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Titre: First-principles study of electronic structure and magnetic properties of doped SnO2 (rutile) with single and double impurities
Auteur: A. Fakhim Lamrani

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Journal of Magnetism and Magnetic Materials 323 (2011) 2982–2986

Contents lists available at ScienceDirect

Journal of Magnetism and Magnetic Materials
journal homepage: www.elsevier.com/locate/jmmm

First-principles study of electronic structure and magnetic properties
of doped SnO2 (rutile) with single and double impurities
A. Fakhim Lamrani a,b, M. Belaiche b,c,e, A. Benyoussef a,c,e, A. El Kenz a,n, E.H. Saidi c,d,e
a
´partement de physique, B.P. 1014, Faculte´ des sciences,
Laboratoire de Magne´tisme et de Physique des Hautes Energies (associe´ au CNRST), URAC, De
Universite´ Mohammed V-Agdal, Rabat, Morocco
b
Laboratoire de Magne´tisme, Mate´riaux Magne´tiques, Micro-onde et Ce´ramique. Ecole Normale Supe´rieure, Universite´ Mohammed V-Agdal, B.P. 9235, Oce´an,
Rabat, Morocco
c
Institute of Nanomaterials and Nanotechnology, MAScIR, Rabat, Morocco
d
Laboratoire de Physique des Hautes Energies De´partement de physique, B.P. 1014, Faculte´ des sciences, Rabat, Morocco
e
Hassan II Academy of Sciences and Technologies, Rabat, Morocco

a r t i c l e i n f o

a b s t r a c t

Article history:
Received 19 August 2010
Received in revised form
27 May 2011
Available online 28 June 2011

Using the augmented spherical wave method, the electronic structure and magnetic properties of the
rutile SnO2 doped with single and double impurities: Sn1 xMnxO2, Sn1 xWxO2, and Sn1 2xMnxWxO2
with x ¼0.0625, have been studied. The scalar-relativistic implementation with a generalized gradient
approximation functional has been used for treating the effects of exchange and correlation. The ground
state of Mn-, and W-doped SnO2 systems have a total magnetic moments of 3 and 2 mB, respectively.
The half-metallic nature appears in Sn1 2xMnxWxO2, which makes them suitable as spintronic systems
with total magnetic moment of 5 mB. The advantages of doping SnO2 with double impurities are
investigated in this work. The total moment of the system, the local magnetic moments of the
impurities, and their oxidation states are also discussed. Since there are two possible couplings
between the impurities, we studied both configurations (ferromagnetic and antiferromagnetic) for
double-impurities-doped SnO2. Magnetic properties and interatomic exchange have been computed for
various distances between Mn and W. The indirect exchange between double impurities has
similarities with the Zener mechanism in transition metal oxides. Based on the interaction between
localized moments, via hybridization between impurities orbitals with the host oxygen, a double
exchange mechanism is proposed to explain the ferromagnetism of our system.
& 2011 Elsevier B.V. All rights reserved.

Keywords:
Impurity-doped SnO2 (rutile)
Electronic structure
Magnetic impurity interaction
Zener mechanism
ASW method

1. Introduction
Recently, it has been shown that oxide-based diluted magnetic
semiconductors ODMS are more suitable for making spintronic
devices in comparison with the non-oxide based DMS. They have
many favorable attributes; such as higher transition temperature
Tc, wide band gap, higher n-type carrier concentration, low cost,
and environmental safety [1].
In the last decades, diluted magnetic semiconductors DMSs
have been investigated extensively since the observation of ferromagnetism (FM) in Mn-doped InAs and GaAs [2]. The observation
of room-temperature FM in various kinds of transition-metal, TM,
ion doped semiconductor oxides ODMSs, such as TM-doped ZnO
[3], TiO2 [4], and SnO2 [5–8], have stimulated great interest.
Tin dioxide (SnO2) has been used for several applications. It is one
of the most interesting materials for the development of transparent

n

Corresponding author.
E-mail address: elkenz@fsr.ac.ma (A. El Kenz).

