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J Supercond Nov Magn
DOI 10.1007/s10948-011-1317-z

O R I G I N A L PA P E R

Ferromagnetism in Mo-doped TiO2 Rutile from Ab Initio Study
A. Fakhim Lamrani · M. Belaiche · A. Benyoussef ·
A. El Kenz · E.H. Saidi

Received: 22 February 2011 / Accepted: 20 September 2011
© Springer Science+Business Media, LLC 2011

Abstract First-principles calculations based on spin density
functional theory (DFT) within the general gradient approximation (GGA) are performed to study the spin-resolved
electronic properties of TiO2 Rutile doped with 6.25 and
12.5% of Mo. The Mo impurity is found spin polarized and
the calculated band structures suggest a 100% polarization
of the conduction carriers. The local moment of Molybdenum is slightly dependent on its concentration. The Fermi
level is shifted to the bottom of the conduction band with increasing concentration of Mo. This leads to the increase of
states density, just above the Fermi level, and consequently
the 4d orbitals are strongly hybridized with Ti 3d ones to
form a d-nature conduction band, without impurity states in
the in-gap region. The Mo-doped TiO2 favors ferromagnetic
ground state which can be explained in terms of p–d hybridization mechanism for 6.25% of Mo, this mechanism
A.F. Lamrani · A. Benyoussef · A. El Kenz ( )
Laboratoire de Magnétisme et de Physique des Hautes Energies
(associé au CNRST) Département de physique, Université
Mohammed V, B.P. 1014, Rabat, Morocco
e-mail: elkenz@fsr.ac.ma
A.F. Lamrani · M. Belaiche
Laboratoire de Magnétisme, Matériaux Magnétiques, Micro-onde
et Céramique, Ecole Normale Supérieure, B.P. 9235, Océan,
Rabat, Morocco
M. Belaiche · A. Benyoussef · E.H. Saidi
INANOTECH (Institute of Nanomaterials and Nanotechnology),
Rabat, Morocco
E.H. Saidi
Laboratoire de Physique des Hautes Energies Département de
physique, Faculté des sciences, B.P. 1014, Rabat, Morocco
M. Belaiche · A. Benyoussef · E.H. Saidi
Hassan II Academy of Sciences and Technologies, Rabat,
Morocco

depends on the Mo concentration. This suggests that the
Mo-doped TiO2 is a promising dilute magnetic semiconductor and may find applications in the field of spintronics.
Keywords Impurity-doped TiO2 (rutile) · Ab-initio
calculation · ASW method · Band structure model · DMS ·
Magnetic properties · Carrier mediated ferromagnetism

1 Introduction
Semiconductors containing small amounts of magnetic impurities, known as dilute magnetic semiconductors (DMS),
have been of interest to the physics and engineering communities for quite some time [1–3]. The intriguing, and potentially technologically useful, property that arises out of
these materials is the possibility of strongly spin polarized
currents. This is electronically possible when either the majority or minority-carrier states dominate at the Fermi energy. In the extreme case of half-metallic materials, one spin
channel is conducting while the other spin channel is strictly
insulating [4]. It is this idea of spin polarized currents that
would allow engineered devices that combine the properties
of magnetism with the traditional semiconductors to create
the so-called spintronic devices.
The electronic structure of the material depends on the
particular host crystal structure and on the magnetic impurity atom. The particular DMS compounds studied here have
crystal structures in which the bonding interactions occur
between the semiconductor s–p orbitals and the magnetic
ion’s d orbitals. The nature of this bonding determines the
physical properties observed in our calculations. It has been
suggested [1, 5] that one of the variables determining the
strength of the exchange interactions is the amount of sp–d

