Ferromagnetic resonance studies of Fe/Ni and Fe/CoNbZr multilayers:
Model and experiments
B. Ramamurthy Acharya, Shiva Prasad, N. Venkataramani, M. Kaabouchi, R. Krishnan et al.
Citation: J. Appl. Phys. 78, 3992 (1995); doi: 10.1063/1.359920
View online: http://dx.doi.org/10.1063/1.359920
View Table of Contents: http://jap.aip.org/resource/1/JAPIAU/v78/i6
Published by the American Institute of Physics.
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!Ferromagnetic resonance
Model and experiments
B. Ramamurthy
studies
of lFe/Ni and FeKoNbZr
multilayers:
Acharya and Shiva Wasada)
Department of Physics, Indian Institute of Technology, Powai, Bombay 400 076, India
N. Venkataramani
Advanced Centerjk
, India
M. Kaabouchi,
Research in Electronics, Indian kstitute of Technology, Powai, Bombay 400 076,
R. Krishnan, and C. Sella
Laboratoire de Magn.&me
et Optique, CNRS, F-92195 Meadon, France
(Received 13 March 1995; accepted for publication 10 June 1995)
Ferromagnetic resonance (FMR) studies were carried out on Fe/Ni and FeKoNbZr multilayers. A
simple model taking into consideration the multilayered nature of the film was used to calculate the
field positions and mode intensities of the experimental spectra. The complicated intensity patterns
of the modes observed in the FMR spectra of the multilayers were explained in terms of model
calculations. The analysis of the spectra showed that the interface in case of these multilayers is not
sharp and suggested the formation of interfacial alloy. 0 1995’ American Institute of Physics.
I. INTRODUCTION
It is known that Ferromagnetic resonance (PMR) is an
interesting tool to characterize magnetic thin films and
multilayers.‘~2 However, FMR spectra in case of multilayers
are very complex, often showing several modes with complicated intensity variationssT4 FMR spectra of many bi-layer
and multilayer films have been explained in terms of simple
models considering these films basically homogeneous with
either a surface layer or some other modifications.’ In principle, the PMR spectra of multilayers cannot be explained
considering the films as homogeneous, because the resonance spectra results from excitations extending up to full
thickness in which the individual layers are exchange
coupled. On the other hand, many theoretical calculations
have been carried out to explain the PMR spectra of
multilayers.“* Many of these calculations are complex and
have not been used to study the dependence of the field and
intensity values of resonance modes on the thickness of individual layers, number of bi-layers, etc. We use a simple
model which is applicable to a multilayer system with magnetic layers, and have been able to account for the field positions and anomalous intensity variations. The calculations
were carried out on similar grounds as were done by Wilts
and Prasad’ in case of non-multilayered ion-implanted magnetic bubble materials. For this study, two type of multilayers, viz., Fe/Ni and FeICoNbZr have been taken which are
also of technical interest?“’
II. EXPERIMENTS
Fe/Ni and Fe/CoNbZr multilayers were prepared by sequential ttiode sputtering,” and rf sputtering,r2 respectively.
The Fe/Ni multilayers have been referred as (t&tm)n where
tFe is the thickness of Fe layer and tNi is the thickness of Ni
layer and n is the number of modulations. The Ni layer was
the topmost layer. The Fe/Ni multilayers studied here have
“Electronic mail: [email protected]
3992
J. Appt. Phys. 78 (6), 15 September 1995
tFe= tNi. The FeKoNbZr multilayers have been referred as
(tFJtCoNbZr)nf1’2, where tCoNbZris the thickness of CoNbZr
layer, iz is the number of Fe layers and n + 1 is the number of
CoNbZr layers. Here the top most and bottom layers were of
CoNbZr. FMR was observed at 9.8 GHz at room temperature.
III. RESULTS
A. Model
AND DISCUSSION
used for the analysis
In perpendicular resonance case, the equation of motion
is given by8*13
(I!$)$!=( Ho-;+H,-4TM)m=k2m, (1)
k”=[HowIy+Hk-4vM],4~M
is saturawhere
tion magnetization, A is exchange constant, m is the magnitude of rf deflection of the magnetization from static equilibrium, H,, is the applied field, Hk is the anisotropy field, and
y is the gyromagnetic ratio gpn/pL, where g is the spectroscopic splitting factor, pE is Bohr magneton. The exchange
constant A is related to spin wave stiffness constant D by the
relation, D/$=ZAIM.