0304-8853/$ - see front matter & 2011 Elsevier B.V. All rights reserved.
doi:10.1016/j.jmmm.2011.06.021

conductors, solid state gas sensors, and catalysts [9]. Many physical
properties of tin dioxide are driven by defects such as oxygen
vacancy. In this sense, SnO2 surfaces are even more important
because of the presence of two possible oxidation states of tin (þ2
and þ4), which favors compositional changes and reconstructions,
when combined with the reduced atomic coordination.
Although the SnO2 (1 1 0) surface is one of the most studied
both theoretically [10–13] and experimentally [9,14,15] its actual
structure is still an open problem of debate because of the
controversial aspects concerning defects and oxygen adsorption
[16]. Several reconstructions are possible depending on both the
preparation conditions and the sample history. Nevertheless, in a
faceted sample, the lowest indices (1 1 0) and (1 0 1) stoichiometric surfaces seem to be the most favored from the thermodynamic point of view [17].
Ogale et al. [5] fabricated Co-doped rutile SnO2 (Sn1 xCoxO2) thin
film samples, using the pulsed-laser-deposition, PLD, technique. They
found that a sizable amount of Co ions, up to x¼ 0.25, is soluble in
rutile SnO2 and that all samples showed a room-temperature FM.
Especially Sn0.95Co0.05O2 film exhibited a giant magnetic moment of

A. Fakhim Lamrani et al. / Journal of Magnetism and Magnetic Materials 323 (2011) 2982–2986

7.5 mB/Co, but the magnetic moment dropped rapidly with the
increase of Co content. Coey et al. [6] have also grown Fe-doped
SnO2 films and found that the doped films are transparent ferromagnet with a Curie temperature of 610 K. Furthermore, Ogale et al.
[5] and Coey et al. [6] reported that FM of these doped samples is
intrinsic. However, Punnoose and Hays reported FM in chemically
synthesized Sn1 xCoxO2 [7], with small magnetic moment of
0.133 mB/Co ion existing in Sn0.99Co0.01O2. Their observations indicate
a metamagnetic origin of the FM in Co- and Fe-doped SnO2. Hong
et al. [8] presented that substrate size and oxygen partial pressure
greatly influence the magnetism of Cr-doped SnO2 film fabricated by
PLD. Hence, the properties of TM-doped SnO2 are sensitive to the
experimental conditions and it is necessary to investigate the
electronic structure and magnetism of TM-doped SnO2 from
the theoretical calculation.
Using density-functional theory, which is implemented in the
well-tested SIESTA code Wang et al. [35] have investigated
electronic structures and magnetic properties of SnO2 doped with
6.25% Mn. The resulting magnetic moment is 3.12 mB, and the
paramagnetism is more stable than ferromagnetism.
The ferromagnetism in DMS materials originates from the
local magnetic moments of the impurities. The dependence of
the energy of the system on the orientation of these local
moments is called the exchange interaction.
The description of the mechanism, which stabilizes the ferromagnetism (FM) is very important to understand in dilute
magnetic semiconductors. The ferromagnetic interactions represent the basic ingredient for understanding the physical properties of doped SnO2. Two mechanisms are proposed to explain
ferromagnetism in diluted magnetic semiconductors. One is
Zener’s p–d exchange mechanism [18,19] and the other is double
exchange mechanism [20,21]. Both methods gave similar predictions for the ferromagnetism; however, no consensus has been
reached about the origin of the ferromagnetism.
Generally, doped oxide semiconductors become ferromagnetic
after creating oxygen vacancies in these systems such as TiO2
doped with Co [22]. To date, there are a few cases where defects
are believed to be the origin of ferromagnetism and each case has
a different physical origin. Mounkachi et al. [36] showed that
higher values of transition temperature, Tc, are attained for high
concentration of vacancy defects sites in (Zn,Mn)O and for small
concentration of vacancy defects sites in (Zn,Mn)(O,N). Rahman
et al. [37] showed that SnO2 has magnetism with defects and
without TM doping. Indeed the bulk SnO2 is non-magnetic, but it
shows magnetism with a magnetic moment around 4.00 mB due
to Sn vacancy (VSn). The magnetic moment comes mainly from O
atoms surrounding VSn and Sn atoms, which couple antiferromagnetically with the O atoms in the presence of VSn.
The aim of the present work is to study oxide-based semiconductors doped with double transition metal impurities (3d–5d)
rather than the traditional single impurities. This can be used to
avoid the oxygen vacancies in double-impurities. The indirect
exchange between double impurities has similarities with the Zener
mechanism in transition metal oxides in contrast to (3d–3d)
impurities such as (Cr, Mn) co-doped TiO2 [23], where no indication
of charge transfer between double impurities has been observed. In
this paper a double exchange mechanism is suggested, it is based
on the interaction between localized moments via hybridization
between impurities orbitals with the host oxygen. This could help
us to understand the ferromagnetism of discussed systems.

