Temperature dependences of surface magnetoelastic constants of ultrathin Fe/GaAs (001) films
The magnetoelastic constants of epitaxial iron films prepared by dc magnetron sputtering on single crystal GaAs (001) substrate in argon atmosphere and covered with a protective Si layer have been investigated in the temperature range 10–300 K by means of the strain modulated ferromagnetic resonan...
Збережено в:
| Дата: | 2012 |
|---|---|
| Автори: | , , , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2012
|
| Назва видання: | Физика низких температур |
| Теми: | |
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/117614 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Temperature dependences of surface magnetoelastic constants of ultrathin Fe/GaAs (001) films / R. Żuberek, K. Nesteruk, K. Fronc, S. Piechota, H. Szymczak // Физика низких температур. — 2012. — Т. 38, № 9. — С. 1058-1061. — Бібліогр.: 20 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-117614 |
|---|---|
| record_format |
dspace |
| spelling |
nasplib_isofts_kiev_ua-123456789-1176142025-02-23T19:26:19Z Temperature dependences of surface magnetoelastic constants of ultrathin Fe/GaAs (001) films Żuberek, R. Nesteruk, K. Fronc, K. Piechota, S. Szymczak, H. К 80-летию Виктора Валентиновича Еременко The magnetoelastic constants of epitaxial iron films prepared by dc magnetron sputtering on single crystal GaAs (001) substrate in argon atmosphere and covered with a protective Si layer have been investigated in the temperature range 10–300 K by means of the strain modulated ferromagnetic resonance. It has been shown that the magnetoelastic constants strongly depend on the thickness of the film. The surface components of the magnetoelastic constants have been determined and analyzed within the Néel and dipolar models. The proposed analysis of experimental data gives chance for deeper insight into mechanisms responsible for magnetostriction of iron thin films. The work was supported in part by Polish MNiSW 2048/B/H03/2008/34 grant. The substrates of GaAs supplied by Institute of Electronic Materials Technology are kindly acknowledged. 2012 Article Temperature dependences of surface magnetoelastic constants of ultrathin Fe/GaAs (001) films / R. Żuberek, K. Nesteruk, K. Fronc, S. Piechota, H. Szymczak // Физика низких температур. — 2012. — Т. 38, № 9. — С. 1058-1061. — Бібліогр.: 20 назв. — англ. 0132-6414 PACS: 75.70.Cn, 75.80.+q, 75.70.Ak https://nasplib.isofts.kiev.ua/handle/123456789/117614 en Физика низких температур application/pdf Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| topic |
К 80-летию Виктора Валентиновича Еременко К 80-летию Виктора Валентиновича Еременко |
| spellingShingle |
К 80-летию Виктора Валентиновича Еременко К 80-летию Виктора Валентиновича Еременко Żuberek, R. Nesteruk, K. Fronc, K. Piechota, S. Szymczak, H. Temperature dependences of surface magnetoelastic constants of ultrathin Fe/GaAs (001) films Физика низких температур |
| description |
The magnetoelastic constants of epitaxial iron films prepared by dc magnetron sputtering on single crystal
GaAs (001) substrate in argon atmosphere and covered with a protective Si layer have been investigated in the
temperature range 10–300 K by means of the strain modulated ferromagnetic resonance. It has been shown that
the magnetoelastic constants strongly depend on the thickness of the film. The surface components of the
magnetoelastic constants have been determined and analyzed within the Néel and dipolar models. The proposed
