAS with linearly polarized X-rays, used in this work, has been proven to be one of the most powerful available probes applied to various interfaces 9,13-18 . The utility of the probe stems from the strong dependence of absorption on the direction of the photon polarization vector (E) with respect to the crystal lattice axis (Fig. 1a); Thus, excited by linearly polarized X-rays, electronic transitions from Ti core levels to the unoccupied d orbital bands contains important information about the orbital symmetry of those states. In general, when the linear X-ray polarization is oriented along the direction of unoccupied orbital lobes, the contribution of these orbitals to the XAS signal is largest 6,33 . Therefore, the X-ray absorption at the Ti L 2,3 -edge for E a-b and E c arises mainly from the unoccupied in-plane Ti d xy /d practically identical for both X-ray polarizations (i.e. [I H -I V ]∼ 0). As seen in Fig. 1b, no significant XLD signal at Ti L 2,3edge is observed in agreement with the expectation 17 . With the sample set at θ = 20 • , a strong XLD signal appears (∼ 15 % of XAS, see Fig. 1c) indicating the splitting of e g and t 2g subbands with the lineshape that agrees well with the previous measurements and calculations 9,[13][14][15][16][17][18] .
However, as seen in Fig. 2, the XLD spectra for our AlO/STO system is atypical and has the reverse XLD lineshape compared to the results reported for prototypical 2DEGs at titanate interfaces [e.g. LaAlO 3 /SrTiO 3 (LAO/STO) and LaTiO 3 /SrTiO 3 (LTO/STO)] 9,14-17 . Specifically, for the Ti t 2g state of the perovsite-perovskite interfaces the negative sign of the first main XLD feature implies that the d xy subband is the lowest energy state in agreement with reported results 9,13-17 . In sharp contrast to this, for AlO/STO, the sign of XLD is reversed (see blue and red arrows in Fig. 2a), i.e. the first feature at ∼ 457.85 eV has a positive sign whereas the second feature at ∼ 458.15 eV is negative, immediately implying that d xz /d yz orbitals are the first available states for interfacial electrons. Therefore, the relative energy position of Ti 3d subbands is unusual d xz /d yz < d xy < d 3z 2 −r 2 < d x 2 −y 2 . In order to understand this anomalous behavior, epitaxial strain was induced by utilizing a large mismatch between the substrates and film [i.e. NdGaO 3 (NGO) substrate for compressive strain ∼ −1.16 % and TbScO 3 (TSO) substrate for tensile strain ∼ +1.29 %]. As shown in Fig. 2b, for the AlO/STO heterostructure on NGO (compressive strain) the lineshape of XLD is similar to that observed for AlO/STO except that the very first feature (at ∼ 457.85 eV) is suppressed. However, for tensile strain on TSO, surprisingly almost all the spectral features are killed and no significant XLD signal is observed.
Next, we quantify the strain effect on the splitting and peak energy shift (see Fig. 3). Generally, the size of the band splitting can be estimated from the peak energy difference of XAS obtained with linear polarized X-rays. First, we analyze the splitting of e g and t 2g subbands at the AlO/STO interface. As shown in Fig. 3a and Supplementary Fig. 4, a direct comparison of the energy position for XAS with in-plane (I V ) and out-of-plane (I H ) orientation of the X-ray polarization reveal that the most pronounced XAS feature for I H is lower in energy than the I V absorption. For AlO/STO without external strain, it yields t 2g (L 3 ) band splitting ∆ t 2g ∼ 50 meV and the e g (L 3 ) band splitting ∆ e g ∼ 80 meV. Unexpectedly, as shown in Fig. 3a e g bands is suppressed and practically vanished while the splitting is enhanced under compressive strain (∼ −1.16 %, NGO substrate). Compared to the band splitting of AlO/STO without external strain, the e g (L 3 ) band splitting ∆ e g under compressive strain (∼ − 1.16 %) increases from ∼ 80 meV to 150 meV, whereas the t 2g (L 3 ) band splitting ∆ t 2g ∼ 30 meV is only weakly decreased. Besides the subband splitting, strain also alters the peak energy position (see Fig. 3b). Specifically, for tensile strain though the splitting is strongly suppressed (see Fig. 3a and Supplementary Fig. 4) the peak energy moves to the positive direction i.e. higher photon energies by ∼ + 75 meV for t 2g (L 3 ) and + 35 meV for e g (L 3 ), respectively. On the other hand, as shown in Fig. 3b, under compressive strain with enhanced band splitting, the four main peaks of Ti XAS at L 2,3 -edge shift towards negative direction by about -38 meV for t 2g (L 3 ) and − 170 meV for e g (L 3 ), respectively.