2. Theoretical method and computational details
The calculations are based on the density-functional theory
[24,25] using the generalized gradient approximation (GGA) with

2983

the Zhang and Yang (ZY) approximation [26], and the localdensity approximation parameterized according to von Barth
and Hedin (VBH) [27]. The calculations were performed using
the scalar-relativistic implementation of the augmented spherical
wave (ASW) method [28–30] 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 Schrodinger’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 [31]. Self-consistency was achieved by
a highly efficient algorithm for convergence acceleration [32]. 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 Hellmann–Feynman force and total energy. The
convergence criterion is fixed to 10–8 Ry in the self-consistent
procedure and charge difference DQ¼10 8 C between two successive iterations.
SnO2 has a tetragonal symmetry in rutile structure. The rutile
structure is characterized by two lattice parameters a ¼4.7373 A˚
and c ¼3.1864 A˚ [33]. The unit cell contains two metal atoms (Sn)
at positions (0, 0, 0) and (1/2, 1/2, 1/2) and four oxygen atoms
(O) at positions 7(u, u, 0; 1/2þu, 1/2 u, 1/2) with u¼0.306.
Each Sn atom is in the central site of an octahedron, which is
formed by four rectangular basal O atoms (O1) and two vertex O
atoms (O2). Using the integer multiples representations of the
primitive lattice vectors a, b, and c of the conventional SnO2 cell,
the geometry of an undoped 2 2 2 super cell containing 48
atoms (Sn16O32) has been determined (Fig. 1a). In order to model
Sn1 xMnxO2, Sn1 xWxO2, and Sn1 2xMnxWxO2, for x¼ 0.0625, one
and two different Sn atoms are substituted (Fig. 1b). Two possible
couplings (FM and AFM) have been considered, between the
double impurities in Sn1 2xMnxWxO2.

3. Results and discussion
As a first step, the electronic structure and the dependence of
the band gap on the exchange-correlation potential of pure SnO2
(rutile) without doping elements have been studied. However, it
is necessary to check which approximation is the appropriate
method for determining the best band gap in agreement with the
known experimental values. The local density approximation
(LDA-VWN) approach was tested for calculating the band structure of the SnO2 unit cell. The result shows that the LDA underestimated the band gap substantially. The calculated value is only
2.9 eV while the experimental one is 3.6 eV [9]. However, the
calculated one based on GGA-VWN is 3.3 eV.
In addition, Fig. 2 shows that near the band edge the valence
band is mainly composed of O-2p orbitals and is full, while the
conduction band is mainly composed of Sn 5s-orbitals and is
empty. The density of states (DOS) of majority and minority spin
are symmetrical. Therefore, there is no evidence of spin
polarization.
Before studying the electronic and magnetic properties of SnO2
rutile doped with double impurities, Sn1 2xMnxWxO2 with
x¼0.0625, the SnO2 rutile doped with single impurities (Mn or
W) was first investigated. The total and partial densities of states
(DOS) for our system are obtained using the tetrahedron method
with Bloch corrections.
The electronic structure of the substitutional Mn at an Sn site
in SnO2 (rutile) has been performed. Fig. 3(a) and (b) shows the

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A. Fakhim Lamrani et al. / Journal of Magnetism and Magnetic Materials 323 (2011) 2982–2986

Fig. 3. The total (a) and Mn 3d partial DOSs (b) of Sn15MnO32.

Fig. 1. (a) Primitive unit cell of rutile SnO2: big gray balls correspond to tin atoms,
small red balls to the oxygen atoms, and green balls to empty spheres. (b) The
2 2 2 super cell of SnO2 after substitution of Mn and W atoms for Sn atoms, the
Sn14MnWO48 unit cell was generated.

Fig. 2. Total DOS of rutile SnO2 with GGA approximation.

total density of states (DOS), and the Mn-3d projected local DOS
(PLDOS) for Mn-doped SnO2. The Mn-3d states are split into four
band levels. Indeed, the first majority-spin states are occupied

