Transport and Magnetism in p-type cubic (Ga,Mn)N

Abstract

The electrical and magnetic properties of p-type cubic (Ga,Mn)N thin films grown by plasma-assisted molecular beam epitaxy are reported. Hole concentrations in excess of 1018 cm-3 at room temperature are observed. Activated behaviour is observed down to around 150K, characterised by an acceptor ionisation energy of around 45-60meV. The dependence of hole concentration and ionisation energy on Mn concentration indicates that the shallow acceptor level is not simply due to unintentional co-doping. Thermopower measurements on freestanding films, CV profilometry, and the dependence of conductivity on thickness and growth temperature, all show that the conduction is not due to diffusion into the substrate. We therefore associate the p-type conductivity with the presence of the Mn in the cubic GaN films. Magnetometry measurements indicate a small room temperature ferromagnetic phase, and a significantly larger magnetic coupling at low temperatures.

Full text

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Transport and Magnetism in p-type cubic (Ga,Mn)N
KW Edmonds, SV Novikov, M Sawicki1, RP Campion, C.R. Staddon, AD Giddings, LX
Zhao, KY Wang, T Dietl1, CT Foxon, BL Gallagher
School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United
Kingdom
1Institute of Physics, Polish Academy of Sciences, 02-668 Warszawa, Poland
The electrical and magnetic properties of p-type cubic (Ga,Mn)N thin films grown by
plasma-assisted molecular beam epitaxy are reported. Hole concentrations in excess of 1018
cm-3 at room temperature are observed. Activated behaviour is observed down to around
150K, characterised by an acceptor ionisation energy of around 45-60meV. The dependence
of hole concentration and ionisation energy on Mn concentration indicates that the shallow
acceptor level is not simply due to unintentional co-doping. Thermopower measurements on
freestanding films, CV profilometry, and the dependence of conductivity on thickness and
growth temperature, all show that the conduction is not due to diffusion into the substrate.
We therefore associate the p-type conductivity with the presence of the Mn in the cubic GaN
films. Magnetometry measurements indicate a small room temperature ferromagnetic
phase, and a significantly larger magnetic coupling at low temperatures.
Introduction
The emerging field of semiconductor spintronics relies on the ability to manipulate the
electron spin in a semiconductor device, thus offering new prospects for non-volatile high
speed information storage and processing. An important milestone in this field was the
discovery of carrier-mediated ferromagnetism in III-V compounds doped with Mn [1].
Intensive efforts have since led to ferromagnetic transition temperatures TC in excess of
150K in (Ga,Mn)As [2,3,4], and an impressive range of prototype devices [5,6,7]. However,
for widespread technological usage of these systems, a TC significantly above 300K is
necessary, which may yet require the development of new materials.
In this context, the Zener mean-field model prediction of room temperature
ferromagnetism in (Ga,Mn)N [8] stimulated much interest. However, an essential ingredient
of this model is a p-type carrier concentration of around 1020 cm-3, a value significantly
higher than the highest hole concentrations so far obtained in GaN. Furthermore, optical
measurements have indicated that the Mn acceptor level lies over 1eV above the valence
band maximum in Wurtzite (Ga,Mn)N [9,10], which is in agreement with density-of-states
calculations [11]. Therefore, in contrast to the case for (Ga,Mn)As, Mn does not appear to
be an efficient acceptor in Wurtzite GaN, and may not be expected to interact strongly with
delocalised charge carriers in the conduction or valence bands. In spite of this, there are
numerous observations of room temperature ferromagnetism in n-type (Ga,Mn)N, even in
cases where no secondary phases have been identified [12]. The origin of the
ferromagnetism in these cases is unresolved, but no conclusive evidence for a coupling
between magnetic and semiconductor properties has been demonstrated, and it appears that
this effect lies outside the Zener model prediction.
It may be expected that Mn incorporation is favoured in the metastable zincblende
(cubic) phase of GaN, since MnN is itself cubic with a similar lattice constant to GaN.

