Ferromagnetism in Semiconductors Doped with Non-magnetic Elements
Y. P. Feng,∗ H. Pan, R. Q. Wu, and L. Shen
Department of Physics, National University of Singapore
J. Ding and J. B. Yi
Department of Materials Science and Engineering, National University of Singapore
Y. H. Wu
Department of Electrical and Computer Engineering, National University of Singapore
(Dated: March 21, 2008)
I.
INTRODUCTION
Electron has two fundamental properties: charge and
spin. The ability to generate, control and detect the motion of charges in either free space or in solid state forms
the basis of modern electronics. Today’s communication,
information processing and data storage technologies are
dominated by semiconducting materials. Compared to
charge, it is rather difficult to generate, control and detect electron spin. Applications of spin-based devices are
so far limited to information storage, and most of the
spin-related materials and devices still rely primarily on
the spontaneous ordering of spins in the form of different
types of magnetic materials. This situation is expected
to change with successful development of spin-based electronics, or spintronics, the new kind of electronics that
seeks to exploit, in addition to the charge degree of freedom, the spin of the carriers.[1]
To make spintronic devices, the primary requirement
is to have a system that can generate a current of spin
polarized electrons, and a system that is sensitive to the
spin polarization of the electrons for detection of electron spin. Most devices also have a unit in between that
changes the current of electrons depending on the spin
states. The simplest method of generating a spin polarized current is to inject the current through a ferromagnetic material. Compared to ferromagnetic metals, if
a magnetic semiconductor can be used as a spin injector
into a nonmagnetic semiconductor, it would facilitate the
integration of spintronics and semiconductor-based electronics. Comparable resistivities of magnetic and nonmagnetic semiconductors could provide efficient spin injection. Therefore, to enable a host of new microelectronics device applications, it is necessary to develop materials which satisfy the following requirements. (i) Since the
ambition is to use materials and devices at room temperature, spin-polarized charge carriers should be available
at room temperature which requires the ferromagnetic
transition temperature to be above room temperature.
(ii) The mobile charge carriers should respond strongly
to changes in the ordered magnetic state so that the fer-
∗ Electronic
address: [email protected]
romagnetism can be electrically tuned. (iii) The material should retain fundamental semiconductor characteristics when doped. In other words, one needs magnetic
semiconductors exhibiting room temperature ferromagnetism.
Ideally, a semiconductor can be made magnetic by including ions that have a net spin into a semiconductor
host.[2] In such an alloy, a stoichiometric fraction of the
constituent atoms is replaced by magnetic ions, typically
magnetic transition metal (TM) atoms. The doped semiconductors are referred as dilute magnetic semiconductors (DMSs) because only a small amount of magnetic
ions is required to make the semiconductor magnetic. In
recent years, considerable work has been devoted to the
study of DMS materials. However, despite of the large
effort and the fact that many materials have been found
to display room-temperature ferromagnetism,[3–17] the
origin of ferromagnetism in these materials continues to
be debated. Some studies reported strong evidence of
phase separation and formation of ferromagnetic clusters
suggesting a nonintrinsic behavior which is not suitable
for technological applications. Many problems remain to
be solved before the materials can be used to build spintronics devices.
Besides magnetic TM doped semiconductors, researchers are now looking for alternative dopants in order
to overcome problems encountered by the former and in
hope to produce practically useful DMSs. Some breakthroughs have been made recently. In this article, we
review progress made along this direction and discuss
possible origins of the unconventional ferromagnetism observed in materials without magnetic element. The current status in TM doped semiconductors and oxides is
briefly discussed in the next section. We focus on DMSs
obtained by nonmagnetic impurity doping in semiconductors and oxides and review the current progress in
Section III (DMSs obtained by doping with elements with
a full d-shell) and Section IV (DMSs obtained by doping
with 2p light elements). Finally in Section V, some concluding remarks are given.
2
II.
MAGNETIC TRANSITION METAL DOPED
SEMICONDUCTORS
Magnetic transition metal (TM) doped III-V semiconductors such as (Ga,Mn)As,[18, 19] (In,Mn)As[20,
21] and (Ga,Mn)N[19, 22] belong to the most widely
studied magnetic semiconductors, and the mechanism
of ferromagnetism in such systems is relatively well
understood.[19, 22] In particular, (Ga,Mn)As has become
one of the best-understood ferromagnets, and it is now
regarded as a textbook example of a rare class of robust
ferromagnets with dilute magnetic moments coupled by
delocalized charge carriers. An extensive review on ferromagnetism in (III,Mn)V semiconductor was given by
Jungwirth et al. recently.[19]
It is known that magnetically doped III-V semiconductors are ferromagnetic for a wide range of carrier
concentrations, from the insulating to highly conducting regimes, owing to different mechanisms.[23] Here, Mn
acts both as an acceptor and as a source of local moments.
