) magnetic perovskites: an ab initio study

August 5, 2014 10:3 WSPC/Guidelines-IJMPB S0217979214502051

International Journal of Modern Physics BVol. 28 (2014) 1450205 (10 pages)c© World Scientific Publishing Company

DOI: 10.1142/S0217979214502051

Electronic structure and magnetic properties of PbMO3

(M = Fe, Co, Ni) magnetic perovskites:

An ab initio study

Aytac Erkisi

Department of Physics Engineering, Hacettepe University,

Beytepe, Ankara 06800, Turkey

Erdem Kamil Yıldırım

Department of Physics, Kırıkkale University, Kırıkkale 71450, Turkey

Gokhan Gokoglu

Department of Physics, Karabuk University, Karabuk 78050, Turkey

[email protected]

Received 26 March 2014Revised 23 June 2014Accepted 30 June 2014Published 5 August 2014

We present the electronic, magnetic and structural properties of the magnetic transitionmetal oxides PbMO3 (M=Fe, Co, Ni) in cubic perovskite structure. The calculations arebased on the density functional theory (DFT) within plane-wave pseudopotential methodand local spin density approximation (LSDA) of the exchange-correlation functional. On-site Coulomb interaction is also included in calculations (LSDA + U). The systems areconsidered in ferromagnetic (FM) and G-type antiferromagnetic (G-AFM) order. FMstructures are energetically more favored than G-AFM and than non-magnetic statesfor all the systems studied. The spin-polarized electronic band structures show thatall the structures have metallic property in FM order without Hubbard-U interaction(Ueff = 0). However, the inclusion of on-site Coulomb interaction (Ueff = 7 eV) opensa semiconducting gap for majority spin channel of PbFeO3 and of PbNiO3 resulting ina half-metallic character. PbCoO3 system remains as metallic with LSDA + U scheme.Bonding features of all structures are largely determined by the hybridizations betweenO–p and d-states of transition metal atoms. The partial magnetic moment of Fe atomin PbFeO3 is enhanced by inclusion of Hubbard-U interaction (2.55 µB ⇒ 3.78 µB).Total magnetic moments of half-metallic PbFeO3 and of PbNiO3 compounds are veryclose to integer values.

Keywords: Oxides; ab initio calculations; electronic structure.

PACS numbers: 71.15.Mb, 71.20.Be, 75.50.Cc

1450205-1

Int.

J. M

od. P

hys.

B D

ownl

oade

d fr

om w

ww

.wor

ldsc

ient

ific

.com

by U

NIV

ER

SIT

Y O

F M

ICH

IGA

N o

n 11

/05/

14. F

or p

erso

nal u

se o

nly.

http://dx.doi.org/10.1142/S0217979214502051

mailto:[email protected]


A. Erkisi, E. K. Yıldırım & G. Gokoglu

1. Introduction

The cubic transition metal oxide materials with perovskite structure (ABO3) are

very important due to their various invaluable physical properties like multiferroic-

ity, i.e., strong coupling between electric and magnetic degrees of freedom. The

perovskite compounds are a large set of combinations of elements with larger size

and 12-coordinated cation (A) and smaller size and 6-coordinated cation (B) con-

structing a BO6 octahedra at the eight corners of a cube. Some perovskites are

largely used as a substrate in growth process of oxide materials, such as high-Tc

layered superconductors and colossal magnetoresistance materials.1 SrSnO3 and

BaSnO3 are known as sensitive to humidity, so they are potential candidates for

humidity sensors.2 On the other hand, BaMnO3 and SrMnO3 have catalytic activity

and are able to dissociate NO and NO2 gases.3–5 BaMnO3 surfaces performed well

in removing NO, when it is doped by La or Mg.3,4 The elevation of NO decomposi-

tion to a large extent makes BaMnO3 a good candidate as a catalyst together with

its low cost and high thermal stability even at temperatures higher than 1200 K.3,4

The preservation of thermal stability leads to conservation of catalytic activity.

