Exchange broadening of EPR line in ZnO:Co
We study the X-band EPR spectra of Co²⁺ in single crystalline Zn₁₋xCoxO (x = 0.001–0.075) thin films grown by plasma-assisted molecular beam epitaxy. By analyzing the EPR linewidth behavior we argue that the exchange-narrowing model, usually applied to Mn-based II-VI DMS, fails here and that a combi...
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| Cite this: | Exchange broadening of EPR line in ZnO:Co / P. Sati, V. Pashchenko, A. Stepanov // Физика низких температур. — 2007. — Т. 33, № 11. — С. 1222-1226. — Бібліогр.: 33 назв. — англ. |
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Sati, P. Pashchenko, V. Stepanov, A. 2010-04-08T12:14:29Z 2010-04-08T12:14:29Z 2007 Exchange broadening of EPR line in ZnO:Co / P. Sati, V. Pashchenko, A. Stepanov // Физика низких температур. — 2007. — Т. 33, № 11. — С. 1222-1226. — Бібліогр.: 33 назв. — англ. 0132-6414 PACS: 76.30.Fc PACS: 76.30.Fc https://nasplib.isofts.kiev.ua/handle/123456789/7713 We study the X-band EPR spectra of Co²⁺ in single crystalline Zn₁₋xCoxO (x = 0.001–0.075) thin films grown by plasma-assisted molecular beam epitaxy. By analyzing the EPR linewidth behavior we argue that the exchange-narrowing model, usually applied to Mn-based II-VI DMS, fails here and that a combined effect of exchange and dipolar broadening can explain the linewidth variation with Co content and temperature. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Exchange broadening of EPR line in ZnO:Co Article published earlier |
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Exchange broadening of EPR line in ZnO:Co |
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exchange broadening of epr line in zno:co |
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Sati, P. Pashchenko, V. Stepanov, A. |
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We study the X-band EPR spectra of Co²⁺ in single crystalline Zn₁₋xCoxO (x = 0.001–0.075) thin films grown by plasma-assisted molecular beam epitaxy. By analyzing the EPR linewidth behavior we argue that the exchange-narrowing model, usually applied to Mn-based II-VI DMS, fails here and that a combined effect of exchange and dipolar broadening can explain the linewidth variation with Co content and temperature.
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Exchange broadening of EPR line in ZnO:Co / P. Sati, V. Pashchenko, A. Stepanov // Физика низких температур. — 2007. — Т. 33, № 11. — С. 1222-1226. — Бібліогр.: 33 назв. — англ. |
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AT satip exchangebroadeningofeprlineinznoco AT pashchenkov exchangebroadeningofeprlineinznoco AT stepanova exchangebroadeningofeprlineinznoco |
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Fizika Nizkikh Temperatur, 2007, v. 33, No. 11, p. 1222–1226
Exchange broadening of EPR line in ZnO:Co
P. Sati1, V. Pashchenko2, and A. Stepanov1
1
Laboratoire Matériaux et Microélectronique de Provence, Case-142
Université Paul Cézanne and CNRS, 13397, Marseille Cedex 20, France
E-mail: anatoli.stepanov@L2MP.fr
2
Physikalisches Institut, Johann Wolfgang Goethe Universität, 1 Max-von-Laue-Strasse
Frankfurt am Main 60438 , Germany
Received March 3, 2007
We study the X -band EPR spectra of Co2 � in single crystalline Zn1�xCoxO (x = 0.001–0.075) thin films
grown by plasma-assisted molecular beam epitaxy. By analyzing the EPR linewidth behavior we argue that the
exchange-narrowing model, usually applied to Mn-based II-VI DMS, fails here and that a combined effect of
exchange and dipolar broadening can explain the linewidth variation with Co content and temperature.
PACS: 76.30.Fc Iron group (3d) ions and impurities (Ti–Cu).
Keywords: electron paramagnetic resonance, diluted magnetic semiconductors.
