Electronic Structure and X-Ray Magnetic Circular Dichroism in (Zn, T)O (T = V, Fe, Co) Diluted Magnetic Semiconductors
The electronic structure of the (Zn, T)O (T = V, Fe, Co) diluted magnetic semiconductors is investigated theoretically from first principles, using the fully relativistic Dirac linear muffin-tin orbital band structure method. The X-ray absorption spectra, X-ray magnetic circular dichroism spectra at...
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Інститут металофізики ім. Г.В. Курдюмова НАН України
2013
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| Цитувати: | Electronic Structure and X-Ray Magnetic Circular Dichroism in (Zn, T)O (T = V, Fe, Co) Diluted Magnetic Semiconductors / L.V. Bekenov, D.V. Mazur, V.N. Antonov, L.P. Germash, A. Ernst // Металлофизика и новейшие технологии. — 2013. — Т. 35, № 1. — С. 1-17. — Бібліогр.: 50 назв. — англ. |
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Bekenov, L.V. Mazur, D.V. Antonov, V.N. Germash, L.P. Erns, t A. 2016-06-30T17:05:15Z 2016-06-30T17:05:15Z 2013 Electronic Structure and X-Ray Magnetic Circular Dichroism in (Zn, T)O (T = V, Fe, Co) Diluted Magnetic Semiconductors / L.V. Bekenov, D.V. Mazur, V.N. Antonov, L.P. Germash, A. Ernst // Металлофизика и новейшие технологии. — 2013. — Т. 35, № 1. — С. 1-17. — Бібліогр.: 50 назв. — англ. 1024-1809 PACS numbers:71.15.Rf, 71.20.Nr,71.55.Gs,75.30.Et,75.50.Pp,78.20.Ls, 78.70.Dm https://nasplib.isofts.kiev.ua/handle/123456789/104059 The electronic structure of the (Zn, T)O (T = V, Fe, Co) diluted magnetic semiconductors is investigated theoretically from first principles, using the fully relativistic Dirac linear muffin-tin orbital band structure method. The X-ray absorption spectra, X-ray magnetic circular dichroism spectra at the Co, Fe, and V L2,3 edges are investigated theoretically. The origin of the dichroism spectra in such compounds is examined. Using the magnetic force theorem, as it is implemented within the multiple scattering theory, the exchange interaction parameters for the transition metal atoms are calculated. За допомогою зонної повністю релятивістської лінійної методи МТ-орбіталей теоретично досліджено з перших принципів електронні структури розбавлених магнетних напівпровідників (Zn, T)O (T = V, Fe, Co). Теоретично досліджено спектри поглинання Рентґенового випромінення і спектри Рентґенового магнетного циркулярного дихроїзму на L2,3-краях поглинання атомів Co, Fe та V. Вивчено природу спектрів дихроїзму в цих сполуках. За допомогою теореми про магнетні сили на основі теорії багатократного розсіяння було обчислено параметри обмінної взаємодії між атомами перехідних металів. Электронная структура разбавленных магнитных полупроводников (Zn, T)O (T = V, Fe, Co) исследована теоретически, исходя из первых принципов, полностью релятивистским линейным методом МТ-орбиталей. Теоретически исследованы рентгеновские спектры поглощения и спектры рентгеновского циркулярного дихроизма на L2,3-краях поглощения атомов Co, Fe и V. Изучена природа спектров дихроизма. С помощью теоремы о магнитных силах на основе теории многократного рассеяния вычислены параметры обменного взаимодействия между атомами переходных металлов. This work was supported by the National Academy of Sciences of Ukraine in the framework of the State Target Scientific and Technology Program of Implementation and Application of Grid Technologies for 2009—2013. en Інститут металофізики ім. Г.В. Курдюмова НАН України Металлофизика и новейшие технологии Электронные структура и свойства Electronic Structure and X-Ray Magnetic Circular Dichroism in (Zn, T)O (T = V, Fe, Co) Diluted Magnetic Semiconductors Электронная структура и рентгеновский магнитный циркулярный дихроизм в разбавленных магнитных полупроводниках (Zn, T)O (T = V, Fe, Co) Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Electronic Structure and X-Ray Magnetic Circular Dichroism in (Zn, T)O (T = V, Fe, Co) Diluted Magnetic Semiconductors |
| spellingShingle |
Electronic Structure and X-Ray Magnetic Circular Dichroism in (Zn, T)O (T = V, Fe, Co) Diluted Magnetic Semiconductors Bekenov, L.V. Mazur, D.V. Antonov, V.N. Germash, L.P. Erns, t A. Электронные структура и свойства |
| title_short |
Electronic Structure and X-Ray Magnetic Circular Dichroism in (Zn, T)O (T = V, Fe, Co) Diluted Magnetic Semiconductors |
| title_full |
Electronic Structure and X-Ray Magnetic Circular Dichroism in (Zn, T)O (T = V, Fe, Co) Diluted Magnetic Semiconductors |
