1. Temperature induced in-plane/out-of-plane magnetization transition in ferromagnetic
Ga 0.93 Mn 0.07 As 0.94 P 0.06 / ( 100 ) GaAs thin films
M. Cubukcu, H. J. von Bardeleben, J. L. Cantin, and A. Lemaître
Citation: Applied Physics Letters 96, 102502 (2010); doi: 10.1063/1.3353997
View online: http://dx.doi.org/10.1063/1.3353997
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2. Temperature induced in-plane/out-of-plane magnetization transition
in ferromagnetic Ga0.93Mn0.07As0.94P0.06/„100…GaAs thin films
M. Cubukcu,1
H. J. von Bardeleben,1,a͒
J. L. Cantin,1
and A. Lemaître2
1
Institut des Nanosciences de Paris, UMR 7588 au CNRS, Université Pierre et Marie Curie,
140 rue de Lourmel, Paris, F-75015 Paris, France
2
Laboratoire de Photonique et Nanostructures, CNRS, Route de Nozay, 91460 Marcoussis, France
͑Received 12 January 2010; accepted 13 February 2010; published online 8 March 2010͒
Phosphorous alloying in the y=0.06 range allows to engineer ferromagnetic
Ga1−xMnxAs1−yPy/͑100͒GaAs thin films with standard x=0.07 Mn doping in which the easy axes
of magnetization can be changed from in-plane to out-of-plane by a small ͑10 K͒ temperature rise.
Ferromagnetic resonance investigations show the reorientation to be induced by the different
temperature dependence of the cubic and uniaxial anisotropy constants. © 2010 American Institute
of Physics. ͓doi:10.1063/1.3353997͔
Ferromagnetic Ga1−xMnxAs thin epitaxial layers have
been intensively studied in the past decade. Their magnetic
properties depend largely on the Mn and the related free hole
concentrations and are further modified by the postgrowth
annealing step required to obtain high critical temperatures.
The highest critical temperatures and magnetization values
were obtained for total Mn doping levels of x=0.10 which
can only be obtained in low temperature nonequilibrium
growth processes as the solubility of Mn is below x=0.01.
GaMnAs thin films are most often epitaxially grown on
͑100͒GaAs substrates. In this case, the lattice mismatch
linked to the Mn doping and the presence of intrinsic defects
introduces a compressive strain of ␧Ϸ0.3% leading to an
in-plane easy axis of magnetization.1–6
Out-of-plane easy
axis orientations can be obtained with GaInAs substrates
which give rise to tensile strain. However GaMnAs layers
grown on GaInAs have a low magnetic homogeneity due to
high dislocation densities. Recently, it has been shown that
additional alloying with phosphorous allows to modify the
epitaxial strain of ͑Ga,Mn͒͑As,P͒ films on ͑100͒ GaAs inde-
pendently from the Mn doping level. Thus Ga1−xMnxAs1−yPy
layers with either in-plane or out-of-plane easy axes of mag-
netizations can be obtained for Mn concentrations of x
=0.05, ... ,0.10.7–10
In particular, a choice of an intermediate
P doping level ͑y=0.06͒ allows to obtain layers with unique
properties; when their uniaxial anisotropy field just compen-
sates the demagnetization field switching of the magnetiza-
tion between in-plane and out-of-plane orientations becomes
possible by a small temperature rise or by application of a
small magnetic field. In this letter we report a combined
ferromagnetic resonance ͑FMR͒, and static magnetization
study of such layers in which we have investigated in detail
the magnetic anisotropies.
50 nm thick Ga1−xMnxAs1−yPy films were grown by low
temperature MBE on GaAs ͑100͒ substrates. The total Mn
concentration was set to x=0.07 and the phosphorous con-
centration to yϷ0.06.7
After the growth the sample was ther-
mally annealed under N2 atmosphere at 250° for 1 h. The
uniaxial strain ␧zz=͑aЌ−arel͒/arel determined by high reso-
lution x-ray diffraction is Ϫ0.11% after the annealing; aЌ is
the lattice parameter parallel to the growth axis and arel is the
lattice parameter of the relaxed layer. The transport proper-
ties were determined by Hall measurements. The magnetiza-
tion of the films was measured by a superconducting quan-
tum interference device. The magnetocrystalline anisotropy
constants and their temperature dependence were obtained
from x-band ͑9 GHz͒ FMR measurements.
