Robust ferromagnetism in highly strained SrCoO3 thin films

Epitaxial strain provides important pathways to control the magnetic and electronic states in transition metal oxides. However, the large strain is usually accompanied by a strong reduction of the oxygen vacancy formation energy, which hinders the direct manipulation of their intrinsic properties. Here using a post-deposition ozone annealing method, we obtained a series of oxygen stoichiometric SrCoO3 thin films with the tensile strain up to 3.0%. We observed a robust ferromagnetic ground state in all strained thin films, while interestingly the tensile strain triggers a distinct metal to insulator transition along with the increase of the tensile strain. The persistent ferromagnetic state across the electrical transition therefore suggests that the magnetic state is directly correlated with the localized electrons, rather than the itinerant ones, which then calls for further investigation of the intrinsic mechanism of this magnetic compound beyond the double-exchange mechanism.


I. INTRODUCTION
In complex oxides, the epitaxial strain in thin film structures provides an essential control parameter to manipulate their corresponding electronic and magnetic ground states due to the interplay among lattice, charge, orbital and spin degrees of freedom. A large group of transition-metal oxide materials have demonstrated the emergence of novel properties through strain engineering, such as enhanced transition temperatures in ferroelectric [1], ferromagnetic (FM) [2] and superconducting [3] orders, as well as emergent exotic electronic states [4][5][6], as widely reported in high quality epitaxially strained thin films.
Among such oxide materials family, particular attention has been payed to perovskite SrCoO3 recently due to its intriguing FM metallic ground state [7,8] in the bulk compound attributed to the double-exchange mechanism proposed by Zener [9]. Here, according to the density functional theory (DFT), the Co d 6 ion antiferromagnetically couples with the ligand hole in the surrounding oxygen p states through the p-d hybridization to form the intermediate spin Co d 6 L state [10,11]. More sophisticated treatment of the correlation effects, using the DFT + dynamical mean field theory (LDA+DMFT) [12], claimed that the local moment in SrCoO3 results from the coherent superposition of different atomic states rather than the intermediate spin state [13].
Motivated by the possible multiferroicity in strained transition-metal oxides [14], the magnetic ground state of strained SrCoO3 was studied using the standard DFT. It was predicted that the ground state changes from a FM metallic state to an antiferromagnetic (AFM) metallic state, with a moderate tensile strain of 2.0% [15,16]. These theoretical predictions triggered a series of experimental studies to examine epitaxially strained SrCoO3 thin films [17][18][19][20]. While most groups have obtained the FM metallic state in SrCoO3 at low strain states, results on highly tensile-strained samples showed large diversity, which is likely due to the lack of good oxygen stoichiometry of the material resulting from the reduction of the oxygen vacancy formation energy due to large tensile strains [17,18,21]. Thus, the intrinsic magnetic and electronic states as well as the underlying mechanism of highly strained SrCoO3 still remain elusive.
In this paper, we report our magnetic study of highly strained SrCoO3 thin films (up to tensile strain of ~3.0%) with excellent oxygen stoichiometry, which is achieved by a new post-deposition ozone annealing process. To our surprise, the robust FM ground state is found in all tensile strained thin films, which is in stark contrast to previous theoretical predictions and experimental reports claiming a transition to AFM state.
Interestingly, we observed a metal to insulator transition along with the increase of the tensile strains. To gain insight into this observation, we carried out DFT+DMFT calculations and found that the orbital occupation changes more strongly with strain than what DFT predicts. Based on this, we propose a super-exchange mechanism with alternating orbital ordering, which is consistent with the robust FM ground state with insulating transport.

