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Defect-induced defect-mediated magnetism in ZnO and carbon-based materials
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2010 J. Phys.: Condens. Matter 22 334210
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IOP PUBLISHING
JOURNAL OF PHYSICS: CONDENSED MATTER
J. Phys.: Condens. Matter 22 (2010) 334210 (5pp)
doi:10.1088/0953-8984/22/33/334210
Defect-induced defect-mediated
magnetism in ZnO and carbon-based
materials
Antonis N Andriotis1 , R Michael Sheetz2 and Madhu Menon2,3
1
Institute of Electronic Structure and Lasers, FORTH, PO Box 1527, 71110 Heraklio, Crete,
Greece
2
Center for Computational Sciences, University of Kentucky, Lexington, KY 40506-0045,
USA
3
Department of Physics and Astronomy, University of Kentucky, Lexington, KY 40506-0055,
USA
E-mail: [email protected], [email protected] and [email protected]
Received 24 November 2009, in final form 1 February 2010
Published 4 August 2010
Online at stacks.iop.org/JPhysCM/22/334210
Abstract
The recent discovery of magnetism in a variety of diverse non-magnetic materials containing
defects has challenged conventional thinking about the microscopic origin of magnetism in
general. Especially intriguing is the complete absence of d electrons that are traditionally
associated with magnetism. By a systematic microscopic investigation of two completely
dissimilar materials (namely, ZnO and rhombohedral-C60 polymers) exhibiting ferromagnetism
in the presence of defects, we show that this new phenomenon has a common origin and the
mechanism responsible can be used as a powerful tool for inducing and tailoring magnetic
features in systems which are not magnetic otherwise. Based on our findings, we propose a
general recipe for developing ferromagnetism in new materials of great technological interest.
The recipe is quite general, although its realization is system specific. In each case, the required
basic step is to find two synergistic codopants, one for providing the unpaired electrons and the
other for facilitating the ferromagnetic coupling.
(Some figures in this article are in colour only in the electronic version)
C60 [4], graphene ribbons [5] and irradiated graphite [6].
A distinguishing feature of these materials is the complete
absence of d or f electrons, traditionally known to be
responsible for the occurrence of magnetic phenomena.
This class also includes non-carbon-based materials such as
defected oxides of rock-salt structure (e.g. CaO) [7], the
hexaborides (e.g. CaB6 , SrB6 ) [8–10], etc.
The second class includes materials in which the magnetic
moments have an extrinsic origin, that is they are due to
their being doped with magnetic ions, preferably from the
3d-transition metal series. These mainly belong to the
technologically important diluted magnetic semiconductors
(DMSs) and include the doped oxides such as ZnO, TiO2 ,
HfO2 , SnO2 and ZrO2 [11–15]; as well as doped GaAs and
other III–V or II–VI compounds [16].
In the present work we review the key features of
magnetism in carbon-based materials (first class) and present
results of state-of-the-art calculations on ZnO systems
Recent reports of the discovery of magnetic features
in technologically derived new materials with diverse
constitutions are a fascinating phenomenon. In some of these
materials magnetic features were exhibited under extreme
fabrication conditions, while in others they were due to doping
with magnetic ions but at a concentration far less than that
which by itself would justify the appearance of magnetism.
Essential to the development of magnetism in any material
is the existence of unpaired electrons, the origin of which may
be attributed to a number of causes. A closer examination of
the origin of unpaired electrons in the new class of magnetic
materials, however, allows one to classify them into two broad
classes [1, 2].
The first class includes materials which exhibit unpaired
electrons as a result of their nano-size and/or the presence
of structural and topological defects. That is, their unpaired
electrons are of intrinsic origin.
