The structural properties of LaRO3 (R=Cr, Mn, Fe): a first-principles calculation

We investigate the structural properties of three lanthanum transition-metal oxides (LaRO3, R=Cr, Mn, Fe) by the first-principles method based on density functional theory. The crystal parameters and electronic structures are calculated for three different oxides. The results show that the magnitude of lattice distortion is the strongest in LaMnO3, and the slightest in LaCrO3 among three compounds. The magnetic ground states of LaCrO3 and LaFeO3 are G-type antiferromagnet. However, for LaMnO3, GGA+U fails to predict the experimental ground state, and only the internal coordinates are relaxed and the experimental lattice constants are fixed, the LDA+U can reproduce the experimental A-type antiferromagnetic state. It is found that Fe-3d electrons in LaFeO3 occupy the localized orbital with the low energy, while Cr-3d and Mn-3d electrons in LaCrO3 and LaMnO3 occupy the relatively wide energy states due to the strong hybridization between d electrons and p electrons of oxygen atoms.


Introduction
Lanthanum transition-metal oxides LaRO 3 (R=Cr, Mn, Fe) display a complex correlation among structural, orbital, magnetic, and electronic degrees of freedom due to the existence of strongly correlated effect between 3d electrons of transition metal atoms. Over the past decades, LaRO 3 compounds have been widely investigated because of their technical importance and the fundamental interest in the physics of their phase transition [1,2,3,4,5,6,7,8]. Among these oxides, LaMnO 3 had attracted considerable attention due to its colossal magnetoresistance, a large variety of phases with remarkably different structural, magnetic and transport properties [9,10], and a large Jahn-Teller (JT) effect [11,12]. The Jahn-Teller effect is often encountered in octahedral complexes of the transition metals, and caused mainly by the presence of molecular orbital of the 3d transition metals [13].
In the present work, we systematically investigate the structural properties and Jahn-Teller lattice distortion for three types of oxides LaCrO 3 , LaMnO 3 , and LaFeO 3 by the first-principles calculation based on density functional theory. The magnetic ground state and spin density of states of three oxides are also studied. , where the red sphere is O atom, the green sphere is La atom, and the yellow sphere is the transition metal atom. The right panel displays a partition of orthogonal supercell (here take LaCrO 3 for example), where J ac represents the exchange interaction parameter between the nearest-neighbor Cr3 and Cr4 atoms in the ac plane and J b exchange interaction parameter between next nearest-neighbor Cr2 and Cr4 atoms. The X, Y, and Z represent the direction of different R-O bonds.

Computational details
In this paper, the first-principles calculation based on density functional theory (DFT) is performed by using the Vienna Ab initio Simulation Package (VASP). The interactions between ions and electrons are described by the projector augmented wave (PAW) method developed by Blöchl [14,15]. The cut-off energy of the plane-wave basis is set to be 650 eV, and the Brillouinzone integration is applied by 8 × 8 × 8 Monkhorst-Pack special k-points. All atoms are fully relaxed with the total energy change less than 10 −6 eV and the force on each ion less than 0.01 eV. The La-5s 2 5p 6 5d 1 6s 2 , O-2s 2 2p 4 , Cr-3p 6 3d 5 4s, Mn-3p 6 3d 5 4s 2 , Fe-3p 6 3d 6 4s 2 are considered as valence electrons. The strong correlation effects of 3d electrons are treated by GGA+U with the Perdew-Bruke-Ernzerhof (PBE) potential. The values of U eff (U-J) are taken as 5 eV for three compounds. For LaMnO 3 , we also compute the total energy and electronic structure using the LDA exchange correlation potential.

The magnetic ground state
To find the magnetic ground state, we first carry out the full structural optimization for LaCrO 3 , LaMnO 3 , and LaFeO 3 in the case of four magnetic configurations, i.e., ferromagnetic (FM), A-type antiferromagnetic (A-AFM), G-type antiferromagnetic (G-AFM), and C-type antiferromagnetic (C-AFM) states, as sketched in Fig.2, and calculate their total energies and magnetic moments, which are shown in Table 1. The magnetic ground states of LaCrO 3 and LaFeO 3 are found to be G-AFM state, which is in agreement with the experiment [7]. For LaRO 3 , the result shows that LaMnO 3 has lower energy in FM state than in A-AFM state by GGA+U, as in previous calculations [19,20,21,22]. And if only the internal coordinates with the experimental lattice constants are optimized by using LDA+U exchange correlation potential, we can reproduce the experimental ground state with A-type antiferromagnetic ordering. According to the energy difference, we derive the exchange coupling parameters J ac (J b ) between R4 and R3 (R2)(see Fig.1 (b)), and simulate the magnetic transition temperature by Monte Carlo method [23], also given in Table 1. For comparison, the experimental transition temperature is also given in Table 1. Our simulated magnetic transition temperature T = 79(550) K for LaCrO 3 (LaFeO 3 ) are lower than 290(750) K of the experimental values [24,25,26], which should be attributed to the U values and computational accuracy. For LaMnO 3 , it is found that the magnetic moment of 3.75µ B obtained from LDA is in agreement with the experimental one of 3.7µ B [27], and the out-of-plane magnetic coupling parameter of -1.85 meV is lower than experimental one of -1.2 meV [28].