Some cubic perovskite structures feature interesting magnetic properties in fer-

romagnetic (FM) and antiferromagnetic (AFM) order. Although most cubic per-

ovskites are known to have insulating electronic structure,1 in a recent study, it

is reported that BaMnO3 structure shows half-metallic properties both in bulk

and surface geometries in view of the density functional calculations within gen-

eralized gradient approximation.6 The most studied BiFeO3 compound is also a

magnetic perovskite with ferroelectric property below ≈ 1103 K and ferromagneti-

cally ordered below 640 K with a magnetic ordering in a single phase.7–10 BiFeO3

exhibits multiferroic phenomenon at ambient temperature having potential appli-

cations in spintronics; magnetically ordered and electrically accessed memory de-

vices.9 BiCoO3 has a C-type AFM structure in its ground state having an insulating

character with 2.11 eV energy band gap.11

In view of technological applications of cubic perovskites explained above, bulk

properties of these materials should be clarified in order to elevate the efficiency. The

PbNiO3 compound synthesized at 800◦C under 3 GPa pressure.12 This was an or-

thorhombic phase in GdFeO3-type structure with space group Pnma. This structure

can be transformed into a LiNbO3-type phase with an acentric space group R3c.

The ferroelectric polarization properties of PbNiO3 have also been investigated.13

These are the high temperature and high pressure phases of the related compound.

To the best of our knowledge, there is a lack of study on electronic structure and

magnetic properties of cubic magnetic PbMO3 (M=Fe, Co, Ni) structures in liter-

ature. Moreover, the effects of on-site Coulomb interaction (LSDA + U), which is

highly desirable in investigation of strongly correlated electron systems like tran-

sition metal oxides, on the magnetic properties of these materials is discussed in

detail. Therefore, our main goal is to perform a comprehensive investigation on

electronic structure of this set of materials within local spin density approximation

1450205-2

Int.

J. M

od. P

hys.

B D

ownl

oade

d fr

om w

ww

.wor

ldsc

ient

ific

.com

by U

NIV

ER

SIT

Y O

F M

ICH

IGA

N o

n 11

/05/

14. F

or p

erso

nal u

se o

nly.



(LSDA) of the density functional theory (DFT). The rest of the paper is organized

as follows: The details of computational methods and numerical parameters used

in calculations are given in Sec. 2. The results of electronic structure calculations

are discussed in Sec. 3. Then paper concludes with a summary in Sec. 4.

2. Computational Details

All the calculations presented in this work have been carried out using the

PWscf code, distributed with the Quantum ESPRESSO package.14,a The exchange-

correlation potential is approximated by LSDA of the DFT.15,16 Ultrasoft pseudopo-

tentials (USPP) are used for all the atoms in composition. The electronic configu-

rations of the atoms in compositions are as follows: Pb: 6s26p25d10, O: 2s22p4, Fe:

3s23p64s23d6, Co: 4s13d8, Ni: 4s23d8.

Bulk structure of cubic perovskite oxide PbMO3 conforms to E21 symmetry

with Pm3m space group consisting of one formula unit of atoms per primitive cell.

Brillouin zone integration is performed with automatically generated 10×10×10 k-

point mesh centered at Γ-point following the convention of Monkhorst and Pack.17

Wavefunctions are expanded in plane wave basis sets up to a kinetic energy cut-

off value of 80 Ry. These values are determined by testing convergence in self-

consistent calculations. Davidson type iterative diagonalization method18 is used in

order to solve Kohn–Sham equations with 1×10−8 Ry energy convergence threshold.

In order to get a smooth electronic density of states (DOS), Methfessel–Paxton

type smearing is applied on fermionic occupation function with 0.02 Ry smearing

parameter. The structure optimization process is performed by Broyden–Fletcher–

Goldfarb–Shanno (BFGS) algorithm which optimizes the ionic coordinates without

breaking symmetry.19 The ionic minimization is carried out until the forces on

the atoms are less than 1 × 10−4 Ry/a.u. and the displacement of the atoms are

converged to less than 0.003 a.u.