and located in the valence band edge while the second majorityspin states are empty and located in the band gap. For the
minority-spin, both levels of electron-empty states are located
in the band gap. In particular, a valence band width of 7 eV for
Sn15MnO32, and 6.8 eV for SnO2 close to the experimental
data (7.5 eV) [34] has been found. Moreover, the calculated
Mn magnetic moment and the total magnetic moment in Sn15MnO32
are, respectively, 2.97 and 3.0 mB to compare to the total magnetic
moment, 3.12 mB, obtained by SIESTA code [35]. So spin-polarization occurs mainly from the Mn site, but the results of calculation
also indicate that the nearest-neighboring oxygen can be polarized upto –0.0018 mB, due to the hybridization between the Mn3d states and the nearest-neighboring O-2p states, which induce
antiferromagnetic coupling between Mn and O. We note that
because Mn (3d54s2) has 7 valence electrons and Mn4 þ (3d3) in
Sn15MnO32, the substitution provides three net electrons. When
the calculated Mn magnetic moment within GGA is more close to
the Mn4 þ electronic configuration, then the occupied electronic
configuration could be 3 electrons in 3d (2 spins up in t2g state
and 1 spin up in eg state). The stability calculations show that the
paramagnetic phase is more stable than the ferromagnetic phase,
this is in agreement with the result obtained by Wang et al. [35]
using SIESTA code.
The electronic structure of Sn1 xWxO2 (rutile) is given in
Fig. 4(a) and (b). This figure shows the total density of states
(DOS), and W-5d projected local DOS (PLDOS). The W-5d energy
levels are split into two levels t2g and eg. The majority-spin t2g
states are partially occupied while the majority-spin eg states are
almost empty. However, the minority-spin states are empty and
closed to the bottom of the conduction band of the SnO2 host.
Here also, the valence band width is 6.9 eV for Sn15WO32.
The total magnetic moment of Sn1 xWxO2, x ¼0.0625 is around

A. Fakhim Lamrani et al. / Journal of Magnetism and Magnetic Materials 323 (2011) 2982–2986

2985

Fig. 4. The total (a) and W 5d partial DOSs (b) of Sn15WO32.

2 mB. The local magnetic moments of W, Sn, and O atoms are 1.6,
0.006 and 0.03 mB, respectively. Our results show that the main
part of the total magnetic moment is strongly localized on the W
site with a magnetic moment of 1.6 mB. This suggests that the W
impurity doped in SnO2 has a magnetic configuration of 5d2. The
additional contributions to the total magnetic moment appear to
come from O and Sn atoms. These values show that the exchange
coupling between the W-5d and O-2p is, ferromagnetic p–d
coupling (FM), due to the absence of the overlapping of orbitals.
Thus, the proposed electronic configuration of SnWO2 is 2 electrons in 5d (2 spins up in t2g state and 0 spin in eg state).
The second step of this study analyze the magnetic properties
and electronic structure of doped SnO2 with double impurities,
which is the mixing between two systems: magnetic insulator Mndoped SnO2 and magnetic metal W-doped SnO2. The double
impurities in SnO2 changes the total DOS near de Fermi level, and
the majority spin around the Fermi level becomes 100% spin
polarized compared to Mn-doped SnO2, and W-doped SnO2.
Fig. 5(a) shows that the valence band shifts to lower energy
compared to Sn15MnO32. However, there is no shift of the valence
band with respect to W-doped SnO2. This is to say, the doped SnO2
with double impurities modifies the total DOS of Mn-doped SnO2.
Since there are two possible modes (ferromagnetic (FM) and
antiferromagnetic (AFM)) of coupling between the double impurities, we studied both configuration (FM and AFM) for doubleimpurities-doped SnO2. These two configurations converged to
parallel spin alignments among the impurities for both cases,
which indicates that the systems prefer FM alignment.
The double-impurities doped systems Sn1 2xMnxWxO2,
x¼0.0625, are expected to have several advantages over the single
impurities. Firstly, Fig. 5(b) shows the partial densities of states
(DOS) for SnO2 doped with double impurities, where both majorityand minority-spin components display a band gap, which indicates

Fig. 5. Calculated spin-polarized density of states (DOS) for Sn14MnWO48; (a) the
total DOS; (b) the partial DOS of Mn-3d and W-5d; (c ) neighboring O-2p states for
3.7 A˚ Mn–W distance.

that the introduction of double impurities Mn and W does not
destroy the semiconducting nature of these materials. Secondly, a
half-metallic nature is a favorable feature for 100% spin polarization
in ground state (Fig. 5(a)). Thirdly, the total magnetic moments of
the system is sufficiently large at 5 mB. Fourthly, the magnetic
interaction between the double impurities should be strong. These
combinations aspects of SnO2 doped with double impurities are also
important for fabricating spintronic devices.
The occupied electronic configurations are 3 electrons in 3d (2
spins up in t2g state and 1 spin up in eg state) for Mn and
2 electrons in 5d (2 spin up in t2g state and 0 spin in eg state) for
W, where we have adopted the symmetry notations of the local
octahedral crystal field, which splits the Mn (3d), and W (5d)
states to the triply-degenerate t2g state and the double-degenerate eg state. Note that Mn and W are located at octahedral

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A. Fakhim Lamrani et al. / Journal of Magnetism and Magnetic Materials 323 (2011) 2982–2986