analysis of experimental data gives chance for deeper insight into mechanisms responsible for magnetostriction
of iron thin films. |
| format |
Article |
| author |
Żuberek, R. Nesteruk, K. Fronc, K. Piechota, S. Szymczak, H. |
| author_facet |
Żuberek, R. Nesteruk, K. Fronc, K. Piechota, S. Szymczak, H. |
| author_sort |
Żuberek, R. |
| title |
Temperature dependences of surface magnetoelastic constants of ultrathin Fe/GaAs (001) films |
| title_short |
Temperature dependences of surface magnetoelastic constants of ultrathin Fe/GaAs (001) films |
| title_full |
Temperature dependences of surface magnetoelastic constants of ultrathin Fe/GaAs (001) films |
| title_fullStr |
Temperature dependences of surface magnetoelastic constants of ultrathin Fe/GaAs (001) films |
| title_full_unstemmed |
Temperature dependences of surface magnetoelastic constants of ultrathin Fe/GaAs (001) films |
| title_sort |
temperature dependences of surface magnetoelastic constants of ultrathin fe/gaas (001) films |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2012 |
| topic_facet |
К 80-летию Виктора Валентиновича Еременко |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/117614 |
| citation_txt |
Temperature dependences of surface magnetoelastic
constants of ultrathin Fe/GaAs (001) films / R. Żuberek, K. Nesteruk, K. Fronc, S. Piechota, H. Szymczak // Физика низких температур. — 2012. — Т. 38, № 9. — С. 1058-1061. — Бібліогр.: 20 назв. — англ. |
| series |
Физика низких температур |
| work_keys_str_mv |
AT zuberekr temperaturedependencesofsurfacemagnetoelasticconstantsofultrathinfegaas001films AT nesterukk temperaturedependencesofsurfacemagnetoelasticconstantsofultrathinfegaas001films AT fronck temperaturedependencesofsurfacemagnetoelasticconstantsofultrathinfegaas001films AT piechotas temperaturedependencesofsurfacemagnetoelasticconstantsofultrathinfegaas001films AT szymczakh temperaturedependencesofsurfacemagnetoelasticconstantsofultrathinfegaas001films |
| first_indexed |
2025-11-24T16:06:10Z |
| last_indexed |
2025-11-24T16:06:10Z |
| _version_ |
1849688452896915456 |
| fulltext |
© R. Żuberek, K. Nesteruk, K. Fronc, S. Piechota, and H. Szymczak, 2012
Low Temperature Physics/Fizika Nizkikh Temperatur, 2012, v. 38, No. 9, pp. 1058–1061
Temperature dependences of surface magnetoelastic
constants of ultrathin Fe/GaAs (001) films
R. Żuberek, K. Nesteruk, K. Fronc, S. Piechota, and H. Szymczak
Institute of Physics, Polish Academy of Sciences, 32/46 Al. Lotników, 02-668 Warsaw, Poland
E-mail: szymh@ifpan.edu.pl
Received April 10, 2012
The magnetoelastic constants of epitaxial iron films prepared by dc magnetron sputtering on single crystal
GaAs (001) substrate in argon atmosphere and covered with a protective Si layer have been investigated in the
temperature range 10–300 K by means of the strain modulated ferromagnetic resonance. It has been shown that
the magnetoelastic constants strongly depend on the thickness of the film. The surface components of the
magnetoelastic constants have been determined and analyzed within the Néel and dipolar models. The proposed
analysis of experimental data gives chance for deeper insight into mechanisms responsible for magnetostriction
of iron thin films.
PACS: 75.70.Cn Magnetic properties of interfaces (multilayers, superlattices, heterostructures);
75.80.+q Magnetomechanical effects, magnetostriction;
75.70.Ak Magnetic properties of monolayers and thin films.
Keywords: magnetoelastic constants, ferromagnetic resonance, iron films.