This class includes
carbon-based materials such as C60 -polymers [3], TDAE0953-8984/10/334210+05$30.00
1
© 2010 IOP Publishing Ltd Printed in the UK & the USA
J. Phys.: Condens. Matter 22 (2010) 334210
A N Andriotis et al
Figure 1. Relaxed [C60 ]2 dimer (top panel) and [C60 ]3 trimer (bottom panel) used in our simulations. The location of every C V in these
structures is among the carbon atoms colored in dark.
containing defects (second class). By analyzing the latter
results in light of the new magnetism reported in the carbonbased material we show the common thread linking the two
completely diverse systems and offer a unified approach to the
creation of magnetism in otherwise non-magnetic materials.
It should be noted that defect-induced magnetism is a
synergistic effect; i.e. it is the synergistic result of two
mutually dependent groups of processes. The first one refers
to the rehybridization of the atomic orbitals (AOs) associated
with the defects themselves (impurity atoms) and/or those
of the surrounding defect ligands [17, 18] and characterized
by many features which have local character. The other
group of processes has long range character and leads to
ferromagnetic coupling (FMC) among the magnetic moments;
these processes depend crucially on the induced charge
transfers, remote molecular orbital (MO) delocalization and
remote MO overlaps [2]. As will be shown in the following,
our results demonstrate that this synergy is achieved in both
of the above introduced classes of materials through the
presence and cooperation of two types of defects which can
act as donor (D) and acceptor (A) sites, respectively. These
provide alternating · · · ADADADADA · · · pathways which
play a significant role in the development of FMC [1, 2].
One widely studied carbon-based polymer structure is the
rhombohedral one (Rh-C60 ) in which the C60 molecules are
mutually connected by 2 + 2 cycloaddition bonds. It has been
shown that the magnetism of these systems is the consequence
of the synergy of the simultaneous presence of two types of
defect, namely the presence of carbon vacancies (CV s) and
the 2 + 2 cycloaddition bonds which provide the alternating
· · · ADADADAD · · · pathways [1, 2]. The magnetic moments
in these systems are provided by the lone electron spins
localized around the CV s. The alternating sequence of CV s
and the 2 + 2 cycloaddition bonds form two synergistic types
of defect that lead to sustainable charge transfers which give
rise to large electric dipole moments [19]. It was proposed
that it is the development of these electric fields which develop
the FMC among the magnetic moments, making the high-spin
states of these systems energetically more favorable.
All our structures are fully relaxed. For the [C59 ]2
and C59 –C60 –C59 shown in figure 1 ab initio density
functional theory (DFT) calculations were carried out with the
B3LYP exchange–correlation functional using the Gaussian 03
software program [20]. In each of these calculations the triplesplit-valence basis set 6-311G containing 3d polarization
functions on heavy atoms was used. The stability of our results
was checked by including dynamic correlation effects using the
UMPW1PW91 hybrid functional. It was found that for both
[C59]2 and C59 –C60 –C59 the triplet state is energetically more
favorable by 790 meV and 470 meV, respectively, exhibiting
long range FMC which, in addition to the distance dependence,
shows substantial anisotropy that could reach 20%. It was
recently shown that the FMC in these cases is the result of the
defect-induced remote overlap of the MOs [2], which exhibit
contributions in both neighborhoods of the spin localization
(i.e. vacancy regions). As a result, the FMC develops over large
distances as this is quite profound in the case of C59–C60 –C59 .
Next we consider the magnetism of doped diluted
magnetic semiconductors (DMSs) and choose ZnO as the
representative host material and investigate two example cases
of doping with two types of atoms (codoping). In the first
example, ZnO is codoped with Co and Cu. We denote the
codoped system as Zn(Co, Cu)O. In the second example, we
considered Zn(Co, Cu)O in the presence O-vacancies (OV ).
In this case we considered the interaction of two (Co, OV )
pairs in the presence of a codoping Cu atom. Our calculations
were performed using first principles density functional
theory (DFT) in the spin polarized generalized gradient
2
J. Phys.: Condens. Matter 22 (2010) 334210
A N Andriotis et al
Figure 2. Supercells of Co- and Cu-codoped ZnO. In all panels, Zn (O) atoms are indicated by the large light colored ball (the small dark
colored ball) while Co (Cu) atoms are indicated by the large medium dark ball (the large dark ball). In the right panel, Co (Cu) atoms are
indicated by the large medium dark ball (the large grey ball). The locations of the OV s are indicated by the small dark ball.
