Oscillations and change of sign in indirect exchange coupling of Fe/Au/Tb trilayer structures
Indirect exchange coupling between Fe and Tb layers through an Au layer showed oscillatory behavior with the thickness of the nonmagnetic metal. Different experimental tools such as polar magneto-optical Kerr effect, ferromagnetic resonance, and magnetotransport were used to investigate Fe/Au/Tb...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2004
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| Цитувати: | Oscillations and change of sign in indirect exchange coupling of Fe/Au/Tb trilayer structures / E. Shypil, A. Pogorily, D. Podyalovsky // Физика низких температур. — 2004. — Т. 30, № 5. — С. 544-550. — Бібліогр.: 36 назв. — англ. |
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irk-123456789-1197232017-06-09T03:04:51Z Oscillations and change of sign in indirect exchange coupling of Fe/Au/Tb trilayer structures Shypil, E. Pogorily, A. Podyalovsky, D. Низкотемпеpатуpный магнетизм Indirect exchange coupling between Fe and Tb layers through an Au layer showed oscillatory behavior with the thickness of the nonmagnetic metal. Different experimental tools such as polar magneto-optical Kerr effect, ferromagnetic resonance, and magnetotransport were used to investigate Fe/Au/Tb trilayers with Au thickness varying from 0 to 3.5 nm, prepared in an MBE system. From the experimental data we reconstruct the dynamics of the Fe and Tb magnetic moments with increasing thickness of the Au interlayer and show for the first time that there is a change of sign in the interaction between Fe and Tb, which is observed experimentally. 2004 Article Oscillations and change of sign in indirect exchange coupling of Fe/Au/Tb trilayer structures / E. Shypil, A. Pogorily, D. Podyalovsky // Физика низких температур. — 2004. — Т. 30, № 5. — С. 544-550. — Бібліогр.: 36 назв. — англ. 0132-6414 PACS: 75.70.Ak, 76.50.+g, 78.20.–e http://dspace.nbuv.gov.ua/handle/123456789/119723 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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English |
| topic |
Низкотемпеpатуpный магнетизм Низкотемпеpатуpный магнетизм |
| spellingShingle |
Низкотемпеpатуpный магнетизм Низкотемпеpатуpный магнетизм Shypil, E. Pogorily, A. Podyalovsky, D. Oscillations and change of sign in indirect exchange coupling of Fe/Au/Tb trilayer structures Физика низких температур |
| description |
Indirect exchange coupling between Fe and Tb layers through an Au layer showed oscillatory
behavior with the thickness of the nonmagnetic metal. Different experimental tools such as polar
magneto-optical Kerr effect, ferromagnetic resonance, and magnetotransport were used to investigate
Fe/Au/Tb trilayers with Au thickness varying from 0 to 3.5 nm, prepared in an MBE system.
From the experimental data we reconstruct the dynamics of the Fe and Tb magnetic moments
with increasing thickness of the Au interlayer and show for the first time that there is a change of
sign in the interaction between Fe and Tb, which is observed experimentally. |
| format |
Article |
| author |
Shypil, E. Pogorily, A. Podyalovsky, D. |
| author_facet |
Shypil, E. Pogorily, A. Podyalovsky, D. |
| author_sort |
Shypil, E. |
| title |
Oscillations and change of sign in indirect exchange coupling of Fe/Au/Tb trilayer structures |
| title_short |
Oscillations and change of sign in indirect exchange coupling of Fe/Au/Tb trilayer structures |
| title_full |
Oscillations and change of sign in indirect exchange coupling of Fe/Au/Tb trilayer structures |
| title_fullStr |
Oscillations and change of sign in indirect exchange coupling of Fe/Au/Tb trilayer structures |
| title_full_unstemmed |
Oscillations and change of sign in indirect exchange coupling of Fe/Au/Tb trilayer structures |
| title_sort |