It has been proposed that if the local exchange between
the carriers and the magnetic ions is large enough, an
impurity band is formed in the energy gap of the host
semiconductor.[24, 25] In a highly insulating system, the
Fermi level is well below the mobility edge of the impurity
band. In this regime ferromagnetism can be explained as
the result of percolation of bound magnetic polarons.[26]
In the more conducting samples, itinerant carriers would
mediate ferromagnetism via a Ruderman-Kittel-KasuyaYosida (RKKY) mechanism.[27] The highest Curie temperature achieved in the (Ga,Mn)As system is 173 K
which was obtained in Mn-doped GaAs prepared using
low temperature annealing techniques.[28–30] This, however, is still too low for actual applications. In order to
make DMS a real technology, materials with a Curie temperature higher than room temperature are needed.
Higher Curie temperature was obtained in heterostructures consisting of Mn δ-doped GaAs and p-type AlGaAs
layers by varying the growth sequence of the structures
followed by low-temperature annealing.[31] However, it is
not certain whether the Curie temperature in such systems can be pushed up to above room temperature.[32]
Mn doping in other III-V semiconductors were also
investigated. (III,Mn)Sb based DMSs belong to the
same category as (Ga,Mn)As and (In,Mn)As. However, their Tc ’s are expected to be lower compared to
the corresponding arsenides due to weaker p-d exchange
and smaller magnetic susceptibility of itinerant holes in
the antimonides.[33, 34] Mn-doped phosphide or nitride
DMSs were predicted to be high Tc ferromagnetic semiconductors based on the kinetic-change model.[33] Solubility of Mn in these materials is also larger than that
in arsenides. However, the nature of magnetic interaction in (III,Mn)P and (III,Mn)N is more complex and
not completely understood.[35]
Studies based on the mean-field Zener model predicts that DMSs with a Tc above room temperature
can be obtained with a right combination of host mate-
rial, carrier concentration, and magnetic impurity (type
and density).[33] In particular, with 5% of Mn and
3.5 × 1020 cm−3 of holes in wide-gap semiconductors,
such as GaN, ZnO and C, these materials should be ferromagnetic at room temperature. First-principles calculations also predict a rather stable ferromagnetism for these
materials.[36, 37] Stimulated by these theoretical predictions, intensive research has been carried out to explore
high Tc DMSs.[6, 38–40] Among the different types of
materials that have been investigated, oxide-based DMSs
have attracted special attention, in particular TiO2,[17]
ZnO[41] and SnO2 [42] based materials.
However, despite considerable theoretical and experimental efforts, the nature of their electronic structure
and the origin of ferromagnetism observed in some DMS
is still under debate. Particularly in TM doped oxides,
there has been no consensus on the origin of ferromagnetism. Whether this is an extrinsic effect due to direct
interaction between the local moments in magnetic impurity clusters (or nanoclusters) or is indeed an intrinsic
property caused by exchange coupling between the spin
of carriers and the local magnetic moments is still not
clear. This is a very important issue because spintronics
requires the carriers to be polarized and this can only
be guaranteed if ferromagnetism is intrinsic. Experimental evidence for carrier-mediated ferromagnetism in oxide
based DMSs is not yet conclusive.
Let’s take ZnO as an example. As a direct, wide
band gap semiconductor, ZnO has potential applications
in UV photonics and transparent electronics. It offers
significant potential in providing charge, photonic and
spin-based functionality. Theoretical predictions suggest that room temperature carrier-mediated ferromagnetism should be possible in ZnO, albeit for the p-type
material. Unfortunately, the realization of the p-type
ZnO has proved difficult. ZnO-based DMS was first
reported for Co-doped thin films by Uedo et al. [41]
The average magnetic moment per Co atom they obtained in Zn0.85Co0.15O films was 2 µB . Since this report, there have been hundreds of reports on ZnO based
DMSs.[6, 38–40] The intensive experimental investigations so far have only produced widely diverging results,
ranging from non-ferromagnetic or ferromagnetic with
extrinsic origins to intrinsic ferromagnetism with various Curie temperatures.[38–40] Although observation of
ferromagnetism in ZnO has been reported frequently in
literature by magnetometry measurement, so far there
has been no report on correlated ferromagnetism in magnetic, optical and electrical measurements. Many reports have raised the serious doubts on the magnetism of
magnetically-doped ZnO.[43] Even though some studies
suggest that with sufficient carrier density, room temperature ferromagnetism can be achieved in (Zn,Co)O,[43–
47] crucial experiment such as optical magnetic circular
dichroism that is designed to give signature of dilute ferromagnetism failed to clarify the issue.[16, 48, 49] The
large disparity in experimental results is mainly caused
by the fact that the properties of TM doped ZnO tend
3
to be very sensitive to the preparation methods and conditions, which in turn makes it difficult to conduct systematic studies.