If the field for uniform precession mode for a layer is
H, , then for that particular layer,
k2=(H0-
H,),
!a
where H,= (WI y- H,+4rM).
Hence k2 is positive or
negative depending on whether the value of the applied field
is greater or smaller than the field for uniform precession
mode for the layer. When k” is positive, the local spin wave
will be exponential. On the other hand, when k” is negative,
the local spin wave will be sinusoidal. Hence the possible
excitations in each layer can be traced for a given value of
Ho. At the interface the solution should satisfy certain
boundary conditions. We have used following boundary conditions at each layer-layer interface as were used by Wilts
and Prasad’
Q 1995 American Institute of Physics
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ml
-=-.M,
m2
4
M2’Ml
dml
-=-dz
A2 dm2
M2
dz .
(3)
The computations are carried out beginning from the film air
interface layer. At the film air and film substrate interface
natural boundary condition viz., (dmldz) = 0 was used. We
gave a particular starting value of m and taking (dmldz) = 0,
calculated the value of m and [dmldz) at the next interface.
From these values, m and (dmldz) at the beginning of the
second layer were calculated using Eq. (3). This process was
carried out for all the layers until the film substrate interface
is reached. The field for resonance can be varied until a value
is found for which the excitation satisfies the boundary condition at the film substrate interface as closely as possible
and has required number of crossings corresponding to that
particular mode. For nth mode, m vs z curve should have
(n- 1) crossing with z-axis. The intensity of the modes can
be calculated once the total excitation is known using the
following expression’4
,d-,p dz)*
z- (Jd
-.
s ,,,=yn2 dz
r
(1
O/l 0)"
(4)
This expression assumes the line widths to be same in
the case of Fe and Ni. As no unambiguous information about
line widths are available in individual layers, intensity calculations were made using Eq. (4). The first mode intensity has
been taken as 100% and the intensities of other modes have
been given relative to this term.
B. Fe/Ni multilayers
The perpendicular FMR spectra of Fe/Ni multilayers
with different modulations are shown in Fig. 1. The spectra
consist of more than one resonance mode, except for the
( 10110) * multilayer which showed only one resonance peak
at 15.61 kOe. In some cases the line shape was not symmetrical and asymmetry was marked on the lower field side
of the highest field mode. The field position of the highest
field mode (first mode) showed a systematic change as t
=t~==tNi was changed from 60 A to 10 A, being the
highest for (60/60)5
multilayer and the lowest for
(1 O/l O)* multilayer. Among the two films with t =40 A,
the field for the first mode for (40/40)5 multilayer was
larger than that for (40/40)* multilayer indicating that the
number of bilayers also effects the field for resonance.
The intensity of second mode was lower than the intensity of the first mode for (20/20)*,
(40/40)5
and
(40/4O)a multilayers. In the case of (60/60)5 multilayer,
the intensity of the second mode was higher than that of the
first one. It is interesting to note that similar intensity behaviour has been reported by Kordecki et aL4 in case of Fe/Ni
multilayers and they have analyzed their results considering
the first mode as surface mode.
Such anomaly in the intensity pattern shows that FMR
spectra of multilayers are complex and cannot be analyzed
by simple calculations considering them as homogeneous
films. In Fe/Ni, both the layers are ferromagnetic and as
mentioned before, the resonance spectra results from excitation extending up to full thickness of the film, in which the
J. Appl. Phys., Vol. 78, No. 6, 15 September 1995
FIG. 1. Experimental F M R spectra of FeNi multilayers measured at 9.8
GHz in perpendicular configuration at room temperature. Absorption derivative has been shown in arbitrary units (A.U.).
individual layers are exchange coupled. One also finds in
these multilayers that the resonance field for highest field
mode is quite different from (o/y) + (49~&f), , where
(4 7rM) aVis average (4 7rM) of Fe and Ni. Also the field for
highest field mode is different for (t/t)” multilayers with
different t though (4 r&f) ay is the same.