LSDA functionals fail to describe strongly correlated electron systems with lo-

calized d and f orbitals. This is mostly encountered in transition metal oxides. In

such a case, the on-site Coulomb interaction with an effective Hubbard U parameter

(LSDA + U) is included. The on-site Coulomb (U) and exchange (J) parameters

are not separately taken into account in the approach of Dudarev et al.,20 but the

difference U−J which is physically meaningful is applied. Then the additional term

due to interactions of the strongly correlated 3d electrons of Fe, Co and Ni is in the

following form:

E(LSDA + U) = E(LSDA) +U − J

2

∑

σ

[Trρσ − Tr(ρσρσ)] . (1)

aQuantum-ESPRESSO is a community project for high-quality quantum-simulation software,based on DFT, and coordinated by Paolo Giannozzi. See http://www.quantum-espresso.org andhttp://www.pwscf.org.

1450205-3

Int.

J. M

od. P

hys.

B D

ownl

oade

d fr

om w

ww

.wor

ldsc

ient

ific

.com

by U

NIV

ER

SIT

Y O

F M

ICH

IGA

N o

n 11

/05/

14. F

or p

erso

nal u

se o

nly.



In the equation above, ρ is the density matrix of 3d states of Fe, Co, or Ni having

spin σ. Hereafter, we call the difference (U − J) as a single parameter Ueff .

3. Results and Discussion

The stability and structural distortions of perovskite oxides are roughly determined

by Goldschmidt tolerance factor that is defined by t = (rA + rO)/√2(rB + rO),

21

where rA, rB , rO are the ionic radii of the A, B cations and oxygen anion, respec-

tively. The values with 0.9 < t < 1.0 are energetically favored in cubic phase, while

the structures with 0.75 < t < 0.9 tend to orthorhombic phase (Pnma space group)

with a tilting of BO6 octahedra yielding lower symmetry. The calculated tolerance

factors of the systems considered are 0.92, 0.95 and 0.98 for PbFeO3, PbCoO3 and

PbNiO3, respectively. This situation enables us to investigate such systems in cubic

E21 crystallographic structure.

Firstly, we investigate the stable crystal structure of cubic PbMO3 (M=Fe,

Co, Ni) compounds in FM order with 5-atom cell by calculating total energies at

more than 20 different volumes. The same procedure is also applied to G-type an-

tiferromagnetic (G-AFM) structure whose crystallographic order is shown in Fig. 1

together with conventional E21 structure. The primitive cell of G-AFM structure

is modeled by a 10-atom supercell, in which the magnetic moment of 3d transition

metal cation (Fe, Co or Ni) is in opposite direction to magnetic moments of six

nearest-neighbor identical atoms. Then, we use Vinet equation of states to obtain

equilibrium structural parameters and ground state energies.22,23 The asymptotic

Fig. 1. The crystal structures of cubic PbMO3 and tetragonal supercell of G-AFM crystalstructure.

1450205-4

Int.

J. M

od. P

hys.

B D

ownl

oade

d fr

om w

ww

.wor

ldsc

ient

ific

.com

by U

NIV

ER

SIT

Y O

F M

ICH

IGA

N o

n 11

/05/

14. F

or p

erso

nal u

se o

nly.



0

20

40

60

80

100

500 650 800 950

∆E

[m

Ry]

Volume [a.u.3]

Ferromagnetic

Antiferromagnetic

0

30

60

90

120

150

500 650 800 950

Volume [a.u.3]

0

30

60

90

120

150

500 650 800 950

Volume [a.u.3]

cba

Fig. 2. The static equation of states of (a) PbFeO3, (b) PbCoO3, and (c) PbNiO3 compoundsin FM and G-AFM order with LSDA + U scheme.

Table 1. The optimized structural parameters, total magnetic moments andpartial magnetic moment of the magnetic atoms in composition for LSDA andLSDA+ U (Ueff = 7 eV) calculations in FM phase.

a (a.u.) B (GPa) B′ µtot (µB) µatom (µB)

LSDA

PbFeO3 7.164 183.1 4.10 3.30 µFe = 2.55PbCoO3 7.060 172.0 1.77 1.78 µCo = 1.26PbNiO3 7.038 183.5 1.42 0.14 µNi = 0.09LSDA+ U

PbFeO3 7.288 156.5 3.73 4.04 µFe = 3.78PbCoO3 7.010 208.1 4.83 0.24 µCo = 0.43PbNiO3 7.095 177.8 5.27 0.92 µNi = 1.05

Table 2. The optimized structural parametersfor LSDA + U (Ueff = 7 eV) calculations inG-AFM phase.

a (a.u.) B (GPa) B′

PbFeO3 7.295 153.5 6.21PbCoO3 7.023 193.4 4.63PbNiO3 7.065 181.3 5.79

standard errors in fitting process are less then ≈ 2% as an indication of accuracy of

the calculations. Murnaghan equation of states also give similar values with ≈ 1%

differences. The static equations of states of PbMO3 compounds in FM and G-

1450205-5

Int.

