4278
IEEE TRANSACTIONS ON MAGNETICS,
VOL.
25.
NO.
5.
SEPTEMBER
1989
Permalloy Multilayers to Reduce the Effects
of
Uniaxial Anisotropy
JOHAN W. WIEBERDINK
AND
KEES
J.
M. EIJKEL
AbstractThe anisotropic magnetoresistance effect of Permalloy
(Ni0.82Fe0.,8) is used in a contactless angle detector
[l].
The uniaxial
magnetic anisotropy in a Permalloy thin film causes a difference be
tween the magnetization and the magnetic field direction. This leads to
a systematic error in the angle detector output. The effects
of
uniaxial
magnetic anisotropy can be reduced by using Permalloy multilayers
with different orientation
of
their anisotropy axes.
A
double layer with
mutually perpendicular anisotropy axes is found to be sufficient for
application in an angle detector. The StonerWohlfarth singledomain
model is used to describe the systematic error of an angle detector using
multilayers.
INTRODUCTION
N OUR research group a contactless angle detector
I
based on the anisotropic magnetoresistance effect (AMR
effect) in a Permalloy thin film has been proposed
[
11.
The
AMR effect is used to detect the direction of magnetiza
tion
E
in the Permalloy film which is influenced by the
magnetic field of a rotatable permanent magnet. The
output signal of the angle detector yields the direction of
magnetization (output angle
8
)
while the object is to
measure the angular position of the magnet (input angle
cp).
The uniaxial magnetic anisotropy of Permalloy causes
a difference between the angles
cp
and
8
resulting in a
systematic error
(cp

e)
of the angle detector (see Fig.
1).
This systematic error is determined by the strength and
direction
of
both the uniaxial anisotropy (UA) and the
magnetic field
E
(Fig.
2).
The UA
is
induced during the
deposition of a Permalloy film and can be oriented with
the aid of an external magnetic field during film growth.
The orientation of the anisotropy axis or easy axis (EA)
and the strength of the UA are characterized by the angle
a!
(Fig.
1)
and the anisotropy field strength
Hk.
It is possible to calculate the systematic error if
CY
and
the ratio
Hk/H
are known. In this way the angle detector
output can be corrected. However, it
is
preferable to elim
inate the effects of the UA in the Permalloy film itself.
Annealing is one wellknown means to reduce the UA
[2],
[3] and in our case a
1.5
h/500"C annealing treatment
proved to be sufficient to meet the requirements, viz.
(cp

e)
I
0.1"
for
H
=
10
kA/m. Another solution
Manuscript received December 1, 1988; revised February
2,
1989. This
The authors are with the University
of
Twente, ELTDM, P.O.
Box
IEEE Log Number 8927698.
work was supported by the Netherlands Technology Foundation
(STW).
217, 7500 AE Enschede, The Netherlands.
Fig. 1.
A
Permalloy
film
with uniaxial anisotropy.
L
Fig. 2. The systematic
error
(p

e)
of the angle detector as a function
of
lp.
exploits the inhomogeneity
of
the magnetic field of the
permanent magnet to reduce the systematic error
[3].
In
this paper a new approach to reduce the effects of UA is
proposed using multilayers
of
Permalloy with different
orientation of their easy axes.
SINGLE
LAYER
We start by describing the magnetic behavior of a sin
gle layer in order to describe the systematic error of an
angle detector using multilayers. For a Permalloy film
with UA in a homogeneous magnetic field the angle
(cp

e)
follows the StonerWohlfarth singledomain
model [4]:
Hk
sin
(cp

e)
=
sin
2(8

CY).
2H
One cannot solve
e(
cp)
explicitely, but (1) can be re
written as an iteration process
(2).
Now
8
(cp)
can be cal
culated for all values of
cp
starting with
eo
=
cp
and the
exact solution can be approximated as accurately as nec
essary.
00189464/89/09004278$01
.OO
0
1989 IEEE
WIEBERDINK
AND
EIJKEL:
REDUCTION
OF
THE
EFFECTS
OF
UNIAXIAL
ANISOTROPY
4279
Alternatively, one can approximate
(cp

0)
(cp)
with the
first two terms of a simple Fourier series derived from
(1).
This Fourier series
(3)
clearly shows how
(cp

0)
de
pends on
cp
and the ratio
Hk/H
and is very appropriate for
describing the systematic error of multilayers.
For a singlelayer Permalloy film we have
Hk
=
450
A/m,
so
the maximum systematic error of the angle de
tector at
H
=
10
kA/m is
1.3"
(Fig.
2).
MULTILAYERS
The effect of the UA in a Permalloy film on the perfor
mance of the angle detector can be reduced by using mul
tilayers of Permalloy with different easyaxis orientation.
This is obvious from the fact that a single layer with two
mutually perpendicular easy axes with equal anisotropy
constants
K,
is magnetically isotropic. The total anisot
ropy energy
E,
of such a film is independent of
0:
Metzdorf
[5]
managed to reorient a part of the anisotropy
in the hard axis direction and realized isotropic Permalloy
films. However, the magnetic properties of these films are
not stable in a magnetic field for the desired operating
temperatures of the angle detector. In order to approxi
mate the ideal situation we realize multilayers with dif
ferent EA orientation.
We used a computer simulation to calculate the system
atic error of a double and fourlayer and determine its
maximum value (Table I). Here, an ideal situation is con
sidered: the
Hk,i
and thickness
ti
of the layers
(i
=
1,
2
or
1