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Additionally, cubic GaN does not display the large polar effects associated with Wurtzite
material, which may influence incorporation. Even though the Mn level is also predicted to
lie deep in the gap in cubic (Ga,Mn)N [11,13], we recently demonstrated that this material
can be highly p-type, with carrier concentrations exceeding 1018 cm-3 at room temperature
[14]. Cubic (Ga,Mn)N may therefore be a more promising candidate than the Wurtzite
phase for room temperature carrier-mediated ferromagnetism. It is important to determine
the origin of the p-type conductivity and investigate the nature of the Mn state in this
material. Here we report on a detailed study of the electrical and magnetic properties of
cubic (Ga,Mn)N films grown on GaAs(001) by molecular beam epitaxy.
Growth and structure
Undoped cubic GaN films and cubic (Ga,Mn)N layers were grown on semi-insulating GaAs
(001) substrates by plasma-assisted molecular beam epitaxy (PA-MBE) using arsenic as a
surfactant to initiate the growth of cubic phase material [15]. Films where grown under N-
rich conditions, which has been found to be necessary for the effective substitutional
incorporation of Mn in hexagonal (Ga,Mn)N [16]. The substrate temperature was measured
using an optical pyrometer. Growth temperatures from 450 to 680oC were used. The active
nitrogen for the growth of the group III-nitrides was provided by an CARS25 RF activated
plasma source. The Mn concentration in the films was set using the in-situ beam monitoring
ion gauge, and calibrated by secondary ion mass spectrometry (SIMS). The growth was
monitored in-situ using RHEED.
Prior to the growth of active nitride layers, a GaAs buffer layer was grown on the
GaAs substrate in order to provide the cleanest possible interface between GaAs and
(Ga,Mn)N, although p-type conductivity was also observed in films in which the GaAs
buffer was absent. In order to ensure electrical isolation as well as rule out the possibility of
Mn diffusion into the GaAs layer being responsible for the observed electrical and magnetic
properties, an undoped cubic GaN (~150nm thick) buffer layer followed by a cubic AlN
buffer layer (50-150 nm thick) was introduced between the GaAs and cubic (Ga,Mn)N
layers in some samples.
The structural properties of the films were studied by x-ray diffraction, using a
Philips X’pert Materials Research Diffractometer. 2θ/ω curves for a series of 300nm thick
(Ga,Mn)N films grown directly on GaAs buffer layers on GaAs(001) are shown in figure 1.
These data confirm that the films are cubic phase and epitaxial with respect to the GaAs
substrate, with no peaks corresponding to hexagonal phase GaN visible. Above Mn
concentrations of around 5%, an additional peak is visible at around 46.4º, which may
correspond to inclusions of GaMn3N or Mn4N secondary phases. Unambiguous
identification of the secondary phase is not possible from this measurement, since GaMn3N
and Mn4N have nearly the same lattice parameter. Antiferromagnetic GaMn3N precipitates
have previously been observed in Wurtzite (Ga,Mn)N at high Mn concentrations [16].
Although Mn4N phases are not usually identified in MBE-grown (Ga,Mn)N, this is a known
room temperature ferromagnet, and undetected inclusions of this or other magnetic
secondary phases may be responsible for the room temperature ferromagnetic properties
observed here as well as elsewhere [17]. For the (Ga,Mn)N (002) reflection, no significant
shift in the peak position on varying the Mn concentration between zero and 10% can be
resolved, due to the large width of the 002 reflection. (Ga,Mn)N layers grown on cubic AlN
buffer layers on GaAs also show only the cubic x-ray diffraction peak, with no obvious
degradation of the structural quality resulting from the presence of the buffer layers.

