Applied Mathematics, 2013, 4, 1320-1325
http://dx.doi.org/10.4236/am.2013.49178 Published Online September 2013 (http://www.scirp.org/journal/am)
A Novel Coupling between the Electron Structure and
Properties of Perovskite Transition Metal Oxides
Ghous Narejo, Warren F. Perger
Electrical Engineering Department, Michigan Tech University, Houghton, USA
Received August 2, 2012; revised January 5, 2013; accepted January 12, 2013
Copyright © 2013 Ghous Narejo, Warren F. Perger. This is an open access article distributed under the Creative Commons Attribu-
tion License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly
cited.
ABSTRACT
The ab-initio computational techniques are employed to extract the coupling between the electronic structure and mag-
netic properties for a wide variety of transition metal oxides. Optimized crystalline structures are computed by employ-
ing Hartree Fock (HF) and Density Functional Theory (DFT) techniques. The hydrostatic pressure is employed upon the
optimized cubic crystalline structures of BaScO3, BaTiO3, BaVO3, BaCrO3, BaMnO3 and BaFeO3 to extract the cou-
pling between the electronic structures and magnetic properties originating due to electron spin polarizations.
Keywords: Coupling; Spin; Strain
1. Introduction
The transition metals and their oxides are widely inves-
tigated by researchers [1-5]. The researchers employed
the empirical, analytical and experimental methods [1-8]
to extract the correlation between the electronic struc-
tures and properties of these materials. However, no ma-
jor success has been reported in finding out the exact
relationship between the crystalline structure and proper-
ties of these materials. We have attempted to investigate
the complex nature of this interdependence existing in
highly correlated physics of these materials. The com-
plexity in these investigations arises due to an interaction
between the electronic structures and properties. The
latter are partially based upon the position of valence
electrons in highly localized d-orbitals. This article ex-
plores the novel cubic perovskite phases for a wide vari-
ety of oxides of Sc-Fe. Later on, the interaction between
these novel perovskite crystalline structures is compared
with the computational results from other sources. An
attempt has also been made to extract the interactions
between the electronic structures and magnetic properties
arising from electron spin polarization.
2. Computational Methods and Paramters
The Crystal09 code is employed to compute the ex-
change energy for the ferromagnetic and antiferromag-
netic phases in each of the transition metal oxides. Fig-
ures 1 and 2 show the periodic crystalline lattice of
perovskite cubic BaTiO3 and BaFeO3 consisting of the
supercells of an optimum size utilized during these com-
putations. These super cells were employed to compute
the optimized crystalline structure and its interaction with
electronic properties arising out of the electron spin po-
larization. Hydrostatic strains are employed for a varying
sizes of electronic structures around optimized crystalline
volume for each perovskite. During these computations
the electronic basis sets for Ba and O were kept same. for
BaScO3, BaVO3, BaCrO3 and BaMnO3 to facilitate the
SCF convergence.
The computational results are reported in Tables 1-5
and shown in Figures 1-8. The optimized crystalline
structure is compared with experiemental values if avail-
able and four additional computations of electronic
structures and properties are performed. The hydrostatic
compression or expansion of each crystalline structure is
achieved by employing expansions and reductions of
volume in small increments.
In this way, five separate computations are done for
each of the crystalline systems. These computations are
repeated for a large variety of crystalline systems to
check the consistency.
Model
Some researchers [5,7,8] have proposed working theo-
retical models for a wide variety of transition metal oxides
C
opyright © 2013 SciRes. AM

G. NAREJO, W. F. PERGER 1321
Figure 1. An octahedral is formed by O atoms having Fe
atom in the middle. Green and red color spheres represent
Ba, O and Fe atoms could not be seen as these are posi-
tioned in the middle of each cage in a perovskite BaFeO3.
Figure 2. An octahedral is formed by O atoms having Fe
atom in the middle. Green and red color spheres represent
Ba and O while grey colored Ti atoms ar e positioned in the
middle of each cage in a perovskite BaTiO3.
Table 1. Computations of fm
E
, fm
exch
E
, afm
E
and afm
exch
E
are done for lattice constant a in cubic BaScO3. The units of
energy are in Hartree.

Åa fm
exch
E afm
exch
E

4.120 −132.8511 −132.6138 −0.2373
−132.8497 −132.6086 −0.2411
4.125 −132.8408 −132.6031 −0.2377
−132.8394 −132.5964 −0.243
4.13 −132.8305 −132.5923 −0.2382
−132.8297 −132.5860 −0.2437
4.135 −132.8211 −132.5817 −0.2394
−132.8194 −132.5749 −0.2455
4.140 −132.8077 −132.5690 −0.2387
−132.8094 −132.5657 −0.2437
Table 2. Computations of fm
E
, fm
exch
E
, afm
E
and afm
exch
E
are done for lattice constant a in cubic BaTiO3. The units of
energy are Hartree.