Diluted magnetic semiconductors (DMS), the mag-
netic properties of which are due to the substitution of
cations by transition-metal (TM) ions, have become a fo-
cus of considerable interest in recent years as essential
materials for practical semiconductor spintronic devices
such as spin filters [1] or spin polarizers [2]. The theoreti-
cal predictions based on the local spin density approxima-
tion (LSDA), triggered extensive studies of ZnO:TM al-
loys with a special focus on ZnO:Co as the most
promising candidate for a room-temperature ferromag-
netic (FM) semiconductor [3]. Many experiments have
been reported on this material fabricated by a variety of
methods [4–6]; however, the magnetic properties of
ZnO:Co still remain a controversial issue since the ob-
served magnetic behavior appears to be strongly depend-
ent on the preparation methods and is poorly reproduc-
ible. Ferromagnetism was reported for thin films and bulk
samples of ZnO:Co with a very large spread of spontane-
ous magnetic moment from 6.1 � B /Co to 0.01 � B /Co ac-
companied by a Curie temperature well above room tem-
perature [4–9]. At the same time the absence of
ferromagnetism and paramagnetic behavior down to
helium temperatures in ZnO:Co were claimed by many
authors [10–16].
On the theoretical side, LSDA has difficulties when
applied to the magnetic state of TM-doped ZnO, since it
does not account for correlations between d-electrons and
leads to a semimetallic FM ground state. Quite surpris-
ingly, an improved version of LSDA, LSDA + U also
leads to controversial results as regards the exchange con-
stant sign between Co 2 � ions in ZnO. Indeed, in their re-
cent paper, Chanier et al. [17] show that the exchange
constants, J out and J in , between nearest-neighbor (NN)
Co ions in the ZnO wurtzite structure are both negative
(AFM) and have the values �9 K and �21 K, respectively.
In contrast, Lee and Chang [18] and Sluiter et al. [19]
have detected a competition between FM J out and AFM
J in in Co-doped ZnO.
The EPR offers an interesting alternative to traditional
magnetic and optical methods providing complementary
information on the electronic properties of transition met-
als ions. For example, EPR is able to probe the exchange
interactions between TM ions by studying the well known
phenomenon of the exchange narrowing of an EPR line.
In this case a broadened line, say, by the magnetic dipole
interaction, �d , is narrowed by a fast dynamics resulting
from the exchange coupling, J . This gives finally a
linewidth �H /Jd� �
2 [20]. Interestingly, the exchange
narrowing picture explains the linewidth of various
Mn-based II-VI DMS at high temperatures [21]. It was
also established, that at low temperatures these DMS ex-
hibit, quite universally, a critical line broadening — a
phenomenon which is also driven by the exchange cou-
pling [22–24]. More recently, the exchange-narrowing
model was confirmed for Zn 1�xMn xO thin films having
various Mn contents [25,26]. To our knowledge, no
© P. Sati, V. Pashchenko, and A. Stepanov, 2007
detailed EPR investigations have been yet performed on
Zn 1�xCo xO.
In this paper we report the X -band EPR experiments
on Zn 1�xCo xO single crystalline thin films, performed in
a wide range of temperature and Co content, which were
undertaken in order to gain more insight into the role
played by the magnetic Co–Co interaction in ZnO:Co.
Zn 1�xCo xO thin films with x = 0.001–0.075 were
grown on sapphire substrates by plasma-assisted MBE
and had thicknesses of about 1�m, the c-axis of the wurt-
zite structure being perpendicular to the film plane. The
conductivity of the films was n-type, with residual carrier
concentrations ne � 10 18 cm �3.
We first discuss the magnetic properties of the studied
ZnO:Co films. The data were obtained using a commer-
cial SQUID magnetometer (Quantum Design MPMS) in
magnetic fields up to 50 kOe and in the temperature range
2 300� K. A pure ZnO film on a sapphire substrate and a
sample holder were examined separately and their signals
were subsequently subtracted from the total magnetic mo-
ment. The Co content x of the studied samples was deter-
mined by energy dispersive x-ray (EDX) microanalysis.