J. M

od. P

hys.

B D

ownl

oade

d fr

om w

ww

.wor

ldsc

ient

ific

.com

by U

NIV

ER

SIT

Y O

F M

ICH

IGA

N o

n 11

/05/

14. F

or p

erso

nal u

se o

nly.



AFM orders are shown in Fig. 2. LSDA + U calculations show clearly that FM

structures have 29.41, 44.14 and 19.85 Ry lower energies than G-AFM structures

for PbFeO3, PbCoO3 and PbNiO3 systems, respectively. This situation indicates

that FM ground states are energetically more favored than G-AFM structures for

all the systems studied. We present the results of structural parameters in Table 1

for both LSDA and LSDA+U calculations in FM order. The parameters of G-AFM

structure in the LSDA+U scheme are presented in Table 2. The equilibrium lattice

constants are approximately ≈ 7 a.u. with small deviations according to system. All

compounds considered can be regarded as hard materials with high bulk moduli

values. Moreover, PbFeO3 system has large pressure derivative of bulk modulus

indicating a strong sensitivity against pressure, since bulk modulus is a monotonic

increasing function of pressure in the range of structural stability.

The inclusion of on-site Coulomb interaction redecorates the electronic structure

yielding dramatic changes in structural parameters as well as in energy band struc-

ture and density of electronic states. The Ueff parameter is chosen as 7 eV for all 3d

transition metals in compositions. The bulk moduli of the systems, except PbCoO3,

are decreased together with slight increase in equilibrium lattice constants. There

are also remarkable changes in total and partial magnetic moments. The magnetic

moment of Fe atoms in PbFeO3 is largely enhanced by inclusion of Hubbard U

(2.55 µB ⇒ 3.78 µB). The details of the interactions can be visualized by consider-

ing electronic band structures and partial electronic DOS of the systems. In Figs. 3

-9

-6

-3

0

3

6

E-E

F(e

V)

majority ↑ minority ↓

-9

-6

-3

0

3

6

E-E

F(e

V)

-9

-6

-3

0

3

6

R Γ X M Γ

E-E

F(e

V)

R Γ X M ΓEDOS ρ(E) [eV-1

]

a

b

c

Fig. 3. Spin-polarized LSDA electronic band structures for (a) PbFeO3, (b) PbCoO3 and(c) PbNiO3 compounds. Total electronic DOS are also included between the band structures.

1450205-6

Int.

J. M

od. P

hys.

B D

ownl

oade

d fr

om w

ww

.wor

ldsc

ient

ific

.com

by U

NIV

ER

SIT

Y O

F M

ICH

IGA

N o

n 11

/05/

14. F

or p

erso

nal u

se o

nly.



-9

-6

-3

0

3

6

E-E

F(e

V)

majority ↑ minority ↓

-9

-6

-3

0

3

6

E-E

F(e

V)

-9

-6

-3

0

3

6

R Γ X M Γ

E-E

F(e

V)

R Γ X M ΓEDOS ρ(E) [eV-1

]

a

b

c

Fig. 4. Spin-polarized LSDA + U electronic band structures for (a) PbFeO3, (b) PbCoO3 and(c) PbNiO3 compounds. Total electronic DOS are also included between the band structures.

and 4, spin-polarized electronic band structures of the systems are presented along

the high symmetry directions in Brillouin zone for LSDA and LSDA + U calcu-

lations, respectively. All the PbMO3 compounds have metallic character in their

ground state due to LSDA scheme. The bands crossing Fermi level (EF ) are 3d

states of Fe, Co and Ni atoms as seen in Fig. 5 in which orbital projected den-

sity of electronic states are given for PbMO3. p-states of oxygen also contribute to

bands around EF . The electronic states of Pb atoms are remarkable at high energy

levels and have no distinct effect on bonding properties. Spin-up and -down states

of PbNiO3 have very similar characteristics yielding very small magnetic moment.