1. Introduction
The films of iron deposited on GaAs have been of
strong interest for their possible applications in magneto-
electronic devices. It was shown that Fe films with thick-
ness of 5 monolayers or more epitaxially grown at room
temperature (RT) on GaAs (001) surfaces, are ferromag-
netically ordered at room temperature with nearly bulk
magnetic moment per atom [1]. It is generally accepted
that magnetic anisotropy essentially control the hysteretic
behavior of ferromagnets and consequently determine most
of the parameters (e.g., coercivity, permeability, energy of
magnetic domain walls) important for practical applica-
tions. Therefore, the understanding of magnetic aniso-
tropies in Fe/GaAs films is of crucial importance for the
development of various spintronic devices. In this particu-
lar case the magnetic anisotropy of the thin films is deter-
mined to a large degree by surface or interface effects. The
interfacial anisotropy does exist not only in the out-of-
plane direction, but can also arise within the plane of the
film. In thin single crystal Fe films on GaAs (001) sub-
strate an uniaxial anisotropy is observed with easy axis in
the [110] direction [2] below a critical film thickness. The
uniaxial magnetic anisotropy has already been observed in
thicker Fe films on GaAs (001) [3,4]. There have been
speculations on the origin of this anisotropy. It was sug-
gested that this anisotropy is related to the presence of a
Fe3Ga2–xAsx at the interface [4]. More results, however,
support the explanation of the uniaxial term by the intrinsic
anisotropy of the dangling bonds at the GaAs (001) surface
[2,3,5,6].
The thickness and stress dependence of magnetoelastic
constants of iron films have also been reported by several
authors (see, e.g., [5,7]). In the present paper we continue
our studies of the magnetoelastic constants of the iron
films with different thickness but with similar stresses at
the surface/interface [6,8]. To explore this problem further
the epitaxial iron films prepared by dc magnetron sputter-
ing on single crystal GaAs (001) substrate in argon atmos-
phere and covered with a protective Si layer have been
investigated from 10 to 300 K by means of the strain mod-
ulated ferromagnetic resonance (SMFMR).
2. Experimental
The Fe films in form of a wedge and the thickness
range from 3 to 6 nm, were grown by dc magnetron sput-
tering on GaAs (001) single crystal substrate at room
temperature. Ar were used as a sputter gas at pressures
of 3·10–1 Pa. Prior to the thin film deposition, polished
semiinsulating GaAs (001) substrates were cleaned in tri-
chloroethylene, methanol and rinsed in deionized water.
Then the substrates were dipped into a solution of
6H2SO4:1H2O2:1H2O (by volume) for 15 min and rinsed
Temperature dependences of surface magnetoelastic constants of ultrathin Fe/GaAs (001) films
Low Temperature Physics/Fizika Nizkikh Temperatur, 2012, v. 38, No. 9 1059
in deionized water. Next the GaAs substrates were dipped
into solution of 10H2O:1HCl without subsequent rinsing
with ultrapure water. After etching procedure the substrate
was immediately mounted to the substrate holder and load-
ed into loadlock chamber of sputtering system. The time
needed to transfer the substrate from HCl solution into
UHV environment with pressure 10–6 Pa not exceeded
20 min. In order to prevent oxidation of magnetic layer, the
iron films were covered with a protective Si layer of 7.5 nm
thick.
3. Ferromagnetic resonance conditions
SMFMR experiments were performed using a standard
X-band spectrometer operating at 9.2 GHz with 100 kHz
field modulation and 130 kHz strain modulation. The dc
magnetic field was applied in the plane of the film along
the [100] and [110] directions. The SMFMR spectra were
analyzed using a coordinate system in which the magneti-
zation of the film M and the external magnetic field H
make angles θ and θH with respect to the film normal and
angles φ and φH with respect to the [100] axis of the film.
In our experiment θH = π/2.
In order to calculate the resonance frequency we have
used the approach developed by Suhl [9]. Considering the
uniaxial and cubic anisotropy energies the free energy den-
sity of the system is
2 2
effsin cos ( ) 2 cosHF MH Mθ φ π θφ= − − + +
4 2 2 2 21 (sin sin 2 sin 2 ) sin cos ( 45 ) .