Discussion
Next, we discuss the atomic structure of AlO/STO interfaces as a key factor to produce the inverse orbital symmetry. As schematically shown in Supplementary Fig. 5, based on the interfacial atomic structure data 32,39 , for the case of γ-Al 2 O 3 spinel and in contrast to the previously reported perovskiteperovskite interfaces, the apical oxygen of Ti-O octahedra is not stable in a spinel-perovskite heterostructure. Thus, at the AlO/STO interface a unique Ti-O pyramid coordination is formed; in this distorted pyramid-like structure, d xz /d yz subband becomes the preferable state for the interfacial electrons (see Supplementary Fig. 5b, c). More importantly, the degenerate d xz /d yz subband can be further split due to the cooperative efefct of spin-orbit coupling and crystal field distortion, yielding an energy separation as large as 60-100 meV 12,19,29 . Therefore, in contrast with all reported data on the (001)-oriented perovskite interfaces with in-plane d xy subband as the lowest energy state, the d xz or d yz subband becomes the lowest energy state for the case of spinel-perovskite heterojunction. As the consequence of the d xz or d yz orbital character of mobile electrons amplified by the spatial confinement along z 40,41 , and regardless of which d xz or d yz is the preferred state, the forbidden electron hopping along the y-(for d xz ) or x-(for d yz ) direction may result in the emergence of the extremely anisotropic "1D" electron gas (see Supplementary Fig. 5c). Furthermore, to understand the impact of epitaxial strain on the XLD signals, we propose a simple model shown in Fig. 4. As seen, under compressive strain (∼ −1.16%) the contraction of the in-plane four oxygens together with the elongation of the apical oxygen ion increases the energy of the in-plane d x 2 −y 2 and d xy orbitals, whereas the energy decreases for out-of-plane d 3z 2 −r 2 and d xz /d yz orbitals 42 . As the result, the energy splitting ∆e g between d x 2 −y 2 and d 3z 2 −r 2 orbitals, as well as the splitting ∆t 2g between d xy and d xz /d yz orbitals of Ti ions is increased. This model agrees well with the experimental observation that both ∆e g and ∆t 2g under compressive strain are increased. On the other hand, under tensile strain, the elongation of the in-plane four oxygen ions and the contraction of the apical oxygen ion pulls the Ti ion inside the pyramid 42 , leading to the reversed effect on the Ti 3d orbital sequence. Therefore, the energy splitting within both e g and t 2g bands is expected to decrease; the corresponding XLD signal will be significantly suppressed due to the strain induced degeneracy.
In conclusion, we have demonstrated that in the spinelperovskite heterostructure -AlO/STO the out-of-plane d xz / d yz states are the lowest lying energy states, which is in the sharp contrast to titanate based perovskite-perovskite heterostructures where the in-plane d xy state is always the ground state of the 2D conduction carriers. Moreover, the impact of strain corroborates that this unusual orbital configuration is directly linked with the altered crystal field at the interface and lattice symmetry breaking of the interfacial TiO 6 octahedra. Our findings provide another interesting route to engineer unusual quantum states with deterministic orbital symmetry beyond those attainable in all (001)-oriented perovskite heterojunctions.
Spectroscopy. XAS/XLD (at room temperature) at Ti L 2,3 -edge with total electron yield (TEY) detection mode (interface sensitive) were carried out at beamline 4.0.2 of the Advanced Light Source (ALS, Lawrence Berkeley National Laboratory). In successive scans, spectra were captured with the order of polarization rotation reversed (e. g., horizontal, vertical, vertical, horizontal) so as to eliminate systematic artifacts in the signal that drift with time. The residual artifact intensity is plotted in Fig. 1 and labeled as background.