Results of various studies on other oxides have been
equally controversial. While some support carrier mediation of ferromagnetism, others show evidence of ferromagnetism contributed by magnetic clusters. It appears
that there exist several competing ferromagnetic mechanisms and their dominances vary from material to material and under different conditions. Recently, Calderón
and Das Sarma analyzed different models for carriermediated ferromagnetism in dilute magnetic oxides and
proposed that a combination of percolation of magnetic
polarons at lower temperature and RKKY ferromagnetism at higher temperature as the reason for the high
critical temperature measured in these materials.[23] In
dilute magnetic oxides, carriers, usually electrons, are
provided by the oxygen vacancies that are believed to
act as shallow donors.[50, 51] This is different from IIIV semiconductors, like (Ga,Mn)As, where the carriers
(holes) are provided by the magnetic impurities themselves which act also as donors (or acceptors). Since
the binding energy of the electrons on the oxygen vacancies is not large enough to keep the electrons bound
up to the high temperature reported for the Tc (∼ 700
K), they suggested that thermally excited carriers also
mediate ferromagnetism via the RKKY mechanism at
sufficiently high temperatures, complementing the bound
polaron picture.
The observed ferromagnetism in magnetic TM doped
DMSs could be due to a number of different origin.[52]
Carrier-mediated ferromagnetism in spatially uniform
ferromagnetic DMSs is certainly possible and the mechanisms are relatively well understood. However, in a
composite material, precipitation of a known ferromagnetic, ferrimagnetic or antiferromagnetic compound can
account for magnetic characteristics at high temperature. Even in the absence of precipitates of foreign compound, alloys can phase separate into nanoscale regions
with small and large concentrations of the magnetic constituent, and high-temperature magnetic properties are
dominated by the regions with high magnetic ion concentrations. In many carrier-doped DMSs, a competition between long range ferromagnetic and short-range
antiferromagnetic interactions and/or the proximity of
the localization boundary lead to an electronic nanoscale
phase separation. Questions then can be asked: Is the
FM observed in DMSs really intrinsic? Are there really strong magnetic interactions between well-separated
magnetic dopants? Available experimental techniques
are unable to provide exclusive evidence to differentiate
the various mechanisms and have difficulties in unambiguous determination of the origin of magnetic signals in
these materials. Theoretical studies also predicted that
clusters of magnetic elements are energetically favored in
some DMSs. For example, through first-principles calculation, Cui et al. [53, 54] predicted that the magnetic Cr
dopants have a clustering tendency in (Ga,Cr)N. Mag-
netic secondary clusters have been shown to be ferromagnetic. Ferromagnetism of the DMSs can thus arise
from magnetic secondary clusters.[9, 48, 55–57] These
extrinsic magnetic behaviors are undesirable for practical applications in spintronics. In a recent study, Prater
et al. found that upon high-temperature annealing in
oxygen, (Zn,Co)O samples which showed magnetic ordering above room temperature as-deposited became insulating and the magnetization drops, suggesting that the
observed magnetic behavior of the oxide is directly related to the presence of intrinsic defects, notably oxygen
vacancies and Zn interstitials.[58] The origin of ferromagnetism in TM doped DMSs is still controversial due to the
possibility of magnetic secondary phases and other source
of magnetism, uncertainty of magnetic interactions.
III.
DMS WITHOUT MAGNETIC ELEMENTS
It is important to note that the vast majority of the
DMSs that have been investigated are semiconductors
or oxides doped with magnetic d atoms having open dn
shells (1 ≤ n ≤ 9) or various combinations of several
magnetic atoms of different kinds. A possible way to
avoid problem related to magnetic precipitate is to dope
a nonmagnetic matrix with nonmagnetic impurity atoms.
Because the dopants, and hopefully their oxides, are not
magnetic, DMSs obtained this way can be free of ferromagnetic precipitates and hence unambiguous DMSs.