We first describe the theoretical calculations based on
model described above for Fe/Ni multilayers and show how
the field positions and intensities of the modes depend on
various parameters such as the individual layer thickness, the
number of bi-layers etc. Here, the saturation magnetization
(47rM) and spin wave stiffness constant (D) for Fe and Ni
were taken from standard reference.15 The g-values were
taken as taken as 2.2 and 2.1 respectively for Ni and Fe.16
Since these are soft magnetic materials,” the Hk values were
assumed to be zero.
Fig. 2(a) shows the model calculations for (tlt)5 multilayers, where t has been varied from 30 A to 80 A. It is
clear from the figure that the field values for both first and
second mode increase with increase in t, even though the
ratio of tFe: tNi, and number of bi-layers are maintained constant. Interestingly, the intensity of second mode also increases with t and for t2 60 A, one finds that the intensity of
the second mode is higher than the first mode. Hence, acAcharya et al.
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3993
2501
I
I
I
!
I
I
I
200
!
I
(a>
1
I
,
tm=m* (t/t) s
1.
1
-
80
70A
22
n
-
-1
P)
&150-
>\
6OA
m
2
500
-2
-c
.22
8
d
i
First Mode
30A
q
5OA
-3
.i?
E
60
5OA 70A
&A’ &&%A
n
i
^.
120
Field
(kOe)
loo-
240r
200
,160
t
1
8
a
!
s
t
a
!
(50/50)”
u
1
(b).
8
,
80-
n=lOm
1
-
23
E
n=9
m
n=8
q
3
60-
8, n=7 w
.eA120 E
2
80-
3
n=6
2
n
FL
0
n=5
L7O
n=4
40 n--3
n=2
017
u
0
19
Field
I
-
Mode _
.
0-J
17.7
18.1
18.5
Resonance
m
Field (kOe)
.
I
I
,
I
I
0
,
2i
(k&f’
FIG. 3. Variation of field position and intensity of first and second modes
calculated for (Fe-M) multilayers with an intermediate layer of 17 A: (a)
with 47rM for a fixed value of D = 305 meV A*, and (b) with D for a fixed
value of 4~rhf = 12.5 kG.
FTG. 2. Variation of field position and intensity of tirst and second modes
calculated for (F&i) multilayers: (a) with t for (t/t)’ and (b) with n for
(50/50)“.
cording to these calculations, the second mode will have
about 35% of the first mode intensity for (40/40)5, whereas
for (70/70)‘, the second mode will have about 170% of the
intensity of the first mode.
Fig. 2(b) shows the results of the model calculations
carried out for (50/50)n multilayers, where n is increased
from 2 to 10. The calculations show that the field for the first
mode is independent of n and remains at 22.30 kOe. This is
an interesting point, realizing that with the change of n, the
total thickness of the films, in which the full excitation extents, keeps on changing. As seen in Fig. 2(b), the field for
the second mode as well as intensity increase with increase
in n. Again for n a7 the second mode becomes more intense
than the first one.
The independence of first mode field position on ‘n.’ is
not surprising when one realizes the following. An excitation
which has no crossing in a single bilayer and matches boundary condition dmldz=O
at the ends of the bilayer has to
satisfy the condition dmldz = 0 at all the interfaces of the
3994
bilayers without any crossing. This is because all the bilayers
are exactly identical and that the value of m from which an
excitation starts in a bilayer is not important. This can be
clearly demonstrated from Fig. 4 also, where mlM has been
plotted as a function of z for (50/50)n multilayers for different values of n as obtained from solution of Eq. (1). We
can notice dmldz = 0 at all the interfaces where one (Fe/Ni)
bilayer joins the other, as well as at the ends. This leads to an
important conclusion that the first mode of a (tllt2)” film
occurs at same field at which (t Ilt2) I occurs. Note that the
above argument will not be valid for the second mode, because in that case we are allowed to have only one crossing
throughout the excitation which can occur only within one of
the bilayers. One can thus also understand why an increase in
total thickness of bilayer causes an increase in the field of
first mode.
The experimental values of first mode field positions
have been compared to theoretical calculations in Table I.
The difference between the first and second mode field positions have been tabulated in Table II. The field positions and
intensities of all the observed modes for different multilayers
have been tabulated in Table III. The model calculations
J. Appl. Phys., Vol. 78, No. 6, 15 September 1995
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Acharya et a/.