4 u
K
Kθ φ θ θ φ+ + − − °
(1)
It is useful to define the anisotropy fields
12 / , 2 /k s u u sH K M H K M= = . (2)
The terms containing Ku represents in plane uniaxial ani-
sotropy energy, K1 is cubic anisotropy constant. The effec-
tive magnetization term consists of saturation magnetiza-
tion and out of plane anisotropy field:
eff4 4 2 /s sM M K Mπ π ⊥= + . (3)
The equilibrium conditions for the magnetization and the
resonance condition for the FMR can be found using the
following equations [9]:
22 2 2 2
2 2 22
1
0, ,
sins
F F F F F
M
ω
θ φ γ θ φθ θ φ
⎡ ⎤⎛ ⎞⎛ ⎞∂ ∂ ∂ ∂ ∂⎢ ⎥= = = −⎜ ⎟ ⎜ ⎟∂ ∂ ⎝ ⎠ ∂ ∂⎢ ⎥∂ ⎝ ⎠∂⎣ ⎦
(4)
where ω is the circular frequency, γ is the giromagnetic
ratio.
For the strain modulated FMR (SMFMR) the
magnetoelastic energy [10] should be added to the free
energy of the system:
eff
ijkl ijklmni j kl i k kl mn i j klME ijklF BB Dα α ε α α ε ε α α ε= + = , (5)
where the first term is linear and second nonlinear func-
tions of the strain. For cubic crystal the linear part of the
magnetoelastic energy can be written as
2 2 2
1 1 11 2 22 3 33
2 1 2 12 2 3 23 1 3 13
( )
2 ( ) ,
ME bF
b
α ε α ε α ε
α α ε α α ε α α ε
= + + +
+ + + (6)
1111 11221 2 1313, 2 , Bb bB B= − = (7)
where b1 and b2 are the magnetoelastic constants, the εij
and αi are the components of strain tensor and the direction
cosines of M with respect to the cubic axes, respectively.
For thin films, in which the thickness (t) of the film is
smaller than the exchange length, the effective anisotropy
and magnetoelastic constants can be written as ([11] and
reference therein)
eff
( ) ( ) ( )
2v s
n n nK K K
t
= + , (8)
where
1 2
( ) ( ) ( )2 s s s
n n nK K K= + (9)
and
eff
( ) ( ) ( )
2v s
n n nb b b
t
= + , (10)
n = u for uniaxial and 1 for in-plane cubic anisotropy and
n = 1 or 2 for magnetoelastic constants. In (9) the contribu-
tions from both interfaces are considered.
4. Experimental results
The SMFMR measurements with dc magnetic field pa-
rallel to [110] direction allow determination of the effec-
tive magnetoelastic constant eff
2b . As examples the FMR
derivative spectra for the film with 4 nm thickness for
magnetic and strain modulation measured at 10 K and RT
are shown in Fig. 1. The temperature dependence of eff
2b
Fig. 1. The typical FMR spectra for field directed along [110]
axis for magnetic and strain modulation measured at 10 K and RT
for the Fe film with the thickness of 4 nm.
Strain
Magnetic
B, mT
FM
R
sp
ec
tra
, a
rb
. u
ni
ts
600
400
200
0
–200
–400
–600
–800
50 60 70 80 90 100
R. Żuberek, K. Nesteruk, K. Fronc, S. Piechota, and H. Szymczak
1060 Low Temperature Physics/Fizika Nizkikh Temperatur, 2012, v. 38, No. 9
for the films with different thicknesses are shown in Fig. 2.
The fitted values of the volume and surface (interface be-
tween GaAs and Fe from one side and Fe/Si from the se-
cond one) magnetoelastic constants for several tempera-
tures are shown in Figs. 3 and 4. The values of the
magnetoelastic constant b2 of bulk bcc Fe [12,13] are also
displayed. The surface magnetoelastic constants seem to
have origin similar to that established for the surface ani-
sotropy.
5. Comparison with the Néel and dipolar models
Usually, in order to compare the surface in-plane cubic
and uniaxial anisotropy constants with the Néel [14,15] or
dipolar [16,17] models the effective anisotropy constant is
written in another way [18]. Assuming that the thickness of
one monolayer is equal d then the thickness of the film will
be equal t = Nd where N is the number of atomic layers in
the film. In ideal structure of the film there are two surface
layers of thickness d and N – 2 volume layers. Then effec-
tive anisotropy constant can be written as
eff
( ) ( ) ( )( 2) 2v ss
n n nK Nd K N d K= − + , (11)
where
1 2
( ) ( ) ( )2 ss ss ss
n n nK K K= + , (12)
and ( )
ss
nK d is the proper surface anisotropy constant calcu-
lated, e.g., in the Néel or dipolar model. The following
dependence between ( )
s
nK and ( )
ss
nK results from Eqs. (1)
and (4):
( ) ( ) ( )
s ss v
n n nK K K d= − . (13)
It means that the measured surface anisotropy constant
( )( )s
nK depends additionally on volume contribution ( 1
vK ).