A. Fabrication and characterization of highly strained SrCoO3 thin films
In previous studies, the strained SrCoO3 samples were typically achieved via in-situ oxygen (or low-pressure ozone) annealing processes, in which the resulting samples usually possess pronounced oxygen vacancy contents. In this study, a two-step method has been developed to achieve the desired high quality epitaxial thin films with great oxygen stoichiometry. First, the brownmillerite SrCoO2.5 thin films (~30 nm) were grown using the pulsed laser deposition method, and then they were post-annealed within ozone (see details in Sec. IV). The elevated annealing temperature (~300 ºC) and high ozone content (5 g/m 3 in 1 bar O2) triggers effectively the phase transformation from brownmillerite to perovskite with excellent oxygen stoichiometry of SrCoO3 [ Fig.   1 providing tensile strains of 1.0%, 2.0%, and 3.0% with respect to the lattice constant (0.3829 nm) of bulk SrCoO3 [7]. As a consequence, the as-grown SrCoO2.5 samples are epitaxially strained on all selected substrates and the crystalline orientations are perfectly correlated with that of the substrates underneath (see Supplemental Material Fig. S1 [22]). It is interesting to note that the oxygen vacancy channels of brownmillerite align along the in-plane (out-of-plane) direction with compressive (tensile) strain states, as evidenced by the presence of the superlattice peaks in the Xray diffraction (XRD) θ-2θ scans [starred peaks in Fig. 1(b)] only for the samples grown on LSAT and STO substrates with compressive strain. Despite different oxygen vacancy orientations, all samples can be nicely transformed into perovskite structure through post-deposition ozone annealing, where the CoO4 tetrahedra are oxidized into the CoO6 octahedra, reflecting in the XRD results as the complete absence of the superlattice peaks and the movement of the pseudo-cubic (001) and (002) diffraction peaks towards the higher angles. Furthermore, detailed X-ray reciprocal space mappings (RSM) along the pseudo-cubic (103) direction [ Fig. 1(c)] were carried out to investigate the epitaxial relationship between thin films and substrates, in which the identical horizontal q values between the films and substrates (marked with red dashed lines) strongly suggest that the post-ozone-annealed SrCoO3 thin films are coherently strained with substrates (see Supplemental Material Tab. S1 for lattice parameters [22]).
Conventionally the tensile strain in fully strained samples would introduce a systematic lattice contraction along the film normal direction. However, such trend clearly breaks down for the film grown on DSO substrate, in which a clear lattice expansion is observed. We speculate that such crystalline structure change might be related with the evolution of lattice symmetry with tensile strain. With STO and LSAT substrates, the samples would be strained into tetragonal phase from its bulk cubic compound; while with DSO substrate, the lattice structure would be largely deformed into orthorhombic phase with lower symmetry. Interesting to note that similar structural anomaly was also observed in the previous theoretical work [15], in which the lattice changes from a high symmetry P4/mmm to a lower symmetry Pmc21 at ~2% tensile strain. The high-quality epitaxial nature of SrCoO3 thin films was further confirmed by the high-resolution transmission electron microscopy (HRTEM) study (see Supplemental Material Fig. S2 [22]), which ascertains that by this post-deposition ozone annealing method the SrCoO3 thin films can be fully strained on the DSO substrates with as high as 3.0% strain without formation of any detectable interfacial defects that would cause strain relaxation otherwise.
As mentioned, the lack of stoichiometry of oxygen concentration in highly strained SrCoO3 samples was a big challenge that researchers suffered in previous studies, where noticeable oxygen vacancies were always formed [18][19][20]. The presence of oxygen vacancies in thin films would strongly modify the corresponding valence states of Co ions as well as their hybridization with oxygen ions. Thus, in order to carefully evaluate the oxygen stoichiometry in our samples, we performed the valence-statesensitive soft X-ray absorption spectroscopy (XAS) at both the Co L-edges and oxygen S4 [22]) further prove the excellent oxygen stoichiometry, since this hybridization peak in oxygen deficient SrCoO2.5 would be dramatically suppressed and shifted toward higher energy (~529.2 eV) [23,24]. With all these careful analyses, we can confirm that the post-deposition ozone annealing method achieves coherently-strained and stoichiometric SrCoO3 thin films.