| title_fullStr |
Electronic Structure and X-Ray Magnetic Circular Dichroism in (Zn, T)O (T = V, Fe, Co) Diluted Magnetic Semiconductors |
| title_full_unstemmed |
Electronic Structure and X-Ray Magnetic Circular Dichroism in (Zn, T)O (T = V, Fe, Co) Diluted Magnetic Semiconductors |
| title_sort |
electronic structure and x-ray magnetic circular dichroism in (zn, t)o (t = v, fe, co) diluted magnetic semiconductors |
| author |
Bekenov, L.V. Mazur, D.V. Antonov, V.N. Germash, L.P. Erns, t A. |
| author_facet |
Bekenov, L.V. Mazur, D.V. Antonov, V.N. Germash, L.P. Erns, t A. |
| topic |
Электронные структура и свойства |
| topic_facet |
Электронные структура и свойства |
| publishDate |
2013 |
| language |
English |
| container_title |
Металлофизика и новейшие технологии |
| publisher |
Інститут металофізики ім. Г.В. Курдюмова НАН України |
| format |
Article |
| title_alt |
Электронная структура и рентгеновский магнитный циркулярный дихроизм в разбавленных магнитных полупроводниках (Zn, T)O (T = V, Fe, Co) |
| description |
The electronic structure of the (Zn, T)O (T = V, Fe, Co) diluted magnetic semiconductors is investigated theoretically from first principles, using the fully relativistic Dirac linear muffin-tin orbital band structure method. The X-ray absorption spectra, X-ray magnetic circular dichroism spectra at the Co, Fe, and V L2,3 edges are investigated theoretically. The origin of the dichroism spectra in such compounds is examined. Using the magnetic force theorem, as it is implemented within the multiple scattering theory, the exchange interaction parameters for the transition metal atoms are calculated.
За допомогою зонної повністю релятивістської лінійної методи МТ-орбіталей теоретично досліджено з перших принципів електронні структури розбавлених магнетних напівпровідників (Zn, T)O (T = V, Fe, Co). Теоретично досліджено спектри поглинання Рентґенового випромінення і спектри Рентґенового магнетного циркулярного дихроїзму на L2,3-краях поглинання атомів Co, Fe та V. Вивчено природу спектрів дихроїзму в цих сполуках. За допомогою теореми про магнетні сили на основі теорії багатократного розсіяння було обчислено параметри обмінної взаємодії між атомами перехідних металів.
Электронная структура разбавленных магнитных полупроводников (Zn, T)O (T = V, Fe, Co) исследована теоретически, исходя из первых принципов, полностью релятивистским линейным методом МТ-орбиталей. Теоретически исследованы рентгеновские спектры поглощения и спектры рентгеновского циркулярного дихроизма на L2,3-краях поглощения атомов Co, Fe и V. Изучена природа спектров дихроизма. С помощью теоремы о магнитных силах на основе теории многократного рассеяния вычислены параметры обменного взаимодействия между атомами переходных металлов.
|
| issn |
1024-1809 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/104059 |
| citation_txt |
Electronic Structure and X-Ray Magnetic Circular Dichroism in (Zn, T)O (T = V, Fe, Co) Diluted Magnetic Semiconductors / L.V. Bekenov, D.V. Mazur, V.N. Antonov, L.P. Germash, A. Ernst // Металлофизика и новейшие технологии. — 2013. — Т. 35, № 1. — С. 1-17. — Бібліогр.: 50 назв. — англ. |
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1
ЭЛЕКТРОННЫЕ СТРУКТУРА И СВОЙСТВА
PACS numbers:71.15.Rf, 71.20.Nr,71.55.Gs,75.30.Et,75.50.Pp,78.20.Ls, 78.70.Dm
Electronic Structure and X-Ray Magnetic Circular Dichroism
in (Zn, T)O (T = V, Fe, Co) Diluted Magnetic Semiconductors
L. V. Bekenov, D. V. Mazur, V. N. Antonov, L. P. Germash*, and A. Ernst**
G. V. Kurdyumov Institute for Metal Physics N.A.S.U.,
36 Academician Vernadsky Blvd.,
UA-03680 Kyiv-142, Ukraine
*National Technical University of Ukraine
‘Kyiv Polytechnic Institute’,
14 Politekhnichna Str.,
03056 Kyiv, Ukraine
**Max Planck Institute of Microstructure Physics,
Weinberg, 2,
D-06120 Halle, Germany
The electronic structure of the (Zn, T)O (T = V, Fe, Co) diluted magnetic semi-
conductors is investigated theoretically from first principles, using the fully
relativistic Dirac linear muffin-tin orbital band structure method. The X-ray
absorption spectra, X-ray magnetic circular dichroism spectra at the Co, Fe,
and V L2,3 edges are investigated theoretically. The origin of the dichroism
spectra in such compounds is examined. Using the magnetic force theorem, as
it is implemented within the multiple scattering theory, the exchange interac-
tion parameters for the transition metal atoms are calculated.
