Existence of La-site antisite defects in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox{LaMO}_3$$\end{document}LaMO3 (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox{M} = \hbox{Mn}$$\end{document}M=Mn, Fe, and Co) predicted with many-body diffusion quantum Monte Carlo

The properties of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox{LaMO}_3$$\end{document}LaMO3 (M: 3d transition metal) perovskite crystals are significantly dependent on point defects, whether introduced accidentally or intentionally. The most studied defects in La-based perovskites are the oxygen vacancies and doping impurities on the La and M sites. Here, we identify that intrinsic antisite defects, the replacement of La by the transition metal, M, can be formed under M-rich and O-poor growth conditions, based on results of an accurate many-body ab initio approach. Our fixed-node diffusion Monte Carlo (FNDMC) calculations of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox{LaMO}_3$$\end{document}LaMO3 (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox{M} = \hbox{Mn}$$\end{document}M=Mn, Fe, and Co) find that such antisite defects can have low formation energies and are magnetized. Complementary density functional theory (DFT)-based calculations show that Mn antisite defects in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox{LaMnO}_3$$\end{document}LaMnO3 may cause the p-type electronic conductivity. These features could affect spintronics, redox catalysis, and other broad applications. Our bulk validation studies establish that FNDMC reproduces the antiferromagnetic state of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox{LaMnO}_3$$\end{document}LaMnO3, whereas DFT with PBE (Perdew–Burke–Ernzerhof), SCAN (strongly constrained and appropriately normed), and the LDA+U (local density approximation with Coulomb U) functionals all favor ferromagnetic states, at variance with experiment.

www.nature.com/scientificreports/ derived from them. At equilibrium, the formation energy of defects determines their relative abundance. However, outside this regime, the relative abundance of defective structures also depends on growth kinetics. Defects with high formation energies will be difficult to form even out of equilibrium. Therefore, the formation energy of defects is a key indicator of their occurrence during natural or artificial growth. For general ABO 3 perovskites, defects are theoretically possible on any of the atomic sites and in defect complexes. In La-based perovskites, a strong focus has been on the formation energy of the oxygen vacancies because these play an important role in the oxygen reduction reaction 22 , oxygen evolution reaction 23 , and ionic conduction 24,25 . However, in non-La-based perovskites, such as YAlO 3 and LuAlO 3 , both Y and Lu antisite defects have been predicted 26 . Similarly, DFT calculations predicted that Ni impurities in BaZrO 3 occupy the A-site under Ni-rich condition 27 . Experiments also found that Y impurities, B-site dopants in BaZrO 3 , occupy the A-site as well in the Y richer phase 28 . These examples raise the question as to the extent La-site antisite defects are relevant in LaMO 3 perovskites.
In this paper, we study the formation energy of antisite defects and oxygen vacancies in LaMO 3 (M = Mn, Fe, and Co) using FNDMC. We establish for LaMnO 3 and LaFeO 3 that the formation energy of antisite defects is low enough to form the defects under M-rich and O-poor chemical conditions. However, in LaCoO 3 , the formation energy of antisite defects is higher for each type of growth conditions studied here. We also show that the antisite defects, as well as the oxygen vacancies, significantly affect the properties of La perovskites. The predicted partial density of states (PDOS) suggests that the antisite defect formation may contribute to the p-type electronic conductivity in LaMnO 3 and may narrow the band gap of LaFeO 3 and LaCoO 3 . In addition, we study the magnetic energy order of the non-defective perovskite crystals. Because even the magnetic ground state is still controversial for some perovskites, we determine the magnetic ground state prior to conducting the defect studies. For LaMnO 3 and LaFeO 3 , FNDMC corroborates the experimental antiferromagnetic (AFM) ground state, but the ground state of pristine LaCoO 3 remains controversial 16 .
The rest of the paper is organized as follows: In "Calculation details" section, we explain how the point defect formation energies are evaluated, including the details of the DFT and FNDMC calculations. In "Results and discussion" section, we discuss the magnetic state of non-defective perovskite crystals. We also discuss the defect formation energies and how the point defects affect electronic conductivity. This work is summarized in "Conclusion" section.