B. Robust ferromagnetism in the highly strained samples
With these high-quality samples, we further investigated their intrinsic magnetic properties. Since the large paramagnetic background of DSO prohibits the direct magnetic measurement of the thin films grown on it, we carried out the element-specific and magnetic-resolved soft X-ray magnetic circular dichroism (XMCD) measurement [25]. Fig. 2(b) shows the measured XMCD spectra of Co L-edges at 20 K, in which the pronounced (~18% at L3 edge) XMCD signals with similar characteristic peaks manifest that all strained SrCoO3 thin films possess robust magnetizations. Fig. 2

(c)
represents the magnetic field dependent XMCD for all three samples, which shows well-defined hysteresis loops, confirming the FM ground states. Using the XMCD sum rule (see Ref. [25] and Supplemental Material Fig. S5 [22]) we calculated the spin and orbital contributions for the total magnetization as around ~1.0 μB/Co and ~0.4 μB/Co, respectively. This result is consistent with the experimentally reported value for bulk SrCoO3 [7] as well as slightly strained (1.0%) thin films [23,24], however, it is in disagreement with some previous theoretical calculations that predicted an AFM ground state for highly strained samples [15,16]. To further investigate the FM state, we carried out temperature-dependent XMCD measurement for all strained samples

C. Strain induced metal to insulator transition
While showing similar and robust FM states, this series of strained SrCoO3 samples exhibit very different electronic properties, as revealed by the temperature dependent electrical transport measurements shown in Fig. 3(a). The SrCoO3 sample grown on LSAT substrate shows a good metallic characteristic with residual resistivity of ~10 -4 ·cm at ~15 K, which is much lower than previously reported values of single crystalline bulk [7] and thin films [24], however consistent with our recent studies of SrCoO3 thin films obtained with ionic liquid gating [26]. This fact again confirms that our ozone-annealed SrCoO3 samples are of high crystalline quality with minimal oxygen vacancy concentration. This temperature dependent curve follows nicely the T 2 relationship, in accordance with the Fermi liquid behavior of this metallic sample.
Interestingly, with the increase of tensile stain, the conductivity is dramatically suppressed and a distinct insulating behavior is developed in the sample grown on DSO.
Specifically, we have observed a more than two orders of magnitude enhancement of resistivity at room temperature between the LSAT and DSO samples. A careful analysis reveals that the temperature dependence of such highly strained sample can be fitted with the three dimensional Mott variable range hopping model [27,28] with (T) = 0 ( 0 ) 1  shows a dramatically reduced room temperature conductivity as compared with all SrCoO3 thin films, and its exponential temperature dependence follows nicely the thermal activated semiconducting behavior.
To provide further insights of the strain induced metal to insulator transition, we measured the optical conductivity spectra for selected SrCoO3 samples as shown in Fig.   3

D. Electronic structure calculations
In order to understand the underlying mechanism, we performed DFT calculations as well as DFT+DMFT calculations. As shown in Fig. 4(a), our spin-resolved density of states (DOS) for relaxed SrCoO3 is quantitatively consistent with the previous calculated result [13]. In contrast to the nearly fully-occupied majority spin states, minority spin states are partially occupied and make primary contribution to the electric conductance, in which the Fermi level crosses mainly at the Co t2g states for relaxed  [22]), i.e., orbital polarization is amplified by correlation effects [30][31][32]. This would result in one electron occupation in the twofold degenerate minority spin xz and yz orbitals, and potentially lead to the cooperative Jahn-Teller effect accompanied by alternating spatial arrangement of xz and yz orbitals. To simulate this situation, we introduced a tiny potential splitting between the xz and yz orbitals, ∆ = 0.1 eV, and carried out DFT+DMFT calculation. As shown in Fig. 4(b), the tiny splitting is enough to separate Khomskii mechanism [33] as schematically shown in Fig. 5(b). We note that a similar FM interaction is realized in lightly-doped CMR manganite [34]. This picture strongly contrasts with the previously predicted AFM ground state by first principles calculations [15]. Indeed, using DFT, we confirmed that AFM ordering is also more stable than FM ordering for 4% strained sample by 0.36 eV per formula unit, which is accompanied by the change of the electron occupation N and the spin moment M on partially filled, are unstable compared with low-spin and high-spin states in the atomic limit [35]. This energetics might be overlooked in the DFT calculations, and the comparison of the total energy between different spin states as well as the examination of xz/yz orbital ordering within the DFT+DMFT framework are desirable but left for future studies.