Table 1. Energy differences between the FM and AFM states of relaxed configurations of the Zn(Co, Cu)O system as obtained within the
LSDA + U method.
System
Configuration
[C59 ]2
C59 –C60 –C59
Zn(3Co2Cu)O
Zn(3Co2Cu)O
Zn(3Co2OV Cu)O
Zn(Co, Cu)O
Figure 1, top
Figure 1, bottom
Figure 2, left
Figure 2, middle
Figure 2, right
Zn(Co)O
[ E(FM) − E(AFM)] (meV)
−790
−470
−43
−1
+9
E FM − E AFM < 0
E FM − E AFM > 0
approximation (SGGA) and the Hubbard-U approximation (to
be denoted as the DFT/SGGA + U method) as implemented
in the Vienna ab initio simulation package (VASP) [21–23].
A plane wave basis set for electronic wavefunction expansion
together with the projector augmented wave (PAW) method
has been used while the cut-off energy was consistently set
to 400 eV in all calculations. The convergence criteria for
−1
the total energy and force were 10−4 eV and 10−2 eV Å ,
respectively. We used the simplified rotationally invariant
DFT + U model developed by Dudaref et al [24] according to
which the U value is taken to be U = U ∗ − J , where U ∗ and
J denote the on-site Coulomb and the exchange interaction,
respectively. The U parameters for the d-states of Zn, Co and
Cu and the p states of O were carefully selected to reproduce
the correct energy locations for the Zn(d) and Co(d) peaks
as well as the correct electronic band gap (≈3.4 eV) for the
Zn(Co, Cu)O system. The U values thus obtained are: Ud;Zn =
10.5 eV, Ud;Co = 3.5 eV, Ud;Cu = 3.5 eV and Up;O = 7.0 eV.
A hexagonal 3 × 3 × 3 cell was employed containing 108 atoms
along with a 2 × 2 × 2 -centered pack for k-vectors.
In figure 2 (left panel) we show the fully relaxed supercell
used in the case of Zn(Co, Cu)O including three Co (indicated
in magenta) and two Cu substitutional impurities (blue)
forming an alternating pathway of Co–Cu–Co–Cu–Co with
the impurities distributed over successive Zn-planes. The
corresponding concentrations for Co and Cu are 3/54 =
5.55% and 2/54 = 3.70%, respectively. In figure 2 (middle
Remarks
E(triplet) − E(singlet)
E(triplet) − E(singlet)
Co(↑)–Cu(↑)–Co(↑)–Cu(↑)–Co(↑)
Co(↑)–Cu(↑)–Co(↓)–Cu(↑)–Co(↑)
Co(↑)–Cu(↓)–Co(↓)
Ud,Zn = 6.5 eV, Ud,Co = 2.5 eV
Ud,Cu = 1.0 eV, Up,O = 0 eV
Ud,Zn = 6.5 eV, Ud,Co = 2.5 eV
Up,O = 0 eV
panel) we show the same supercell as in the left panel, but here
the distribution of the Co and Cu atoms is more widely spread
although not necessarily over consecutive Zn-planes. In the
right panel of figure 2, we show a supercell of the same size
as the previous ones containing two (Co, OV ) pairs (Co and
OV , being indicated by magenta and blue, respectively) and
one Cu atom (shown in orange). In this case the corresponding
concentrations for the pairs (Co, OV ) and Cu are 2/54 =
3.70% and 1/54 = 1.85%, respectively.
In table 1 we summarize the results of our calculations for
the total energy differences between ferromagnetic (FM) and
antiferromagnetic (AFM) states for the three configurations.