Calculation details
Formation energy of defects. The formation energies of oxygen vacancy V O and intrinsic transition metal antisite defects on the La site M La (M = Mn, Fe, and Co) were evaluated in the neutral state by using the following equations: Here, E bulk is the total energy of perovskite supercells with no defects, E V O is an isolated oxygen vacancy, E M La is an isolated antisite defect, and µ X is the chemical potential of the atomic species X . The formation of chargeneutral oxygen vacancy reduces the neighboring cations. The influence of charge-neutral antisite defect formation on the neighboring ions is discussed in "Atomic distortions around the antisite defect" section. The effects of electron and hole doping are discussed in the supplemental information (SI). The chemical potential ( µ X ) and the defect formation energies ( �E(V O ) and �E(M La ) ) for different equilibrium states are characterized by the solids or gases present during growth. The calculated total energies for the materials were used to determine the chemical potentials to simulate several equilibrium states and are listed in Table 1.
Relaxation of defective and bulk structures. The Vienna Ab Initio Simulation Package (VASP) 67 was used to relax the atomic positions. The total energy and orbital eigenenergies convergence criteria for the selfconsistent field (SCF) process were both 1 × 10 −5 eV/simulation cell. The atomic positions were relaxed until the maximum residual force was less than 0.01 eV/Å. We found that the defect formation energy does not significantly change when the structure is altered to the one obtained with a different functional choice (details available in the SI). The lattice vectors were fixed at the reference values listed in Table 1. For LaCoO 3 , we used the same calculation settings as our previous work 16 . To calculate the chemical potentials and cohesive or formation energies of bulk structures, the atomic positions were also fixed at the reference data values in Table 1. For LaMnO 3 and LaFeO 3 , we used the Perdew-Burke-Ernzerhof (PBE) functional 68 to relax the atomic positions of both bulk and defective structures. The core electrons were replaced using the projector augmented wave (PAW) method 69 . The plane-wave cutoff energy was 520 eV, which converged the total energy of LaMnO 3 within 14 meV/atom. The k-mesh spacing was smaller than 0.50 Å −1 , which converged the total energy of LaMnO 3 within 2.4 meV/atom. The same calculation settings were used to obtain the LaMnO 3 , LaFeO 3 , and LaCoO 3 www.nature.com/scientificreports/ AFM and FM energy differences. The cohesive or formation energies of the bulk systems listed in Table 1 were calculated using PBE 68 and strongly constrained and appropriately normed (SCAN) functionals 70 .
FNDMC calculations' details. We performed FNDMC calculations with the high-performance QMC-PACK code 71,72 with the Nexus workflow management software 73 . We used the Slator-Jastrow-type trial wave functions 74 . The Jastrow factor consisted of one-, two-, and three-body terms. The orbitals of the Slater determinants were obtained with the local density approximation with Coulomb interaction potential (LDA+U) method 30 . Further details of the LDA+U calculations are written in the next subsection. The time step was dt = 0.01 a.u. −1 , and the associated errors were 5 meV/atom for LaMnO 3 and LaFeO 3 54,75 and less than 20 meV/ atom for LaCoO 3 16 . The target population of walkers was 2000 or larger for our main results (the SI discusses a few exceptions). We used twist-averaged boundary conditions and size extrapolation to estimate the one-and two-body finite size effects (details in the SI). For LaFeO 3 , E V O and E bulk in Eq. (1) were taken from our previous FNDMC results 75 .
Tuned LDA+U trial wave function. We used the Quantum ESPRESSO package 76 to run the LDA+U calculations. We used the norm conserving pseudopotentials 54,75,77 , whose accuracy has been verified in our previous works 54,75,77 . The cutoff energy was 350 Ry, which converged the total energy of LaCoO 3 within 1 meV/ atom. The k-mesh size was identical to the twist-averaging mesh size (details in the SI). The energy convergence criterion for the SCF process was 5 ×10 −6 Ry or smaller. The Hubbard U contribution was applied to the 3d electrons of Mn, Fe, and Co. We optimized the U value for Mn (Fe) to minimize the FNDMC total energy of the bulk LaMnO 3 ( LaFeO 3 ): U opt = 3 eV for Mn and 6 eV for Fe. We optimized the U value for Co to minimize the FNDMC total energy of every bulk system: U opt = 6 eV for LaCoO 3 and Co and U opt = 5 eV for CoO and Co 3 O 4 . We consistently used the U opt values for our LDA+U calculations throughout the paper. We also used LDA+U with the optimal U values to obtain the PDOS of the perovskites because the FNDMC tuning of DFT+U has been reported to improve the reliability of DFT to study physical properties 40,78,79 .