Structure parameters
The degree of Jahn-Teller distortion can be reflected by three R-O bond lengths and R-O-R bond angles in RO 6 octahedron. In Table 2 we present the equilibrium lattice constants, normal mode  a bit larger than the experimental data for three compounds. In LaCrO 3 , three bond lengths, i.e., Cr4-O3 (O7), Cr4-O4 (O8), Cr4-O9 (O11), are nearly equal, and the relative ratio of bond length in the Y direction to the X (Z) direction is 0.098% (0.148%). In comparison, in LaMnO 3 the bond length in the Y direction is obviously larger than that in the X (Z) directions with relative ratio 10.97% (9.39%). For LaFeO 3 the bond length in the Y direction is slightly larger than that in the X (Z) directions with relative ratio 0.544% (0.368%). Moreover, we measure the magnitude of JT distortion by calculating the normal mode parameters [12,32], where X,Y,Z directions are marked in Fig.1. The Q 2 and Q 3 of LaMnO 3 is larger than those of LaCrO 3 and LaFeO 3 , as shown in Table 2. For three compounds, the bond angles, i.e., O3 (O7)-R-O4 (O8), O7-R-O11, O8-R-O11, have a slight deviation from the perpendicular angles each other. All above results indicate that the lattice distortion of LaMnO 3 is the most pronounced, LaFeO 3 is relatively slight, and the JT distortion of LaCrO 3 is almost ignorable. Additionally, the R-O-R bond angles exhibit a large deviation from the 180 degree in the perovskite structure, which also suggests the occurrence of structural distortion. The JT distortion can also be further explained by the electronic structure of 3d electrons in transition metal atoms.  Fig.3 shows the total and partial density of states (DOS) for G-AFM-LaCrO 3 , A-AFM-LaMnO 3 , and G-AFM-LaFeO 3 . It is found that three types of compounds are semiconductor. The LaCrO 3 has the largest energy gap of 3.1 eV, the energy gap of LaMnO 3 is 0.875 eV, close to other calculated results of 0.90 eV [22], and that of LaFeO 3 is 2.56 eV. The partial density of states of R atoms, three types of O atoms around it, and one La atom in three compounds are presented in Figs. 3 (a), 3 (b) and 3 (c), respectively, in order to clarify the orbital hybridization and ligand change around R atoms. We can see that the valence energy states are mainly contributed by the R-3d and O-2p electrons with a small contribution of La-5d electrons. There exists strong orbital hybridization between O-2p electrons and Cr (Mn)-3d electrons in LaCrO 3 (LaMnO 3 ). For LaCrO 3 and LaFeO 3 , three p orbitals of O3 and O4 atoms in the XY plane exhibit a slight exchange splitting, while no exchange splitting is found for three p orbitals of O9 atom along the Z direction (see Figs. 3 (a) and 3 (c)). In comparison, the p orbitals of O3 and O4 atoms in LaMnO 3 have obvious exchange splitting, and three p orbitals of O9 atom are also slightly asymmetry, as shown in Fig. 3 (b). Under the action of the octahedron crystal field with low symmetry, three Cr4-d electrons in LaCrO 3 do not apparently occupy the d xy ,d yz ,d xz orbitals. The d electrons of Mn atom also occupy widely the five orbitals, i.e., d xy ,d yz , d xz , d 3z2−r2 ,d x2−y2 , due to the strong hybridization between 3d electrons and 2p electrons of O atoms.

Electronic structure
In addition, it is found that the valence energy states of LaFeO 3 are separated into two parts. The energy states ranging from -8 eV to -6 eV are contributed by Fe-3d electrons and small O-2p electrons, and those from -5 eV to 0 eV are contributed by O-2p electrons and La-5d electrons. Compared with that of LaCrO 3 and LaMnO 3 , the orbital hybridization of LaFeO 3 between O-2p and Fe-3d electrons becomes weak. The Fe-d electrons orbital in LaFeO 3 is very localized and has a small energy scale ranging from -7.1 eV to -6.1 eV due to small orbital hybridization between Fe-3d electrons and O-2p electrons.

Conclusions
In summary, we have investigated the magnetic ground state, structure parameters, electronic density of states in LaCrO 3 , LaMnO 3 and LaFeO 3 by the first-principles calculation. The results show that the magnetic ground states of LaCrO 3 and LaFeO 3 are G-type antiferromagnetic state, which is in agreement with the experimental results. For LaMnO 3 , it is found that the ferromagnetic ground state has lower energy than the antiferromagnetic state in the case of optimizing both internal coordinates and lattice constants based on GGA+U, and the A-type antiferromagntetic state can be obtained if only optimizing the internal coordinates with the experimental lattice constants based on LDA+U. The lattice distortion of LaMnO 3 is the most pronounced among three compounds. Compared with the d electrons in LaCrO 3 and LaMnO 3 , the d electrons in LaFeO 3 have small energy splitting and occupy the very localized orbital.

Acknowledgement
This work is funded by the National Nature Science Foundation of China (Grant Nos. 11204064 and U1304518)