Strain-Induced Modulation of Spin Configuration in LaCoO3

For oxides with octahedron ligand field, such as perovskite, spinel, and mullite, unit occupancy of eg orbital plays a key role in governing the catalytic performance of oxygen redox in the application of renewable energy storage and conversion. The magnetic configurations greatly influence the eg occupancy of these oxides. In this work, using the perovskite LaCoO3 as an example, we use density functional theory (DFT) calculations to achieve an intermediate spin configuration corresponding to unit-like eg occupancy via strain schemes. We determined that the introduction of strain by changing lattice constants effectively tailors electronic configurations. The low-spin (t2⁢g6⁢eg0), intermediate-spin (t2⁢g5⁢eg1), and high-spin (t2⁢g4⁢eg2) configurations are obtained with the strain γ < 1.0%, 1.0% ≤ γ < 4.0%, and γ ≥ 4.0%, respectively. To obtain the eg unit occupancy practically, Ba with a larger ionic radius relative to La is inserted into A site to replace La elements, introducing tensile strain to the pristine LaCoO3. The Ba substitution of La leads to the desirable spin configuration with the unit-like eg occupancy. These findings provide a scenario on how to precisely control the unit occupancy of eg via defect induced strain.


INTRODUCTION
The development of oxygen catalysts plays a significant role in accelerating the oxygen redox reaction in energy storage and conversion devices. In relation to the discovery of highly efficient non-precious catalysts like oxide, one needs to perform in-depth access with regard to the relation between the crystal structure and the catalytic property. Electronic structures are the fundamental origin of excellent catalytic performances of materials (Suntivich et al., 2011a;Maitra et al., 2013;Li et al., 2016;Gani and Kulik, 2018;Wang et al., 2019a;Zhang et al., 2019;Xu et al., 2020). For perovskites, e g orbital occupancy is one of the effective descriptors in illustrating catalytic behavior. In the 1970s, Matsumoto et al. (1977b) first proposed that e g orbital features in bulk transition metal oxides could reflect the catalytic trend of oxygen reduction reaction (ORR). They pointed out that the formation and filling of a σ * band due to the interaction between e g orbital of transition metal ion and oxygen molecular orbital greatly affects the ORR activity (Matsumoto et al., 1977a,b). To date, this bulk descriptor has been widely used to understand and predict the catalytic performance of oxides. For instance, Wei et al. (2017) demonstrated that e g occupancy of the active cation in octahedral sites is an efficient descriptor for the ORR/OER activities of spinel. They proposed that a moderate e g filling (e g ≈ 1) at the octahedral site can optimize ORR/OER activity. A similar conclusion in terms of e g filling was further drawn in double perovskites (Jiang et al., 2018).
In 2010, Shao-Horn and colleagues presented research that confirmed that the e g filling of transition metal ions in surface accounts for the ORR/OER activity of perovskites (Suntivich et al., 2011a,b). They found that maximum activity can be achieved when e g orbital is occupied by a single electron for OE(R)R reaction. In contrast to traditional band theory, they assumed that a localized e g electron in an orbital directed toward an O 2 molecule from the surface B cations is essential for ORR/OER. The use of the surface e g filling promotes the accurate prediction of catalytic activities for ORR/OER over oxides. The probe of surface e g filling is very challenging even to date. Compared with hard X-ray absorption spectroscopy (XAS), the soft XAS in principle enables one to access the surface properties depending on the incident energy and the corresponding modes. Shao-Horn and colleagues (Hong et al., 2015) claimed that the e g occupancy in their previous studies (Suntivich et al., 2011a,b) was estimated on the basis of the oxidation state and spin state derived from bulk-sensitive measurements, i.e., hard X-ray absorption and magnetometry. In 2018, in their other review (Kuznetsov et al., 2018), they also mentioned that the values of e g fillings were estimated from ex situ measurements or obtained from computed binding energies of oxygenated species on the surface. Therefore, the surface e g descriptor in current reports fails to be solid. It could be more reasonable to be a bulk descriptor. In any case, the importance of Shao-Horn's work reveals the relation between the e g unit filling of bulk materials and the catalytic properties, even if the relation between bulk and surface remains inaccessible so far. Therefore, the e g unit filling of bulk, rather than the surface, is the key to ensure high catalytic efficiency.