Results and discussion
Cohesive or formation energies and energy differences of magnetic states given by FNDMC and DFT. The total energies of the materials listed in Table 1 were calculated to obtain the chemical potentials, µ La , µ M , and µ O , for different chemical equilibrium conditions. The chemical potentials were used to calculate the defect formation energies with Eqs. (1) and (2). To verify the results, the calculated cohesive energies were compared with the available experimental data 24,80,[82][83][84][85][86][87][88][89] (Table S1 in the SI). The differences between calculated and experimental cohesive energies are shown in Fig. 1. The experimental and FNDMC numerical values are listed in Table 1 in the SI. To quantitatively assess the reliabilities of different methods, the mean squared deviations (MSD) were calculated from the experimental data for the cohesive energies. The MSDs were 0.046(4) (eV/atom) 2 for FNDMC, 0.158 (eV/atom) 2 for PBE, and 0.562 (eV/atom) 2 for SCAN: FNDMC gave the lowest MSD. Because the experimental cohesive energies were not found for Co 3 O 4 and LaCoO 3 , we alternatively  www.nature.com/scientificreports/ compared the formation energies in Table 2: FNDMC reproduced the experimental values significantly better than the DFT approximations that were considered. We also calculated the energy differences between FM and AFM states of the perovskites. These differences are listed in Table 3. A negative (positive) value indicates that the AFM (FM) state is more stable. For both LaMnO 3 and LaFeO 3 , the AFM ground state was reported experimentally 53,90 . Our FNDMC calculations reproduced the AFM ground state for both materials. For LaFeO 3 , the functionals all reproduced the AFM ground state. SCAN agrees well with FNDMC (FMDMC: −0.08(1) vs. SCAN: −0.08 eV). However, none of the DFT functionals that we tested gave the AFM ground state for LaMnO 3 .
Determining the magnetic ground state for LaCoO 3 is rather more complex than for LaMnO 3 and LaFeO 3 because different spin states of the cobalt ion are nearly degenerated. Here, we briefly discuss the main results of our previous work 16 . The ground state of bulk LaCoO 3 , Co 3+ , was reported experimentally in 1957 to be low spin (LS) t 6 2g e 0 g at low temperature (T<30 K) and therefore non-magnetic (NM) 91 . However, experiments in recent years have challenged this idea [92][93][94][95][96] . It is argued that at elevated temperatures, the LS Co 3+ transitions into a high-spin/low-spin mixture; at temperatures above 500K, the ground state is completely high-spin (HS; t 4 2g e 2 g ) Co 3+91 . In our FNDMC calculations, we found that the ground state of LaCoO 3 at 0 K is an HS AFM 16 state. Using FNDMC, the magnetic state energy ordering was revealed to be HS-AFM < HS/LS-FM < HS-FM < LS < intermediate spin-FM. The FNDMC total energy difference between the most and second-most stable states (i.e., HS-AFM and HS/LS-FM) was 0.15 eV, which indicates an HS-AFM ground state. Table 3 shows the energy differences of HS-AFM−HS/LS-FM. SCAN and LDA+U reproduce FNDMC; PBE does not.
From the above discussion, we conclude that FNDMC is better at evaluating the energies related to the perovskite systems. Therefore, we used FNDMC to evaluate the defect formation energies.

Local magnetization of point defects.
A point defect was introduced into the bulk supercell with the AFM ordering because this is the ground state of the bulk structures and we target the formation energy of an  www.nature.com/scientificreports/ isolated point defect. We optimized the magnetic moment around the point defect to minimize the total energy. Figure 2 shows the total energies of defects in LaMnO 3 , antisite defects or oxygen vacancies, for different magnetic moments around the defect. The blue lines are the FNDMC results, and the orange lines are the LDA+U results. The total energies are shown as the relative differences from the lowest value. The minima of FNDMC and LDA+U agreed with each other. The antisite defect was magnetized by 4 or 6 µ B in LaMnO 3 , whereas the oxygen vacancy is not magnetized. Because FNDMC and LDA+U agreed with each other in terms of the magnetization of point defects in LaMnO 3 , we simply used LDA+U to determine the magnetization of defects used for the FNDMC calculations for LaFeO 3 and LaCoO 3 . For LaFeO 3 , we obtained 5 µ B /defect for the antisite defect and 0 µ B /defect for the oxygen vacancy. For LaCoO 3 , we obtained 4 µ B /defect for the antisite defect and 0 µ B /defect for the oxygen vacancy. In all the perovskites, the transition metal antisite defects have finite local magnetizations, but the oxygen vacancy does not. Figure 3 illustrates the main result of this research: the antisite defect and oxygen vacancy formation energies of LaMO 3 ( M = Mn , Fe, and Co) for different chemical equilibrium conditions. In the case of LaMnO 3 and LaFeO 3 , the antisite defect formation energies are almost always significantly lower than the oxygen vacancy formation energies. For LaMnO 3 , a very small antisite defect formation energy (0.51(12) eV) was predicted at the chemical potentials, where MnO, MnO 2 , and LaMnO 3 coexist. Similarly, in the case of LaFeO 3 , the antisite formation energy at the O-poor condition limit, where LaFeO 3 ,Fe, and FeO coexist, was predicted to be almost zero (0.016(95) eV). The antisite defect formation energies in LaCoO 3 are always high (> 2.5 eV), and the formation of antisite defects at equilibrium appears to be very difficult. In summary, our results suggest possible antisite defect formation in LaMnO 3 and LaFeO 3 for M-rich and O-poor conditions because the formation energy appears to be much lower than the oxygen vacancy (Fig. 4) that is often reported in perovskite materials. Table 4 summarizes the formation energies of the oxygen vacancy at the O-rich limit (i.e., µ O = 0.5 · E(O 2 ) ) obtained with different methods. Our FNDMC calculations nearly reproduced experimental estimates of the oxygen vacancy formation energies for LaMnO 3 and LaFeO 3 . This corroborates the accuracy of our FNDMC calculations for defects. Among the DFT results, the PW91+U method also nearly reproduced the experimental results 97,98 , but the others did not. These previous DFT calculations without the Hubbard U correction overestimated the oxygen vacancy formation energies for the LaMnO 3 case. The Hubbard U correction tends to decrease the vacancy formation energy. For the LaCoO 3 case, the previous DFT calculations with the Hubbard U correction all underestimated the oxygen vacancy formation energy compared to our FNDMC results.