oscillations and change of sign in indirect exchange coupling of fe/au/tb trilayer structures |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2004 |
| topic_facet |
Низкотемпеpатуpный магнетизм |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/119723 |
| citation_txt |
Oscillations and change of sign in indirect exchange
coupling of Fe/Au/Tb trilayer structures
/ E. Shypil, A. Pogorily, D. Podyalovsky // Физика низких температур. — 2004. — Т. 30, № 5. — С. 544-550. — Бібліогр.: 36 назв. — англ. |
| series |
Физика низких температур |
| work_keys_str_mv |
AT shypile oscillationsandchangeofsigninindirectexchangecouplingoffeautbtrilayerstructures AT pogorilya oscillationsandchangeofsigninindirectexchangecouplingoffeautbtrilayerstructures AT podyalovskyd oscillationsandchangeofsigninindirectexchangecouplingoffeautbtrilayerstructures |
| first_indexed |
2025-07-08T16:29:19Z |
| last_indexed |
2025-07-08T16:29:19Z |
| _version_ |
1837096931997777920 |
| fulltext |
Fizika Nizkikh Temperatur, 2004, v. 30, No. 5, p. 544–550
Oscillations and change of sign in indirect exchange
coupling of Fe/Au/Tb trilayer structures
Elena Shypil, Anatoly Pogorily, and Dmitriy Podyalovsky
Institute of Magnetism, National Academy of Sciences of Ukraine
36-b Vernadsky Ave., Kiev 03142, Ukraine
E-mail: elena@imag.kiev.ua
Received August 20, 2003
Indirect exchange coupling between Fe and Tb layers through an Au layer showed oscillatory
behavior with the thickness of the nonmagnetic metal. Different experimental tools such as polar
magneto-optical Kerr effect, ferromagnetic resonance, and magnetotransport were used to investi-
gate Fe/Au/Tb trilayers with Au thickness varying from 0 to 3.5 nm, prepared in an MBE sys-
tem. From the experimental data we reconstruct the dynamics of the Fe and Tb magnetic moments
with increasing thickness of the Au interlayer and show for the first time that there is a change of
sign in the interaction between Fe and Tb, which is observed experimentally.
PACS: 75.70.Ak, 76.50.+g, 78.20.–e
Introduction
Rare earth–transition metal (RE–TM) alloys and
compounds have been of fundamental and practical in-
terest for many years [1]. The presence of various ex-
change interactions (RE–RE, TM–TM, RE–TM)
makes understanding of physical processes compli-
cated, though on the other hand they show the way to
create new magnetic materials with novel properties.
There are well known examples of high-energy perma-
nent magnets created on the basis of RECo5 and mag-
neto-optical media for rewriteable memory storage
based on RE–CoFe amorphous films. The main feature
of these artificial materials is the ferrimagnetic order-
ing, meaning that RE and TM magnetic sublattices
are oriented antiparallel with perpendicular aniso-
tropy and have a compensation point at a definite
composition. The major source of the perpendicular
magnetic anisotropy is known to be single-ion aniso-
tropy of the RE ion, which possesses an orbital angu-
lar momentum [1]. This is also valid for RE/TM
multilayer films, where an interface region gives the
main contribution to the perpendicular anisotropy
[2,3]. The exchange interaction in this system is fairly
complex: the magnetic moments of the 3d shells of the
TM atoms are thought to participate in the direct in-
teraction exchange, whereas the orbital moments of
the deep 4f shells of the RE atoms need mediation of
the conduction electrons for their indirect exchange
[4]. The polarization of conduction electrons as a re-
sult of spin interaction with the TM sublattice also
has a significant influence on the exchange interaction
in the RE sublattice, which is manifested, for exam-
ple, in a steep rise of the Curie temperature (TC) for
the Tb–Fe alloy [5] compared with the TC for pure
terbium [6]. According to the RKKY (Ruderman–
Kittel–Kasuda–Yosida) model the polarization oscil-
lates in strength and sign with increasing distance
from the magnetic ion.