In Fig. 1, we show the resistivity and magnetization of
an annealed Ga0.93Mn0.07As0.94P0.06 layer. The resistivity is
metallic with a value of Ϸ20 m ⍀ cm at 5 K in spite of the
P doping which shifts the Mn level deeper into the band gap.
The saturation magnetization at T=5 K is 42 emu/cm3
. The
critical temperature determined from the resistivity data is
TcϷ85 K.
In Fig. 2, we show the angular dependences of the uni-
form mode spectra in the ͑110͒ plane at several temperatures.
The magnetic anisotropy constants ͑Fig. 3͒ were determined
from a fit of these variations with the standard Smit–Beljers
formalism.11,12
The free energy expression used to determine
the anisotropy constants is as follows:
E = − MH · cos ␪ cos ␪H + sin ␪ sin ␪H cos͑␸ − ␸H͒
− 2␲M2
sin2
␪ − K2Ќ cos2
␪ −
1
2
K4Ќ cos4
␪
−
1
2
K4ʈ
͑3 + cos 4␸͒
4
sin4
␪ − K2ʈ sin2
␪ sin2
ͩ␸ −
␲
4
ͪ,
a͒
Electronic mail: vonbarde@insp.jussieu.fr.
0 30 60 90 120 150 180 210 240
0
10
20
30
40
50
Temperature (K)
Magnetization(emu/cm
3
)
1.8
2.1
2.4
2.7
3
ρρρρxx
(10
-2
ΩΩΩΩ.cm)
3.3
FIG. 1. ͑Color online͒ Magnetization as a function of temperature ͑square,
black͒ for a magnetic field H=1000 Oe applied parallel to ͓001͔ direction
͑left axis͒. Electrical resistivity ͑right axis͒ as a function of temperature
͑open circle, blue͒.
APPLIED PHYSICS LETTERS 96, 102502 ͑2010͒
0003-6951/2010/96͑10͒/102502/3/$30.00 © 2010 American Institute of Physics96, 102502-1This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
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3. where all symbols have their usual definition.5,12
The Landé
g-factor has equally been evaluated from the angular varia-
tion. It is different from g=2.00 and varies from g=1.91 at
4 K to 1.95 at 60 K. The assumption of a constant g-factor of
2.00 would have led to different K values. The corresponding
anisotropy fields ͑Fig. 3͒ defined as 2Ki/M can then be di-
rectly deduced. As shown in Fig. 3 at T=4 K we have the
for x=0.07 unusual situation that the cubic anisotropy fields
dominate the magnetic anisotropy; however, with increasing
temperature they decrease rapidly to zero and the perpen-
dicular uniaxial anisotropy field becomes dominant at T
Ͼ40 K. The perpendicular uniaxial field H2Ќ is comparable
but slightly inferior below 30 K and becomes superior above
this temperature. Its value is however small and positive
whereas a similar doped GaMnAs layer on ͑100͒ GaAs has
typical K2Ќ value of −70 000 erg/cm3
.
In FMR we observe at T=4 K an easy in-plane axis
along ͓100͔, which with increasing temperature switches at
T=40 K to an out of plane ͓001͔ direction. With increasing
temperatures the FMR spectra become quasi isotropic for
in-plane rotations.
The free energy density E at zero applied field can now
be calculated from these K values. In Fig. 4, we show E as a
function of the crystalline orientation for several tempera-
tures. These three-dimensional ͑3D͒ plots illustrate clearly
the change of the anisotropy from in-plane to out-of-plane
with the temperature. The in-plane anisotropy changes also
with temperature; the easy in-plane orientation shifts mo-
notonously from near ͓100͔ for T=4 K to1–10
T=60 K.
Figures 5 and 6 show the magnetization hysteresis
FIG. 4. ͑Color online͒ 3D plot of free energy densities at different tempera-
tures calculated from the anisotropy constants given in Fig. 3. Energy
minima occur near the ͓100͔ direction at 4 K and shift to the ͓001͔ direction
as the temperatures increases.