TABLE I. Calculated and’experimental values of first mode field position~in
the perpendicular FMR spectra of (Fe/Ni) multilayers. Parameters : D(Fe)
=281 meV A2; D(Ni)=364 meV A’; .D(interlayer) ~306 meV A*
4n-M(Fe)=21.45 kG, 4n&4(Ni)=6.91 kG, 4rrM(interlayerj=
12.5 kG.
TABLE III. The experimental and calculated values of mode location and
intensity of perpendicular FMR spectra corresponding to different (Fe/Ni)
multilayers. Parameters : D(Fe)=281 meV As; D(Ni)=364 meV A*;
D(interlayer)=306 meV As 4n&f(Fe)?21.45
kG, 4nM(Ni)=6.91
kG,
4rrM(interlayer)=
12.5 kG.
First mode held position in kOe
Inter-layer
thickness
Calculated
!tdtNi)”
No.
in A
Experimental
No diiussion
with diffussion
1
2
3
4
(60/60)5
i40/40]5
(40/40)8
(20/20)8
20.23
19.71
19.02
17.25
22.51
22.03
22.03
21.55
20.98
19.82
19.45
17.51
21
17
19
15
However, the results from model calculations do not
agree with the experimental data on following points:
(1)The experimental field values were about lo%-20%
smaller than those calculated, the largest variation being observed for (20/2O)s multilayer. For example, in (60/60)5
the first mode occurs at 20.23 kOe, as compared to the calculated value of 22.57 kOe.
(2) The field positions for the first mode for (40/40)5
and (40/40)8 are not the same. This is in contradiction with
the model calculations.
TABLE II. The difference between the first and second mode positions in
the perpendicular FMB spectra of (Fe/Ni) multilayers : calculated and experimental values.
CtFJtNJn
in A
1
2
3
4
(60/60)5
C40/40)5
@O/40)8
QO/iO)*
Difference between first and second mode
tield positions (kOe)
Experimental
Calculated
1.07
1.40
0.98
1.97
1.13
1.53
0.89
1.90
J. Appl. Phys., Vol. 78, No. 6, 15 September 1995
Intensity(%)
Sample
Mode No.
Exp.
Calc.
Exp.
(60/60)5
1
2
3
4
20.23
19.16
18.21
16.87
20.98
19.48
18.12
16.12
100
107
1.1
0.3
100
139
0.2
2.9
(4014015
1
2
19.71
18.31
19.82
18.20
100
18.4
100
23.7
(40/40)8
1
2
19.02
18.03
19.45
18.55
100
42.5
100
64.0
(20/20)8
1
2
17.26
15.28
17.52
15.03
100
2.1
100
0.45
CalC.
(4
agree with the experimental results regarding following
points
(1) The field value for the first mode for (60/60)5
multilayer is higher compared to that of (40/40)5
multilayer, as predicted by the model calculation. Also, the
field for the first mode is higher for (40/4O)s in comparison
to that of (20/2O)s.
(2) The difference between first and second mode field
positions is higher for (40/40)5 multilayer than that of
(60/60)5
multilayer. The results for (40/4O)s
and
(20/2O)s multilayers are compared in a similar way. The
difference between first and second mode field positions for
(40/40)5 multilayer is higher than that of (40/4O)s. These
results agree well with model calculations as seen from Table
II.
(3) When we compare the spectra for (40/40)5 with that
of (60/60)5 multilayers, we observe that the intensity of the
second mode is higher than the first mode for (60/60)5,
whereas it is not so for (40/40)5. This result again agrees
with the model prediction.
No.
Mode location (kOe)
Therefore, though there is an agreement between the experimental intensity pattern and the relative field positions
for films with different Fe layer thicknesses, the absolute
values of resonance fields calculated using the model are
higher in comparison to the experimental values. The large
discrepancies between the experimental and calculated first
mode positions cannot be explained in terms of errors in
thickness measurements, because the values of the mode positions calculated expecting -t5% error in thickness values
were still higher than the experimentally observed ones.
These discrepancies may not be due to the anisotropy field as
Hk is very small for these multilayers, as mentioned earlier.