Oscillatory interlayer coupling between ferromag-
netic metal layers separated by nonmagnetic metal
spacer has been observed in many systems: Fe/Cr,
Fe/Cu, Fe/Al, Fe/Ag, Fe/Au, Fe/Pd [7]. Non-
magnetic layers adjacent to the ferromagnetic layers
become spin polarized and these atoms develop mag-
netic moments [8,9]. As the interlayer thickness is
varied, the exchange coupling of the magnetic layers
is found to vary in sign, oscillating between anti-
ferromagnetic and ferromagnetic coupling. This is
manifested, for example, as an oscillation in the mag-
nitude of the GMR effect with increasing separation
of the magnetic layers [10,11].
The authors of Refs. 12 and 13 investigated
Co/X/Gd multilayers with X = Pt, Cu, Y, hoping to
see oscillatory behavior of the coupling. However, in
contrast with the results of Gd/Y/Gd [14] and
Co/Cu/Co [15], where the oscillatory behavior of
the coupling is well known, no oscillation of the cou-
pling was found.
© Elena Shypil, Anatoly Pogorily, and Dmitriy Podyalovsky, 2004
Hoffmann and Scherschlichtis reported their study
of Tb and Fe multilayers separated by different non-
magnetic metal interlayers (Au, Ta, Pt) [16]. It was
shown that the net magnetic moment of this system os-
cillates weakly with interlayer thickness, although the
indirect coupling did not show a change in sign.
In this article we describe measurements of Fe/x
Au/Tb, x = 0–35 Å, bi- and trilayers carefully grown
under clean conditions in an MBE system, to investi-
gate the effect of interlayer thickness. We show that
oscillations of the net magnetic moment are seen in
magneto-optical, magnetotransport, and magnetic re-
sonance measurements. Moreover, we demonstrate for
the first time experimentally that the indirect coup-
ling changes sign with interlayer thickness.
Experimental details
Two sets of Fe/Au/Tb trilayers were prepared on
quartz and silicon substrates by electron-beam evapo-
ration in an MBE system having a background pres-
sure of 1·10–10 Torr and a pressure of better than
1·10–9 Torr during the film growth. To minimize
interdiffusion of the layers the substrate temperature
during evaporation was kept near 0 oC. The rate of
evaporation did not exceed 0.4 Å/s and was con-
trolled with a calibrated quartz crystal monitor. Sam-
ples on quartz substrates were protected with 30 Å
thick layer of Al2O3, whereas samples on Si substrate
were capped with 30 Å Au layer. Polar magneto-opti-
cal Kerr effect (PMOKE), ferromagnetic resonance
(FMR), and magnetotransport methods were used to
characterize the films magnetically. PMOKE was
measured at room temperature using a 630 nm laser in
an applied field up to 1.8 T perpendicular to the film
plane. The FMR was measured at room temperature
by means of conventional modulation rf spectrometer
at 9.41 GHz with an applied magnetic field (up to
0.7 T) in the film plane. Extraordinary Hall effect
(EHE) and magnetoresistance (MR) of the trilayers
were measured using standard techniques. The re-
quired five electrical contacts were made on the film
samples using Ag paint, and the offset voltage in the
Hall configuration was compensated in zero magnetic
field. Hall voltages (in the range of millivolts for the
film on the quartz substrate and a few tenths of a mil-
livolts for those on the silicon substrate) were mea-
sured, using a 1 mA current with an applied field of 9
kOe perpendicular to the film plane, whereas the MR
measurements were done with field both in plane and
perpendicular to it. The thickness of the individual
layers, 3 monolayers for Fe (dFe = 3 ML) and 3
monolayers for Tb (dTb = 3 ML), were chosen on the
basis of the previous experiments in which the ferri-
magnetic ordering of Fe/Tb multilayer has been
shown [17]. Also it was shown for the control films
that the 3 ML = 8 Å Fe film is ferromagnetic at room
temperature, whereas the 3 ML = 12 Å Tb film is pa-
ramagnetic down to 5 K [18].