For the lowest concentration (x � 0 005. ), the x value was
determined by magnetic measurements.
In Fig. 1 we show the temperature dependence of the
inverse static magnetic susceptibility, � �1( )T , measured
at H �10 kOe and H c for x � 0 052. .
A linear increase of � �1( )T at higher temperatures can
be fitted to the Curie–Weiss law �
� � �1( ) ( ( )) / ( )T T x C x ,
with the usual notation for
( )x and C x( ). Note that the
curve in Fig. 1 is representative of many experiments in two
respects, namely, i) for all measured samples the sign of
is
found to be negative, ii) the continuous increase of
with x
is also observed.
The inset of Fig. 1 shows the magnetization of the
Zn1�xCoxO film with x � 0 052. as a function of magnetic
field at T � 2 K. As expected from the results on weakly
Co-doped ZnO films [27], M H( ) curves reveal a consid-
erable magnetic anisotropy of Co
2+
in the wurtzite lattice.
In order to probe the exchange interactions in ZnO:Co,
we have compared the experimental data with the results
of simulations in the framework of a cluster model. Our
conclusion is that both | |J in and | |J out exceed10 K and are
negative in ZnO:Co [28].
We turn now to our EPR results. The X -band EPR
spectra were recorded using a Bruker EMX spectrometer
equipped with a standard TE102 cavity and a continuous
helium flow cryostat that allows temperature scans be-
tween 4 and 300 K. The films with an area of 3 � 3 mm
were mounted on a quartz rod sample holder. The angle
between the c-axis of the films and the direction of the
static magnetic field H was controlled by a goniometer
with a precision better than � 0 25. � .
In Fig. 2 we present the low-temperature EPR spectra
of ZnO:Co samples with different Co 2 � concentration
measured at 9.4 GHz for H c| | . For the lowest x the reso-
Exchange broadening of EPR line in ZnO:Co
Fizika Nizkikh Temperatur, 2007, v. 33, No. 11 1223
T, K
50 100 200 250 300150
0
M
,
/C
o
�
B
0
10 20 30 40 50
2.0
1.5
1.0
0.5
H, kOe
4
3
2
1
�
–
1
3
–
3
,
1
0
m
o
l
cm
Fig. 1. Temperature dependence of the inverse magnetic sus-
ceptibility for a Zn1�xCoxO sample with x � 0052. taken at
H �10 kOe and H c . The solid line is the Curie–Weiss law.
The inset shows M vs H plot for the same sample at T � 2 K
and for H c|| and H c .
a
b
2800 2900 3000 3100 3200
x < 0.001
x = 0.003
x = 0.018
x = 0.052
x = 0.075
J = 0.0085 cm–1
J = 0.0295 cm–1
1500 2250 3000 3750 4500
H, Oe
Fig. 2. EPR spectra taken at 7 K and for H c|| on Zn1�xCoxO
films with different Co content. Note that the upper scale cor-
responds only to the sample with x � 0.001 (a). EPR spectrum
of the sample with x � 0003. shown on an enlarged scale. The
vertical bars indicate the positions of two exchange pair spec-
tra characterized by two different exchange constants (b).
nance spectrum consists of eight equally spaced compo-
nents resulting from the hyperfine interaction of the elec-
tron spin of Co 2 � and its nuclear spin, I � 7 2/ . The main
EPR spectrum originates from the low-lying doublet
S /z � � 1 2 of a S � 3 2/ ground-state manifold and its po-
sition is determined by the following spin Hamiltonian
�spin � � �� B z z z z zg H S DS A S I|| ||
2 , (1)
where g || .� 2 236, D � �2 76 1. cm and A || .�
� �16 1 10 4 1cm
were inferred from experiments for the lowest x
[27,29,30]. Additionally EPR spectra of Co 2 � exchange
pairs are observed and shown in detail in Fig. 2,b. (Details
of the pairs spectra interpretation will be published in our
forthcoming paper.) With increasing of the Co concentra-
tion the observed hyperfine structure (HFS) first becomes
poorly resolved, for x � 0 003. , and then completely disap-
pears for x � 0 02. due to a line broadening. This line
broadening is our main concern here.