In the above calculations since the values of 4~M and D for
Fe and Ni are well established, we find no other reason for
the differences in the experimental and calculated spectra
other than the existence of an intermediate layer between the
two. Formation of such an interface layer is considered to be
common in the case of multilayers and has been reported in
case of FelNi, Fe/Co etc. by different workers using different
methods.Y*“~‘7~‘8Hence, we assumed that a part of each of Fe
and Ni layers constitute an intermediate alloy layer with
47rM and D values in between the values corresponding to
Fe and Ni.
We first assumed an intermediate layer 17 A thick for
(40/40)5 multilayer and varied the 47rM value for a given
value of spin wave stiffness constant D. Fig. 3(a) shows the
variation of first and second mode field location and intensity
with the 47rM value. It is clear from the figure that these
parameters increase with an increase in 4 TM of the intermediate layer. The second mode intensity shows a large dependence on 4rrM of the intermediate layer. Similar calculations
were made where the D values were varied but for a fixed
value of of 4~rM (experimentally it has been shown that D
values for Fe,Ni, --x alloys lie between 460 meV A2 to 140
meV A2 for 0s X> 0.6).19 Fig. 3(b) shows the results. Here
D values higher than that of Ni have also been used for the
interlayer just for illustration. The field location for lirst and
second modes decreases with the increase in D. Here again,
Acharya eta/.
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3995
nesses less than 15 A, we expect a complete mixing of Fe
and Ni. As mentioned, the ( 1O/l O)* sample showed only
one resonance peak at a field of 15.61 kOe. This field could
not be explained by assuming a partial mixing, because the
highest fields obtained were always higher than the experimental value, irrespective of the thickness of the interlayer.
For example, if we consider an interlayer of 9 A thickness
with 47&l= 13 kG and D = 350 meV A2, we obtain a first
mode at 16.8 kOe under the model calculations. We then
assumed that a homogeneous alloy film has been formed due
to total mixing of the Fe and Ni, and calculated the 4rrM
using the equation
0
100
Distance
200
300
from the topmost
400
500
layer (A}
FIG. 4. Plot of m/M vs z as obtained from solution of E?q.(l), where m/M
has been given in arbitrary units (A.U.). The continuous vertical Iines indicate interface between two bilayers, whereas the dotted lines indicate the
interface between Fe and Ni layers.
the second mode intensity showed a large variation with D.
The experimental resonance field position and intensity have
also been shown in Figs. 3(a) and 3(b). These results show
that the resonance field locations and intensities are strongly
dependent on the parameters selected for the intermediate
layer. These large variations in the field locations and intensities of different modes help in finding out the best fit for the
experimental results. The best fits were found out using field
locations and intensities of all the modes.
Calculations were made varying the intermediate layer
thickness and other parameters. Here when an interlayer of
thickness ‘6 is assumed, it is supposed to extend into Fe and
Ni layer equally by a depth of (a2). The thickness of the last
layer on the substrate side is taken less by 10 A to account
for any interfacial mixing or oxidation at film-substrate interface. Three parameters viz., 4rM, A and thickness of the
interfacial layer, were varied to get best fits. The best fits thus
obtained for different samples are shown in Table III for four
samples. As mentioned earlier, ( 1011 0)8 multilayer showed
only one resonance mode. The experimental spectrum for
this multilayer could not be fitted using model calculations
and this case will be discussed later. From these results we
note that
(9
(ii)
The values of field positions for resonance modes obtained from model calcuiations agree with the experimental values within an error of 5%.
The agreement between experimental and calculated
intensity patterns is good as earlier. For example, The
intensity for second mode is higher than the first mode
for (60/60)5, whereas it is not true for (40/40)5.
When an interlayer of 15 A is assumed for the
(,20/20)8 multilayer, 75% of the Fe and Ni is assumed to be
present in the alloy, leaving only 5 A of pure metal layer.
Hence, in the case of multilayers with individual layer thick3996
assuming this to be the uniform precession mode in a uniform film. The 4rM = 12.3 kG was obtained from this
equation which matches well with the 47rM value of 12.5
kG obtained for the interface layer in the calculations for the
other samples.