Copper-doped ZnO was among the first such systems that have been investigated. In a systematic theoretical study of ZnO doped with 3d TM elements using the Korringa-Kohn-Rostoker (KKT) Green’s function method based on the local density approximation,
Sato and Katayama-Yoshida initially predicted that ZnO
doped with 25% Cu is nonmagnetic.[36] However, it
was realized later that this was due to the effect of a
small supercell (high Cu concentration) in the calculation, such that it was necessary to place Cu atoms both
above/below each other in adjacent basal planes (with a
separation of 5.20 Å) and on adjacent cation positions
within a single basal plane (with a separation of 3.25
Å). Further theoretical studies at lower doping concentrations predicted that ZnO doped with 6.25%[59] and
3.125%[60] Cu are ferromagnetic. In these first principles studies, based on local spin density approximation (LSDA)/LSDA+U and generalized gradient approximatin (GGA)/GGA+U, respectively, the Cu atoms were
separated by at least 6.1 Å. Feng[61] later examined the
effect of Cu separation and the stability of the FM state
in (Zn,Cu)O and clarified that when the Cu atoms are
separated by 5.20 Å along the c-axis the FM state is
favored, but when the Cu atoms are separated by 3.25
Å within the basal plane the AFM state is favored, but
the AFM state has higher total energy compared to the
FM state at larger Cu separation. Therefore, it was
concluded that ferromagnetic semiconductors can be obtained by doping Cu into ZnO.
5.0
5.0
4.0
4.0
3.0
3.0
2.0
2.0
1.0
1.0
Energy (eV)
Incidentally, the initial experiment on Cu-doped ZnO
thin films prepared by combinatorial laser molecularbeam epitaxy method failed to detect ferromagnetism
down to 3 K.[62] However, ZnO thin films doped with
0.3% Cu prepared with pulsed-laser deposition were
shown to be ferromagnetic by magnetic circular dichroism spectra.[48] Further studies devoted to Cu-doped
ZnO, with samples of different Cu concentrations, by
Lee et al.[63] provided additional experimental confirmation of ferromagnetism in Cu-doped ZnO. More recently,
Buchholz et al. reported room temperature FM in p-type
ZnO thin films but nonferromagnetic behavior in n-type
Cu-doped ZnO at room temperature.[64]
Ferromagnetism in Cu-doped ZnO was reexamined recently by Ye et al.[65] using accurate full-potential linearized augmented plane-wave and DMol calculations
based on density functional theory. Each Cu dopant was
found to carry a magnetic moment of 1 µB . For ZnO
doped with 12.5% Cu, the FM state was found energetically favored by 43 meV compared to the AFM state
which lead to an estimated Tc of about 380 K. More importantly, ferromagnetism was predicted for both n-type
and p-type samples. Subsequently, Hou et al. observed
ferromagnetism in carefully prepared n-type Cu-doped
ZnO thin films.[66] In this study, a series of Cu-doped
ZnO thin films was prepared on glass substrate by dc reactive magnetron sputtering, to reduce the influence of
ferromagnetic impurities. All the films, ranging from 2
to 12% Cu doping, were found ferromagnetic at room
temperature and the moment per Cu ion was found to
decrease with increasing Cu concentration and nitrogen
doping. The results confirm that ferromagnetism can be
mediated by itinerant electrons in Cu-doped ZnO.
Besides ZnO, GaN is another wide gap semiconductor that was predicted to hold the possibility of a DMS
with a Curie temperature above room temperature.[33]
Motivated by the success of ferromagnetism in Cu-doped
ZnO, Wu et al.[67] carried out first-principles calculations
based on spin density functional theory to study the magnetic properties of GaN doped with 6.25% of Cu. Using
a supercell which consists of 2×2×2 wurtzite GaN units,
with one or two Ga atoms substituted by Cu, they found
that each Cu dopant induces a magnetic moment of 2.0
µB which is larger than that of Cu-doped ZnO.[65] Furthermore, the calculated band structure (Fig. 1) shows
that Cu-doped GaN is half metallic with the majority
spin being semiconducting and the minority spin being
metallic with sufficient unfilled states above the Fermi
level. Calculations based on two Cu atoms at the largest
possible separation of 6.2 Å in the supercell indicated
that the FM state is the ground state and its energy is
50 meV lower than that of the AFM state. Based on this
significant energy difference, Wu et al. predicted that Cudoped GaN should be a room temperature DMS, similar
to Cu-doped ZnO.
The above prediction was confirmed recently by Lee
et al. using an implantation and subsequent annealing
process.[68] In their experiment, 1 MeV Cu2+ ions were
Energy (eV)
4
0.0
-1.0
-2.0
0.0
-1.0
-2.0
-3.0
-3.0
-4.0
-4.0
-5.0
-5.0
-6.0
-6.0
-7.0
-7.0
G A
H K
G
(a) Majority spin
M L
H
G A
H K
G
M L
H
(b) Minority spin
FIG. 1: Band structure of the majority spin (a) and the minority spin (b) of GaN doped with 6.25% Cu, calculated using
DFT/GGA. The Fermi level is set to zero. Reprinted with
permission from Ref. [67], R. Q. Wu et al. Appl. Phys. Lett.