It can be emphasized that 3d electronic states of magnetic transition metal are

responsible for the metallicity of these systems.

In Fig. 6, spin-polarized LSDA + U calculated electronic densities of states are

shown. As clearly seen, the Hubbard U interaction has remarkable effects on elec-

tronic structure. In the majority spin channels of PbFeO3 and PbNiO3 compounds,

an energy gap appears by the inclusion of Ueff . These energy gaps are 1.36 eV and

0.96 eV for PbFeO3 and PbNiO3, respectively, both are direct band gaps at M

point. These materials become half-metallic with a semiconducting band structure

for one spin state, while the other spin state conveys a metallic conduction. As a

typical property of half-metals, the total magnetic moments of these systems are

very close to integer values; µPbFeO3= 4.04 and µPbNiO3

= 0.92 µB, since the elec-

tronic states about EF are solely occupied by minority spins. Hubbard U interaction

1450205-7

Int.

J. M

od. P

hys.

B D

ownl

oade

d fr

om w

ww

.wor

ldsc

ient

ific

.com

by U

NIV

ER

SIT

Y O

F M

ICH

IGA

N o

n 11

/05/

14. F

or p

erso

nal u

se o

nly.



-2

-1

0

1

2

ED

OS

ρ(E

) [e

V-1

]

O-p

Fe-d

Pb-s

-2

-1

0

1

2

ED

OS

ρ(E

) [e

V-1

]

-2

-1

0

1

2

ED

OS

ρ(E

) [e

V-1

]

O-p

Co-d

Pb-p

Pb-s

-2

-1

0

1

2

ED

OS

ρ(E

) [e

V-1

]

-2

-1

0

1

2

-10 -8 -6 -4 -2 0 2 4 6

ED

OS

ρ(E

) [e

V-1

]

E-EF(eV)

O-p

Ni-d

Pb-p

Pb-s

-2

-1

0

1

2

-10 -8 -6 -4 -2 0 2 4 6

ED

OS

ρ(E

) [e

V-1

]

E-EF(eV)

a

b

c

Fig. 5. Spin-polarized LSDA orbital projected electronic DOS for (a) PbFeO3, (b) PbCoO3 and(c) PbNiO3 compounds.

repels the electronic states to lower energies via changing Fermi energy. Especially

in the case of PbFeO3, the energetic difference between the majority and minority

spins of Fe–3d states are widened with almost zero density of up spin states at

EF . This is the cause of large increase in Fe magnetic moment upon inclusion of

Ueff . The p-orbital of oxygen is also slightly disturbed by the inclusion of Ueff . The

bonding properties of all structures are mainly determined by the hybridizations

between d-states of transition metal atoms and O–p states. p-states of Pb atom

1450205-8

Int.

J. M

od. P

hys.

B D

ownl

oade

d fr

om w

ww

.wor

ldsc

ient

ific

.com

by U

NIV

ER

SIT

Y O

F M

ICH

IGA

N o

n 11

/05/

14. F

or p

erso

nal u

se o

nly.



-2

-1

0

1

2

ED

OS

ρ(E

) [e

V-1

]

O-p

Fe-d

Fe-p

Pb-s

Pb-p

-2

-1

0

1

2

ED

OS

ρ(E

) [e

V-1

]

-2

-1

0

1

2

ED

OS

ρ(E

) [e

V-1

]

O-p

Co-d

Co-s

Pb-p

Pb-s

-2

-1

0

1

2

ED

OS

ρ(E

) [e

V-1

]

-2

-1

0

1

2

-10 -8 -6 -4 -2 0 2 4 6

ED

OS

ρ(E

) [e

V-1

]

E-EF(eV)

O-p

Ni-d

Pb-p

Pb-s

-2

-1

0

1

2

-10 -8 -6 -4 -2 0 2 4 6

ED

OS

ρ(E

) [e

V-1

]

E-EF(eV)

a

b

c

Fig. 6. Spin-polarized LSDA+U orbital projected electronic DOS for (a) PbFeO3, (b) PbCoO3

and (c) PbNiO3 compounds.

take place at high energy levels with no distinct effect on bonding and conduction

properties.