In order to separate the linewidth caused by the HFS
from the total one we used the following procedure. The
observed EPR spectra were modeled by eight (2I+1)
Lorentzian components corresponding to the HFS transi-
tions. The resonance fields of the eight Lorentzian were
fixed by the position of the center of gravity of the
hyperfine octet in accordance with the observed g-factor.
Then, we calculate the individual position of each compo-
nent using A ||. The full width at half maximum, �H, of in-
dividual HFS components were adjusted to get the best
agreement with the recorded signal.
Fig. 3 shows the linewidth obtained in this way as a
function of both Co content and temperature. As it may be
seen from the inset of Fig. 3, �H grows almost linearly
with x. This is in significant disagreement with previ-
ously reported data on Mn-doped DMS. In this latter case
and at low x � 01. a rapid decrease of �H is observed sug-
gesting the exchange narrowing of an initially broadened
line. Another important feature of the observed linewidth
behavior is its temperature dependence shown in Fig. 3.
�H decreases as the temperature is decreased from 100 K
to 60 K and remains almost constant at temperatures
below � 60 K down to 4 K.
The fast decrease of �H T( ) can be naturally explained
by the temperature dependence of the spin lattice relax-
ation time of Co 2 � ions, since it is observed even at low-
est x. However, the «plateau» below 60 K has clearly a
magnetic origin. As we mentioned above, according to
previously reported EPR data on Mn-doped DMS, one
would expect that �H increases as the temperature is
decreased due to the fluctuations of antiferromagne-
tically coupled TM ions. Therefore the independence of
�H T( ) on temperature can be interpreted as the absence
of any such coupling between Co 2 � contributing to the
observed line.
It is clear that the exchange narrowing scenario is rather
unlikely in ZnO:Co, since simple estimates of �H xM /J� 2 ,
in the case where the second moment M 2, stems from the
magnetic dipole or Dzyaloshinskii–Moriya interaction, lead
to a negligible linewidth, which is about two orders of mag-
nitude smaller than the observed one.
The situation changes, however, if one considers M 2
arising from the single ion anisotropy �A . In this case
�H x D /J� ( )2 2 gives a linewidth of several kOe i.e. much
larger then the observed one. This is an indication that �A
of Co 2 � should be included in the unperturbed Hamil-
tonian �0 which determines the structure of the energy lev-
els between which the EPR absorption takes place. Here the
exchange modulation of a broadened line cannot be effec-
tive, because �A does not commute with �ex.
Kopvillem has developed a theory of the second moment
in the case where �0 includes the single ion anisotropy and
Zeeman terms �Z while the exchange and the dipole inter-
actions were considered as perturbations [31]. The underly-
ing physical picture is the following. The �A and �Z split
the energy spectrum of the spin system into a series of
quasi-discrete bands whose widths depend on the magnetic
dipole and exchange interactions among the paramagnetic
centers. In its turn the EPR spectrum splits up into a series of
fine-structure components corresponding to the magnetic
dipole transitions | , | ,S m S mS S� � � �1 . Under these con-
ditions the second moment is given by
M b P b J P J Pjk
k
jk jk jk2
2
1 2
2
3� � ��[ ] , (2)
where the summation is over all lattice sites, b jk �
� �( ) ( cos ( ))||3 2 1 32 2 2 3/ g /rB jk jk�
, J jk are the exchange
constants and Pi are numerical constants having the fol-
lowing values in the case of S � 3 2/ and the transition be-
tween m /S � � 1 2: P1 1125� . , P /2 3 4� � , P /3 3 8� .