89, 062505 (2006). Copyright @ American Physical Society.
implanted into GaN with a dose of 1×1017 cm−2 at room
temperature which was followed by rapid thermal annealing of the samples at 700, 800, and 900 ◦ C, respectively,
for 5 min. Both samples annealed at 700 and 800 ◦ C
were found ferromagnetic at room temperature. Figure 2
shows the magnetization-field (M − H) curves at room
temperature (300 K) of as-implanted and annealed samples. The sample annealed at 900 ◦ C did not show ferromagnetism, possibly due to clustering of Cu during the
annealing process. Even though the estimated saturation
magnetization of 0.057 µB and 0.27 µB per Cu atom for
the samples annealed at 700 and 800 ◦ C, respectively, are
much smaller than the value (2 µB /Cu atom) predicted
by the first-principles calculations,[67], the experimental
evidence of room temperature ferromagnetism of Cu implanted GaN is encouraging.
This, however, was cautioned by Rosa and Ahuja[69]
who investigated structural and electronic properties of
Cu-doped GaN using density functional theory (DFT)
within GGA. They considered two configurations where
the Cu atoms are separated along the [0001] direction by
5.23 Å (far configuration) and 3.22 Å (close configuration). Their results of total energy calculations indicated
that the close configuration has a lower energy (by 0.4
eV/cell) and therefore more stable than the far configuration. Due to atomic relaxation, the spin polarization
on the Cu atom in the GaN lattice is rather small, leading
to rather weak ferromagnetic behavior.
Ferromagnetism in Cu-doped ZnO and GaN can be
explained based on the p-d hybridization mechanism.[70,
71] Here the d orbitals of Cu hybridizes strongly with the
p orbitals of its neighboring anions (oxygen or nitrogen)
of the host semiconductor, resulting in spin polarization
of the neighboring anions with large magnetization. They
couple ferromagnetically or anitiferromagnetically with
5
FIG. 2: Magnetization-field (M − H) curves at room temperature (300 K) for the as-implanted GaN:Cu sample, and
samples annealed at 700 and 800 ◦C after the Cu implantation. Reprinted with permission from Ref. [68], J.-H. Lee,
et al. Appl. Phys. Lett. 90, 032504 (2007). Copyright @
American Institute of Physics.
the dopant. Other dopants in turn couple to the spin
polarized anions in the same way for an energy gain, resulting in an indirect FM coupling among dopants.
Very recently, room temperature ferromagnetism was
also found in Cu-doped GaN nanowires.[72] The saturation magnetic moments in the hot-wall chemical vapor deposited single-crystalline GaN nanowires doped
with 1% and 2.4% Cu were measured to be higher than
0.86 µB /Cu at 300 K. The author attributed the ferromagnetism to p-d hybridization between Cu and N ions,
which induces delocalized magnetic moments and longrange coupling.
Besides Cu, other IIA non-magnetic elements such
as Pd[73] have been considered as possible dopants for
DMSs.
IV.
DMS BY ANION DOPING WITH 2p LIGHT
ELEMENTS
Carbon can exist in a number of polymorph such as
graphite, diamond, graphene, nanotubes, and fullerene.
None of these show magnetism. However, various recent
studies indicate that defects in carbon system can lead to
magnetization.[74–87] Motivated by this idea, Pan et al.
considered carbon as a possible dopant for ZnO based
DMS.[88] Using first-principles method based on DFT
within LSDA, they considered various possible point defect forms of carbon in ZnO and concluded that substitution of carbon for oxygen results in spin polarization.
A magnetic moment of 2.0 µB was found for each carbon, contributed mainly by the carbon p orbitals. The
neighboring Zn atoms and the second nearest neighboring oxygen atoms also contribute a small part to the overall magnetic moment. Strong coupling between the carbon p orbitals, oxygen p orbitals, and the zinc d orbitals
Density of States
were found, as shown by the projected density of states
(PDOS) shown in Fig. 3. The interaction results in the
splitting of the carbon 2p orbitals near 2.3 eV. The spinup bands are fully occupied while the spin-down bands
are partially filled (Fig. 4). Further calculations showed
that ferromagnetic coupling between magnetic moments
of different impurity sites is energetically favored compared to the AFM state. This energy difference of 63
meV per pair of C dopants is significant enough to make
Zn(O,C) a room temperature ferromagnet.