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Transport properties
Four-point electrical measurements were performed on ~3x3mm squares with evaporated
Ti/Al/Ti/Au ohmic contacts in the corners. The contacts were annealed at 440ºC for five
minutes. Standard low frequency AC lock-in methods were used for the measurements, with
excitation currents typically in the range 100nA-1µA.
Hall effect measurements unambiguously reveal that the cubic (Ga,Mn)N samples
are p-type. In contrast, nominally undoped GaN films grown under the same N-rich
conditions are highly n-type, with n~2x1019 cm-3 at room temperature. Hole density and
mobility, obtained from room temperature Hall measurements in fields up to 0.7T, are
shown in figure 2 for samples both with and without AlN buffer layers. The hole density
pHall generally increases with increasing Mn up to ~4%, reaching a plateau or decreasing
slightly above this value. This plateau coincides with the appearance of a secondary phase in
the x-ray diffraction data discussed above. For samples grown with Mn concentration
around 0.5 to 1%, denoted by the hashed area in figure 2, we find that samples are highly
insulating, and the hole density and mobility cannot be measured accurately. Below 0.5%
Mn, samples grown directly on GaAs show a small Hall resistance which changes sign with
decreasing temperature, indicating the presence of parallel conducting n- and p-type regions,
while for samples grown on cubic AlN buffer layers, only p-type conduction is observed. In
the conducting samples, the mobility µHall is consistently in the range 200-350 cm2V-1s-1,
comparable to or larger than the values obtained elsewhere for carbon doped p-type cubic
GaN [18]. The origin of the observed conducting-insulating-conducting behaviour with
increasing Mn concentration is presently unknown, but is reproducible.
The variation of room temperature Hall hole density and mobility in the cubic
(Ga,Mn)N layers with growth temperature for constant Mn flux is shown in figure 3. As is
evident from figures 2 and 3, the p-type behaviour depends on the Mn concentration, but is
robust against changes to other growth conditions. Samples grown at temperatures between
450 and 680°C, and also with varying thickness of AlN or GaAs buffer layers, show no
systematic variation in the obtained values of hole density and mobility. In addition, we
have investigated the effect of varying the film thickness. For thicknesses below around
100nm, the conductivity is significantly decreased, which can be ascribed to the increased
influence of interfacial defects. However, for thicker films the conductivity is almost
independent of the film thickness, showing that the p-type conductivity is a bulk property of
the (Ga,Mn)N films rather than being due to surface or interface layers.
Having established the p-type conductivity in the cubic (Ga,Mn)N layers, it is
important to discuss its origin. Aside from Mn, possible p-type dopants in GaN include Mg,
Be, and C. Mg or Be contamination can be ruled out as there is no source of Mg or Be in the
growth chamber. SIMS measurements identify the presence of unintentional C and O
doping in the films, with concentrations in the range 1019-1020cm-3. C is a known p-type
dopant in cubic GaN [18]. However, we find n-type conductivity in layers grown without
Mn but with similar background C levels. This is a strong indication that the p-type
conductivity is associated with the presence of Mn.
Since Mn is a well-known p-type dopant in GaAs, parallel conduction due to
diffusion into the substrate must be considered. The absence of any systematic dependence
of the p-type conductivity on thickness, growth temperature, or the presence of AlN buffer

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layers is strong, if not conclusive, evidence against this. To further investigate this
possibility, the conduction in the layers close to the surface of the films was investigated by
capacitance-voltage profilometry. This yielded a carrier density in the top ≈50nm which is
comparable to the value obtained from Hall measurements. However, this technique is
rather sensitive to input parameters and film roughness so again cannot be considered
conclusive. As a final test, the GaAs substrate was etched away in H2O2:H3PO4 solution.
Following etching, the films tended to either crack or roll into cylinders due to the very
large strain. Four-point Hall measurements could not be performed on such films. However,
electrical contacts could be formed at either end of the cylinders using Ag epoxy. The
cylinders were found to be electrically conducting, with a room temperature resistance of
around 105Ω, comparable to the value obtained in unetched films where contacts were made
by this method. Seebeck effect measurements were performed on the (Ga,Mn)N cylinders,
by placing one end of the cylinders in contact with a heated metal probe. The thermoelectric
power was positive for our (Ga,Mn)N cylinders, which demonstrates that the freestanding
(Ga,Mn)N layers are p-type. Measurements on p- and n-type GaAs and GaN control
samples in the same experimental set-up yielded the expected positive and negative sign of
thermoelectric power, respectively. This confirms that the measured p-type conductivity is
due to the cubic (Ga,Mn)N layer, and not due to diffusion into the GaAs substrate.
Figure 4 shows the temperature-dependence of pHall and µHall in three cubic
(Ga,Mn)N films on AlN, with varying Mn concentration. For all three films, pHall shows
activated behaviour above around 150K, while the mobility increases with decreasing
temperature, indicating that phonon scattering is dominant in this regime. The rate of
decrease of pHall is slower than is typically observed in either Mg-doped Wurzite GaN
[19,20,21,22] or C-doped zincblende GaN [18], which indicates that the acceptor level is
rather shallow in the present samples. We can quantify this using the standard expression:
p pN
NNp
ad
()
−−
where Ea is the acceptor ionisation energy, Na and Nd are the acceptor and donor densities,
ga is the acceptor degeneracy which we set equal to 4, and Nv is the effective valence band
density of states, given by
Nm k Th
v h B
= 2 2()/
π
The hole effective mass in GaN, mh*, is not well known, but is typically found to be in the
range 1-2mo [23,24,25]. Here we use an intermediate value of 1.5m0, although the choice of
mh* does not affect the value of ∆Ea obtained by fitting the experimental data.
NgE k T
B
d
vaa
()
(/ )exp(/)
+
= −∆
(1)
3 2/3*
(2)
From the measured Hall hole densities we obtain values of ∆Ea of around 45-
60meV, which decreases with increasing Mn concentration, as shown in the inset to figure
4. This compares to ∆Ea=215meV [18] for C in cubic GaN. A decreasing ∆E with
increasing acceptor concentration, as found here, is commonly observed in p-type GaN
[21,22]. Na and Nd cannot be separately extracted from this fitting procedure, although we
obtain the difference (Na-Nd) in the range 1018-1019 cm-3. This is two orders of magnitude
smaller than the Mn concentration measured by SIMS, suggesting that only a fraction of
incorporated Mn is electrically active. We expect that compensation is very large in these
samples, since nominally undoped samples grown under otherwise identical conditions are
strongly n-type, with Nd~1020 cm-3. The values obtained from the above fitting procedure
should be viewed with caution, since the above equations neglect acceptor level broadening,
screening of the acceptors by valence holes, and non-parabolicity of the valence band edge,
all of which may be important at these high impurity densities [21,22]. However, the