Results and discussion
Two periods of oscillation
Understanding of the magnetic coupling via differ-
ent spacers between TM and RE layers (in ferromag-
netic or paramagnetic state) is lacking. However, the
phenomenon of magnetic coupling for two TM ferro-
magnetic layers separated by a nonmagnetic spacer is
better understood [7,10,19,20]. Information about the
properties of this latter system can be useful in under-
standing the nature of coupling that is being investi-
gated here. It was shown that the amplitude of the
coupling strength (exchange constant) and the period
of oscillations depend on the material and thickness of
interlayer, whereas the phase of the exchange cou-
pling oscillations depended upon the properties of the
ferromagnetic layers.
Theoretical works for noble-metal spacers based on
the RKKY model have predicted two oscillations of the
interlayer coupling with the spacer thickness, reflect-
ing the topological properties of the Fermi surface [21]:
Jinter(d) = 1/d2[A1 sin (2�d/�1 + �1) +
+ A2 sin (2�d/�2 + �2)]
(1)
where Jinter(d) is the interlayer exchange energy as a
function of the spacer thickness d; A1, A2 are the am-
plitudes and �1, �2 are the periods of the energy os-
cillations. The phases and the amplitude ratio A1/A2
have been found to depend critically on sample quali-
ty and ferromagnetic layer thickness. It is only for a few
trilayers that two periods of oscillations and anti-
ferromagnetic coupling have been observed for spac-
ers thinner than 3–4 ML, e.g., for Fe/Au/Fe [22].
In Fig. 1 the PMOKE signal measured at room
temperature is plotted as a function of Au film thick-
ness for Fe/Au/Tb trilayers (top inset), prepared on
a quartz substrate. For a free Fe layer we observed an
unsaturated signal (bottom inset), while the Fe/Tb
bilayer showed a rectangular loop with perpendicular
anisotropy [18] (right bottom quadrant). With the in-
troduction of 1 ML of spacer layer (dAu = 3 Å), the
PMOKE loop showed that the magnetic moments of
the Fe and Tb layers are no longer perpendicular to
the film plane. For trilayers with different dAu we ob-
served very narrow loops with no remanence and with
a kink, clearly showing two regions with different
magnetic susceptibilities. We suppose that the low-
field susceptibility is a measure of indirect exchange
between Fe and Tb via Au. The difference of the loops
Oscillations and change of sign in indirect exchange coupling of Fe/Au/Tb trilayer structures
Fizika Nizkikh Temperatur, 2004, v. 30, No. 5 545
for the control Fe film with dFe = 8 Å and for trilayers
shows that interaction between Fe and Tb layers still
exists. Fragments of the loop at magnetic fields over
the kink show that the Fe magnetization is affected by
the Au. The PMOKE angle was taken at the kink
point. The loop indicates the rotation of the magnetic
moments of the layers from the film plane (at H = 0)
with increasing perpendicular magnetic field: the po-
sition of the kink (values of PMOKE angle and mag-
netic field) oscillates as dAu increased. Oscillations of
the Kerr angle with Au thickness having one clear pe-
riod of about 8 Å and some feature of the second pe-
riod of 26 Å are observed.
Oscillation of the magnetic moment as a function
of Au for thickness greater than 20 Å was seen in sput-
tered multilayers of [Fe/Au/Tb]12 by Hoffman and
Scherschlicht [16]. The first period (8 Å, that is
2.8 ML) observed by us on trilayers correlates well
with that seen on multilayers. Interestingly, in gen-
eral we observed both periods for the Fe/Au/Tb sys-
tem, that is 2.8 ML and 8.9 ML. These correlate well
with the oscillation periods 2.5 and 8.6 ML, which
were measured for the Fe/Au/Fe system [23] and
also with the values of 2.5 and 8.6 ML extracted [24]
from measurements of the Au Fermi surface. The facts
that the feature of the second oscillation period ap-
pears and also the high amplitude ratio, A1max/A1min,
show that the growth conditions for the trilayers were
good and the interface is sharp. The amplitude ratio of
PMOKE angle, A /A1 1max min
� � , seen in our work,
which is proportional to the net magnetic moment, are
evaluated as 1.26–1.33 for trilayers on the quartz sub-
strate and 1.64 for the silicon substrate.