Relative abundance of antisite defects in LaMnO 3 and LaFeO 3 .
Our FNDMC calculations suggested a relative abundance of antisite defects; however, no direct observations of antisite defects were found in the literature review. This lack could be due to the difficulty in observing these antisite defects. Because the transition metal atom has fewer electrons (25,26, and 27) than the La atom (57), the antisite defects would be masked by the La atom and cannot be easily observed in the transmission electron microscopy experiments. Similarly, x-ray diffraction experiments would not observe the antisite defects unless they are ordered. These reliable FNDMC results of antisite defects formation could accelerate their discovery in perovskites. Figure 5 shows the relaxed structure around the antisite defect in LaMO 3 (M=Mn, Fe, and Co). The antisite defect shifts from the original La site position towards some of the surrounding oxygen atoms. This is attributed to the significantly smaller ionic radii of Mn 3+ , Fe 3+ , and Co 3+ (respectively 0.785, 0.785, and 0.75 Å) compared to that of La 3+ (1.172 Å) 106 . Table 5 compares the distances between the antisite defect and surrounding O atoms with those between the La atom and surrounding O atoms in the bulk structure. This table clarifies that the antisite defect selectively bonds with some specific O  Table 6. The TM-O distances are smaller or TM's coordination number is larger when the TM's formal charge is larger. For the LaMnO 3 case, the antisite-O distances are slightly larger than the TM-O distances in the bulk LaMnO 3 , and the antisite's coordination number is also smaller. Therefore, the antisite defect's formal charge is smaller than + 3. For the LaFeO 3 case, whereas the antisite-O distances are shorter than the TM-O distances of bulk LaFeO 3 and Fe 2 O 3 , the antisite's coordination number is smaller. Therefore, the formal charge of the antisite defect cannot be decided  www.nature.com/scientificreports/   www.nature.com/scientificreports/ based on distances and coordination. Similarly, the antisite's formal charge in LaCoO 3 cannot be decided: the antisite-O distances are smaller than the TM-O distance in the bulk LaCoO 3 but the antisite's coordination number is smaller. In order to estimate the formal charge of the antisite defects, we calculated their Bader charges [107][108][109][110] for the electronic densities given by LDA+U method. For the LaMnO 3 case, Mn atoms in the bulk structure have larger Bader charge (1.67 e) than the antisite defect's (1.43 e). This supports the discussion in the prior paragraph that the antisite defect's formal charge is smaller than +3. For the LaFeO 3 case, the antisite defect has the same Bader charge as the Fe atoms' in the bulk structure (1.78 e). However, the Fe atoms labeled "(reduced)" in Figure 5 have smaller Bader charges (1.59 e): their formal charges are smaller than +3. On the other hand, for the LaCoO 3 case, the antisite and the other Co ions have similar Bader charges to the Co atoms' in the bulk LaCoO 3 .