Perovskite oxides contain different spin configurations in a given system. For instance, LaCoO 3 exhibits three spin configurations of low (t 6 2g e 0 g ), intermediate (t 5 2g e 1 g ), and high spin (t 4 2g e 2 g ). For e 1 g , the unit occupancy contributes to a moderate hybridization between d z 2 and oxygen 2p orbital to achieve an optimized catalytic activity. To date, much effort has been paid to improve the catalytic activity of LaCoO 3 by tuning its electronic structures. For example, the spin state of Co was adjusted by changing particle sizes of LaCoO 3 or doping Fe atom at Co sites to boost the catalytic performance (Zhou et al., 2016;Duan et al., 2017). However, the precise control of the specific intermediate spin configuration is still challenging. In principle, strain technology, defects, and interfacing are alternative schemes (Zhao et al., , 2019(Zhao et al., , 2020a, among which the strain technology is one of the widely adopted schemes to tune electronic properties and thereby tailor the reactivity of materials. Mavrikakis et al. (1998) proposed that the strain changes the reactivity of transition metal surface by shifting the d-band center; this model is general and suitable for a number of metal surfaces to successfully explain chemical behaviors of materials under strain (Hammer et al., , 1997Holmblad et al., 1996;Kratzer et al., 1996;Hammer and Norskov, 2000;Liu et al., 2011). In addition, for the widely used platinum catalyst, a compressive strain of 1% can induce activity enhancement of more than 300% for ORR (Strasser et al., 2010;Escudero-Escribano et al., 2012;Asano et al., 2016;Escudero-Escribano et al., 2016). Wang et al. (2019b) found that the control of the thickness of twodimensional transition metal at atomic level can achieve finetuning intrinsic strain. Moreover, the activity of oxygen reduction and hydrogen evolution reactions can be improved by more than an order of magnitude relative to corresponding nanoparticle counterparts. For oxides, strain primarily impacts the orbital characteristics, like energy level arrangement of the d subset and its occupancy, and consequently, the catalytic properties. The different strain along in-plane and out-of-plain direction can remove degenerate of e g orbital, and alter the occupancy of d z 2 (Freeland et al., 2011;Pesquera et al., 2012).
Although strain technology has been proven to be effective, the physics behind it remains inaccessible, and the modulation of e g occupancy is not explored yet. Here, we use cubic LaCoO 3 as a model catalyst to systematically investigate the effect of strain on electronic configurations closely relevant for catalytic performance, such as d-band center and electron spin arrangements. We focus on the strain induced by modifying lattice in the absence of octahedral distortions. When the uniform strains were applied, the magnetic moment of Co atom showed step-like behavior versus strain (γ < 1.0%, Mag Co : 0.0 µ B ; 1.0% ≤ γ < 4.0%, Mag Co : 1.406 µ B ; γ ≥ 4.0%, Mag Co : 2.561 µ B ). The substitution of La by large-radius Ba introduces strain leading to the e g unit-like occupancy. Significantly, the lower oxidation state of Ba compared with La leads to a magnetic moment localized at the Co atom in Ba substitution-modified LaCoO 3 larger than that of the equivalent strained defect-free LaCoO 3 . This work provides insights into the precise control of e g unit occupancy via defect induced strain.

