Review
First-principles investigations of structural, electronic and magnetic properties of cubic LaMnO
3M. Dine El Hannania, D. Racheda,, M. Rabaha, R. Khenatab,, N. Benayada, M. Hichourb, A. Bouhemadouc
aFaculte´ des Sciences, De´partement de Physique, Universite´ Djillali LIABES de Sidi-Bel-Abbe`s 22000, Alge´rie
bLaboratoire de Physique Quantique et de Mode´lisation Mathe´matique de le Matie`re (LPQ3M), Universite´ de Mascara, Mascara 29000, Alge´rie
cLaboratory for Developing New Materials and their Characterization, Department of Physics, Faculty of Science, University of Setif, 19000 Setif, Algeria
a r t i c l e i n f o
Available online 20 May 2009 Keywords:
Perovskite FP-LMTO
Electronic properties Magnetic properties
a b s t r a c t
Using first-principle density functional calculations, the structural, electronic and magnetic properties of cubic perovskite LaMnO3were studied by means of the full- potential linear muffin-tin orbital method. Calculations were performed within the local spin density approximation (LSDA) to the exchange correlation potential. The magnetic phase stability was determined from the total energy calculations for both ferromag- netic (FM) and non-magnetic (NM) phases. Our calculations show that the magnetic phase is more stable than the non-magnetic phase. To our knowledge the elastic constants of this compound have not yet been measured or calculated, hence our results serve as a first quantitative theoretical prediction for future study. Additionally, the band structure, the density of state and the magnetic moments were analyzed.
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Contents
1. Introduction . . . 81
2. Method of calculations . . . 82
3. Results and discussion. . . 82
3.1. Structural properties and phase stability . . . 82
3.2. Elastic properties . . . 83
3.3. Electronic structure and magnetic properties. . . 85
4. Conclusions . . . 85
References . . . 85
1. Introduction
The ABO3-type perovskite crystals have been exten- sively studied, because of their technical importance and the fundamental interest in the physics of their phase transition [1]. They are among the most important examples of ferroelectric materials. The perfect perovskite Contents lists available atScienceDirect
journal homepage:www.elsevier.com/locate/mssp
Materials Science in Semiconductor Processing
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doi:10.1016/j.mssp.2009.04.002
Corresponding author. Tel.:+213 48 54 43 44.
Corresponding author. Permanent address: Universite´ Djillali Liabe`s, Faculte´ des Sciences, De´partement de Physique, Sidi-Bel-Abbe´s 22000, Alge´rie. Tel.:+213 48 54 43 44.
E-mail addresses:[email protected] (D. Rached), [email protected] (R. Khenata).
structure is very simple and has full cubic symmetry in which the body center position is occupied by B atoms, the edges by A atoms and the face centers by oxygen atoms in Pm3m space group. A large number of the perovskites exhibits a wide variety of low temperature structural distortions associated with lattice instability of the prototype structure, including ferroelectrics, antiferro- electric and antiferrodistortive.
Among these perovskites, the LaMnO3shows a great potential of technological applications in fuel cells [2], magnetoresistive devices and spintronics[3]. This materi- al exhibits puzzling physical properties related to a complex interplay between orbital, magnetic, charge and structural degrees of freedom. This includes colossal- magnetoresistance (CMR) effects and a large variety of phases with remarkably different structural, magnetic and transport properties.
This compound is also characterized by its very rich phase diagram depending on the doping concentration, temperature and pressure, being either an antiferromag- netic (AF) insulator, ferromagnetic (FM) metal, or charge- ordered insulator[4,5]. At ambient condition, the MnO6
octahedra in LaMnO3 are strongly tilted with respect to the ideal cubic perovskite, and also significantly distorted by a collective Jahn-Teller (JT) effect[6].
From a theoretical point of view, a several first principles calculations were made for LaMnO3 material by a variety of methods. Tyer et al. [7]and Banach and Temmerman[8], reported some results on electronic and magnetic properties of this compound. These authors[7,8]
used the self-interaction corrected (SIC) within the local spin-density (LSD) theory [9,10]. Trimarchi and Binggeli [11] have used the first-principle ultrasoft pseudopoten- tial method within LDA+U to study the structural and electronic properties of LaMnO3. Evarestov et al. [12];
Nicastro and Pattersson [13]; Munoz and Harrison [14]
and Ravindran et al. [15] have studied the magnetic properties of LaMnO3, in particular the energetic of ferromagnetic and antiferromagnetic phases by using the linear combination of atomic orbitals (LCAO) and the linearized augmented plane wave (LAPW) methods, respectively.