Åa fm
exch
E afm
exch
E

4.00 −138.4905 −138.7541 0.2636
−138.7533 −138.7532 −0.0001
4.005 −138.4785 −138.7403 0.2618
−138.7396 −138.7394 −0.0002
4.01 −138.4663 −138.7265 0.2602
−138.7259 −138.7125 −0.0134
4.015 −138.4546 −138.7132 0.2586
−138.4554 −138.7125 0.2571
4.02 −138.4427 −138.6996 0.2569
−138.6990 −138.6989 0.0001
Table 3. Computations of fm
E
, ex ch
E
, afm
E
and exc h
E
are done for lattice constant a in cubic BaVO3. The units of
energy are Hartree.


Åa fm
exch
E afm
exch
E

4.049 −145.2346 −143.9615 −1.2731
−145.0421 −143.9616 −1.0805
4.054 −145.2010 −143.9488 −1.2522
−145.2075 −143.9489 −1.2586
4.059 −145.2231 −143.9360 −1.2871
−145.3132 −143.9362 −1.377
4.064 −145.1868 −143.9234 −1.2634
−145.1926 −143.9235 −1.2691
4.069 −145.1994 −143.9108 −1.2866
−145.1770 −143.9110 −1.266
Table 4. Computations of fm
E
, fm
exch
E
, afm
E
, and afm
exch
E
are done for lattice constant a in cubic BaCrO3. The units of
energy are Hartree.


Åa fm
exch
E afm
exch
E

3.8436 −151.8259 −150.3628 −1.4631
−151.8267 −150.3763
3.8486 −151.8586 −150.3475 −1.5111
−151.8283 −150.3609
3.8536 −151.9614 −150.3326 −1.6288
−151.8653 −150.3381
3.8586 −151.8034 −150.3179 −1.4855
−151.7902 −150.3232
3.8636 −151.7371 −150.3032 −1.4339
−151.8065 −150.3085

G. NAREJO, W. F. PERGER
1322
Table 5. Computations of fm
E
, fm
exch
E
, afm
E
and afm
exch
E
are done for lattice constant a in cubic BaMnO3. The units
of energy are Hartree.

Åa fm
exch
E afm
exch
E

3.80 −34.8595 −157.2687 122.4092
−156.8650 −157.2736
3.85 −65.2846 −156.8965 91.6119
−158.2801 −156.9355
3.90 −159.0151 −156.8844 −2.1307
−157.9015 −157.2532
3.95 −64.0915 −157.2102 93.1187
−157.5813 −156.9111
4.00 −159.0042 −157.2003 −1.8039
−157.6340 −156.8992
Figure 3. Exchange energy vs. lattice strain for cubic
BaScO3. A decrease in exchange energy can be seen for the
compression of lattice. The straight line is drawn to signify
the linearity of the trend.
Figure 4. Exchange energy vs. lattice strain for cubic
BaTiO3. A decrease in exchange energy can be seen for the
compression of lattice. There is smaller deviation from the
linear trend.
Figure 5. Exchange energy vs. lattice strain for cubic
BaVO3. A slight increase in the exchange energy can be seen
for the compression of lattice. The nonlinear dependence of
the exchange energy on lattice strain is more pronounced.
Figure 6. Exchange energy vs. lattice strain for cubic
BaCrO3. A decrease in exchange energy can be seen for the
compression of lattice. The oscillatory character of ex-
change energy is also persistent.
Figure 7. Exchange energy vs. lattice strain for cubic
BaMnO3. The nonlinear dependence of the exchange energy
on the compression of lattice can be observed. Exchange
energy has slightly increased with the compression of the
lattice in this case.