За допомогою зонної повністю релятивістської лінійної методи МТ-
орбіталей теоретично досліджено з перших принципів електронні струк-
тури розбавлених магнетних напівпровідників (Zn, T)O (T = V, Fe, Co). Те-
оретично досліджено спектри поглинання Рентґенового випромінення і
спектри Рентґенового магнетного циркулярного дихроїзму на L2,3-краях
поглинання атомів Co, Fe та V. Вивчено природу спектрів дихроїзму в цих
сполуках. За допомогою теореми про магнетні сили на основі теорії бага-
тократного розсіяння було обчислено параметри обмінної взаємодії між
атомами перехідних металів.
Электронная структура разбавленных магнитных полупроводников (Zn, T)O
(T = V, Fe, Co) исследована теоретически, исходя из первых принципов, пол-
ностью релятивистским линейным методом МТ-орбиталей. Теоретически
исследованы рентгеновские спектры поглощения и спектры рентгеновского
Металлофиз. новейшие технол. / Metallofiz. Noveishie Tekhnol.
2013, т. 35, № 1, сс. 1—17
Оттиски доступны непосредственно от издателя
Фотокопирование разрешено только
в соответствии с лицензией
© 2013 ИМФ (Институт металлофизики
им. Г. В. Курдюмова НАН Украины)
Напечатано в Украине.
2 L. V. BEKENOV, D. V. MAZUR, V. N. ANTONOV et al.
циркулярного дихроизма на L2,3-краях поглощения атомов Co, Fe и V. Изу-
чена природа спектров дихроизма. С помощью теоремы о магнитных силах
на основе теории многократного рассеяния вычислены параметры обменного
взаимодействия между атомами переходных металлов.
Key words: diluted magnetic semiconductors, electronic structure, exchange
interaction, magnetic properties, X-ray magnetic circular dichroism.
(Received August 28, 2012)
1. INTRODUCTION
Spintronics or spin-transport electronics has attracted much attention
due to its technologically potential applications. Diluted magnetic
semiconductors (DMSs) obtained by doping the host semiconductor
with magnetic element impurities can be used for spintronics devices
[1]. The starting materials, which were expected to be the promising
candidates for spintronics, are Group III—V materials, such as (Ga,
Mn)As with the highest Curie temperature of 110 K [2]. Other candi-
dates are transition metal doped Group III nitrides, phosphides and
semiconducting oxides. Dietl et al. [3] predicted theoretically that
transition element doped semiconducting materials such as GaN and
ZnO have a Curie temperature TC higher than room temperature. After
the report of TC = 280 K in (Zn1−xCox)O [4], there have been many re-
ports on ZnO-based DMSs showing high TC [5].
As a wide-band-gap Group II—VI semiconductor, ZnO has recently
been considered as a base material for transparent DMSs. Since ZnO has
an energy band gap in the ultraviolet region (3.3 eV) and a large exciton
binding energy (60 meV at room temperature) and can be made highly
conductive by appropriate doping, it has attracted considerable atten-
tion as a material for optoelectronic device applications. Recently, it has
been reported that V doping can cause ferromagnetism (FM) in ZnO.
However, not much work has been done on the system and the results
obtained so far are rather controversial. There have been a number of
reports on the growth of (Zn1−xCox)O films [4, 6, 7] and characterization
of their structural, magnetic and optical properties. However, substan-
tial disagreement as to the magnetic and optical properties of magnetic
alloys has been found. Despite the partial success, the nature of the host-
impurity couplings, and of the ferromagnetic interactions in transition
metal doped oxides, is not very well understood. The accumulated expe-
rience of experiments with thin films of magnetically doped semicon-
ductors indicates a high sensitivity of the samples to the technology of
their preparation and subsequent heat treatment [8].
The interest of previous investigations was to a great extent concen-
trated on the nature of the magnetic interactions in the DMSs. In the
ELECTRONIC STRUCTURE AND X-RAY MAGNETIC CIRCULAR DICHROISM 3
present study, we focus our attention on X-ray absorption spectra
(XAS) as well as X-ray magnetic circular dichroism (XMCD) in the
(Zn, T)O (T = V, Fe, Co) DMSs. The XMCD experiments measure the
difference of the absorption of X-rays with opposite (left and right)
directions of circular polarization. The XMCD is a powerful tool to
study the element-specific local magnetic interactions, and it reflects
the spin and orbital polarizations of the local electronic states. The
XAS and XMCD in the Co-doped ZnO were measured by several groups
[9—26]. Field and temperature dependences of the XAS and XMCD
spectra at the V L2,3 edges in the (Zn, V)O were reported by Ishida et al.
[27]. They found a linear increase of the XMCD signal with external
magnetic field H, which indicates that the paramagnetic signal domi-
nates the XMCD signal and that the ferromagnetic component is small,
consistent with their magnetization measurements. The XAS and
XMCD at the Fe L2, 3 edges in the Fe-doped ZnO were measured by sev-
eral groups [28—31] as well.