The above discussions lead us to conclude that the interface between Fe and Ni is not sharp. It is seen that the agreement between the theoretical and experimental values is
good, considering the simplicity of the model. These fits
were obtained when the intermediate layer thicknesses were
assumed to be of the order of 15-20 A indicating that an
intermediate alloy layer of 15-20 w is formed in these multilayers. Similar results were obtained by us by conversion
electron MGssbauer spectroscopic studies of rf sputtered
Fe/Ni multilayers. The low angle x-ray diffraction gave
rather ill defined Bragg peaks. This could be because of the
fact that Fe and Ni have similar x-ray absorptions. Morever,
Fe and Ni readily form solid solution and therefore, the
mixed layer is thicker than usually encountered in multilayers. It is worth pointing out that in case of Ni/Ti multilayers,
the interfacial dead layer was found to be 14 A.21
It is important to mention that normally one expects the
concentration of Fe and Ni layers to vary continuously in the
intermediate layer leading to a gradual variation of properties. In the present calculations we have approximated this
by a single intermediate layer having particular magnetic
properties for the simplicity in calculations. So the magnetic
parameters given above for intermediate alloy layer should
be treated as a sort of average value only.
C. Fe/CoNbZr
multilayers
In this section we report the results of our study on
Fe/CoNbZr multilayers. This study is different from the one
reported on Fe/Ni in the following ways:
(1) In these multilayers, one of the layer is an alloy, which is
known to be useful as a recording head material.
(2) Here, the relative thicknesses of the samples are also
varying. This is unlike Fe/Ni multilayers where tFe
-tNi*
(3) The CEMS study was carried out on exactly same series
of multilayers which showed the formation of an intermediate alloy layer.‘” From CEMS study, an estimate of
thickness of undiffused Fe layer was also obtained.
J. Appl. Phys., Vol. 78, No. 6, 15 September 1995
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Acharya et al.
TABLE N. The experimental and tabulated values of mode location and
intensity of perpendicular FMR spectra corresponding to different
(FeKoNbZr) multilayers. Parameters : D(Fe)=281 meV A*; D(CoNbZr)
=210 meV A*; D(interiayer)=230
meV A” 4rrM(Fe)=21.45
kG,
4?rM(C!aNbZr)=g
kG, 4z-M(interlayer)=
12 kG [16.0 kG for
(36/36)‘7+‘R].
Mode location (kOe)
Sample
(1 H/36)“+‘”
CdC.
Exp.
talc.
20.60
N.O.
19.96
19.31
18.41
20.37
20.24
19.98
19.58
19.05
100
4.54
0.03
0.05
100
0.58
4.13
0.14
0.59
21.87
21.67
21.36
N.O.
20.20
20.06
21.85
21.72
21.47
21.09
20.57
19.95
100
.9
7.98
0.2
100
.6
3.83
0.13
Sl
.03
1
2
3
22.44
N.O.
21.72
22.97
2271
22.20
100
4.4
100
0.78
1.98
1
2
3
3
5
6
7
8
20.69
20.6@
20.45
20.40
20.26
20.20
19.93~
19.51
21.10
21.02
20.87
20.66
20.40
20.07
19.71
19.32
100
a
23.5
a
9.18
a
0.45
0.45
100
0.03
7.67
0.03
1.62
0.01
0.46
0.01
1
2
3
4
5
20.44
20.22
19.77
19.45
19.05
20.54
20.42
20.18
19.85
19.49
100
8.48
1.7
0.04
0.21
100
9.47
2.55
0.87
0.3 1
“Experimentally comes as a shoulder; difficult to measure intensity.
(4) Here we have one extra layer of CoNbZr, whereas the
number of Fe and Ni layers were equal in case of Fe/Ni
multilayers.
In Table IV we show the field position and intensity for
five different multilayers. We observed that, for fixed
koNbzr = 36 A, the increase of tFe causes an increase of
field of first mode. On the other hand, if tFe is kept constant
at 69 A, the increase in tCoNbZrcauses a decrease in first
mode field value. This is interesting result, which indicates
that the increase in the layer thickness of large 4 TM material
is responsible for the increase in the field value of first mode,
contrary to the increase in layer thickness of small 4-rrM
value. However, it should be remarked that, when tCoNbZr
was changed for fixed tt+, the total number of layers were
kept constant, while it was not the same in the other case. As
far as the intensity is concerned, the intensity of the second
mode does not show significant change with either change in
tFe Or bNbZr.