Fig. 6. Model of double exchange mechanism for SnO2 doped with double
impurities.

centers formed by O ions, and t2g states are lower in energy than
the eg states.
The oxidation states of the two impurity ions are determined
from the charge carrier’s occupancy in the d-orbital. Fig. 5(a), (b),
and (c) show the total density of states (DOS) and TM (3d,5d)
projected local DOS (PLDOS) for Sn1 2xMnxWxO2. Half-metallic
electronic structure for majority spin d states of both Mn and W,
have been obtained. That is, the conduction electrons at the Fermi
level, Ef, are 100% polarized. The minority spin Mn-3d states are
seen to be hybridized slightly with the conduction band (see
Fig. 5(b)), the Fermi level cuts the majority spin t2g for Mn and W
in Sn1 2xMnxWxO2 (correspond to partially occupied atomic-like t2g
states), the eg orbitals of Mn-3d are completely filled in contrast to
eg of W. The minority spin states of both Mn and W are electronempty. Thus, the oxidation states of the two impurity ions of Mn
and W located in Sn1 2xMnxWxO2 turn out to be þ3 and þ5,
respectively, where the occupied electronic configuration may be
4 electrons in 3d (2 spins up in t2g state and 2 spins up in eg state)
and 1 electron in 5d (1 spin up in t2g state and 0 spin in eg state),
respectively. We infer that the two impurity Mn3 þ and W5 þ in
Sn1 2xMnxWxO2 are coupled ferromagnetically via the double
exchange interaction, resulting in a strong ferromagnetic moment
of 5 mB. Using these calculations, the local magnetic moments of the
two impurities Mn and W are 3.8 and 0.7 mB, respectively. These
results suggest electron occupancies of d4 (Mn3 þ ) and d1 (W5 þ ).
The ferromagnetic configuration for Mn–W distance of 3.7 A1
is stable, since starting from the antiferromagnetic configuration
the self consistent calculation converge to the ferromagnetic one.
In Fig. 5(b) one can see the strong hybridization between Mn-3d
and W-5d states via the host oxygen. Further, it is clearly seen in
Fig. 5(c) that some new states emerge in the Mn 3d majority spin
noteworthy from PLDOS. There occurs charge transfer from W to
Mn, and accordingly W and Mn are likely to have nominal W5 þ
(d1) and Mn3 þ (d4) configuration, respectively. As a result, the
electron occupancy at Mn site increases, and so W has reduced
spin magnetic moment of 0.7 mB as compared to 1.6 mB in W only
doped SnO2. The charge transfer from W to Mn, Fig. 6, is expected
to disturb the Jahn–Teller distortion at Mn sites and concomitantly make a system metallic. Further, it will cause the mixedvalence occupancies for (W4 þ W5 þ ) and (Mn4 þ Mn3 þ ) ions,
and the consequent double-exchange-like interaction is expected
to induce the ferromagnetism in (W, Mn) co-doped SnO2.
In order to examine the energetic stability of parallel and
antiparallel alignment of double impurities in SnO2, the difference
between FM and AFM configurations has been calculated; it
shows the stability of ferromagnetic configuration. Ferromagnetic
alignment has half-metallic electronic structure.

4. Conclusion
The augmented spherical wave method has been used in order to
study the electronic structure and magnetic properties of the rutile
SnO2 doped with single and double impurities: Sn1 xMnxO2,
Sn1 xWxO2, and Sn1 2xMnxWxO2 with x¼0.0625. The display of

both majority- and minority-spin band gap indicates that the
introduction of double impurities does not destroy the semiconducting nature of these materials. The co-doped system,
Sn1 2xMnxWxO2, exhibits half-metallic behavior, which make it
suitable as spintronic system with high total magnetic moment
(5 mB). The ground state of Mn-, and W-doped SnO2 systems have a
total magnetic moments of 3 and 2 mB, respectively. The oxidation
states of the two impurity ions are determined from the charge
carrier occupancy in the d-orbital. So, the oxidation states of the two
impurity ions of Mn and W located in Sn1 2xMnxWxO2 turn out to
be þ3 and þ5, respectively. The difference between FM and AFM
configurations has been calculated, it shows the stability of half
metal ferromagnetic system. A tendency of charge transfer from W
to Mn ions has been observed, this tendency causes the mixedvalence occupancies between W and Mn, and accordingly the
double-exchange-like interaction is expected to induce the ferromagnetism in this system.

Acknowledgments
The authors would like to thank V. Eyert for fruitful discussion
concerning the ASW program PACKAGE.
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