2. COMPUTATIONAL DETAILS
The calculations of the electronic structure of (Zn, T)O (T = V, Fe, Co)
DMSs were performed for a 3a×3a×1c and 3a×3a×2c supercells of the
wurtzite-type ZnO unit cell with one or two of the Zn ions replaced by
T. The supercell calculations were performed for the compositions
x = 0.0556 (1/18) and x = 0.02778 (1/36) using the simple trigonal
P3m1 (No. 156) space group. The substitutional (Zn1−xCox)O positions
are illustrated in Fig. 1 for 72-atom ZnO unit cell containing two sub-
stitutional Co atoms x = 0.0556 (2/36). The Co atom has four O nearest
neighbours: three O atoms at the distance of 1.949 Å and one O atom at
Fig. 1. Schematic representation of the 3a×3a×2c supercell of the wurtzite-
type ZnO unit cell with two of the Zn ions replaced by Co ones. Small open cir-
cles show the oxygen vacancy in close vicinity of the Co2 atom.
4 L. V. BEKENOV, D. V. MAZUR, V. N. ANTONOV et al.
1.950 Å. The second-neighbour shell consists of 12 Zn atoms: six at the
distance of 3.196 Å and six at 3.172 Å.
The details of the computational method are described in our previous
papers [32—34], and here we only mention some aspects specific to the
present calculations. The calculations presented in this work were per-
formed using the spin-polarized relativistic linear-muffin-tin-orbital
(SPR LMTO) method [35, 36] for the experimentally observed lattice
constants a = 9.588 Å, c = 5.16 Å for wurtzite-type ZnO [37]. The crystal
structure was optimized using the Vienna ab initio simulation package
(VASP) [38—40]. For the LMTO calculations, we used the Perdew—Wang
[41] parameterization of the exchange-correlation potential. Brillouin
zone (BZ) integrations were performed using the improved tetrahedron
method [42] and charge self-consistency was obtained on a grid of 95 k
points in the irreducible part of the BZ. To improve the potential, we in-
cluded additional interstitial spheres. The basis consisted of Co and Zn s,
p, d and f, O s, p and d, and empty spheres s and p LMTOs.
3. RESULTS AND DISCUSSION
3.1. (Zn, Co)O and (Zn, Fe)O DMSs
3.1.1. Energy Band Structure
Figure 2 presents total and partial density of states for 72-atom ZnO
wurtzite unit cell containing one CoZn substitution (x = 0.03) in the local
spin density approximation (LSDA) and a ferromagnetic arrangement of
the Co moments. The O 2s states are located mostly between −19.7 to
−18.7 eV below the Fermi level (not shown) and the p states of O are found
between −8.7 eV to −1.8 eV. The spin splitting of the O p states is quite
small. Zn d states occupy the energy interval between −8.8 and −1.8 eV
and hybridize strongly with the O 2p states. The Co 3d impurity states hy-
bridize well with the O 2p conduction band, which gives a metallic charac-
ter solution. The crystal field at the CoZn site (C3v point symmetry) causes
the splitting of Co d orbitals into a singlet a1 ( −2
3 1z
d ) and two doublets e (dyz
and dxz) and e1 (dxy and −2 2x y
d ). In close vicinity to the Fermi level, a very
strong narrow two-peak structure of the minority-spin Co dxz and −2 2x y
d
states is found (see the insert in the bottom panel of Fig. 2). The energy
splitting between the two peaks is around 14 meV. The Fermi level is situ-
ated at the shoulder of the second high-energy peak. Peaks of dxz and
−2 2x y
d symmetry occur in the minority-spin channel at 0.45 to 0.67 eV
above the Fermi level. The energy interval from 0.6 to 0.7 eV above the
ELECTRONIC STRUCTURE AND X-RAY MAGNETIC CIRCULAR DICHROISM 5
Fermi level is occupied by −2
3 1z
d states with minority-spin.
The magnetic moment in the (Zn, Co)O unit cell is 3.947μB. Our band
structure calculations yield the spin magnetic moment of 3.412μB for
the Co atoms in (Zn1−xCox)O (x = 0.03). The induced spin magnetic mo-
ments at the O first neighbour sites are of 0.048μB and 0.173μB, for
longer and shorter distant O atoms, respectively. Twelve Zn ions in the
second neighbour shell couple ferromagnetically to the substitutional Co
ion with spin magnetic moments from 0.014μB to 0.043μB. The orbital
moments at the Zn and O sites are small with the largest one at the O
Fig. 2. The LSDA total [in states/(cell eV)] and partial [in states/(atom eV)]
densities of states for the O, Zn and substitutional Co ions in (Zn1−xCox)O
(x = 0.03) [43]. The insert is a blow-up of the Co d partial density of states
close to the Fermi energy. The Fermi energy is at zero.