The sign change of the coupling
Furthermore, we present direct evidence for the
change in the sign of the coupling, alternating be-
tween ferromagnetic and antiferromagnetic interac-
tion. From studies of RE–TM amorphous alloy films it
is known that the sign of the Hall resistivity changes
at the compensation composition due to the change in
spin direction [25–28], meaning that either the Fe or
Tb magnetic moment dominates in the perpendicular
anisotropy. For Tb/Fe multilayers with different
layer thickness it was also shown that the Hall voltage
dependence is determined by the interface [29,30].
For Fe/Au/Tb trilayers the indirect exchange be-
tween Fe and Tb goes by means of polarized conduc-
tion electrons of Au. As the two magnetic moments,
Fe and Tb, separated by a thin Au spacer with the in-
crease of its thickness gradually come into the film
plane, at a small spacer thickness they make some an-
gle with the film plane and hence some perpendicular
exchange of indirectly coupled Fe and Tb still exists.
Namely polarized conduction electrons of Au become
the main carriers of this exchange. On the other hand
the Au layer has the lowest electrical resistivity in the
trilayer studied (2.2·108
�·m at T = 293 K against 10
and 120·108
�·m for Fe and Tb, respectively [31]).
This means that magnetotransport methods, particu-
larly the extraordinary Hall effect, can be very infor-
mative for these samples.
Magnetotransport data plotted in Fig. 2 for two
sets of trilayers, prepared on quartz and silicon sub-
strates (to increase the range of investigated spacer
thickness), show oscillations of the Hall resistivity
and magnetoresistance (MR) with Au thickness. The
thickness of the Fe and Tb layers was kept the same at
8 Å and 12 Å, respectively, while the thickness of the Au
layer was increased. We observed alternate («right»
and «left») loops for the extraordinary Hall effect for
different interlayer thickness, showing a sign change
of the interaction (Fig. 2). The Hall resistivity in
Figs. 2,a,c, where an Au layer is interposed between
Fe and Tb films, also shows that the magnetic mo-
ments of Fe and Tb are no longer strong perpendicular
to the film plane. This further shows that the Au film
presents an indirect interaction between Fe and Tb
with some perpendicular component of magnetization
still remaining.
Also shown (Fig. 2,c) is the Hall resistivity for a
bilayer Fe (8 Å)/Tb (12 Å) without Au in between. It is
apparent that the positive («right») EHE loops corre-
spond to the parallel coupling, while the negative
(«left») EHE loops are displayed for the antiparallel
546 Fizika Nizkikh Temperatur, 2004, v. 30, No. 5
Elena Shypil, Anatoly Pogorily, and Dmitriy Podyalovsky
0 5 10 15 20 25 30 35 40 45 50 55
4
6
–2.0 –1.0 1.0 2.0
–20
–10
0
10
20
–0.1 0 0.1
0
0.2 Fe/Tb
Fe/3 Au/TbÅ
Fe
�
P
M
O
K
E
an
gl
e,
�
,
m
in
Au interlayer thickness, Å
Tb
Au
Fe
,
ar
b
.u
n
its
H, T
0
Fig. 1. Oscillation of PMOKE angle for Fe/x Au/Tb
trilayers as a function of dAu (quartz substrate). Top in-
set: Schematic diagram of trilayer. Bottom inset: PMOKE
loop for the trilayers compared with the control 8 Å Fe
film. Arrows show the kink at a critical field Hcr where
the susceptibility changes. Bottom right quadrant: Fe/Tb
bilayer shows rectangular loop with perpendicular aniso-
tropy [18].
arrangement (Figs. 2,a,c). The MR variation as a
function of Au interlayer thickness in transverse and
perpendicular geometries is plotted in Figs. 2,b,d. In-
crease in the MR is observed at the periods of the
EHE-resistivity modulations, where the antiparallel
coupling of Fe and Tb magnetic moments occurs. This
is apparent for the samples with low Au thickness (the
set of samples prepared on the Si substrate). As the
MR signal was very low, the MR maximum could
be checked only for the second AFM state (dAu =
= 15–20 Å). The same trend of MR increase for the
antiparallel coupling is seen at higher Au thickness
(the set of samples prepared on the quartz substrate).