COMPUTATIONAL MODELS AND SETUPS
All calculations are performed in the framework of spin-polarized density functional theory (DFT), using the projector-augmented wave (PAW) method (Kresse and Joubert, 1999), as implemented in VASP code (Kresse and Furthmüller, 1996). The exchangecorrelation interaction is treated in the generalized gradient approximation (GGA) of Perdew, Burke, and Ernzerhof (PBE) (Perdew et al., 1996). To describe the electronic correlation effect of 3d electrons of Co element, the DFT+U method (Anisimov et al., 1991) with a U eff of 2.8 eV was employed. The energy cutoff for the plane-wave basis is set to be 550 eV. The calculated lattice parameters of LaCoO 3 are a = b = c = 3.811 Å, which agree well with previous theoretical and experimental results (Ganguly and Vasanthacharya, 1986;Kushima et al., 2010;Rivadulla et al., 2013). A Monkhorst-Pack -centered 11 × 11 × 11 k-point mesh was used for Brillouin zone sampling. Accordingly, for the 2 × 2 × 2 supercell, the 7 × 7 × 7 k-point mesh was adopted. The magnitude of the force acting on each atom to be allowed to relax is less than 0.01 eV/Å. The substitutional energy per Ba atom in La 1−x Ba x CoO 3 with different composition x is defined as where E La 1−x Ba x CoO 3 and E LaCoO 3 are the total energy of Ba substitution-modified LaCoO 3 and pristine LaCoO 3 . E La 2 O 3 bulk , E BaO bulk , and E O 2 are the energy of bulk La 2 O 3 , bulk BaO, and oxygen gas, respectively.

Electronic and Elastic Properties of LaCoO 3
Prior to exploring the effect of strain on the electronic properties of bulk LaCoO 3 , it is necessary to first calculate the electronic structures with effective on-site coulomb-exchange interaction parameter U eff varying from 1.0 to 4.6 eV. Figure 1 presents the calculated bandgap of bulk LaCoO 3 (see Figure 2A) under different U eff . It is found that the bulk LaCoO 3 exhibits metallic properties for U eff < 1.8 eV. And, with the U eff increasing beyond 1.8 eV, the bandgap occurs. When U eff value of 2.8 eV was employed, a bandgap of 0.441 eV was observed which is in good consonance with experimental results (Chainani et al., 1992;Abbate et al., 1993;Arima et al., 1993). Therefore, we adopted the U eff of 2.8 eV in the following discussions. As shown in Figure 2B, the degenerate 3d orbitals of the free Co atom are split into t 2g and e g bands under the restriction of cubic symmetry of LaCoO 3 . The valence bands and the conduction bands are attributed to t 2g and e g , respectively. This indicates that six d electrons of trivalent Co ion fully occupied t 2g orbitals, agreeing well with non-magnetic ground states of LaCoO 3 (Abbate et al., 1993). Besides, there is significant hybridization O-2p and Co-3d, suggesting a strong covalent bond between Co and O. The empty states at the energy of 4.0 eV above Fermi level are the La 4f states. The Bader charge analysis suggests that the calculated charge transfer of La is +2.071e, close to its formal charges of +3e. The charge transfer of Co and O atom is +1.355e and −1.142e, respectively. This deviation of the charge transfer from the corresponding formal charges +3e and −2e further confirms the covalent feature of Co-O bond. In our DFT analysis for the effect of strain on the spin arrangement of LaCoO 3 , the strain is achieved by equally changing lattice parameters along with a, b, and c directions. The strain is evaluated by γ = (a s − a)/a × 100%, where a s and a are the lattice constants of strained and strain-free structure, respectively. The corresponding strain energy of LaCoO 3 is defined as E = E s − E, where E s and E denote the total energy of strained and strain-free structure, respectively. Figure 2C shows the curve of the strain energy E of LaCoO 3 versus γ. The minimum E occurs at γ = 0, corresponding to the unstrained system.
To assess the strain effect on electronic configurations within a reasonable strain range, we first determined the ultimate strain of LaCoO 3 by calculating the strain-stress curve. It is evident that stress increases with strain and reaches a peak at 18%, as shown in Figure 2C. The ultimate strain of 18% suggests a good resistance to stress for LaCoO 3 , which makes it possible to synthesize multicomponent perovskites by partially substituting La or Co, reflecting the diversity of perovskite-type oxides (Peña and Fierro, 2001;Smit et al., 2006). When the strain becomes larger than ultimate strain, the system is subject to attack by vacancy defects or high-temperature effects, etc., and the consequent collapse of crystal structures (Topsakal et al., 2010;Akhoundi et al., 2019).