In the same table we also include the results for the energy
differences between the singlet and triplet states for the two
C60 -polymeric configurations shown in figure 1. As indicated
in the table, for the configuration shown in the left panel of
figure 2, the FM alignment of the Co atoms is energetically
more favorable than their AMF coupling by 43 meV. In the
FM configuration the Cu atoms acquire substantial magnetic
moment (≈0.59 μB ) and are aligned ferromagnetically with
respect to the Co atoms while in the AFM case the Cu atoms
acquire magnetic moment of the same magnitude as in the
FM case and align as follows: Co(↑)–Cu(↑)–Co(↓)–Cu(↑)–
Co(↑). For the configuration shown in the middle panel of
figure 2 we find the FM and AFM states to be isoenergetic,
with the FM state slightly more stable (by 1 meV). The
fact that in this configuration the codopants do not form
3
J. Phys.: Condens. Matter 22 (2010) 334210
A N Andriotis et al
C60 -based polymers and in Zn(Co, Cu)O. Our investigations
at the SGGA + U level of approximation led us to the
conclusion that, in Zn(Co, Cu)O, the Cu mediation is attributed
to the spin polarization of Cu; this plays a role analogous
to that of the spin polarization of the free electrons which
mediate the RKKY interaction. Furthermore, it is found that
the interaction of the (Co, OV ) pairs (found to be coupled
antiferromagnetically [25]), retains this feature even in the
presence of Cu codopants (figure 2 right panel). On the
other hand, Lin et al [30] demonstrated experimentally the
enhancement of Zn(Co)O ferromagnetism by Li codoping;
They suggest that in Zn(Co, Li)O the Li codopants may
be inducing an indirect exchange in the form of the bound
magnetic polaron. For the same Zn(Co, Li)O system, Sluiter
et al [31], working at the U = 0 level, proposed that
the Li codopants induce charge transfers which result in the
enhancement of the magnetic moments of the Co ions while
bringing their d-states closer to the optimal values for double
exchange.
Based on our findings we propose that a more general
and predictive recipe for developing DMDI ferromagnetism in
new materials of great technological interest can be suggested.
The recipe is quite general, although its realization is system
specific. In each case, the required basic step is to find two
synergistic codopants, one for providing the unpaired electrons
and the other for facilitating the FMC. Our findings further
propose that this complementarity of the codopants may be
achieved if the pair of codopants are able to act as a donor–
acceptor pair. DMDI magnetism appears to be applicable for a
wide variety of non-traditional magnetic materials, and can be
very effective in DMS materials in particular.
It has to be pointed out that the proposed complementarity
and synergistic nature that should exist between the codopants
does not necessarily imply similarities in the nature of
the developing FMC among the defect-induced magnetic
moments. The nature of the FMC is expected to differ
from system to system, as it depends on the nature of the
defects and the dopants, the defect-induced hybridizations, the
concentration of the codopants, etc. This becomes apparent
from the systems (C60 -based polymers and Zn(Co, Cu)O)
investigated in the present work as discussed in the above. Our
work proposes that in order for such a FMC to be developed
it is necessary that the two codopants form alternate pathways
of the donor–acceptor type. This appears to be the conclusion
from the experimental findings of Straumal et al [32] which we
became aware of after the submission of our manuscript. They
present strong evidence that ferromagnetism in pure and Mndoped ZnO originates through crystallographic imperfections
with the magnetic moments located at vacancies present in the
grain boundaries, the latter forming a foamlike network around
the non-magnetic ZnO grains. Interestingly, it is found that
ferromagnetism appears only if the specific grain boundary
area, sGB , exceeds a certain threshold value, presumably for
ensuring the development of continuous foamlike networks.
In view of the above, we can understand the fact that
no ferromagnetism was found in substitutional Zn(CoAl)O
while enhanced ferromagnetism was found if the Al occupies
interstitial sites [33]. Similarly, it is not surprising that
alternating pathways gives support to our argument that the
enhancement of ferromagnetism is related to the establishment
of the alternating donor–acceptor pathways. Finally, in the
configuration shown in the right panel of figure 2, oxygen
vacancies OV , shown in red, are introduced next to Co ions
(shown in magenta). Anticipating that the (Co, OV ) pairs can
induce long range interaction in the presence of additional ndoping [25], we checked their behavior in the case of p-doping.