In some cases [11] the volume anisotropy constant for
the uniaxial anisotropy is equal to zero and therefore both
surface anisotropy constants are the same ( ( ) ( ) s ss
u uK K= ).
The in-plane surface cubic anisotropy constant obtained
from linear dependence of the effective anisotropy constant
on inverse film thickness is less than calculated one by
1
vdK . For the films with the same surface anisotropy con-
stant but different volume anisotropy constant the linear
dependence surface anisotropy constant ( 1
sK ) on the vol-
ume anisotropy constant ( 1
vK ) is observed (see for in-
stance Fig. 4 in paper [11]).
Usually magnetic anisotropy and magnetostriction have
the same origin. Therefore, in the case of magnetoelastic
constant the same problem appears as in magnetic anisot-
ropy constant and, consequently, the same formula for
simulating surface magnetoelastic constant ( 2
sb ) and prop-
er surface magnetoelastic constant ( 2
ssb ) should be used
2 2 2
s ss vb b b d= − . (14)
According to literature (e.g., [19]) the dependence of
the magnetoelastic constants on the thickness of magnetic
layer arises as an intrinsic or an extrinsic effect. The intrin-
Fig. 2. The temperature dependence of eff
2b for films with differ-
ent thicknesses.
b 2 ,
1
0
J/
m
6
2
t = 3.6 nm
t = 4.4 nm
t = 5.8 nm
t = 4.0 nm
T, K
Fig. 4. The fitted values of the volume magnetoelastic constants
for several temperatures. The values of magnetoelastic constant
b2 of bulk bcc Fe are also displayed.
Films
Bulk
7
6
5
4
3
b 2V
,
10
J/
m
6
2
Fig. 3. The fitted values of the surface (interface between GaAs
and Fe from one side and Fe/Si from the second one) magneto-
elastic constant b2 for several temperatures.
T, K
–1.6
–1.8
–2.0
–2.2
–2.4
–2.6
–2.80 50 100 150 200 250 300
2
,
10
J/
m
b 2s
–4
2
Temperature dependences of surface magnetoelastic constants of ultrathin Fe/GaAs (001) films
Low Temperature Physics/Fizika Nizkikh Temperatur, 2012, v. 38, No. 9 1061
sic effect is related to the broken symmetry of atoms at the
interface (see, e.g., the well-known Néel model [14,15]).
According to the Néel model the surface magnetoelastic
tensor, ss
ijklB , for the bcc structure and for (001) surface
has cubic symmetry and magnetoelastic constant ( 2
ssb ) is
equal to [15]
2 1313
42 ( ),
9
ss ss
sb B n p mr= = + (15)
where ns is the density of surface atoms and p for the bcc
iron is equal to – 1.5326·10–23 J, mr = 12.0·10–23 J. Then
3 2 3 2· ·2 20.57 10 J/m , and 0.5 10 J/mss sb b− −= = − (16)
which is about several times smaller than values obtained
in experiment.
The extrinsic effects arise mainly due to the misfit dis-
locations, interdiffusion and even due to the surface rough-
ness. The relatively large scatter of the experimental data
seen in Figs. 3, 4 suggests that interface Fe–GaAs is not
flat but rather rough. The roughness was shown to give
considerable contribution to the surface anisotropy and
magnetostriction [20]. The roughness depends on various
factors which are difficult to remove.