J Supercond Nov Magn

hybridization between the host and impurity. Recently, Titanium dioxide TiO2 -based materials have received considerable attention. This is due to its widespread technologically
applications in many fields such as photovoltaic solar cells
[6], photocatalysis [7], and spintronic devices [8]. More recently, TiO2 has attracted much attention as an electronic
material, and attempts at employing it as a high-k material
[9] and in resistive random access memory (RRAM) [10]
devices have been made. Diluted magnetic semiconductors
based on TiO2 have the potential to enable room temperature spintronics [8]. Reviews on TiO2 properties in relation
to its applications can be found elsewhere [11, 12].
More remarkably, room-temperature ferromagnetism
was reported in Co-doped anatase TiO2 by Matsumoto et al.
[8] using a combinatorial molecular beam epitaxy (MBE)
technique. This work motivated intensive studies on the
structural and physical properties of this material [13–17].
Considerable experimental and theoretical studies on the
electronic structure and the magnetism of anatase TiO2 doped by other transition metals (TM) such as Mn, Fe,
Ni, V and Cr [14, 18–21] have also been performed, and
it is found that both V- and Cr-doped anatase TiO2 exhibit
room-temperature ferromagnetism [18–20]. We know that
TiO2 has three commonly encountered polymorphs in nature: anatase, rutile and brookite. Interestingly, in 2002, Park
et al. [22] have successfully grown ferromagnetic (FM) Codoped rutile TiO2 films by reactive co-sputtering, and the
Tc was estimated to be above 400 K for Co content of 12%.
Motivated by these, electronic and magnetic properties of
Co-, Mn-, Fe-, Ni- and Cu-doped rutile TiO2 [23–26] have
been investigated both experimentally and theoretically. The
Fe-doped rutile TiO2 exhibits FM ordering above 350 K
[24].
The purpose of the present work is to investigate the
magnetism and the electronic structure of Mo-doped rutile
TiO2 by using the first-principles band calculations. The effects of Mo concentration, on electronic structure and magnetic properties, have been investigated. The Mo-doped rutile TiO2 has a stable FM ground state. The Mo doping modifies the band structure of TiO2 and generates carriers in the
conduction band.

2 Method of Calculation
The Rutile TiO2 crystallizes in a tetragonal cell (a =
4.594 Å, c = 2.959 Å, space group P42/mnm). Each Ti
atom is bonded to four nearest and two second nearest oxygen neighbors. The Mo-doped structures were constructed
by using the 48-atom 2 × 2 × 2 supercell (16 Ti and 32
O atoms). In this study, we replace Ti atoms by one, and
two Mo atoms corresponding to concentration ratios of
x = 1/16, and 2/16 in Ti1−x Mox O2 , which are close to the

experimentally reported values [22, 27]. As the concentration of Mo increasing, the lattice parameters of Mo-doped
TiO2 exhibit a slight variation and a small elongation along
the c-axis, which is similar to the experiment [28]. Comparing to the TiO2 rutile phase, the Mo–O bond lengths in
the supercells are considerably longer than Ti–O (first nearest neighbors) and slight shorter than Ti–O (second nearest
neighbors). The distortions will be useful to the substitution
of Mo for Ti in the TiO2 rutile phase [29].
Ferromagnetic stability is determined through the total
energy difference ( E) of the super cell between antiferromagnetic (AFM) state and ferromagnetic (FM) state.
The FM state is more stable (AFM state is more stable) if
E > 0 ( E < 0). The calculations are based on densityfunctional theory [30, 31] using the generalized gradient approximation (GGA) with the Engel and Vosko EV approximation [32], and the local-density approximation parameterized according to Vosko Wilk and Nusair VWN [33].
The calculations were performed using the scalar-relativistic
implementation of the augmented spherical wave (ASW)
method [34–36] based on the atomic sphere approximation
(ASA). In this method, the wave functions are expanded
in atom-centered augmented spherical waves, which are
Hankel functions and numerical solutions of Schrödinger’s
equation, respectively, outside and inside the so-called augmentation spheres. In order to optimize the basis set, additional augmented spherical waves were placed at carefully
selected interstitial sites. The choice of these sites as well as
the augmentation radii were automatically determined using the sphere-geometry optimization SGO algorithm [37].
Self-consistency was achieved by a highly efficient algorithm for convergence acceleration [38]. The Brillouin zone
(BZ) integrations were performed with an increasing number of k-points (6 × 6 × 8) in order to ensure convergence
of the results with respect to the space grid. The geometry
was fully relaxed using Hellman–Feynman force and total
energy. The convergence criterion is fixed to 10−8 Ry in the
self-consistent procedure and charge difference Q = 10−8
between two successive iterations.
The radius of Mo4+ ion is equal to that of Ti4+, and
their values of ionization potentials are close to each other.
MoO2 has a distorted structure of rutile with c/a = 0.574,
compared to a value of 0.644 for TiO2 rutile. Bond lengths
between Mo in the chains of edge-sharing octahedra alternate between 251 and 311 pm, compared to a constant value
of 296 pm between Ti in rutile [39, 40]. Thus, rutile TiO2
should be easily doped with Mo4+, and at high doping levels the material should exhibit a semiconductor to metal
transition. It is worth pointing out that the substitutional Mo
at the body-centered (or the base-centered) Ti site in a supercell, helps reduce the distortion of the tetragonal lattice
through full structural relaxation.