In this case we find that in the presence of Cu codopants the FM
and AFM alignment of the Co atoms are almost isoenergetic
with the AFM configuration being more stable by 9 meV (as
shown in table 1). This indicates that Cu codopants, acting as
acceptors, cannot contribute to FMC in a way analogous to that
of a donor-type codopant (hydrogen) as shown in [25].
The results presented in the above support the role of
complimentary pairs of defects in inducing magnetism in
otherwise non-magnetic materials belonging to two widely
differing classes with no apparent correlation between them.
In both classes, the two kinds of defect usually form
structures (pathways) of alternating effective donor and
acceptor crystal sites leading to the development of electron
charge and spin density like waves (CDW and SDW,
respectively). Interestingly, these features are reminiscent of,
on the one hand, the characteristics of the layered magnetic
materials [26, 27] and, on the other hand, McConnell’s
theory [28, 29] of magnetism of the charge-transfer organic
salts.
In each codoped system, the defects of one type contribute
unpaired electrons and, therefore, are responsible for the
development of the magnetic moments. The process of
creation of unpaired electron can be considered to be defect
or impurity specific but at the same time it is influenced
by the electronic structure of the host lattice. Key factors
playing a significant role in the creation of unpaired electrons
include, the type of defects or impurities themselves, the point
group symmetry of their lattice positions, their spin and crystal
field band splittings as well as their band-filling factors, the
directionality of the bonding orbitals and the hybridization
of the AOs associated with the defects and their surrounding
ligands. However, in order for ferromagnetism to develop,
the magnetic moments created by the first group of defects
have to be coupled through a long range correlation. This is
made possible through the mediation of the other type of defect
and the mutual interaction between the two groups of defects.
This interaction may result in induced charge transfers, remote
molecular orbital (MO) delocalizations as well as their remote
overlaps. Thus, the essence of the codoping is that one of the
codopants induces or provides the unpaired electrons, while
the other codopant mediates the FMC among them giving, thus,
the characteristic of a defect-mediated defect-induced (DMDI)
magnetism in the codoped systems. The major advantage of
DMDI magnetism is that it enables the coupling among the
magnetic moments to be developed even for defect/impurity
concentrations smaller than those dictated by the percolation
threshold [1, 2, 19, 25].
This is, in fact, what has been demonstrated with our
results shown in table 1, from which it is clear that long
range mediated interactions develop upon codoping in both the
4
J. Phys.: Condens. Matter 22 (2010) 334210
A N Andriotis et al
ferromagnetism was found only within specific ranges of
codopant concentrations as, for example, was found in the Ndoped Zn(Co)O [34], or not found at all as in the case of Zn(Co,
Cu)O [Zn0.928Co0.062Cu0.01 O] [35], although in this case the
presence of Cu was found to enhance the magnetization of
Zn(Co)O at low temperatures.
[13] Prellier W, Fouchet A and Mersey B 2003 J. Phys.: Condens.
Matter 15 1583R
[14] Fitzgerald C B, Venkatesan M, Dorneles L S, Gunning R,
Stamenov P, Coey J M D, Stampe P A, Kennedy R J,
Moreira E C and Sias U S 2006 Phys. Rev. B 74 115307
[15] Spaldin N A 2004 Phys. Rev. B 69 125201
[16] Mahadevan P and Zunger A 2004 Phys. Rev. B 69 115211
[17] Mpourmpakis G, Froudakis G E, Andriotis A N and
Menon M 2003 Phys. Rev. B 68 125407
[18] Mpourmpakis G, Froudakis G E, Andriotis A N and
Menon M 2005 Phys. Rev. B 72 104417
[19] Andriotis A N, Menon M, Sheetz R M and
Chernozatonskii L 2003 Phys. Rev. Lett. 90 026801
[20] Frisch M J et al 2003 Gaussian 03, Revision A.1 (Pittsburgh,
PA: Gaussian, Inc.)