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remarkably low value of ∆Ea obtained, together with its dependence on Mn concentration,
provides further evidence that the p-type conductivity in these samples is related to the
presence of Mn, rather than simply being due to unintentional co-doping by carbon.
At the lowest Mn concentration, freeze-out of carriers occurs rapidly with decreasing
temperature, and the conductivity becomes too low to accurately measure below around
220K. At higher concentrations, a change of slope of pHall is observed at around 150K.
Deviations from activated behaviour at low temperatures are frequently observed in p-type
GaN in which there is significant compensation [19-22], and are usually ascribed to the
onset of impurity band conduction [26]. In systems with competing valence and impurity-
band conduction, the measured pHall has a minimum value at the temperature where the
conductivity of the valence and impurity band channels is equal, followed by an increase up
until pHall is equal to the impurity band density, which is usually temperature-independent
[26]. The measured pHall can be expressed as a weighted sum of two terms:
pp
pp
+µµ
12
where µ1, µ2, p1 and p2 are respectively the mobility and density of valence and impurity
band carriers.
p
Hall=
+
()
µµ
1 122
2
1222
(3)
In the present case, qualitatively different behaviour is observed to those reported in,
e.g. refs [19-22]. pHall reaches a plateau at around 150K, and then at lower temperatures
decreases further, although more slowly than observed at higher temperatures. This
behaviour can also be reproduced using the expression above, but only if pVB and pIB are
both thermally activated (rather than metallic). Figure 5 shows a fit to the data in figure 4
for the sample with 4.2% Mn, with p1 given by equation 1 and p2 = p0 exp(-∆E2/kBT). We
obtain a good agreement with experiment using ∆Ea=50meV, ∆Ε2=15meV, µ1/µ2=10, and
assuming that the ratio of mobilities is independent of temperature.
The activated carrier density, together with the not too dissimilar mobilities between
the two channels, suggests that p2 may not be associated with an impurity band in the
present case. The origin of this second conducting channel in these samples is not clear;
however it is unlikely to be associated with an interfacial layer, since quantitatively similar
behaviour is observed, at this Mn concentration, between samples grown with and without
the AlN buffer layer.
Magnetic properties
Magnetic measurements are performed in a SQUID magnetometer, with magnetic fields of
up to 4000Oe applied in the plane of the sample. Room temperature SQUID measurements
for a 4.2% cubic (Ga,Mn)N/AlN/GaAs(001) sample are shown in figure 6. A temperature-
independent linear background due to the diamagnetic substrate has been subtracted from
the data. Similar to earlier reports of magnetism in (Ga,Mn)N, we find a ferromagnetic
signal in all the cubic (Ga,Mn)N films studied here, which persists above 400K. Comparing
the measured room temperature ferromagnetism to the Mn concentration measured by
SIMS, we obtain a magnetic moment of only around 0.1 µB / Mn, indicating that most of the
Mn in the sample is not contributing to the room temperature coupling. The origin of this
signal is not presently known, however it has been noted that there are several MnxNy
phases which have a ferromagnetic transition temperature above room temperature [17],
which could account for the observed behaviour. Here we take the view that, in order to