III. SUMMARY
To summarize, this work demonstrated a robust FM state in SrCoO3 thin films under tensile strain beyond the critical strain value above which a transition from FM to AFM was predicted. We found the coexistence of the ferromagnetism and insulating transport behavior in highly strained samples, indicating a different mechanism being responsible for the FM ordering in the strained thin films rather than the Zener's double-exchange mechanism. Based on the DFT+DMFT calculations indicating strong orbital polarization under strain, we propose orbital ordering to induce the FM super-exchange interaction with the splitting inside minority bands, which might finally cause a full gap.
Furthermore, these results clearly highlight the importance of excellent oxygen stoichiometry for the studies of strained engineered complex oxides.

A. Synthesis of high quality SrCoO3 thin films
Brownmillerite SrCoO2.5 thin films were grown by a customized reflection high-energy electron diffraction (RHEED) assisted pulsed laser deposition system, at a growth

C. Electrical transport and magnetic property measurements
A Physical Property Measurement System (PPMS, Quantum Design) with lock-in amplifiers (Model SR830 DSP, Stanford research systems) was employed to measure the temperature dependent resistivity, in which four-probe method was employed to eliminate the contact resistance. Temperature dependent magnetization was measured using a Magnetic Property Measurement System (MPMS 3, Quantum Design) with the temperature ramping up from 4 K to 300 K after a 2 T field cooling. In order to avoid the influence of the strong paramagnetic signal from DyScO3 substrate, we measured the remnant magnetization with zero-field, while for other measurements, the magnetic field of 2 T was applied during the measurements.

D. Optical conductivity measurement
The reflectivity spectra were measured at room temperature with a spectrometer

E. X-ray absorption measurements
Soft X-ray absorption spectra (XAS) at Co-L edges and O-K edge were carried out at the magnetic field (2 T) was applied along the beam incident direction, and circularly polarized X-ray was employed. The XAS spectra presented in this work were taken at 300 K, while the XMCD spectra were taken from 3 K to 300 K. For the TEY mode, the signal was obtained by collecting the total electron yield current from the sample, which is therefore a surface sensitive technique. While for the FY (LY) mode, the signal was a collection of the fluorescence (luminescence) intensity from the whole sample, and therefore is bulk sensitive. It is worth noting that due to the self-absorption effect of FY, we observed clear different L2/L3 peak ratios between FY and TEY modes.

F. Electronic structure calculations
We carry out density functional theory (DFT) calculations using Vienna ab initio Simulation Package (VASP) [36] with the projector augmented wave method [37] and the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional [38]. We used for  will be solved self-consistently [44]. To solve the impurity model, we use the hybridization-expansion version of the continuous-time quantum Monte-Carlo method [45] at T = 0.02 eV = 232 K. We keep only density-density components of so that the efficient segment algorithm is utilized [46].
For the double-counting correction , we used the procedure proposed in Ref. [47]: Here, is the number of Co d orbital times 2 (spin), i.e., 10. Σ ( ) is the Co d electron self-energy as a function of fermionic Matsubara frequency = (2 + 1) . Using this formula, is updated at each DMFT iteration. This method has been successfully applied to describe metallic systems [47]. The electron spectral functions are computed using the self-energy that is analytically continued to the real frequency axis by the maximum entropy method [48].