6 L. V. BEKENOV, D. V. MAZUR, V. N. ANTONOV et al.
first neighbour sites (−0.011μB). The orbital magnetic moment at the Co
site is 0.353μB and is parallel to the spin moment. It is well known that
the physical properties of ZnO are very sensitive to different kinds of
defects in the crystal. In spite of numerous experimental studies, there
is still controversy as to what the relevant native defects of this oxide
are. Single-crystal ZnO has always been observed to contain Zn excess or
oxygen deficiency [44]. The Zn excess can be accommodated in part by
the presence of zinc interstitials or oxygen vacancies. Experiments have
been inconclusive as to which of these is the predominant defect. Results
presented in the literature point toward both possibilities and different
interpretations have even been taken on the same set of experimental
data (see, e.g., [45]). However, several authors pointed out that oxygen
vacancies were the predominant defect. Their conclusions were based on
calculation of reaction rates [45], diffusion experiments [46] as well as
electrical conductivity and Hall effect measurements [47]. To investi-
gate the influence of possible oxygen vacancies on the electronic struc-
ture of the (Zn1−xCox)O DMSs, we perform the LMTO band structure cal-
culations with two of the Zn ions replaced by Co with different environ-
ments. The supercell calculations were performed for the composition
x = 0.0625 (2/36). We create an oxygen vacancy in the first neighbour-
hood of the second cobalt along z direction. The oxygen vacancy has four
nearest neighbour atoms: three Zn atoms at the distance of 1.9496 Å and
one Co atom at 1.9505 Å. The lattice relaxation was found to be very im-
portant in the presence of the oxygen vacancy. The lattice relaxation
causes the shift of the Co2 atom and the three Zn atoms toward the va-
cant site by 0.13 Å and 0.24 Å, respectively.
3.1.2. X-Ray Absorption and XMCD Spectra at the Co L2,3 Edges
Figure 3 presents experimental XAS and XMCD spectra [25] of
(Zn, Co)O at the Co L2,3 edges together with the spectra calculated in
the LSDA. The X-ray absorption spectrum at the Co L3 edge is rather
complicated and consists of two major structures: peak b at around
780.9 eV with a low energy shoulder a at 780 eV and double peak c at
781.6—782.4 eV with high energy fine structure d at 784 eV. As may be
seen from the top panel of Fig. 3, the calculations for the ideal crystal
structure with one substitutional Co1 atom (full curve) provide the X-
ray absorption intensity only at the peaks a and b. The full explanation
of the spectra is only possible by taking crystal imperfections, such as
oxygen deficiency, into account. The oxygen vacancy (with lattice re-
laxation taken into account) strongly affects the shape of the XAS
spectra. As may be seen from Fig. 3 (top panel), the X-ray absorption
from the Co2 atoms with the oxygen vacancy (dashed line) mostly de-
termines the shape of the major double peak c. Thereby, our calcula-
tions including oxygen deficiency reproduce the shape of the Co L3 X-
ELECTRONIC STRUCTURE AND X-RAY MAGNETIC CIRCULAR DICHROISM 7
ray absorption spectrum quite well except for the high energy struc-
ture d. It might be that the additional satellite structure at the high-
energy tail of the Co L3 XAS appears due to many-body effects. This
question needs an additional theoretical investigation using an appro-
priate many-body treatment. The theoretically calculated Co L2,3
XMCD spectra are in good agreement with the experiment (lower panel
in Fig. 3). The high-energy minimum at around 782 eV was found to be
due to the oxygen vacancy in the (Zn, Co)O DMS.
3.1.3. X-Ray Absorption and XMCD Spectra at the Fe L2,3 Edges
The XAS and XMCD spectra at the Fe L2,3 edges in Fe doped ZnO were
measured by several groups [28—31]. Figure 4 presents experimental
XAS and XMCD spectra [29] of (Zn, Fe)O at the Fe L2,3 edges together
with the calculated ones. The line shape of the XAS spectrum at the Fe
L3 edge in the (Zn, Fe)O DMS shows a two-peak structure with a major
peak at 710 eV and a smaller one at 708.5 eV. The major peak possesses
an additional high-energy shoulder. As may be seen from the top panel
of Fig. 4, the calculations for the ideal crystal structure with one sub-
Fig. 3. X-ray absorption (top panel) and XMCD (lower panel) experimental
spectra [25] (circles) of (Zn1−xCox)O (x = 0.07) at the Co L2,3 edges and theoreti-
cally calculated spectra [43] for the Co1 without any additional defects (full
lines) and Co2 with the oxygen vacancy (dashed lines) ions. The experimental
spectra were measured at H = 7 T and T = 20 K [25].
8 L. V. BEKENOV, D. V. MAZUR, V. N. ANTONOV et al.
stitutional 3
1
Fe +
ion (full curve) provide the X-ray absorption intensity
at the major peaks only. The oxygen vacancy strongly affects the shape
of the XAS spectra. As may be seen from Fig. 4 (top panel), the X-ray
absorption from the
+2
2
Fe atoms with the oxygen vacancy (dashed line)
mostly determines the shape of the low energy peak at 708.5 eV.
Thereby, our calculations including oxygen deficiency reproduce the
shape of the Fe L3 X-ray absorption spectrum quite well except for
high-energy structure at 711—714 eV. It might be that the additional
satellite structure at the high-energy tail of the Fe L3 XAS appears due
to many-body effects. The theoretically calculated Fe L2,3 XMCD spec-
tra are in good agreement with the experiment (lower panel in Fig. 4).
The low energy minimum at around 708.5 eV was found to be due to the
oxygen vacancy in the (Zn, Fe)O DMS. The theory does not produce the
fine structure corresponding to the high-energy satellite structure at
around 711—714 eV.