From the above it is clear that there is a con- siderable theoretical work on LaMnO3 compound.
We note that there exist limited theoretical studies of structural properties. Moreover, the first-order elastic constants of this compound are among the properties which are not yet established. We therefore think that it is worthwhile to perform these calculations. The aim of this work is to give a detailed description of the structural stability, elastic and electronic properties by using the full-potential linearized muffin-tin orbital (FP-LMTO) method, in order to complete the exciting experimental and theoretical works on this compound.
This paper is organized as follows: In Section 2, we give a brief description of the method used and details of the calculations. In Section 3, the structural parameters, elastic constants, band structure and the magnetic properties are presented and analyzed. Conclusions are drawn in the last section.
2. Method of calculations
The ternary LaMnO3 compound crystallizes in the cubic structure. The space group is (Pm3m-221). The La atom is located at (0.0; 0.0; 0.0), Mn atom at (0.5;0.5;0.5) and the oxygen atom at (0.5;0.5;0.0). The calculations reported in this work were carried out by means of the full-potential linear muffin-tin orbital [16,17] within the framework of density functional theory (DFT). In this method the space is divided into an interstitial region (IR) and non-overlapping (MT) spheres centered at the atomic sites. In the IR region, the basis set consists of plane waves.
Inside the MT spheres, the basis sets are described by radial solutions of the one particle Schro¨dinger equation (at fixed energy) and their energy derivatives multiplied by spherical harmonics.
In order to achieve energy eigenvalues convergence, the charge density and potential inside the muffin-tin spheres are represented by spherical harmonics up to lmax¼6, while in the interstitial region, 9170 plane waves with energies up to 133.61 Ry were included in the calculation. The RMT are taken to be 3.406, 1.943 and 1.589 a.u for La, Mn and O, respectively. The exchange- correlation (XC) effects are treated by the local density approximation (LDA) and local spin density approxima- tion (LSDA) schemes[18]. The self-consistent calculations are considered to be converged when the total energy of the system is stable within 105Ry. The integrals over the Brillouin zone are performed up to 18 k-points in the irreducible Brillouin zone (IBZ), using the tetrahedron method[19].
3. Results and discussion
3.1. Structural properties and phase stability
In order to calculate the ground states properties of LaMnO3 compound, the total energies are calculated in both non-magnetic (NM) and FM phases for different volumes around the equilibrium cell volumeV0. The plots of the calculated total energies versus reduced volume for this compound in both phases are given inFig. 1. It is seen from theE(V) curve, that the FM phase is stable than the NM phase at ambient conditions, which is consistent with experimental results and other theoretical works.
The calculated total energies are fitted to the Birch’s equation of state [20] to determine the ground state properties such as the equilibrium lattice constanta0, the bulk modulus B0 and its pressure derivative B0. The calculated equilibrium parameters (a0,B0andB0) in both phases are given inTable 1, which also contains results of previous calculations as well as the experimental data.
In comparison with the experimental data, the computed lattice constantausing LDA and LSDA deviates from the measured ones within 4.9–4%. We can also mention that our result concerning the LSDA-lattice constant, along the theoretical study of Banach and Temmerman[8], which localizes the ferromagnetic structure of the LaMnO3
compound between 3.68 and 3.77 A˚. The value of the bulk modulus indicates that the magnetic phase is less
hard than the non-magnetic phase. The calculated LDA and LSDA bulk moduli values are twice larger than the available theoretical values. This could be attributed to the use of the local density approximation which known to underestimate the lattice constant and overestimate the bulk modulus compared to generalized gradient approx- imation (GGA) used by Fuks et al.[23].