Strain-Driven Spin-Arrangement Transition in LaCoO 3
Magnetic behaviors of materials arise from its spin arrangement. The results for the magnetic moment localized at Co atom (Mag Co ) under various strain (γ) are shown in Figure 3A and Supplementary Tables S1, S2. The main feature of the curve is that Mag Co exhibits step-like change with strain in the calculated range from γ = −4.0 to 30%, reflecting low, intermediate, and high spin configurations. For strained LaCoO 3 with intermediate-and high-spin configurations, the magnetic moment of Co increases with strain. This positive correlation between magnetic moment and strain is a general behavior, which was observed in various materials (Kushima et al., 2010;Hsu et al., 2018;Zhao et al., 2020b). Given the slight variation in the magnetic moment over each terrace, we take the average values over the corresponding strain range as the DFT calculated Mag Co , listed in Table 1. From Figure 3A, for γ < 1.0%, system manifests non-magnetic behavior. As strain increases (γ ≥ 1.0%), LaCoO 3 becomes ferromagnetic. Within γ = 1.0-4.0%, the values of Mag Co maintain at around 1.406 µ B . When γ ≥ 4.0%, the average Mag Co is 2.561 µ B . Owing to the dependence of magnetic  moment on the U eff parameter of the DFT+U method (Anisimov et al., 1991;Knížek et al., 2005), the calculated magnetic moments and actual magnetization values differ. Although a large U eff value can be used to obtain the magnetic moment consistent with the experimental value, this would lead to the wrong estimation of the ground state energy (Tolba et al., 2018). To ensure the accuracy of results, we calculated the magnetic moments localized at Co atoms with U eff = 3.0, 3.3, 3.5, 3.8, and 4.0 eV, for γ = 0.0, 2.0, and 8.0% (Supplementary Table S1). It is found that there is only a slight variation in the magnetic moment localized Co atom within the reasonable range of U eff values (more information, see Supplementary Table S1), indicating the accuracy of our conclusion on the spin configuration transition. Furthermore, the previous theoretical investigation has shown that the strained LaCoO 3 has an intermediate-spin and high-spin configuration at a strain of 3 and 11%, respectively, which is consistent with the results in this work (Kushima et al., 2010).
To seek the physical origin of the step-like dependence of Mag Co on the strain, we analyze the electronic structures by calculating the d-band center and corresponding orbital occupancy (Figures 3B,C; for detailed data, see Supplementary  Tables S2, S3). It is observed that t 2g and e g bands are spindegenerate for γ < 1.0% ( Figure 3B). However, in the case of γ ≥ 1.0%, the spin degeneracy is lifted, and the degenerate d bands split into two bands. The corresponding spin splitting is estimated by the gap of d-band center between the majority α-spin and minority β-spin, presented in Figure 3B. The spin splitting increases with γ. As compared with the t 2g band, the degree of spin splitting is significantly larger in e g , which is accompanied by the change of the octahedral field splitting. The octahedral field splitting is assessed by the gap of d-band center between the t 2g and e g with same spin states. It is noted that the predominant change of the octahedral field split concentrates in majority α-spin d orbitals. The majority α-spin t 2g and e g band centers show step-like descent as γ increases. Especially, the majority α-spin e g -band center becomes lower than the t 2g -band center when γ ≥ 4.0%. This indicates the smallest octahedral  Table 1). We further quantify the d band-filling numbers by integrating the projected densities of states with respect to energy up to the Fermi level. N filling e g , α , N filling e g , β , N filling t 2g ,α , and N filling t 2g , β were used to denote t 2g and e g filling in different spin states. The corresponding data are listed in Supplementary Table S3. Figure 3C reveals that N filling e g , α increases with