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understand the magnetic properties of (Ga,Mn)N, it is important to study the system as a
whole rather than concentrating only on the small room temperature ferromagnetic part (we
note however that the opposite approach is frequently taken in the experimental literature
surrounding (Ga,Mn)N). We therefore study the behaviour at low temperatures, in order to
investigate the part of the Mn magnetic moment which does not take part in the high
temperature coupling.
The high temperature ferromagnetic phase appears to be temperature-independent
below around 200K. Therefore, subtracting magnetisation curves measured at 50K from
those measured at lower temperatures should allow us to identify the magnetic behaviour of
the remainder of the film. This procedure is followed in figure 7. At low Mn concentration
(0.3%), the relative magnetisation ∆M(H,T)=M(H,T)-M(H,50K) is linear with the external
magnetic field both at 15K and 5K, characteristic of paramagnetic behaviour. Different
behaviour is observed at 4.2% Mn concentration. A large increase of the magnetisation is
observed on going from 15K to 5K, with a clear hysteresis. The effect develops further on
lowering of the temperature to 2 K. This is a clear indication of a magnetic coupling
between the Mn ions in this sample. Similar magnetisation curves have been reported for
insulating hexagonal (Ga,Mn)N films [27], interpreted as having spin-glass characteristics.
The glassy behaviour was ascribed to antiferromagnetic superexchange interactions between
the substitutional Mn, which are naturally frustrated within the Wurzite lattice. The
zincblende lattice also allows for frustrated antiferromagnetism [28], however the Mn
concentration in the present case seems too low to expect significant nearest-neighbour
interactions.
On the other hand, the present samples exhibit p-type conduction, which is expected
to favour a ferromagnetic alignment of substitutional Mn. Indeed, the magnetisation curves
of figure 7 are reminiscent of those observed for highly p-type (Zn,Mn)Te single crystals
[29]. Even though the samples of ref. [29] exhibited insulating behaviour at low
temperatures, recent inelastic neutron measurements indicated local ferromagnetic ordering
mediated by weakly localised holes [30]. However, other mechanisms may also give rise to
ferromagnetic ordering at low temperatures in p-type materials, including percolation of
bound magnetic polarons [31], or virtual transitions between valence and impurity bands
[32]. Clearly, more work is required to resolve this issue.
Summary
We have clearly demonstrated p-type conduction in cubic (Ga,Mn)N films grown on
GaAs(001) by PA-MBE. Temperature-dependent Hall measurements indicate that the
acceptor ionisation energy is around 50meV, which is shallower than any known acceptor
level in GaN. The dependence of hole concentration and ionisation energy on the Mn
concentration demonstrates than the shallow acceptor level is related to the presence of Mn,
although the hole concentration is around two orders of magnitude smaller than the Mn
concentration measured by SIMS, probably due to the presence of a large n-type
background doping. The p-type conduction is in contrast to the n-type behaviour more
usually found in Wurtzite (Ga,Mn)N, and is an essential ingredient for Zener-like carrier-
mediated ferromagnetism [8]. Much higher hole concentrations will be necessary to realise
the predicted room temperature ferromagnetism according to this model, however the
present result suggests that cubic (Ga,Mn)N may be a good candidate system to achieve
this. Magnetometry results show the presence of a magnetic ordering at low temperatures

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(~10K), which is reminiscent of the ferromagnetism mediated by weakly localised holes in
(Zn,Mn)Te, and thus may be related to the p-type conduction.
Acknowledgements
The work was supported by EU projects FENIKS (EC: G5RD-CT-2001-00535) and
CELDIS (ICA1-CT-2000-70018), the EPSRC (UK), and Polish KBN grant PBZ-KBN-
044/P03/2001. KWE is supported by the Royal Society (UK). We thank Jas Chauhan and
Dave Taylor for processing the van der Pauw samples and for etching of the freestanding
layers. Valuable discussions with Tomas Jungwirth, Henri Mariette, Joel Cibert, David
Ferrand, Piotr Bogusławski, Maria Kaminska, and Andrzej Twardowski are acknowledged.
Figure 1. ω-2θ plots of 300nm thick (Ga,Mn)N films on GaAs(001), with Mn
concentrations 0.22%, 2.5%, 6.6%, 10%.
2030 4050 60 70
1
10
100
1000
Counts per sec
ω/2θ