Under compression, the calculation shows that LaMnO3 will undergo a structural phase transition from M to NM phase. The structural phase stability is determined by calculating the Gibbs free energy for both phases (G¼Etot+PV–TS). Since the theoretical calculations are performed at 0 K, the Gibbs free energy becomes equal to the enthalpy H¼Etot+PV [24]. At a given pressure a stable structure is one for which the enthalpy has its minimum value and the transition pressure (Pt) is calculated at which the enthalpies for the two phases are equal. We can avoid this construction and obtain this information directly from Fig. 1 by determining the comment tangent between the two E(V) curves.
The calculated value for the transition pressure from FM to NM phase turn out to be 130.75 GPa. This pressure is accompanied by transition volumes 0.75 and 0.76 for NM and FM phase, respectively.
3.2. Elastic properties
The elastic properties play an important part in providing valuable information about the binding char- acteristic between adjacent atomic planes. Anisotropic characters of binding and structural stability are usually defined by the elastic constantsCij. These constants have been often related to the shear modulusG and Young’s modulusY, which are frequently measured for polycrys- talline materials when investigating their hardness. The elastic moduli require knowledge of the derivative of the energy as a function of the lattice strain. In the case of cubic system, it is possible to choose this strain in such a way that the volume of the unit cell is preserved. Thus for the calculation of elastic constants C11, C12 and C44 for these compounds we have used the Mehl method[25], which have been applied with successful results in our previous work[26,27]. For the calculation of the elastic constantsC11andC12, a volume conserving orthorhombic strain tensor is used
1þd 0 0
0 1d 0
0 0 1=ð1d2Þ 2
64
3
75. (1)
Application of this strain leads to the following total energy:
EðdÞ ¼EðdÞ ¼Eð0Þ þ ðC11C12ÞV0d2þOðd4Þ, (2) whereV0 is the volume of the unit cell and E(0) is the energy of the unstrained lattice at volumeV.
For the calculation of the elastic constantC44, a volume conserving monoclinic tensor is used
1 d=2 0
d=2 1 0
0 0 4=ð4d2Þ 2
64
3
75, (3)
which changes the total energy into
EðdÞ ¼EðdÞ ¼Eð0Þ þ12C44V0d2þOðd4Þ. (4) 240
-19745.00 -19744.95 -19744.90 -19744.85 -19744.80 -19744.75 -19744.70 -19744.65 -19744.60
Magnetic Phase Non-Magnetic Phase
Total Energy (Ryd)
260 280 300 320 340 360 380 400 420 Volume (a.u)3
Fig. 1.Calculated total energy as a function of volume in the cubic perovskite phase for both non-magnetic and magnetic phases of LaMnO3.
Table 1
Calculated lattice constanta0(in A˚), bulk modulusB0(in GPa) and the pressure derivative (B0) of LaMnO3 for the ferromagnetic and non- magnetic phases.
This work a0(A˚) B0(GPa) B0
LSDA 3.739 220.91 5.118
3.904a,b,c 118.7c 3.903d
3.930e
LDA 3.708 263.56 4.391
aRef.[21].
bRef.[22].
cRef.[23].
dRef.[8].
eExpt. from Ref.[8].
For isotropic cubic crystal, the bulk modulus is given by
B¼13ðC11þ2C12Þ: (5)
On the other hand, the shear and the Young’s moduli are related to the microscopic elastic constants by means of the following equations:
G¼9BY=ð3BþYÞandY¼ ðC11C12þ3C44Þ=5. (6) Our calculated elastic constants Cij, the shear and the Young’s moduli for the magnetic phase (M) are summar- ized inTable 2. It is clear that this compound exhibits a small value ofC44. From the elastic constants we obtain the anisotropy parameterA¼(2C44/(C11–C12)¼1.64. This indicates that this compound is highly anisotropic. Also, Table 2
Calculated elastic constants of LaMnO3in its stable structure.
C11(GPa) C12(GPa) C44(GPa) G(GPa) E(GPa)
LaMnO3 234.52 214.10 16.8 14.16 49.15
-10 -10
-8 -6 -4 -2 0 2 4 6 8 10
EF Total
Dashed dot 4f La Dash dot dot 5p La
DOS, st./[eV*cell]
Energy (eV)
-10 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0
EF Mn 3d
DOS, st./[eV*cell]
Energy (eV)
-5 0 5 10
2s O 3d Mn
-5 0 5 10
eg t2g
Fig. 2.Total and partial DOS (a) and partial DOS of Mn atom (b) of LaMnO3in cubic perovskite phase.
the calculated positive value of the elastic constants is indicative of the stability of this compound in its cubic perovskite structure. According to the theoretical study of Banach and Temmerman[8], which states that the stable ferromagnetic structure appear with reducing the volume of the antiferromagnetic structure, and consequently, the cubic FM structure has comparatively smaller lattice constant and higher bulk modulus than the AF structure.