-400 -200 0 200 400
-40
-20
0
20
40
Magnetization(emu/cm3)
Magnetic Field (Oe)
4K
20K
60K
H//[001]
H1
H2
H3
FIG. 5. ͑Color online͒ Magnetization curves as a function of the magnetic
field applied along Hʈ ͓001͔; T=4 K ͑square, black͒, T=20 K ͑circle, red͒,
and T=60 K ͑triangle, blue͒.
-400 -200 0 200 400
-40
-20
0
20
40
Magnetization(emu/cm
3
)
Magnetic Field (Oe)
H//[100]
FIG. 6. ͑Color online͒ Magnetization curves as a function of the magnetic
field applied along Hʈ ͓100͔; T=4 K ͑square, black͒, T=20 K ͑circle, red͒,
and T=60 K ͑triangle, blue͒.
0 20 40 60 80 100
E(10
3
erg/cm
3
)
-25
-20
-15
-10
-5
H=500 Oe
H3
=180 Oe
H2
=140 Oe
θθθθ ((((degree))))
H=0 Oe
H1
=100 Oe
[001] [100]
FIG. 7. ͑Color online͒ Free energy density as the function of ␪ for different
values of a magnetic field H applied parallel to ͓001͔.
0 20 40 60 80 100 120 140 160 180
2600
2800
3000
3200
3400
3600
3800
4000
4200
[00-1][110]
MagneticField(Oe)
θθθθΗΗΗΗ
((((degree))))
4K
20K
40K
60K
[001]
FIG. 2. ͑Color online͒ Angular dependence of the FMR resonance field
͑symbols͒ in the out-of-plane configuration; the simulated angular variations
͑solid lines͒ are obtained from the coefficients given in Fig. 3 and the
g-values of g=1.91 at 4 and 20 K, g=1.93 at 40 K, and g=1.95 at 60 K.
0 20 40 60 80
0
4000
8000
12000
16000
20000
AnisotropyConstants(erg/cm3)
Temperature (K)
K2⊥⊥⊥⊥
K2////////
K4⊥⊥⊥⊥
K4////////
-200
0
200
400
600
800
1000
H2⊥⊥⊥⊥
H2////////
H4⊥⊥⊥⊥
H4////////
4ππππM
AnisotropyField(Oe)
FIG. 3. ͑Color online͒ Anisotropy constants ͑left͒ and anisotropy fields
͑right͒ as a function of temperature; the demagnetization field is equally
given. The symbols are experimental results; lines are guide for the eyes.
102502-2 Cubukcu et al. Appl. Phys. Lett. 96, 102502 ͑2010͒
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4. curves M͑H͒ with the magnetic field applied parallel to ͓001͔
or ͓100͔ for different temperatures T=4 to 60 K. For the easy
axis orientations ͓100͔ for TϽ40 K and ͓001͔ for T
Ն40 K we observe square loops with coercive fields vary-
ing from HC=45 Oe at 4 K to HC=3 Oe at 60 K. At T=4
and 20 K when the easy axis is in-plane the curves M͑H͒
with Hʈ ͓001͔ ͑Fig. 5͒ show a double loop characteristic of a
noncoherent magnetization reversal. This can be understood
as follows: at magnetic fields of 150 Oe the Zeeman term is
dominant and orients the magnetization out of plane; with
decreasing field strength the equilibrium orientation switches
gradually in the ͓100͔ direction—the easy axis for zero ap-
plied field—due to the influence of the magnetocrystalline
anisotropy fields. The corresponding free energy curves in
the ͑010͒ plane for different applied fields H1, H2, and H3 are
shown in Fig. 7. A similar behavior has already been re-
ported in low doped ͑Ga,Mn͒As layers with x=0.03 in which
a strain compensating intermediate GaInAs layer had been
grown.4
In such layers the uniaxial strain is also very weak
but the magnetization and critical temperatures of these lay-
ers are reduced by the low Mn content.
In summary, we have shown that P alloying allows to
obtain quaternary Ga1−xMnxAs1−yPy layers with x=0.07 in
which the easy axis of magnetization which is in-plane at
low temperatures TϽ20 K can be changed to out-of-plane
͓001͔ by raising the temperature or applying a small mag-
netic field of Ϸ102
Oe.
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