0.22%



1
10
100
1000
2.5%



1
10
100
1000
6.6%



1
10
100
1000
GaAs
(004)
GaAs
(002)
β β β β-GaN
(002)
10%

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Figure 2. Room temperature Hall hole density and mobility versus Mn concentration for
(Ga,Mn)N/GaAs (squares) and (Ga,Mn)N/AlN/GaAs (circles). For both series, samples
grown with Mn concentration close to 1%, marked by the hashed region in each figure, are
found to have either very low conductivity or be fully insulating at room temperature.
0246810
1E16
1E17
1E18
02468 10
0
100
200
300
Hole mobility, µHall (cm
2V
-1s
-1)


Hole density, pHall (cm-3)
(Ga,Mn)N/GaAs
(Ga,Mn)N/AlN/GaAs

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400 500 600700
1E16
1E17
1E18
0
100
200
300

Hole density, p / cm
-3
Growth Temperature (K)
Hole mobility (cm
2V
-1s
-1)
Figure 3. Room temperature Hall hole density and mobility versus growth temperature for a
series of cubic (Ga,Mn)N films on GaAs.

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Figure 4. (a) Hole density, and (b) hole mobility, extracted from Hall measurements, versus
temperature for cubic (Ga,Mn)N layers on AlN buffers on GaAs(001), for Mn
concentrations 4.2% (filled squares), 2.5% (open squares) and 0.22% (circles). The lines in
(a) indicate the fitted curves to the activated hole densities, as described in the text. Inset of
(a): acceptor ionisation energies extracted from the fits.
1E16
1E17
1E18
0
24
40
50
60
70
(a)
∆Ea (meV)
Mn concentration (%)


pHall (cm-3)




0.00 0.010.02
-1)
0.03
100
1000
10000
(b)
µHall (cm2V-1s-1)


1/T (K

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Figure 5. Measured hole density for (Ga,Mn)N/AlN/GaAs(001) (points); calculated pHall
assuming two activated contributions p1 and p2 (lines).
0.000 0.005 0.010 0.015 0.020 0.025
1/T (K
1E15
1E16
1E17
1E18
p2
p2


pHall (cm-3)
-1)

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Figure 6. Magnetisation hysteresis curves for a cubic (Ga,Mn)N/AlN/GaAs(001) sample
with 4.2% Mn, after substracting a linear background due to the diamagnetic substrate.
-3000 -2000 -10000 10002000 3000
-3
-2
-1
0
1
2
3
250K
2K


M (emu)
H (Oe)

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Figure 7. Magnetisation after removing the high TC contribution, ∆M(T)=M(T)-M(50K)
versus magnetic field, for temperature T=5K and 15K, for (Ga,Mn)N samples with Mn
concentration 0.3% (upper panel) and 4.2% (lower panel).
-20000 20004000
-2
0
2
4
2K
15K
5K
4.2% Mn