J Supercond Nov Magn

3 Results and Discussion
First, the electronic structure of pure rutile TiO2 without
doping elements has been checked. The overall band structure of the present ASW result is consistent with existing
results [41–45]. As usual in the GGA approximation, the rutile TiO2 band structure and density of states are shown in
Fig. 1, it can be seen that the valence band of rutile at the
vicinity of the Fermi level mainly provided by the O atom
2p orbital, while the conduction band mainly provided by
the Ti atom 3d orbital. The valence band comprising mostly
oxygen 2p states is filled and the mostly Ti 3d conduction
band is empty. TiO2 is insulator; the Ti-derived 3d band are
split approximately into t2g and eg sub bands by octahedral
crystal field.
In order to understand the electronic structure of the ferromagnetic Ti15 MoO32 , the band structure, the total and partial spin densities of states (DOSs) have been calculated.
The spin-resolved band structure of the supercell is given
in Fig. 2. It shows a half metallic behavior with the majority spin being metallic with sufficient unfilled states above
the Fermi level. These unfilled states behave like free holes,
although slightly localized. The 100% polarization of conductions carriers, suggests that Mo-doped TiO2 may be used
for spin injection, where highly polarized spin current is desired, and the minority spin being insulating. In order to
understand the mechanism which stabilizes the FM state in
Mo-doped TiO2 , it is important to analyze the total and partial spin densities of states (DOSs). Figure 3a shows the total DOS of FM Ti15 MoO32 . It is clearly seen that the Mo
doped TiO2 has introduced new states in the energy gap,
resulting in a half metallic characteristics of the doped system. Meanwhile, partial DOS of Mo-4d and O-2p are given
in Fig. 3. As can be seen, the majority spin channel of Mo4d overlaps with that of O-2p at the Fermi level E f . These
characters indicate a strong hybridization between Mo and

Fig. 1 Calculated partial density of states (DOS) for rutile TiO2

Fig. 2 Spin-resolved band structure of Rutile Ti0.9375 Mo0.0625 O2
along selected high symmetry directions, (a) spin up bands and (b) spin
down bands. The energy zero is chosen to be at the Fermi energy

Fig. 3 (Color online) Calculated spin resolved density of states (DOS)
for Ti0.9375 Mo0.0625 O2 : (blue) the partial DOS of O-2p, (green) the
Ti-3d, and (red) the Mo-4d states. Fermi level is set at zero

J Supercond Nov Magn
Table 1 Total energy (E tot ) and Fermi energy (E f ) of Ti1−x Mox O2

Ti1−x Mox O2 (FM)

E tot (Ry)

E f (Ry)

−38609.028987

0.658807

−45000.476589

0.707407

−45000.361878

0.694088

x = 0.0625
Ti1−x Mox O2 (FM)
x = 0.125
Ti1−x Mox O2 (AFM)
x = 0.125

Fig. 5 Calculated spin resolved density of states (DOS) for antiferromagnetic Ti0.875 Mo0.125 O2