Also the influence of substrate on the phase of os-
cillations can be seen in a comparison of the two sets.
One observes that Hall resistivity oscillations having
the same periods for the two sets of samples demon-
strate some shift of phases (Figs. 2,a,c). It is quite
plausible that the Fe layers (being only 3 ML thick)
prepared on quartz and silicon substrates (with differ-
ent surface energies) are not the same and, having
some structural differences, may affect the phase of
the exchange coupling oscillations.
Ferromagnetic resonance
FMR is known to be one of the most powerful ex-
perimental techniques in the study of ultrathin film
magnetic properties. The main advance for our case is
the high sensitivity providing detailed information
about the magnetic and structural quality of thin films
up to monolayer; moreover, that resonance can spread
to the paramagnetic region [32].
FMR data shown in Fig. 3 display oscillations of
the resonance field with Au interlayer thickness for
two sets of trilayers, prepared on quartz and silicon
substrates. Both kinds of them were chosen among
other insulating materials to be used as substrates,
with signals that do not overlap the FMR signals of
the trilayers.
The Hres oscillations correlate well with mag-
neto-optical and magnetotransport measurements as
well. For the sets of trilayers prepared on the quartz
substrate one can see the similar dependences for the
Oscillations and change of sign in indirect exchange coupling of Fe/Au/Tb trilayer structures
Fizika Nizkikh Temperatur, 2004, v. 30, No. 5 547
0 5 10 15 20 25 30 35
0
0.8
d
Au interlayer thickness, Å
0 5 10 15 20 25 30 35
–0.03
0
0.03
c
Fe
Au
Tb
Fe
Tb
Au
Fe
Tb
M
R
,%
M
R
,%
c
m
0 10 20 30
0
0.3
0.6
AFM
E
H
E
Magnetic field
b
0 10 20 30
–0.8
0
0.8
AFM
FM
FM
0.5
a
Magnetic field
E
H
E
,1
0
6
–
E
H
E
,10
6
–
·
c
m
·
�
�
Fig. 2. (a,c) Extraordinary Hall effect resistivity and
(b,d) magnetoresistance (perpendicular – white triangles
and transverse – black triangles) as a function of Au
interlayer thickness. Samples on (a,b) quartz substrate;
(c,d) silicon substrate. The change of sign in extraordi-
nary Hall effect loops is shown at the left of (a and b);
the top «right» loop corresponds to positive values of
EHE resistivity in (a), the lower, «left» loop corresponds
to the negative values in (a). Inset in (c): Schematic of
the Fe and Tb magnetization orientations as a result of
coupling via the Au spacer.
0 5 10 15 20
240
260
280
300
320
100 200 300 400
15Å 238
H, mT
12Å 247
9Å 279
6Å 265
dAu= 3Å 299
I
n
t
e
n
s
i
t
y
Fe/Tb 331
b
H
H
e
e
s
s
,
,
m
m
T
T
Au interlayer thickness, Å
0 10 20 30
180
200
220
240
260
100 200 300 400
12Å185
I
n
t
e
n
s
i
t
y
H, mT
9Å190
6Å222
245 dAu= 3Å
Fe/Tb 253
Fe 243 mT
a
r
r
Fig. 3. Resonance fields (Hres ), obtained (with magnetic
field up to 0.7 T, applied in film plane and an rf fre-
quency of 9.41 GHz) from FMR data, plotted as a func-
tion of Au interlayer thickness for two sets of samples on
quartz (a) and on silicon substrate (b). FMR signals as a
function of magnetic field are also shown at the right,
where the resonant fields are also indicated in these figures.
PMOKE and FMR signals for dAu > 15 Å, where the
maxima of the Kerr angle and Hres are found at the
same Au thickness, dAu = 20, 26, and 35 Å. (Figs. 1
and 3,a). They correspond to AFM coupling for the
magnetotransport data (Fig. 2,a). Samples prepared
on the silicon substrate demonstrate AFM coupling at
dAu = 9 Å (Figs. 2,c and 3,b).