[21] Kresse G and Furthmuller J 1996 Comput. Mater. Sci. 6 15
[22] Kresse G and Furthmuller J 1996 Phys. Rev. B 54 11169
[23] Hafner J 2008 J. Comput. Chem. 29 2044
[24] Dudaref L S, Botton G A, Savrasov S Y, Humphreys C J and
Sutton A P 1998 Phys. Rev. B 57 1505
[25] Pemmaraju C D, Hanafin R, Archer T, Braun H B and
Sanvito S 2008 Phys. Rev. B 78 054428
[26] Baibich M N, Broto J M, Fert A, NguyenVanDau F, Petroff F,
Eitenne P, Creuzet G, Friederich A and Chazelas J 1988
Phys. Rev. Lett. 61 2472
[27] Samant M G et al 1994 Phys. Rev. Lett. 72 1112
[28] McConnell H M 1967 Proc. R. A. Welch Found. Conf. 11 144
[29] Breslow R K R, Jaun B and Xia C-Z 1982 Tetrahedron 38 863
[30] Lin Y H, Ying M, Li M, Wang X and Wen C 2007 Appl. Phys.
Lett. 90 222110
[31] Sluiter M H F, Kawazoe Y, Sharma P, Inoue A, Raju A R,
Rout C and Waghmare U V 2005 Phys. Rev. Lett.
94 187204
[32] Straumal B B, Mazilkin A A, Protasova S G, Myatiev A A,
Straumal P B, Schutz G, van Aken P A, Goering E and
Baretzky B 2009 Phys. Rev. B 79 205206
[33] Chang G S, Kurmaev E Z, Boukhvalov D W, Finkelstein L D,
Moewes A, Bieber H, Colis S and Dinia A 2009 J. Phys.:
Condens. Matter 21 056002
[34] Assadi M H N, Zhang Y B and Li S 2009 J. Appl. Phys.
106 093911
[35] Zhang Y B and Li S 2008 Appl. Phys. Lett. 93 042511
Acknowledgments
The present work is supported through grants by DOE (DEFG02-00ER45817 and DE-FG02-07ER46375).
References
[1] Andriotis A N, Sheetz R M, Richter E and Menon M 2005
Europhys. Lett. 72 658
[2] Andriotis A N, Sheetz R M, Lathiotakis N N and
Menon M 2009 Int. J. Nanotechnol. 6 164
[3] Makarova L, Sundquist B, Hohne R, Esqulnazi P,
Kopelevich Y, Schar P, Davidov V A, Kashevarova L S and
Rakhmanlna A V 2001 Nature 413 716
[4] Narymbetov B, Omerzu A, Kabanov V V, Tokumoto M,
Kobayashi H and Michailovic D 2000 Nature 407 883
[5] Yamashiro A, Shimoi Y, Harigaya K and Wakabayashi K 2003
Phys. Rev. B 68 193410
[6] Esquinazi P, Spemann D, Hohne R, Setzer A, Han K H and
Butz T 2003 Phys. Rev. Lett. 91 227201
[7] Elfimov I S, Yunoki S and Sawatzky G A 2002 Phys. Rev. Lett.
89 216403
[8] Young D P, Hall D, Torelli M E, Fisk Z, Sarrao J L,
Thompson J D, Ott H R, Oseroff S B, Goodrich R G and
Zysler R 1999 Nature 397 412
[9] Matsubayashi K, Maki M, Tsuzuki T, Nishioka T and
Sato N K 2002 Nature 420 143
[10] Young D P, Fisk Z, Thompson J D, Ott H R, Oseroff S B and
Goodrich R G 2003 Nature 420 144
[11] Stoneham A M, Pathak A P and Bartram R H 1976 J. Phys. C:
Solid State Phys. 9 73
[12] Venkatesan M, Fitzgerald C B and Coey J M D 2004 Nature
430 630
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