Fig. 4 (Color online) Calculated spin resolved density of states (DOS)
for Ti0.875 Mo0.125 O2 : (blue) the partial DOS of O-2p, (green) the
Ti-3d, and (red) the Mo-4d states. Fermi level is set at zero

its neighboring O atoms. Therefore, it is the p–d exchange
mechanism that is responsible for ferromagnetism in Modoped TiO2 . Furthermore, in order to explore the magnetic
properties for Ti0.9375 Mo0.0625 O2 , the total magnetization of
the cell is 2 μB , which is the signature of a half-metallic behavior. Our results show that the main part of this magnetic
moments is strongly localized on the Mo site with a magnetic moment of 1.4 μB , the nearest neighbor host atoms are
weakly polarized with induced moments of +0.037 μB on
nearest neighbor Ti sites and −0.003 μB on nearest neighbor
O site between two Mo atoms, which indicates the nearest
neighbor O-2p electrons prefer AFM alignment to Mo 4d.
Substitution of two Ti atoms by Mo gives a dopant
concentration of 12.5%. The total energies calculated for
the two states; ferromagnetic (FM) and antiferromagnetic
(AFM), show that the FM state, is the ground state, and its
energy is 114.711 mRy lower than that of the AFM state
(Table 1), this is due to a difference in electronic structure (Fig. 4). The Fermi energy increases with increasing
Mo concentration it is 0.659 and 0.707 for x = 0.0625 and
0.125, respectively.
Total DOS profiles computed for Ti0.875 Mo0.125 O2 are
shown in Fig. 5. It is clearly shown that both majorityand minority-spin components display a long the conduc-

tion band, (the Mo impurity band overlaps fully with the
Ti conduction band) which indicates that the introduction
of Mo-destroy the semiconducting nature of these materials. It is shown that it is possible to optimize the hybridization, by increasing the concentration. So, the Mo impurity
band overlaps fully with the Ti conduction band, the lowest
Mo level is a donor band, with localized electrons. Compared with the undoped TiO2 , the remarkable feature in energy band for Mo-doped TiO2 is that the Fermi level shifts
upward into the conduction band which indicates that the
materials is n-type metallic. Impurities states and the Fermi
level are close to the bottom of the conduction band of the
host system. This leads to a free flow of charge carriers between the impurities and host, which is the most important
criteria for fabricating spintronic devices. Like the free flow
of charge carriers in the entire system, the half-metallic nature is observed from the density of states (DOS), with a gap
of 3.88 eV. Figure 5 compares partial DOS of Ti and Mo d
states. Remarkably, both DOS profiles above the E f show
essentially similar shapes that is, the Mo 4d orbital spreads
over the entire region of the conduction band, implying that
Mo is strongly hybridized with Ti and O. Furthermore, electron charge density distribution around Ti and Mo atoms coincide well with each other, being another support for the
strong hybridization between Ti and Mo. As a consequence
of strong Ti–Mo hybridization, each Mo atom releases two
electrons to the conduction band, originating from the fact
that the Fermi level shift to the bottom border of the conduction band, E f lies at 0.71 eV. This leads to optimize the hybridization between the host and impurities. It is important
to note that the conductivity in TiO2 is due to the delocalization of Ti 3d states, and electrons generated by Mo doping.
The mechanism that stabilizes the FM state in Mo-doped
TiO2 x = 0.125 is the same as that given in the study of
doped ZnO with double impurities, Zn1−2x Fex Cox O [43].

J Supercond Nov Magn

In the Ti1−x Mox O2 , x = 0.125, there is no indication of
Zener’s double exchange (absence of charge transfer) or
p–d hybridization mechanism. In this case one needs to invoke another exchange mechanism between Mo, such as the
RKKY-type exchange interaction mediated by Ti 4s carriers
or conduction carriers induced by oxygen vacancies.

4 Conclusion
In summary, the electronic structure and magnetic properties
of Mo doped TiO2 system in the rutile structure, have been
studied by carrying out the first-principle calculations in
GGA formalism. Our results show that alloys posses a band
of well-defined spin, which is primarily due to hybridization of Mo 4d and O 2p orbitals. This band renders that the
material has an apparent half-metallic character. The results
also indicate that by increasing the concentration of molybdenum it is possible to develop systems where the highest
occupied impurity states overlap well with the conduction
band minimum. The magnetic interaction is sensitive to position of the Fermi level, these results rule out the possibility
of ferromagnetic order originating from RKKY interactions.
Acknowledgement The authors would like to thank V. Eyert for
fruitful discussion concerning the ASW program PACKAGE.

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