Atomic distortions around the antisite defect.
The Bader charges of La atoms in the bulk LaMO 3 ( ∼2.14 e) are significantly larger than the antisite defects' . Therefore, the antisite defects could disturb the local charge neutrality. Positively charged antisite defects could be more easily formed when the Fermi energy is lower. It remains to be investigated in the future how the antisite defect formation energies depend on the defect charge and Fermi energy. The neutral defects do not depend on the Fermi energy and are thus an upper bound for the formation energies of these defects. While very high or very low Fermi energies may lower the energies of charge defects below the neutral ones, the existence of charge defects will not change the main conclusion of this work since it can lower their formation energy further.
Defect's contributions to the density of states. Figure 4 shows the PDOS of LaMnO 3 without defects, with antisite defects, and with oxygen vacancies. The PDOS of LaFeO 3 and LaCoO 3 are given in the SI. The total magnetizations were obtained in DFT, without the restriction used in FNDMC that constrains the magnetization value to be an integer. We obtained different total magnetization from the trial wave functions for LaMnO 3 with antisite defects (4→5.05 µ B ) and for LaMnO 3 with oxygen vacancies (0→0.15 µ B ). However, the energy differences were less than 0.016 eV/atom. LDA+U with the optimal U values yielded by FNDMC reproduced earlier reports that the bulk LaMO 3 (M = Mn, Fe, and Co) are insulators. However, the LaMnO 3 band gap given by LDA+U was 0.08 eV, which is significantly smaller than the experimental values, 1.7 and 1.9 eV 111,112 . In our previous work, PBE+U also underestimated the band gap (0.2 eV) and FNDMC reasonably reproduced the experimental value (2.3(3) eV) 54 . DFT with a hybrid functional also gave 2.3 eV 113 so the Hubbard U correction alone would not be enough to obtain the band gaps of LaMnO 3 . The LaFeO 3 band gap given by LDA+U was 2.77 eV, which is close to a reported value of 2.37 eV, which was produced by applying Tauc models to experimental data 114 . The LaCoO 3 band gap given by LDA+U in our work 16 was 1.94 eV, which is significantly larger than the experimental band gap of 0.5 eV 115,116 . However, these experiments reported a non-magnetic state, whereas we found the AFM state for a theoretical defect-free material. The reasons of disagreement between theory and experiments on the magnetic ground state of LaCoO 3 remains a subject of active research. Regarding the gap, we found that the band gap of the NM state of LaCoO 3 is 1.390 eV by LDA+U, which is closer to the experimental value.
Among the bulk structures, only LaMnO 3 has small density of states (DOS) around the Fermi energy, in agreement with an experiment 111 . They found that states exist around the Fermi level originating mainly from e g orbitals of the d-shell in Mn. They also observed that a large splitting exists between t 2g and e g orbitals, and a small splitting is also in the e g orbitals. They explained that the small splitting is attributed to the Jahn-Teller distortions of the octahedral crystal field. Consequently, a significantly smaller band gap exists for LaMnO 3 than for the other two perovskites in our results. Our results show that point defects can turn LaMnO 3 metallic. Figure 4b and c indicate that antisite defects (oxygen vacancies) yield p-type (n-type) conductivity: antisite defects (oxygen vacancies) cause the Fermi energy to shift toward the valence (conduction) band. The shift of Fermi energy with charge neutral oxygen vacancies may be because of reduction of the system. Formation of +2 charged oxygen vacancies may inversely shift the Fermi energy toward the valence band. For LaFeO 3 and LaCoO 3 , the antisite defects create defect energy levels in the band gap of the bulk structure. As a result, the band gap is reduced from 2.37 to 0.65 eV for LaFeO 3 and from 1.92 to 1.11 eV for LaCoO 3 . The oxygen vacancies also narrow the band gap of LaCoO 3 from 1.92 to 1.12 eV and make LaFeO 3 conductive, producing an isolated DOS peak around the Fermi energy; the experimental disappearance or narrowing of the band gap could be evidence of formation of point defects.

Conclusion
We studied the charge neutral antisite defects and oxygen vacancy formation energies of LaMO 3 (M = Mn, Fe, and Co) by FNDMC. Our calculations predicted a relative abundance of antisite defects for the cases of M = Mn and Fe, comparable with or higher than the oxygen vacancies, at the M-rich and O-poor conditions.
The transition metal atoms studied have significantly fewer electrons (25, 26, and 27) than La (57). Therefore, the presence of antisite defects should be difficult to observe in transmission electron microscopy experiments because the presence of antisite defects would be masked by the La atoms on the same column. However, we found that antisite defects affect the electronic and magnetic properties of the perovskite host. Our PDOS analyses showed that the antisite defects make the LaMnO 3 metallic introducing holes and energy levels inside the band gap of LaFeO 3 and LaCoO 3 . Mid gap levels could be a signal that antisite defects have formed in experiments. Our FNDMC calculations also showed that the antisite defects have local magnetization.

Data availability
The calculation data for the results in this study is available from the corresponding authors on request.