3.2. (Zn, V)O DMS
3.2.1. Electronic Structure
Figure 5 presents LSDA total and partial density of states for the ZnO
Fig. 4. X-ray absorption (top panel) and XMCD (lower panel) experimental
spectra [29] (circles) of (Zn1−xFex)O at the Fe L2,3 edges and theoretically calcu-
lated spectra for the
3
1
Fe
+
without any additional defects (full lines) and
2
1
Fe
+
with the oxygen vacancy (dashed lines) ions.
ELECTRONIC STRUCTURE AND X-RAY MAGNETIC CIRCULAR DICHROISM 9
wurtzite unit cell containing one V substitution. The O s states are locat-
ed mostly between −21.0 and −19.7 eV and the O p states are found be-
tween −9.6 eV and −3.0 eV. The spin splitting of the O p states is quite
small. Zn d states occupy the energy interval between −9.6 eV and
−3.0 eV and hybridize strongly with the O p states. The majority-spin V
−2
3 1z
d structure is found in close vicinity to the Fermi energy between
−0.2 eV and 0.7 eV (see the insert in the bottom panel of Fig. 5).
Very strong and narrow peaks of the majority-spin V bonding dxy and
dyz states are located between −0.4 eV and −0.8 eV. The corresponding
Fig. 5. The LSDA total [in states/(cell eV)] and partial [in states/(atom eV)]
densities of states for the O, Zn and substitutional V ions in (Zn1−xVx)O
(x = 0.06) [48]. The insert is a blow-up of the V d partial density of states close
to the Fermi energy. The Fermi energy is at zero.
10 L. V. BEKENOV, D. V. MAZUR, V. N. ANTONOV et al.
anti-bonding states are from 0.2 eV to 0.6 eV. Narrow peaks of dxy and
dyz symmetry occur in the minority-spin channel at around 1 eV above
the Fermi level. The energy interval from 1.4 eV to 2.2 eV above the
Fermi level is occupied by the dxz, 2 2
3x y
d
− and −2
3 1z
d minority-spin states.
We also investigated the electronic and magnetic structures of the
(Zn1−xVx)O DMSs with two of Zn ions replaced by V. The supercell calcu-
lations were performed for the compositions x = 0.1111 (2/18),
x = 0.0625 (2/32) and x = 0.0555 (2/36). We found that vanadium at-
oms placed at different Zn sites show very little selectivity of site oc-
cupancy. Besides, different geometries with ferromagnetic and anti-
ferromagnetic (AFM) configurations are found to be energetically
nearly degenerate, the difference in the total energies between ferro-
magnetic and antiferromagnetic solutions was found to be less than
3 meV per a formula unit. Still in most cases, the ferromagnetic solu-
tions are lower in total energy in comparison with the antiferromag-
netic solutions. However, for fully relaxed lattice we found that the
AFM ordering has lower total energy in comparison with the FM one.
3.2.2. XAS and XMCD Spectra
The X-ray absorption and X-ray magnetic circular dichroism of the di-
lute magnetic semiconductor (Zn, V)O at the V L2, 3 edges have been in-
vestigated by Ishida et al. [27]. They found that 90% of the V ions were
presumably strongly antiferromagnetically coupled, and the ferro-
magnetic component was below the detection limit of XMCD.
Since the real structure and chemical composition of (Zn1−xVx)O was
not known, we performed numerous calculations fitting XAS and
XMCD spectra to the experimental results. The fitting parameters
were positions of V atoms, Zn excess atoms, various oxygen vacancies
and the magnetic order of V atoms. The best fit is shown in Fig. 6,
which presents the calculated XAS as well as XMCD spectra of the
(Zn1−xVx)O DMS at the V L2,3 edges compared with the experimental da-
ta [27]. In this model, V atoms substitute cations and are antiferro-
magnetically ordered. Also, they are positioned at the largest possible
V1—V2 distance of 5.53 Å. Relevant XMCD signal occurs only in the
presence of an oxygen vacancy located in the first neighbourhood of
the second V2 atom along z direction. Adding Zn excess atoms also im-
proves the agreement between theory and experiment. The X-ray ab-
sorption spectrum at the V L3 edge is rather complicated and consists
of two major peaks c and d at 515.6 eV and 517 eV, respectively, with
two additional low energy shoulders a and b at 513.8 eV and 514.6 eV
and a high energy shoulder at 518 eV. As can be seen from the top panel
of Fig. 6, the calculations for the ideal crystal structure with two sub-
stitutional AFM ordered V1 atoms (full curve) provide the X-ray ab-
sorption intensity only at the peak c and the shoulder b. The full expla-
ELECTRONIC STRUCTURE AND X-RAY MAGNETIC CIRCULAR DICHROISM 11
nation of the spectra is only possible by considering crystal imperfec-
tions. We investigate the influence of two types of crystal defects on the
XAS and XMCD spectra, namely, oxygen deficiency and Zn excess. The
oxygen vacancy strongly affects the shape of the XAS spectra.