5. Conclusion
We have grown epitaxial iron films on single crystalline
GaAs (001) substrates with Ar as a sputtering gas. The
films were covered with Si overlayers. The magneto-
striction constants have been measured by SMFMR meth-
od. The small FMR linewidth of the measured films indi-
cates a high crystalline quality of the Fe layers. It has been
found that magnetostriction constants are composed of
surface and bulk contributions dependend on temperature.
The bulk magnetoelastic constants were equal to the values
found for bulk Fe. The surface anisotropy and surface
magnetostriction are related first of all to the effects of
broken symmetry of atoms at the interfaces. This observa-
tion seems to be related to tetragonal strain due to lattice
mismatch.
Acknowledgments
The work was supported in part by Polish MNiSW
2048/B/H03/2008/34 grant. The substrates of GaAs sup-
plied by Institute of Electronic Materials Technology are
kindly acknowledged.
1. M. Zolfl, M. Brockmann, M. Kohler, S. Kreuzer, T.
Schweinbock, S. Miethaner, F. Bensch, and G. Bayreuther,
J. Magn. Magn. Mater. 175, 16 (1997).
2. M. Brockmann, M. Zolfl, S. Miethaner, and G. Bayreuther,
J. Magn. Magn. Mater. 198–199, 384 (1999).
3. J.J. Krebs, B.T. Jonker, and G.A. Prinz, J. Appl. Phys. 61,
2596 (1987).
4. A. Filipe, A. Schuhl, and P. Galtier, Appl. Phys. Lett. 70, 129
(1997).
5. R. Koch, M. Weber, K. Thurner, and K.H. Rieder, J. Magn.
Magn. Mater. 159, L11 (1996).
6. R. Zuberek, E. Mosiniewicz-Szablewska, H. Szymczak, K.
Fronc, K. Swiatek, and F. Stobiecki, Physica B 284–288,
1237 (2000).
7. G. Wedler, J. Walz, A. Grener, and R. Koch, Surf. Sci. 454–456,
896 (2000).
8. R. Zuberek, K. Fronc, A. Szewczyk, M.U. Gutowska, H.
Szymczak, and M.R.J. Gibbs, Czech. J. Phys. 52, Suppl. A,
169 (2002).
9. H. Suhl, Phys. Rev. 97, 555 (1955).
10. V.V. Eremenko and V.A. Sirenko, Magnetic and Magneto-
elastic Properties of Antiferromagnets and Superconductors,
Cambridge Scientific Publishers (2008); in: Modern Trends
in Magnetostriction Study and Application, M.R.J. Gibbs
(ed.), Kluwer Academic Publishers (2001).
11. G. Bayreuther, M. Dumm, B. Uhl, R. Meier, and W. Kipferl,
J. Appl. Phys. 93, 8230 (2003).
12. Y. Ohta and M. Shimizu, J. Phys. F: Met. Phys. 12, 1045
(1982).
13. J.A. Rayne and B.S. Chandrasekhar, Phys. Rev. 122, 1714
(1961); Q. Xing, T.A. Lograsso, M.P. Ruffoni, C. Azimonte,
S. Pascarelli, and D.J. Miller, Appl. Phys. Lett. 97, 072508
(2010).
14. L. Néel, J. Phys. Rad. 15, 225 (1954).
15. R. Zuberek, D. Zymierska, and H. Szymczak, Acta Phys.
Pol. A 85, 439 (1994).
16. H.J.G. Draaisma and W.J.M. de Jonge, J. Appl. Phys. 64,
3610 (1988).
17. T. Szumiata, H. Szymczak, and R. Zuberek, IEEE Trans.
Mag. MAG-29, 3132 (1993).
18. R. Zuberek, K. Fronc, W. Paszkowicz, and H. Szymczak,
J. Magn. Magn. Mater. 283, 28 (2004).
19. U. Gradman, T. Durkop, and H.J. Elmers, J. Magn. Magn.
Mater. 165, 56 (1997).
20. H. Szymczak, M. Rewienski, and R. Zuberek, J. Magn.
Magn. Mater. 139, 151 (1995).
|