This implies that the calculated FM—elastic constants are relatively large. Moreover, we expect that these elastic constant computed using our bulk modulus (Eq. (5)) overestimates the corresponding AF values because the bulk modulus in the antiferromagnetic structure is less than those of the ferromagnetic structure. Since the true (experimental) values of the bulk modulus and the elastic constants of the (AF) structure are not available, the magnitude of this overestimation is difficult to estimate.
To the best of our knowledge, the elastic properties of this compound have not yet been measured or calculated.
Hence our results can be considered as a prediction study.
The requirement of mechanical stability in this cubic structure leads to the following restrictions on the elastic constants, C11–C1240, C4440, C11+2C1240.
The elastic constants in Table 2 obey these stability conditions, including the fact that C12 must be smaller than C11. Our calculated elastic constants also obey the cubic stability conditions, meaning thatC12oBoC11.
3.3. Electronic structure and magnetic properties
To further elucidate the nature of the electronic band structure, we have calculated the total and atomic site projected densities of states (PDOS) for LaMnO3 in its cubic perovskite phase. These are displayed in Fig. 2.
We define the majority spin component to be the one that contains the largest number of electrons. The overall DOS profiles are in fairly good agreement with previous (APW+lo) results[23]. From the partial DOS we are able to identify the angular momentum character of the different structures. Following Fig. 2 we should emphasize that there are three distinct structures in the density of electronic states separated by gaps. The lowest structure in the energy range between 20.97 to 19.34 eV (not shown in figure) is essentially dominated by O-2s states with minor contributions from Mn-3d and La-6s, 5p and 5d states. The second structure between9.36 eV up to the Fermi energy (EF) correspond to O-2p, Mn-4s and 3d states with minor contributions from La-5p and 4f states.
The Mn-3d states are split into a doublet with eg
symmetry and triplet with t2g symmetry, respectively.
It is readily apparent that the Mn-3d states are energe- tically degenerate with the O-2p states in the valence band (VB), indicating that there are finite covalent interactions between these states, which are mainly responsible for the formation of the valence band below the Fermi level. The total DOS in the vicinity of the Fermi level (EF) shows a gap of about 1.80 eV for spin down electrons, which is in good agreement with the estimated experimental gap 1.7 eV[28]and the calculated gap (2 eV) by Fuks et al.[23]. For both cases, spin up and spin down,
the Fermi level (EF) crosses the DOS, indicating the metallic character for LaMnO3 compound. In the third structure (conduction band) is mainly dominated by La-4f states with small contributions of Mn-3d states.
Spin polarized self consistent band structure calcula- tions have been very successful in calculating and predicting the magnetic moments using LSDA approxima- tion. The magnetic moments for La and O are 0.0631 and 0.0599mb (where mb is the Bohr magnetic), but the magnetic moment of the Mn atoms is found to be equal 2.247mb. Due to the localization of the spin polarized charge around the Mn atom, this value is slightly smaller than the total magnetic moment (2.632mb). The value of the magnetic moment of O atom according to atomic positions induced that these moments are coupled ferromagnetically with local moments of Mn3+. Our calculated values of the magnetic moment are in good agreement with those calculated by the generalized- gradient-corrected relativistic full-potential LAPW meth- od for the AF and FM states[15].
4. Conclusions
We have performed first-principle FP-LMTO calcula- tions of the structural electronic and magnetic properties of LaMnO3 in its cubic perovskite phase. The calculated pressure at which this compound undergo a structural phase transition from ferromagnetic to non-magnetic phase are found to be equal 130.75 GPa. We have shown the magnetic moment of Mn atom is higher than the other magnetic moment at La and O atoms, closer to the total magnetic moment. We are not aware of any experimental or theoretical data for the elastic properties of this compound in cubic perovskite phase and so our calcula- tions can be used to cover this lack of data for this compound.
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