4
3
2
1
0
−1
−2
−3
−4
1
0.5
0
−0.5
−1
−1.5
2
1
0
−1
−2
−3
100
0
−100
−200
−10
Zn:d
O:p
C:p
Total
−5
0
Energy (eV)
5
10
FIG. 3: Total (top panel) and local density of states for the
carbon dopant, nearest neighbor Zn atom and the next nearest neighbor O atom, calculated using first-principles method
based on DFT within LSDA. The Fermi level is indicated by
the dashed vertical line.
To verify the theoretical prediction, Pan et al. prepared C-doped ZnO films using pulsed-laser deposition.
Three samples with estimated carbon concentrations of
0, 1 and 2.5%, respectively, were prepared. Careful characterization of the samples showed that the pure ZnO
film without carbon doping is nonmagnetic, whereas both
C-doped ZnO films show ferromagnetism at room temperature (inset in Fig. 5). Based on the measured temperature dependence of magnetization (Fig. 5), the Curie
temperatures of both films should be higher than 400 K.
The measured saturation magnetization (Fig. 6) yields a
magnetic moment per carbon in the range of 1.5−3.0 µB
which is in good agreement with the theoretical prediction. XPS measurement also revealed existence of carbon
in carbide form which is an indication that carbon substitutes for oxygen in ZnO.
Ferromagnetism in C-doped ZnO is significant not only
because it is a room temperature DMS, but also because it represents a whole class of new materials whose
magnetic properties are determined solely by the interaction between the carriers in p rather than d or f atomic
shells. In addition to C-doped ZnO, room temperature
ferromagnetism was observed recently in nitrogen doped
ZnO.[89] Using pulsed laser deposition, Yu et al. prepared nitrogen embedded ZnO films. The presence of ni-
4
4
3
3
Energy (eV)
Energy (eV)
6
2
1
0
Γ
H
K
A
Γ
2
1
0
Γ
H
K
A
Γ
FIG. 4: Band structure of C-doped ZnO, calculated using
first-principles method based on DFT within LSDA. One oxygen atom is replaced by carbon in a 72-atom supercell (3×3×2
primitive cells). The Fermi level is indicated by the dashed
horizontal line.
FIG. 5: Ms (T )/Ms (5K) versus temperature for samples
doped with 1% (target concentration 1%) and 2.5% (target
concentration 5%) of carbon, respectively. The solid lines are
a guide for the eye. The inset shows the hysteresis loop of
the sample with 2.5% carbon taken at 300 K. Reprinted with
permission from Ref. [88], H. Pan, et al. Phys. Rev. Lett.
99, 127201 (2007). Copyright @ American Physical Society.
trogen ions in the films was confirmed by the secondary
ion microscopic spectrum and by Raman experiments.
The films were found ferromagnetic at room temperature.
The authors attributed the unexpected ferromagnetism
to electron transfer from the completely filled d-orbits of
Zn to the defect state.
The concept of anion doping was first proposed by
Kenmochi et al. in 2004 for creating DMS based on
CaO[90, 91]. Using the KKR method within the LSDA,
Kenmochi et al. studied the electronic structure and
magnetic properties of B-, C- or N-doped CaO, as well
as Ca vacancies.[90] In particular, they compared the
total energies of FM state and spin-glass state in each
case. It was found that the FM state is more stable than
the spin-glass state in Ca(O,C) and Ca(O,N). However,
the spin-glass state is more stable than the FM state
in Ca(O,B), while the Ca vacancies do not induce any
magnetic moment. Figure 7 shows their calculated total
DOS and the partial density of 2p-states at B, C and N
FIG. 6: The room-temperature saturation magnetization Ms
and the magnetic moment per carbon in the carbide state
(carbide carbon) as a function of the measured carbon concentration of the C-doped specimens. The carbon concentration
in the sample was estimated by SIMS measurements, while
the percentage of carbon in the carbide state was estimated
by XPS measurements. Reprinted with permission from Ref.
[88], H. Pan, et al. Phys. Rev. Lett. 99, 127201 (2007).
Copyright @ American Physical Society.
sites in the ferromagnetic state. A deep impurity band is
pushed up into the band gap of CaO. The large exchangesplitting energy between majority spin states and minority states leads to a high-spin ground state. Based
on the partially occupied narrow and highly-correlated
deep-impurity bands, Kenmochi et al. proposed Zener’s
double-exchange as mechanism for the origin of the ferromagnetism in Ca(O,C) and Ca(O,N).