Model calculations were made for the multilayers considering the actual thickness of individual layers. The values
of 43-M and D were taken from standard references as before. For CoNbZr, the value of 4 TM was determined experiJ. Appl. Phys., Vol. 78, No. 6, 15 September 1995
Fist mode field position in kOe
Calculated
Intensity(%)
Exp.
Mode No.
TABLE V. Calculated and experimental values of first mode field position in
the perpendicular FMR spectra of (FeKoNbZr) multilayers. Parameters :
D(Fe)=281 meV A*; D(CoNbZr)=210 meV A’; D(mterlayer)=230 meV
A” 4rrA4(Fe)=21.45 kG, 4rrM(CoNbZr)=8 kG, 4rrM(interlayer)=
12 kG.
No.
in .A
Experimental
No diffussion
With diffussion
1
2
3
(36/36)‘7+‘”
(69/36)13+ uz
(115/36)‘jtm
20.60
21.87
22.44
21.29
22.75
23.47
20.37
21.85
22-97
4
5
6
(69/36)‘3+“2
(69/60)13+‘”
(69/90)13+‘”
21.87
20.63
20.44
2275
2200
21.46
21.85
21.10
20.54
mentally for a thicker single layer of CoNbZr film as 7800
2200 G. The value of exchange constant was determined by
FMR spectra of a single layer material of same
composition,2’ which was 0.5X 10m6 erg/cm (D=210 meV
A”). As before, the initial calculations were made without
assuming formation of interfacial alloy layer. The first mode
field positions have been given in Table V. As in the case
Fe/Ni, the field positions were higher than the experimental
values.
Even when an error of -+5% in thickness measurement
of Fe and CoNbZr layers is allowed, the discrepancy in the
calculated and experimental field positions could not be accounted for.
However, the following points can definitely be noted
from the calculations. Like experimental results, the first
field position does decrease with tFe for fixed tCoNbZr.Also,
the field position decreases with increase of the field position
decreases with increase of tcoNbzrfor fixed tFe. This confirms
our earlier conjecture that the thickness of high 47rM material causes different kind of change in comparison to the
increase in thickness of lower 41rM material.
Similar to our earlier results, we decided to carry out
calculations assuming interfacial layer. Our earlier CEMS
studies had shown that, in case of the film with t,=24
A
50% of the Fe in the Fe layer had formed an al1oy.s So, one
can assume that 6 8, on each side of the 24 A Fe layer has
been used to form an alloy layer.
The model calculations for the field positions and intensities of the spin wave spectra were made in the following
way.
(a)
(b)
and A values, were varied starting with average
values of these parameters corresponding to Fe and
CoNbZr layers.
The intermediate layer thickness of such layer on the
Fe side as 6 A, as deduced by CEMS studies of these
films (as discussed above).
~TM
The calculated and experimental values of field position
and intensities of the FMR spectra for different films are
tabulated in Table IV. The best agreement between experimental and calculated spectra was obtained when an interlayer was considered such that 6 A on each side in Fe layer
Acharya et al.
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3997
and CoNbZr layer has formed an ahoy layer to give a total
interlayer thickness of 12 A. In this case also, the thickness
of the last layer on the substrate side is taken less by 10 A to
account for any interfacial mixing at the film-substrate interface. In the above calculations, the parameters assumed for
the interlayer were same for all the films. It can be seen from
Table IV that the agreement between the theoretical and experimental values are good. The thickness of - 12 A for
the interlayer was estimated by the analysis.
IV. CONCLUSIONS
The FMR spectra of Fe/Ni and Fe/CoNbZr multilayers
consist, in general, of more than one mode. The position and
intensity of the modes showed large variations with a change
in the thickness of the individual layer and the number of
bi-layers. These results were explained in terms of a model
calculation under the assumption of an inter-facial ahoy layer.
We could get good agreement in the field positions and intensities of various modes with experimental values.
ACKNOWLEDGMENTS
One of the authors (B.R.A.) acknowledges the Council
of Scientific and Industrial Research, New Delhi, for financial support.
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