strain. In contrast, the minority β-spin t 2g bands exhibit a reverse filling trend. The rise of majority α-spin e g band-filling number results in the enhancement of magnetic moment and the transition of spin configuration. N filling t 2g ,α and N filling e g , β under strain were observed to be roughly constant. This follows from 3d 6 electron configuration of trivalent Co ion and the d-orbital splitting under the octahedral field. The projected density of states of Co atoms (Figures 4ae) indicates that with strain increasing the minority β-spin t 2g states shift upward with relative to Fermi level, whereas electrons gradually fill majority α-spin e g states. Based on the analysis of the octahedral field, spin splitting, and d-orbital filling, we obtained low-spin, intermediate-spin, and high-spin arrangements in the corresponding octahedral field, illustrated in

Effect of Ba Substitution in LaCoO 3 on Magnetic Properties
Strain could be achieved through introduction of defect or epitaxial substrate, etc. To apply tensile strain in LaCoO 3 , we used Ba with a larger radius than La to partially replace La atom of LaCoO 3 (Ba 2+ : 1.61 Å, La 3+ : 1.36 Å) (Shannon, 1976 (Ba c+f1+f2+f3 ) (see Figure 5). Here, c, b, f, and e denote corner, body center, face center, and edge center sites, respectively. Ba c , Ba c+b , and Ba c+f1+f2+f3 denote Ba occupying the dispersive La sites to form Ba uniformdistributed structures (Figure 5). Other Ba substitutional defects distributed unevenly instead. The Ba substitutions can be formed due to the small substitutional energies of −0.356, −1.076, −1.083, −1.418, −1.415, −0.766, −1.076, 0.402, and 0.071 eV. The overall substitutional energies manifest the stability of the structure, reflecting the possibility of substituted perovskite compounds with the formula of A 1−x A x B 1−x B x O 3 (Peña and Fierro, 2001). In experiments, various R 1−x A x CoO 3 (R = La, Pr, and Nd; A = Ba, Sr, and Ca), with x ranging from 0 to 0.5, have been successfully synthesized (Muta et al., 2002;Khalil, 2003;Masuda et al., 2003;Kun et al., 2013). For our investigated Ba substitution-modified LaCoO 3 , the charge transfer of Ba is +1.552 to +1.577e, close to its formal charges of +2e ( Table 2). The charge transfer of La approaches to its formal charge (+3e) with a value of about +2.0 e.
The consequence of the introduction of Ba substitution at La site causes the lattice expansions. In this work, the uniform distribution of Ba atoms promotes homogeneous elongation of lattice constants along with a, b, and c directions (Ba c : a s = b s = c s = 0.96%; Ba c+b : a s = b s = c s = 1.31%; Ba c+f1+f3 : a s = b s = c s = 1.74%; Ba c+f1+f2+f3 : a s = b s = c s = 2.05%) ( Figure 6A). For the systems with uneven distributions of Ba atoms (Ba c+f1 , Ba c+f2 , Ba c+e1 , Ba c+e2 , and Ba c+b+f1 ), especially Ba c+b+f1 , the structures derivate away from cubic symmetry (see Figure 6A), resulting in anisotropic physical properties of Co atoms. The lattice expansion-induced strain corresponds to the intermediate-spin strain range of defect-free LaCoO 3 (1.0-4.0%) (Figure 6A). The corresponding magnetic moments of each Co atoms are listed in Table 2 and Supplementary Table  S4. For Ba c+b+f1 substitutional defect modified LaCoO 3 , the magnetic moments of Co atom are largely different, with an average value of 2.157 µ b ranging from 1.606 to 2.761 µ b (Supplementary Table S4 and Figure 6B). In the case of slight deviation from cubic structures (Ba c+f1/f2/e1/e2 ), Co atoms have the same magnetic moments (Ba c+f1 : 1.834 µ b ; Ba c+f2 : 1.836 µ b ; Ba c+e1 : 1.834 µ b ; Ba c+e2 : 1.833 µ b ) ( Figure 6B and Table 2). For the systems with uniform Ba distribution, Ba c , Ba c+b , Ba c+f1+f3 , and Ba c+f1+f2+f3 , eight Co atoms in each structure are equivalent and possess the same magnetic moment (Ba c : 2.111 µ b ;   O atoms, Q Co and the charge transfer of Co owing to the valence electronic configuration difference between Ba 