As can be seen from Fig. 6 (top panel), the X-ray absorption from the
V2 atoms with the oxygen vacancy (dashed line) contributes to the ma-
jor peak c and significantly determines the intensity of the peak d and
the high energy shoulder e. To investigate the Zn excess on the XMCD
spectra, we placed an extra Zn atom into the tetrahedral interstitial
position, which is 2.1916 Å apart from the V2 site. The X-ray absorp-
tion from the VZn atoms with the Zn excess atom (dotted line) contrib-
utes to the major peaks c and d as well as to both the low energy shoul-
ders a and b. Thereby, our simulation including oxygen deficiency and
Fig. 6. Top panel: theoretically calculated (thick full line) [48] and experimen-
tally measured [27] (circles) X-ray absorption spectra of (Zn1−xVx)O at the V
L2,3 edges. Full line presents the X-ray absorption spectrum without any addi-
tional defects. Dashed and dotted lines present the XA spectra with the oxy-
gen vacancy (the contribution of the V2 sublattice as in Fig. 1) and Zn excess
atom, respectively. Bottom panel: theoretically calculated (thick full line) and
experimentally measured [27] (circles) XMCD spectra at the V L2,3 edges.
Dashed and dotted lines present the XMCD spectra with the oxygen vacancy
and Zn excess atom, respectively.
12 L. V. BEKENOV, D. V. MAZUR, V. N. ANTONOV et al.
Zn excess reproduces the shape of the V L3 X-ray absorption spectrum
quite well (see thick curve in top panel of Fig. 6). The lattice relaxation
was found to be very important in the presence of the oxygen vacancy
as well as the Zn excess.
The XMCD spectrum at the V L3 edge is also rather complicated and
consists of a small positive peak at 513.8 eV, a negative fine structure at
514.6 eV, a negative major peak at 515.6 eV, and a positive major peak
at 517.7 eV with a shoulder at 516.4 eV. The V L2 XMCD spectrum con-
sists of two major fine structures, a negative peak at 521.8 eV and a pos-
itive one at 523.3 eV. The theory is not able to reproduce the shape and
relative intensity of the V L2, 3 XMCD spectra for the ferromagnetically
ordered V atoms, with one and two V substitutions per unit cell. The
theory strongly overestimates (from one to two orders of magnitude) the
dichroism signal and produces non-adequate shape of the spectra. On the
other hand, the theory produces an almost vanishing XMCD signal for
the AFM ordering of vanadium substitutional V ions for the ideal crys-
tal structure without any kind of defects due to cancellation of the
XMCD spectra with opposite spin directions. We should mention that
any shift from the antiferro- to the ferrimagnetic ordering will increase
the intensity of the final XMCD spectra due to the reduction of the com-
pensation of the XMCD spectra from V ions with opposite spin direc-
tions. Such a shift may be caused by an applied external magnetic field
or different kinds of defects and imperfections in the lattice. The exper-
imental measurements were performed in an external magnetic field of
7 T [27]. We have performed the calculations with an external magnetic
field applied along z direction and, indeed, obtained the spectra in-
crease, but only by approximately 10 to 20%. We found that only the
defects cause a significant difference. As can be seen from the lower
panel of Fig. 6, the theoretically calculated XMCD spectra with an oxy-
gen vacancy (dashed line) resemble the experimental spectra quite well.
An additional consideration of the Zn excess atoms (dotted curve) leads
to further improvement between the theory and the experiment. One
should mention that we obtain better agreement between the theory and
the experiment in the X-ray absorption rather than in the XMCD spec-
tra. The energy splitting between the two major peaks of the V L3 XMCD
spectrum was found to be smaller than the experimentally measured
one. The reproduction of the shape of the V L2,3 XMCD spectra is a quite
difficult task because the rather weak final XMCD signal is derived
from two large signals occurring from the V atoms with opposite spin
directions. In this case, we have to take into account different crystal
defects in a particular sample with quite precise relative concentration.
However, the type and concentration of possible defects in a sample is
not always well known. On the other hand, the extreme sensitivity of the
XMCD signal may be considered as a useful tool to reveal the details of
the composition by modelling numerically different types of defects and
ELECTRONIC STRUCTURE AND X-RAY MAGNETIC CIRCULAR DICHROISM 13
comparing the theoretically calculated XMCD spectra with the experi-
mentally measured ones.
3.2.3. Exchange Interactions
To describe the magnetic properties of (Zn1−xVx)O, we calculated ex-
change interactions between magnetic moments using the magnetic
force theorem as it is implemented within the multiple scattering theo-
ry [49]. The structural model, elucidated from our XAS and XMCD
simulations, was utilized for calculations of the corresponding elec-
tronic structure and exchange parameters using the KKR Green func-
tion method in the multiple scattering representation [50]. The sche-
matic representation of the exchange interaction between the magnetic
moments of the nearest neighbours is shown in Fig. 7.