G. NAREJO, W. F. PERGER 1323
Figure 8. Exchange energy vs. lattice strain for cubic
BaFeO3. A decrease in exchange energy can be seen for the
compression of lattice showing a linear dependence on the
strain.
known as manganites perovskites. The crystalline ge-
ometry and properties of cubic BaMnO3 may be well
suited to the quantum mechanical model. These models
advocate a delicate balance between the crystalline field
and Hund’s pairing energy. The crystalline field in these
models originates due to a coulombic force between the
electrons and atomic centers. The electrostatic fields par-
tially attributed to these crystalline fields are intricately
interdependent. The interaction between the crystalline
field and Hund’s pairing energy for the relaxed as well as
the strained crystalline structures is interpreted from this
model here. The phenomenon of ferromagnetic spin ex-
change, depending upon the highly correlated electrons
in a crystal field, is also accommodated in the model. It is
assumed that the ferromagnetic or antiferromagnetic
properties due to electron spin polarization depend upon
the crystal field of the strained lattice structure. This
model can also be applied to manganites (AMO3), titan-
ates (ATiO3) and vanadates (AVO3) as the crystal field
splitting is predominant and is relevant in all the material
systems discussed as in ref. [7].
The Hamiltonian for a typical transition metal oxide
may be
2
g
g
effhund te
H
HHH (1)
The
g
e
H
term in Equation (1) may expresse the en-
ergy component due to eg valence electrons of the transi-
tion metals

-bonded with the p-valence electrons for
O atoms in placed in an octahedral complex. The 2
g
t
H
term expresses the energy component due to t2g electron
which are -bonded the p-electrons of O atoms. π
The term expresses the Hund energy for
electrons hund
H
2tg
hundHi i
i
H
JSS (2)
The second energy component in Equation (1) is at-
tributed to electrons localized at t2g suborbital
2
22
g
tg tg
tijij
H
JS S (3)
Equation (4) splits the
g
e
H
term further

†
g
ij
eizijU
iij
H
Ltaa H

 




 



(4)
In Equation (4), the subscripts i and j express the
nearest neighbors on ionic sites, †
i
a


and j a



are the
creation and annihilation operators respectively. The
term t in Equation (4) expresses the kinetic energy of eg
electrons in BaMnO3, BaCrO3 and BaFeO3 and electro-
static energy term U. The Equation (4) takes into account
the kinetic energy of electrons delocalized due to strains
on the

-bonded eg and p-orbitals. The electrons hop
between the cation and anion sites termed as i and j.

†ij ij
ij
ttaa


 




 

(5)
ij oij
t





t (6)
The electrostatic energy term U expresses the on-site
electron correlation in transition metal cations resulting
in the electron localization on transition metal sites. The
symbol t in Equation (5) is the hopping integral for elec-
trons transferred under the action of strains between ions
i and the nearest neighbors j. Hund’s energy consists of
energy components due to t2g and eg electrons which are
well-localized on each transition metal site due to elec-
tron correlations as shown in Equation (7).
2e
g
g
HUU U
t
JHHH


(7)
It is assumed that the term

 in Equation (8) may
be related with the change in the crystal field energy
originating due to external strain. The term i
iT

ex-
presses the change in the orbital spin angular momentum
due to the effect of strain.
i
i
T  
 (8)
3. Results and Discussion
The computational results are shown in Tables 1-5 and
Figures 3-5. It is observed that the computational values
of energy due to spin polarizations are coupled with
electronic structures. The results are also plotted in Fig-
ures 3-5. The oscillations in energy for the BaVO3,
BaCrO3 and BaMnO3 show that the coupling between the
electronic structures and valence electrons are fairly
complex. In Tables 1-5, the
f
m, E
f
m
exch
E, afm and
represent the energies arising from ferromagnetic
and antiferromagnetic spin polarizations.
E
afm
exch
E
The primary effect of the external pressure on the
transition metal oxides is to compress or expand their

G. NAREJO, W. F. PERGER
1324
bond lengths connecting the transition metal and oxygen
atoms in a perovskite. The expansion and contraction of
the bond length result in the weakening or strengthening
of the electron interactions within crystal structures
among the transition metal eg electrons and oxygen p
electrons. The interactions between electrons and ions
couple them in a complicated manner.
Moreover, these interactions are facilitated by the
strains only if there are enough numbers of electrons in
eg valence orbitals. This phenomenon can be observed in
the computational results obtained for BaCrO3, BaMnO3
and BaFeO3. Less variations in energy as a function of
lattice strains for some oxides is a function of the local-
ized nature of the t2g and eg electron orbitals.
The oxides of transition metal have varied number of
electrons in their highly correlated d-orbitals. The con-
tracted wavefunctions of d electrons in BaScO3, BaTiO3,
BaVO3, BaMnO3 and BaFeO3 experience the varied de-
gree of competitive forces of the coulomb repulsion ver-
sus hybridization. The former tries to localize the elec-
trons at atomic lattice sites while the latter favors the
overlaps with p- and d-orbitals of O and transition metal
to delocalize these electrons. The forces of coulomb re-
pulsion and hybridization are varied by lattice strain. A
trend can be seen in all computations as there is a con-
sistent decrease in energy for the compression and in-
crease in energy for expansion of lattice volume. The
chemical bond in transition metal oxides is a combina-
tion of covalent and ionic parts. The covalent and ionic
parts vary as the transition metal ionic radius increases
from Sc to Fe. The contribution of ionic bonding is in-
creased as the number of electrons in transition metals
are increased with more impact on the energy as a func-
tion of lattice strain. The computational results of
BaScO3, BaTiO3, BaVO3, BaCrO3, BaFeO3 show sig-
nificant variations in chemical bonding from strongly
covalent to moderately ionic in nature for the materials
tested.
From the computed results shown in Tables 1-6, an
increase in the energy is observed for spins polarized in
same direction for all crystalline systems tested confirm-
ing the coupling between the crystalline structure and
electron spin polarization.
4. Concluding Remarks
We have employed first principles computations to ex-
tract the coupling between the crystalline structure and
electron spin polarization. The optimized crystalline
structures are computed by a variety of methods for each
of the transition metal oxides. Later on, the coupling be-
tween the electronic structure and electron spin polariza-
tion is determined by computing the energy for the spins
aligned in the parallel as well as antiparallel polariza-
Table 6. Computations of fm
E
, fm
exch
E
, afm
E
, and afm
exch
E
are done for lattice constant a in c ubic BaFeO3. The units of
energy are Hartree.