2+ and La 3+ , Q Co wo_strain , excluding the charge change resulting from lattice relaxation. The total charge transfer of Co atoms varies from +1.40 to +1.45e, differing from the value in strain-free LaCoO 3 (+1.335 e) ( Figure 6C]. The Ba valence states indeed induced the variation in charge transfer of Co ( Figure 6D) Table S4). Meanwhile, the small Mag Co of 1.781, 1.783, 1.606, and 1.752 µ b are observed on Co 1 , Co 4 , Co 6 , and Co 7 atoms associating with the corresponding small Q Co wo_strain of 0.037, 0.040, 0.037, and 0.020e. However, Co 3 atom in Ba c+b+f1 -modified LaCoO 3 is an abnormal case. The magnetic moment localized at Co 3 site is 2.761 µ b despite the small Q Co wo_strain of 0.032e. Further analysis suggests that the charge transfer of Co 3 site, using the charge state of Co atom of pristine strain-free LaCoO 3 as benchmark, is 0.036e, which is almost the same as Q Co wo_strain . Therefore, the valence state of Ba dominates the charge transfer in Co 3 site, eventually leads to large magnetic moment localized at Co 3 site. Overall, the Ba substitutional defect-modified LaCoO 3 possesses intermediatespin configurations. The values of magnetic moments localized at Co atoms deviating from the 1.5 µ b of pristine strained intermediate spin LaCoO 3 results from the different electronic configurations between Ba and La. And, the degree of deviation depends on the magnitude of the charge transfer of Co atoms following from the different valence states between Ba and La.
The projected density of states of Co atom reveals that the systems with Ba c , Ba c+b , and Ba c+f1+f2+f3 substitutional defect hold similar orbital occupations, which differs from Ba c+f1+f3 substitution modified LaCoO 3 (Figures 7A-D). The d-orbital filling exhibit that, for Ba c+f1+f3 , the minority βspin t 2g filling increases accompanied by reducing majority αspin e g filling, compared with the defective LaCoO 3 including Ba c , Ba c+b , and Ba c+f1+f2+f3 substituents (Supplementary Figure S3), which contributes to the small magnetic moment. The defective systems with a small magnetic moment, Ba c+f1 , Ba c+f2 , Ba c+e1 , and Ba c+e2 , have similar d-orbital occupation as Ba c+f1+f3 (Supplementary Figure S4). All these features of d-orbital occupation are found in different Co atoms of Ba c+f1+f3 substitution modified LaCoO 3 (Supplementary Figure S5). Ba substitutional defects induce a unit-like e g occupancy resulting in a moderate interaction between Co active center and oxygen-related adsorbates, which contributes to the reduction of the OER/ORR thermodynamic overpotential. Therefore, Ba substitution defect modified LaCoO 3 is promising for oxygen redox catalytic reactions.

CONCLUSION
In summary, we explored the dependence of spin configurations on strain in LaCoO 3 via DFT calculations. We found that strain by manipulation lattice constants can tune crystal field splitting and spin splitting, resulting in the transition of spin arrangement. The important e g unit occupancy was achieved via applying tri-axial uniform strain ranging from 1.0 to 4.0%. To achieve the strain effects practically, the substitution of La by Ba with larger ionic radius effectively introduces strain, leading to the unit-like occupancy of e g . Notably, there is larger magnetic moment localized at Co atom in Ba substitution modified LaCoO 3 relative to the equivalent strained defect-free LaCoO 3 , due to the lower oxidation state of Ba than La. The response of spin configuration on strain induced by defect enables precise control of the unit occupancy of e g during the catalyst design process.

DATA AVAILABILITY STATEMENT
The datasets generated for this study are available via the corresponding author or other researchers following publication.

AUTHOR CONTRIBUTIONS
LW performed the DFT calculations. LW, JL, and WW wrote this manuscript. WW administrated the project. MW provided the computational resources. HW, KL, YS, and ZL advised the research work.