The strongest magnetic interactions were found between V atoms
only if there is either an oxygen atom or an oxygen vacancy in between
(see Fig. 7, a and 7, b, respectively). Thereby, one can distinguish two
different vanadium atoms: V1 far from and V2 close to an oxygen va-
cancy. The exchange interaction between V1 and V2 atoms is very small
since the atoms are separated by 5.53 Å and there is no connecting at-
om in between. The V1—V1 exchange interaction is mediated mainly by
the oxygen between the vanadium atoms and is positive leading to a
ferromagnetic order in this pair (see
11
01
J at zero relaxation in Fig. 8, b).
This behaviour changes by replacing the oxygen by a vacancy (V2—V2
Fig. 7. Schematic representation of magnetic interactions between V atoms in
(Zn1−xVx)O: two V atoms substituting Zn positions with an oxygen in between
(a); two V atoms within an oxygen vacancy in between (b); V1—V2 pair (see the
text for explanation) (c). The dashed line in (b) shows ideal wurtzite structure.
14 L. V. BEKENOV, D. V. MAZUR, V. N. ANTONOV et al.
pair) in accordance to our structural model. Removing the oxygen atom
kills the exchange interaction between the neighbouring vanadium mo-
ments (see
22
01
J at zero relaxation in Fig. 8, b). However, the atoms
around the vacancy experience strong relaxations and this promotes an
antiferromagnetic order in this pair. Our simulations show that the ex-
change interaction is very sensitive to these atomic movements.
We found that the most substantial changes of Jij occur when the
neighbouring Zn atoms move towards the vacancy (see inset in Fig. 8),
while relaxations of V and O atoms are insignificant for the magnetic in-
teraction. According to our structural optimizations, the shift of the Zn
atoms is about 0.26 Å. Due to these relaxations, the exchange parameters
for the first neighbours
22
01
J were changed from 0 meV in the non-relaxed
geometry to −16 meV. The exchange interaction between the second
neighbours also experiences significant changes, and, in the relaxed ge-
ometry, it is positive. This suggests that the V2—V2 pair with an oxygen
vacancy is antiferromagnetic. The vanadium pairs V1—V1 without oxygen
vacancies remain ferromagnetic, although the value of the exchange pa-
rameters
11
01
J reduces from 5.8 meV in the non-relaxed case to 2.6 meV
after relaxation. The critical temperature, estimated within the random
Fig. 8. Critical temperatures (a) and exchange parameters (b) for (Zn1−xVx)O
calculated for various positions of atoms around an oxygen vacancy [48]. In-
set shows scheme of movements of Zn atoms towards the vacancy.
ELECTRONIC STRUCTURE AND X-RAY MAGNETIC CIRCULAR DICHROISM 15
phase approximation, is about 120 K in the relaxed geometry.
The most important question is why the relaxations of Zn atoms
around the vacancy lead to such substantial changes of magnetic inter-
actions. The Zn states are deep in the valence bands and do not hybridize
with the V states, which are located close to the Fermi level (see Fig. 5).
Relaxations of oxygen atoms were found to be very small and do not
change magnetic properties of (Zn1−xVx)O. However, the hybridization
between V 3d and oxygen 2p states is strongly affected by the relaxa-
tions of the Zn atoms, which is evidently crucial for the magnetic inter-
actions in this system. Our analysis of the density of states and occupa-
tion numbers yields a significant increase of the hybridization between
V 3d and O 2p states. This is governed by stronger d—d hybridization be-
tween Zn atoms moved towards the vacancy and, at the same time, due
to decreasing the hybridization between these Zn 3d and O 2p states.
4. SUMMARY
The theory reproduces the shape and energy positions of major fine
structures of the Co and Fe XAS and XMCD spectra at the L2,3 edges in
(Zn, Co)O and (Zn, Fe)O DMSs reasonably well. We show that oxygen
deficiency is responsible for some fine structures of the Co and Fe L3
XAS and XMCD spectra.
The shape of the V L2,3 XMCD spectra might be explained only by sug-
gesting the AFM ordering between the V ions situated at the largest pos-
sible V
↑
—V
↓
distance from each other. The XMCD signal appears as su-
perposition of very intensive dichroic signals from V ions with opposite
spin directions. The relevant XMCD signal is obtained only in the pres-
ence of an oxygen vacancy located in the first neighbourhood of the sec-
ond V atom. Adding extra Zn atoms improves the agreement between the
theory and the experiment. The lattice relaxation was found to be very
important in the presence of the oxygen vacancy as well as Zn excess.
The structure obtained from the comparison of the XMCD spectra
and theoretical simulations was used to study magnetic properties of
(Zn, V)O DMSs. Using the magnetic force theorem, as it is implemented
within the multiple scattering theory, we have calculated the exchange
interaction parameters for the V atoms. We have found that magnetic V
ions form two magnetic pairs, one ferromagnetic and another antifer-
romagnetic, which interact weakly with each other. The antiferromag-
netic order in one of the pairs is due to the presence of an oxygen vacan-
cy and strongly relaxed positions of neighbouring Zn atoms.
ACKNOWLEDGMENTS
This work was supported by the National Academy of Sciences of
16 L. V. BEKENOV, D. V. MAZUR, V. N. ANTONOV et al.
Ukraine in the framework of the State Target Scientific and Technolo-
gy Program of Implementation and Application of Grid Technologies
for 2009—2013.
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