Dinh et al.[92] extended the above work to alkalineearth-metal-oxide, MgO, CaO, BaO and SrO. They discussed the origin of the ferromagnetism through the calculation of the electronic structure and exchange coupling constant by using the pseudo-potential-like selfinteraction-corrected local spin density. The Monte Carlo
method was also used to predict the Curie temperature.
It was shown that the stability of half-metallic ferromagnetism induced by C in the alkaline-earth-metal-oxide
host materials is improved by taking the electron selfinteraction into account, compared with the standard local density approximation (LDA) case, and the C’s 2p
electron states in the bandgap become more localized resulting in the predominance of the short-ranged exchange
interaction. All alkaline-earth-metal-oxides were found
half-metallic ferromagnetic. It was proposed that the ferromagnetic double exchange mechanism is predominant
for all materials considered, except for Mg(O,C) at high
C concentration. Tc of Mg(O,C) is predicted to be the
highest at 10% C doping, while that of other alkalineearth-metal-oxides increases monotonously.
Very recently, the method was further explored theoretically in BeO by Shein et al.[93] and in SrO by Elfimov
et al.[94] Results of first-principles calculation based on
DFT within GGA, carried out by Shein et al.[93] using a
72-atom supercell Be36 O35 X (X = B, C, N), suggest that
7
FIG. 7: Total DOS per unit cell in CaO with Ca vacancies, and DOS (solid lines) and partial density of p-states (dashed lines)
at B [1(b)], C [1(c)], and N [1(d)] site per atom in Ca(O,X) (X = B,C and N) in the ferromagnetic state, respectively. The
impurities are doped up to 5 at%. The Fermi energy is set to zero. The upper and lower sides of the figures stand for the DOS
of up and down spin states respectively. Reprinted with permission from Ref. [90], K. Kenmochi, et al. Jpn. J. Appl. Phys.
43, L934 (2004). Copyright @ The Japan Society of Applied Physics.
in the case of a partial substitution of boron, carbon, or
nitrogen atoms for oxygen atoms in the BeO system, a
spontaneous spin polarization of the 2p states of impurity atoms takes place, and the Be(O,X) systems become
either a semiconducting magnet Be(O,B) or half-metallic
magnets [Be(O,C) and Be(O,N)], in which conduction is
due to the 2p spin states of the anion alone. In a very
recent publication,[94] Elfimov et al. presented a theoretical argument, based on first-principles calculations
within LSDA and LSDA+U, combined with some experimental support that substitution of nitrogen for oxygen in simple band insulators (e.g. SrO) is sufficient to
produce DMS. The substitution of nitrogen for oxygen
in simple nonmagnetic oxides leads to holes in nitrogen
2p states which form local magnetic moments. Because
of the very large Hund’s rule coupling of nitrogen and
oxygen 2p electrons and the rather extended spatial extent of the wave functions these materials are predicted
to be ferromagnetic metals or small band gap insulators.
The theoretical calculations with regard to the basic electronic structure and the formation of local magnetic moments were supported by experimental studies conducted
on Sr(O,N) grown by solid-state chemistry methods.
Meanwhile, Feng and coworkers extended their theoretical studies on 2p light element doping to other semiconductors and oxides and predicted ferromagnetism in a
number of systems, including C-doped CdS,[95] C-doped
AlN,[96], N-doped ZnO,[97], etc. Similar behaviors as
that of C-doped ZnO were found in these materials.
The mechanism for ferromagnetism in these anion
doped magnetic materials is still not understood for their
particular electronic structure and magnetic properties.
DMSs produced by anion doping typically have a low
doping concentration but enough mobile carriers. Only
2p electrons of dopants and hosts contribute to the magnetism. The origin of ferromagnetism in these materials
challenges our current understanding of ferromagnetism
of DMS. The existing theories of DMS cannot be applied
because they are based on d and f orbitals but there
are no such orbitals in materials doped with light elements. There are several important differences between
the 2p and the 3d orbitals which determine the different
magnetic properties of DMS doped with 2p light element
(anion) and 3d TM (cation). First, the anion 2p bands
of the light element (LE) are usually full in ionic states,
leaving no room for unpaired spins compared to 3d bands
of TM. Secondly, the spin-orbit interaction of p states is
considerably reduced compared to that of d states since it
scales with the fourth power of the atomic number. Consequently, spin relaxation of DMS doped with 2p light
elements is expected to be suppressed by up to two orders of magnitude in comparison with 3d cation doped
DMS [98]. Thirdly, valence electrons in p states are more
delocalized than those in d or f states and have much
larger spatial extensions which could promote long-range
exchange interactions. Therefore, despite suffering from
low solubility[88, 99, 100], DMS doped with 2p light elements can be weak ferromagnets in a highly ordered and
low doping concentration.