Åa fm
exch
E afm
exch
E

3.984 −165.3002 −164.6210 −0.6792
−165.3014 −164.6329 −0.6685
3.989 −165.2919 −164.6123 −0.6796
−165.2931 −164.6254 −0.6677
3.994 −165.2836 −164.6046 −0.679
−165.2848 −164.6173 −0.6675
3.999 −165.2754 −164.5965 −0.6789
−165.2766 −164.6092 −0.6674
4.004 −165.2673 −164.5896 −0.6777
−165.2684 −164.6020 −0.6664
tions. It is observed that the compression of the the bulk
crystal results in the lowering of the the energy confirm-
ing the fact that the former is intricately coupled with the
latter.
It is seen that the coupling between the electronic
structure and electronic polarization varies with the oc-
cupation of electrons in the outermost orbitals. During
computations, it has been observed that the compression
lowers the electron energy in the transition metal oxides
of Sc-Fe. The lowering of the polarization energy may be
attributed to the stronger coupling between transition
metal eg and O p-orbitals forming a

-bond.
5. Acknowledgements
One of the authors (WFP) gratefully acknowledges the
support of the Office of Naval Research Grant N00014-
01-1-0802 through the MURI program.
REFERENCES
[1] R. Gopalan and V. Chandrasekharan, “Room temperature
multiferroism and magnetoelectric coupling in BaTiO3-
BaFe12O19 System Srinivas,” Solid State Communications,
Vol. 149, No. 9-10, 2009, pp. 367-370.
[2] J. P. Velev, P. A. Dowben, E. Y. Tsymbal, S. J. Jenkin,
and A. Caruso, “Interface Effects in Spin-Polarized Me-
tal/Insulator Layered Structures,” Surface Science Reports,
Vol. 63, No. 9, 2008, pp. 400-425.
doi:10.1016/j.surfrep.2008.06.002
[3] J. B. Goodenough, “Electron-Lattice Interactions in Man-
ganese-Oxide,” Perovskites, Fundamental Materials Re-
search, 2002, pp. 127-133.
[4] C. N. R. Rao, “Transition Metal Oxides,” Annual Review
of Physical Chemistry, Vol. 40, 1989, pp. 291-326.

G. NAREJO, W. F. PERGER
1325
doi:10.1146/annurev.pc.40.100189.001451
[5] S. Horiuchi, Y. Okimoto, R. Kumai and Y. Tokura,
“Quantum Phase Transition in Organic Charge-Transfer
Complexes,” Science, Vol. 299, 2003.
[6] J. P. Velev, C.-G. Duan, J. D. Burton, A. Smogunov, M.
K. Niranjan, E. Tosatti, S. S. Jaswal and E. Y. Tsymbal,
“Magnetic Tunnel Junctions with Ferroelectric Barriers:
Prediction of Four Resistance States from First Princi-
ples,” Nano Letters, Vol. 9, No. 1, 2009, pp. 427-432.
doi:10.1021/nl803318d
[7] I. Sumio, O. Satoshi and M. Sadamichi, Physics of Tran-
sition Metal Oxides, 1997.
[8] Y. Tokura and N. Nagaosa, “Orbital Physics in Transi-
tion-Metal Oxides,” Science, Vol. 288, No. 462, 2000, pp.
462-468.