The above formula clearly indicates that the exchange
and magnetic dipole interactions are responsible for a
linewidth broadening but it cannot be employed directly
to calculate the linewidth in ZnO:Co for the following
1224 Fizika Nizkikh Temperatur, 2007, v. 33, No. 11
P. Sati, V. Pashchenko, and A. Stepanov
�
H
,
O
e
500
400
300
200
100
0 20 40 60 80 100
T, K
g
||
�H
500
�
H
,
O
e
400
300
200
100
Co content
0
0.02 0.04 0.06 0.08
g
||
2.4
2.3
2.2
2.1
2.0
Fig. 3. Temperature dependence of the EPR linewidth for
x � 0018. . The inset shows �H (the left scale) and g || (the right
scale) in a function of the Co content.
reasons. As was pointed out by Kittel and Abrahams, in
the case of very diluted paramagnets (x �� 01. ), when only
the magnetic dipole interaction is taken into account, the
ratio M /M4 2
2 1�� (where M 4 is the fourth moment) and a
resonance line is better described by a cut-off Lorentzian
line with �H M�� 2
1 2/ [32]. The summation in the M 2 and
M 4 formulae, which have to be carried out over the occu-
pied sites only, is replaced by the sum over all crystal sites
so that both moments are proportional to the con-
centration of magnetic ions, as well as the linewidth
�H xM M� 2
3 2
4
1 2/ // .
To adapt this approach to the case treated in [31] one needs
an estimate of M 4 . Let us first note that the second moment (2)
is a sum of pair contributions coming from the dipole and ex-
change interactions between different Co 2 � sites. It is easy to
show that with the choice of �0 made above the perturbation
Hamiltonians, �ex and �d , will cause additional transitions at
frequencies �0 � �( )pJ qbjk jk , where �0 is the unperturbed
frequency and p and q are constants of the order of unity. Thus
M 2 is simply proportional to ( )pJ qbjk jk
k
�� 2 in agree-
ment with Kopvillem’s formula. Quite similarly the leading
term in M 4 , which is proportional to x, can be written as
( ) .p J qbjk jk
k
�� 4 Using these estimates one can recover a
linear dependence of the linewidth on the magnetic ion concen-
tration, �H x M� 2
1 2/ , which is in qualitative agreement with
our experimental data.
Another interesting point is the role played by the ex-
change interaction in the mechanism of linewidth forma-
tion. As we explained above, a pair of Co 2 � spins cou-
pled by the exchange constant J contributes to EPR
spectrum at frequencies (or magnetic fields) which are
proportional to this particular value of J . Hence if one
puts in (2), for example, J � 10 K (an estimate for the
nearest neighbor exchange integral in ZnO:Co) �H of the
order of several teslas will be obtained, which is certainly
meaningless. Therefore we should restrict the sum to
those pair contributions which do not exceed the experi-
mentally observed �H.
Some guidelines on how to do this provide our pair spec-
trum presented in Fig. 2,b. In fact the exchange-pair transi-
tions shown in this figure are both involved in the main reso-
nance line broadening, but the ones with J � �0 0295 1. cm ,
which are too far in the wings, do not contribute to the ob-
served linewidth. One can argue, by comparing the ex-
change constants obtained in this work with those found for
ZnO:Mn [33], that in the case of J � �0 0295 1. cm we are
dealing with fifth or sixth neighbor in the ZnO lattice. Thus,
we have arrived at an important conclusion that a large num-
ber of Co 2 � neighbors in ZnO lattice (n � 5) have no effect
on the observed linewidth. This could bring an explanation
for the experimentally established absence of strong
antiferromagnetic fluctuations at low temperatures in
ZnO:Co.
In summary, we have reported the X -band EPR studies
of single crystalline Zn 1�xCo xO (x = 0.001–0.075) thin
films grown by plasma-assisted molecular beam epitaxy.
By analyzing the EPR linewidth behavior, we show that a
combined effect of the exchange and dipolar broadening
plays an important role in the mechanism of linewidth
formation in this material.
The authors thank C. Deparis and C. Morhain for the
sample preparation. Two of us (V.P. and A.S.) dedicate
this article to the memory of their dear mentor, Anatolii
Illarionovich Zvyagin, an eminent scientist and wonder-
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