The FMR signals as a function of magnetic field
present the dynamics of magnetic moments in
Fe/Au/Tb trilayers. The first FMR signal shown is
for the control 8 Å thick Fe film (at the right in
Fig. 3,a). For the 8 Å Fe/12 Å Tb bilayer Hres is
shifted to higher fields, indicating the appearance of
PMA in bilayers due to the Fe–Tb interaction [18].
Introduction of 1 ML of Au at the interface causes a
significant decrease of the resonance field compared to
that of the 8Fe/12Tb bilayer. Now Hres is almost the
same as for the control Fe film. With further increase
of Au thickness the resonance field decays, followed
by its oscillation between ferromagnetic and anti-
ferromagnetic coupling. For the antiparallel coupling
the shape of the FMR line is much wider than for the
parallel ordering. The resonance fields are higher for
samples prepared on the silicon substrate, again show-
ing the influence of the substrate on the Fe layer [33].
The experimental values of Hres for the parallel orien-
tation, substituted into the known Kittel equation [34]
�
�
�
H H Mres res eff( )4 (2)
(where � = 2�f is the microwave frequency, f =
= 9.38 GHz, � � g /B � is the gyromagnetic ratio, g is
the spectroscopic splitting factor, and � is Planck’s
constant), give the effective magnetization 4�Meff,
which includes the input of perpendicular anisotropy
due to the change of form factor and to the growth
anisotropy, as well. Meff and � measured by FMR
and PMOKE for the trilayers with different Au thick-
ness, prepared on the quartz and silicon substrates,
are shown in Fig. 4. Analysis of these data shows that
for both sets of samples up to the Au thickness dAu <
< 15 Å the FMR and PMOKE data dependences cor-
relate, whereas at dAu > 15 Å the dependences are
found to be in antiphase, i.e., the maximum of the
one correlates with the minimum of the other. This
means that dAu = 15 Å is some critical distance for
strong coupling between Fe and Tb. Earlier in a
Mössbauer study of Fe/Tb multilayers with different
layer thickness it was shown that the radius of cou-
pling between Fe and Tb is about 7–15 Å [35]. Hence
at interlayer thickness less than 15 Å both direct (hy-
bridization of the Fe and Tb bands) and indirect
(RKKY) interactions via the spacer exist, while at
higher thickness only the indirect interaction occurs.
The main feature of the direct interaction between Fe
and Tb layers is the perpendicular anisotropy. When
a spacer appears between them and grows in thickness
the input of the direct interaction gradually decreases
while the input of indirect interaction grows. Our
data show that at dAu > 15 Å the long-range indirect
interaction between Fe and Tb layers has the advan-
tage. At this condition the magnetic moment of the
Fe and the induced magnetic moment of the Tb are in
the film plane, and measurements by experimental
methods with different geometry (FMR and
PMOKE) give the opposite results.
Substrate effect
Note that in the PMOKE dependence for the sam-
ples on the Si substrate (Fig. 4,d), the sample with
dAu= 9 Å, showing AFM coupling in FMR and EHE,
demonstrated a minimum in PMOKE, contrarily to
samples on the quartz substrate. This can be explained
by the substrate effect.
We did not use any seed layer (e.g., Ta, Ag, Cu,
etc.) while preparing trilayers on Si substrates, as the
latter might affect the trilayer interactions. In general
using two kinds of substrates and different experimen-
tal methods we got information about the main fea-
548 Fizika Nizkikh Temperatur, 2004, v. 30, No. 5
Elena Shypil, Anatoly Pogorily, and Dmitriy Podyalovsky
0 6 12 18 24 30 36
0,2
0,4
d
Silicon substrate
H�
Quartz substrate
Au interlayer thickness, Å
0 6 12 18 24 30 36
0
5
10
15
c
Silicon substrate
HII
Quartz substrate
0 6 12 18 24 30 36
4
6 bH�
0 6 12 18 24 30 36
10
15
20
25 aHII
P
M
O
K
E
an
g
le
,
,
m
in
u
te
s
�
P
M
O
K
E
an
g
le
,
,
m
in
u
te
s
�
FM
R
d
at
a,
M
,m
T
e
ff
FM
R
d
at
a,
M
,m
T
e
ff
Fig. 4. Meff (a and c) from FMR measurements and � (b
and d) measured by PMOKE for trilayers with different
Au thickness, prepared on quartz (a and b) and silicon (c
and d) substrates.