4. Conclusion

The electronic, magnetic and structural properties of the magnetic transition metal

oxides PbMO3 (M=Fe, Co, Ni) in cubic perovskite structure have been investigated

in detail with considering different magnetic orders. On-site Coulomb interaction

1450205-9

Int.

J. M

od. P

hys.

B D

ownl

oade

d fr

om w

ww

.wor

ldsc

ient

ific

.com

by U

NIV

ER

SIT

Y O

F M

ICH

IGA

N o

n 11

/05/

14. F

or p

erso

nal u

se o

nly.



has been included in calculations (LSDA+U), which is usually vital in investigation

of highly correlated electron systems, such as transition metal oxides. The FM and

G-AFM orders have been studied. For all three compounds, FM ground states are

energetically more favorable than G-AFM and than nonmagnetic states. The spin-

polarized electronic band structures exhibit a metallic property in FM order without

inclusion of Hubbard-U interaction (Ueff = 0). But, LSDA+U calculations present

rather interesting results. The on-site Coulomb interaction (Ueff = 7 eV) opens an

electronic band gap for majority spin channel of PbFeO3 and of PbNiO3 resulting

in a half-metallic character. As a typical property of half-metallic compounds, total

magnetic moments of PbFeO3 and of PbNiO3 compounds are very close to integer

values. These materials can have possible applications in spintronics with half-

metallic conduction and large magnetoresistance.

Acknowledgments

This research was supported in part by TUBITAK (The Scientific & Technological

Research Council of Turkey) through TR-Grid e-Infrastructure Project, part of the

calculations have been carried out at ULAKBIM Computer Center.

References

1. B. Meyer, J. Padilla and D. Vanderbilt, Faraday Discuss. 114, 395 (1999).2. L. M. Feng et al., J. Phys. Chem. Solids 69, 967 (2007).3. H. Iwakuni et al., Appl. Catal. B: Environ. 74, 299 (2007).4. H. Iwakuni et al., Bull. Chem. Soc. Jpn. 81, 1175 (2008).5. J. Zhu and A. Thomas, Appl. Catal. B: Environ. 92, 225 (2009).6. G. Gokoglu and H. Yildirim, Comput. Mater. Sci. 50, 1212 (2011).7. C. Michel et al., Solid State Commun. 7, 701 (1969).8. A. M. Abakumov et al., Chem. Mater. 23, 255 (2011).9. G. Calatan and J. F. Scott, Adv. Mater. 21, 2463 (2009).

10. G. L. Yuan and S. W. Or, J. Appl. Phys. 100, 024109 (2006).11. M.-Q. Cai et al., J. Chem. Phys. 126, 154708 (2007).12. Y. Inaguma et al., J. Am. Chem. Soc. 133, 16920 (2011).13. X. F. Hao et al., Phys. Rev. B 86, 014116 (2012).14. P. Giannozzi et al., J. Phys.: Condens. Matter 21, 395502 (2009).15. W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965).16. P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964).17. H. J. Monkhorst and J. D. Pack, Phys. Rev. B 13, 5188 (1976).18. E. R. Davidson, J. Comput. Phys. 17, 87 (1975).19. H. B. Schlegel, J. Comput. Chem. 3, 214 (1982).20. S. L. Dudarev et al., Phys. Rev. B 57, 1505 (1998).21. V. M. Goldschmidt, Die Naturwissenschaften 21, 477 (1927).22. P. Vinet et al., J. Phys. C 19, L467 (1986).23. R. E. Cohen, O. Gulseren and R. J. Hemley, Am. Mineral. 85, 338 (2000).

1450205-10

Int.

J. M

od. P

hys.

B D

ownl

oade

d fr

om w

ww

.wor

ldsc

ient

ific

.com

by U

NIV

ER

SIT

Y O

F M

ICH

IGA

N o

n 11

/05/

14. F

or p

erso

nal u

se o

nly.

) magnetic perovskites: an ab initio study

Documents