It is reasonable to assume that alignment of magnetic
moments in 2p LE doped DMS is achieved through the pp coupling interaction between the impurity p states and
the host p states at the top of the valence band, similar to
p-d hybridization in some of the TM doped DMSs. This
interaction follows essentially from quantum mechanical
level repulsion, which “pushes” the minority states upward, crossing the Fermi level. Consequently, the p states
split into more stable threefold t2 states which are either
fully occupied or completely empty. The symmetry and
wave function of the impurity 2p state are similar to those
of the top valence band of the III-nitride and II-oxide
which consists mostly of anion p orbitals. Therefore,
a strong p-p coupling interaction between the impurity
state and valence band state is allowed near the Fermi
level. Substitution of C for N in AlN or C/N for O in
ZnO introduces impurity moments as well as holes. Dif-
8
ferent from Mn ions in (Ga,Mn)As which polarizes spin
of holes in opposite direction, the spin density near each
anion impurity in 2p LE doped DMS tends to align parallel to the moment of the impurity ion under the p-p
interaction. The strong p-p interaction leads to stronger
coupling between impurity and carrier spin orientations.
Sufficiently dense spin-polarized carriers are able to effectively mediate an indirect, long-range ferromagnetic coupling between the 2p LE dopants. The spatially extended
p states of the host and the impurity are able to extend
the p-p interaction and spin alignment to a large range
and thus to facilitate long-range magnetic coupling between the impurities. This model based on p-p coupling
interaction gives a reasonable explanation to the experimentally observed ferromagnetism in ZnO doped with a
small amount of carbons [88]. In this model, free carriers
play an essential role in mediating the spin alignment in
such DMS.
V.
been put forward to explain the unexpected magnetism
in such systems. First-principles methods, particularly
that based on the density functional theory, have played
a very important role in the study of DMSs and is expected to continue to play such a role in providing theoretical understanding to the phenomena and in predicting
new DMS materials. Different from other computational
approaches, the first-principles method solves the quantum mechanical problem self-consistently and it does not
require any experimental input or empirical parameters.
It is, therefore, ideal for studying physical properties of
new materials and for predicting new materials. With
advances in computational algorithms and availability
of high performance computing resources, first-principles
method can now be used to model and study more realistic and complicated systems. First-principles methods
are thus indispensable in the study of DMSs. They will
continue to be used to provide theoretical understanding
and the physical insights for the magnetic materials and
to provide guidance to experimental studies.
CONCLUDING REMARKS
The discovery of ferromagnetism in semiconductors
and oxides doped with non-magnetic elements opens a
new pathway to new magnetic materials without conventional magnetic elements. Following this approach, new
materials may be developed to meet the materials requirements of spintronics which TM doped semiconductors or oxides promised to but so far unable satisfactorily
to deliver.
As pointed out by Shein et al.,[93] magnetization of
a nonmagnetic host as a result of its doping by nonmagnetic 2p impurities can be expected for a wide class
of related systems. As the hosts, one can take such
well-known ionic insulators as III-V, II-VI semiconductors/oxides. The dopants should be chosen so that the
orbital energies of their p states be higher than the p band
of oxygen (anion) of the matrix, so that these states be
localized in the energy gap of the initial crystal to ensure
the conditions for their spontaneous spin polarization.
Understanding the origin of ferromagnetism in systems
consisting of only elements with s and p electrons is essential for further development. Research in this direction
is still in the infant stage and no complete theory has
Magnetic ordering is a collective phenomenon. Monte
Carlo simulation is useful in studying the statistical
behavior, and particularly in predicting Curie temperature. With input from first-principles calculations,
Monte Carlo simulation will continue to play an important role in further study of DMSs. Theoretical modeling
is essential in establishing a theory of ferromagnetism in
DMSs. Existing theories such as RKKY, polaron percolation, etc. each works well for some materials but
cannot explain the magnetic ordering in other materials.
There may be different mechanisms of ferromagnetic coupling in different materials and it would be a challenging
task to establish a complete ferromagnetic theory that
works for all DMSs. To reach this goal, it is also necessary to improve experimental techniques in materials
growth and characterization, to provide unambiguous evidence for origin of magnetism in DMSs. In order to draw
meaningful conclusions, it is crucial to conduct systematic studies using different characterization methods. A
concerted effort between theorists, computational scientists and experimentalists shall lead to a complete understanding of magnetic behavior of DMSs and practically
useful DMSs.
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