tures of interactions and also about the substrate ef-
fect. Always the signal for samples on the Si substrate
was about one order of magnitude less than on the
quartz. This shows that some amount of Fe did not
participate in the coupling (because of the appearance
of silicides at the Si/Fe interface) [33] and the inter-
action did not give a significant perpendicular aniso-
tropy input. In other words, the Fe and Tb moments
were in-plane (or nearly so) for the Si substrate and
out-of-plane for the quartz. As a result, the PMOKE
method, which is sensitive to the perpendicular input,
showed a maximum for the samples on the quartz sub-
strate and a minimum for those on Si.
Dynamics of the Fe and Tb magnetic moments
Now we can construct the dynamics of the Fe and
Tb magnetic moments with an Au interlayer starting
with an Fe/Tb bilayer. Without an Au layer, perpen-
dicular magnetic anisotropy is observed in Fe/Tb
interface, similar to that which is observed in amor-
phous Fe–Tb films close to the compensation composi-
tion: the Fe and Tb magnetic moment vectors are anti-
parallel to one another and perpendicular to the film
plane. This is seen from the PMOKE and from the
large FMR resonance field data. Only one ML of Au
interposed between Fe and Tb layers is enough to de-
crease sharply this short-range magnetic interaction.
This is supported by the change of the loop shape in
PMOKE [18] as well as by the sharp decrease of the
FMR resonance field. With further increase of the Au
spacer thickness the magnetic moment vectors change
their mutual orientations, coming closer and closer to
the film plane, as seen from the EHE and FMR data.
Comparison of the PMOKE, FMR, and EHE data
show that when dAu > 15 Å presumably the main char-
acter of the Fe–Tb interaction is the indirect ex-
change. This interaction is observed up to 12 ML
of Au, with an oscillation period of 2.8 ML. At the
minima of the oscillations sharp increases in the MR
are seen, showing a change of sign for the long-range
exchange interaction. It is known that the MR is
a measure of the type and strength of antiparallel
coupling [36].
The most significant feature of the oscillating mode
for the indirect exchange interaction is the weak decay
of the modulation amplitude [16]. The presence of os-
cillations up to 15–17 MLs of Au cannot be expected
from RKKY theory (the r–3 or r–2 decay for a ferro-
magnetic layer is expected). This coupling feature is
unique and needs further investigation.
Conclusions
In summary, carefully prepared Fe(3 ML)/x
Au/Tb(3 ML) trilayers under clean conditions dis-
play oscillations in the exchange interaction, which
can be seen with different methods of characteriza-
tion. The experimental results correlate well with ex-
isting experimental and theoretical data. For the first
time it is shown experimentally that:
i) Fe and Tb layers separated by a thin Au layer
couple their magnetic moments parallel or antiparallel
for different Au thickness, i.e., the sign of the ex-
change interaction oscillates;
ii) EHE is a powerful tool for studying indirect ex-
change coupling;
iii) at a spacer thickness within the radius of Fe–Tb
coupling (7–15 Å) both short- and long-range ex-
change interactions coexist, while at higher spacer
thickness the indirect interaction has the advantage;
iv) the substrate can affect the features and sign
of the coupling .
We are grateful to Jagadeesh S. Moodera, Francis
Bitter Magnet Lab, MIT, Cambridge, Massachusetts,
USA, for stimulating this work, to Tae Hee Kim for
sample preparations, and to Geetha Berera for experi-
mental assistance.
This work was supported by STCU Grant No. 1086.
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