Magnetisation (emu)
H (Oe)
-0.2
-0.1
0.0
0.1
0.2
15K
5K
0.3% Mn

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1 H. Ohno, H. Munekata, T. Penney, S. von Molnar, and L.L. Chang, Phys. Rev. Lett. 68, 2664
(1992)
2 K.C. Ku, S.J. Potashnik, R.F. Wang, S.H. Chun, P. Schiffer, N. Samarth, M.J. Seong, A.
Mascarenhas, E. Johnson-Halperin, R.C. Myers, A.C. Gossard, and D.D. Awschalom, Appl. Phys.
Lett. 82, 2302 (2003)
3 D Chiba, K. Takamura, F. Matsukura, and H. Ohno, Appl. Phys. Lett. 82, 3020 (2003)
4 KW Edmonds, P. Boguslawski, K.-Y. Wang, R.P. Campion, N.R.S. Farley, B.L. Gallagher, C.T.
Foxon, M. Sawicki, T. Dietl, M.B. Nardelli, and J. Bernholc, Phys. Rev. Lett. 92, 037201 (2004)
5 H. Ohno, D. Chiba, F. Matsukura, T. Omiya, E. Abe, T. Dietl, Y. Ohno, and K. Ohtani, Nature
408, 944 (2000)
6 Y. Ohno, D.K. Young, B. Beschoten, F. Matsukura, H. Ohno, and D.D. Awschalom, Nature 402,
790 (1999)
7 C. Rüster, T. Borzenko, C. Gould, G. Schmidt, L.W. Molenkamp, X. Liu, T.J. Wojtowicz, J.K.
Furdyna, Z.G. Yu, and M.E. Flatte, Phys. Rev. Lett. 91, 216602 (2003)
8 T. Dietl, H. Ohno, F. Matsukura, J. Cibert, and D. Ferrand, Science 287, 1019 (2000)
9 R.Y. Korotkov, J.M. Gregie, and B.W. Wessels, Appl. Phys. Lett. 80, 1731 (2002)
10 T. Graf, M. Gjukic, M.S. Brandt, M. Stutzman, and O. Ambacher, Appl. Phys. Lett. 81, 5159
(2002)
11 B. Sanyal, O. Bengone, and S. Mirbt, Phys. Rev. B 68, 205210 (2003)
12 S.J. Pearton, J. Appl. Phys. 93, 1 (2003) and references therein
13 A. Janotti, S.-H. Wei, and L. Bellaiche, Appl. Phys. Lett. 82 766 (2003)
14 S.V. Novikov, K.W. Edmonds, A.D. Giddings, K.Y. Wang, C.R. Staddon, R.P. Campion, B.L.
Gallagher, and C.T. Foxon, Semicond. Sci. Technol. 19, L13 (2004)
15 T.S. Cheng, L.C. Jenkins, S.E. Hooper, C.T. Foxon, J.W. Orton and D.E. Lacklison, Appl. Phys.
Lett. 66, 1509 (1995)
16 S. Kuroda, E. Bellet-Amalric, R. Giraud, S. Marcet, J. Cibert, and H. Mariette, Appl. Phys. Lett.
83, 4580 (2003)
17 M. Zając, J. Gosk, E. Grzanka, M. Kaminska, A. Twardowski, B. Strojek, J. Szczytko, and S.
Podsiadlo, J. Appl. Phys. 93, 4715 (2003)
18 D.J. As, U. Kohler, M. Lubbers, J. Mimkes, and K. Lischka, Physica Status Solidi A 188, 699
(2001); ibid., J. Phys. Condens. Matter (2001)
19 T. Tanaka, A. Watanabe, H. Amano, Y. Kobayashi, I. Akasaki, S. Yamazaki, and M. Koike, Appl.
Phys. Lett. 65, 593 (1994)
20 W. Gotz, N.M. Johnson, J. Walker, D.P. Bour, and R.A. Street, Appl. Phys. Lett. 68, 667 (1996)
21 P. Kozodoy, H. Xing, S.P. DenBaars, U.K. Mishra, A. Saxler, R. Perrin, S. Elhamri, and W.C.
Mitchell, J. Appl. Phys. 87, 1832 (2000)
22 D. Lancefield and H. Eshghi, J. Phys. Condens. Matter 13, 8939 (2001)
23 K. Kim, W.R.L. Lambrecht, B. Segall, and M. van Schilfgaarde, Phys. Rev. B 56, 7363 (1997)
24 M. Suzuki and T. Uenoyama, Jpn. J. Appl. Phys. 1 34, 3442 (1995)
25 J.S. Im, A. Moritz, F. Steuber, V. Harle, F. Scholz, and A. Hangleiter, Appl. Phys. Lett. 70, 631
(1997)
26 D.A. Woodbury and J.S. Blakemore, Phys. Rev. B 8, 3803 (1973)
27 S. Dhar, O. Brandt, A. Trampert, K.J. Friedland, Y.J. Sun, and K.H. Ploog, Phys. Rev. B 67,
165205 (2003)
28 J.K. Furdyna, J. Appl. Phys. 64, 29 (1988)
29 M. Sawicki, L. van Khoi, L. Hansen, D. Ferrand, L.W. Molenkamp, A. Waag, and T. Dietl, Phys.
Stat. Sol. B 229, 717 (2002)
30 H. Kępa, V.K. Le, C.M. Brown, M. Sawicki, J.K. Furdyna, T.M. Giebultowicz, and T. Dietl, Phys.
Rev. Lett. 91, 087205 (2003)
31 A.C. Durst, R.N. Bhatt, and P.A. Wolff, Phys. Rev. B 65, 235205 (2002)
32 V.I. Litvinov and V.K. Dugaev, Phys. Rev. Lett. 86, 5593 (2001)