*
4)
are equal and the angle between the EA of
subsequent layers is exactly
n/2
(doublelayer) or
n/4
(fourlayer). The influence of exchange and magnetostatic
interaction between the layers is neglected.
A ferromagnetic exchange interaction between the lay
ers would try to align their magnetization and would cause
an additional decrease
of
the systematic error. An anti
ferromagnetic exchange interaction or a magnetostatic in
teraction would try to direct the magnetizations antipar
allel and would increase the systematic error.
The computer simulation uses the iteration method
(2)
with the corresponding
ai
to calculate the exact magneti
zation direction in each layer of a multilayer film. The
average magnetization direction of a film,
e(cp),
is de
fined as the average value of
8;
over the number of layers.
The averaging mechanism that occurs in the angle detec
tor includes the nonlinear AMR effect, but for
H
>>
Hk
both averaging mechanisms provide approximately equal
results. Table I shows the maximum values of
(cp

6
)
(
cp)
as
a
function of the number of layers (ver
TABLE
I
MAXIMUM
OF
((0

6
)
((0)
OF
MULTILAYERS
FOR
DIFFERENT VALUES
OF
Hk/H
H,/H
=
((0

e),,,
Func_tion
(in degrees)
0.2
0.1 0.05
((0

e
~(0)
Singlelayer
5.8
2.9
1.5
sin
(2~)
Doublelayer
0.57 0.15
0.036
sin
(4~)
Fourlayer
0.014 0.0089
0.000056
sin
(8~)
tical) and the value of
Hk/H
(horizontal). In the last col
umn the shape of
(cp

e
)
as a function of
cp
is given.
From Table I it is clear that (5) approximates the system
atic error of multilayers
(
a,
=
0):
with
C1
=
1,
C2
=
1,
and
C4
=
2.5
(5)
with
n
being the number of layers. The same result can
be obtained by using
(3)
for the successive Permalloy lay
ers of a film. One simply has to add the expressions for
(cp

ei)
(
cp)
to obtain
(cp

6
)
(cp).
In case of a double
layer the sin
(2cp)
term is eliminated and in case of a four
layer the sin
(4cp)
term is also eliminated.
In a nonideal situation the above terms are not com
pletely eliminated due to differences in the
Hk,i,
ti,
and
a;
of the layers, caused by technological inaccuracies. In that
case,
(cp

0
)
(cp)
can be approximated with the first
three terms of a Fourier series
(6).
The coefficients
c,
,
c2,
and
c4
denote the strength of the corresponding Fourier
terms and depend on the ratio
Hk/H
and the technological
accuracy. The constants
6,,
a2,
and
64
represent the phase
of the Fourier terms and depend on the field direction at
cp
=
0
with respect to
a,.
The quality factors
q,,
q2,
and
q4
defined in
(6)
are independent of
Hk/H.
They indicate
the success of the technological realization. For an ideal
doublelayer we find
q1
=
0,
while an ideal fourlayer
yields
q1
=
q2
=
0.
(cp

e)(,)
=
c,
sin
(2cp
+
6,)

c2
sin
(4cp
+
6,)
+
c4
sin
(8cp
+
6,)
+
Hk
=
q1

sin
(2cp
+
6,)
2H
If
(cp

6
)
(cp)
is determined for a multilayer, the an
isotropy field strength of the Permalloy can be calculated
from the Fourier coefficients in
(6).
This is, of course, an
approximation of the actual anisotropy field strengths
Hk,i
of
the different layers. The value of the ani_sotropy
field strength calculated this way will be called
Hk.
It is
4280
I
IEEE TRANSACTIONS
ON
MAGNETICS,
VOL.
25.
NO.
5,
SEPTEMBER
1989
derived from the first term in
(6)
which is completely
present
doublelayer:
'fik
=
2
H
4
r
fourlayer:
fik
=
2H
4 .
2/25
J
(7)
TECHNOLOGY
The Permalloy (82 at
%
Ni and 18 at
%
Fe) films are
RF sputtered on oxidized silicon wafers and a fixed bias
field of
2
kA/m is used during film growth to direct the
easyaxis orientation. In order to realize multilayers with
different EA in our sputtering system it is necessary to
break the vacuum and rotate the wafer by hand.
In our case, the bias field is too weak to induce a new
EA in the next layer
so
the EA of the previous layer is
continued
[6].
We used an intermediate layer of chro
mium to interrupt the continuity of the Permalloy film
growth. Chromium is very suitable because a thin layer
of
3
nm is sufficient for magnetic separation
[7]
while the
resistivity of Cr is relatively high. Therefore, the Cr layer
hardly influences, that is, shortcircuits, the AMR effect
in the Permalloy layers (thickness
25
or
50
nm) and does
not disturb the AMR signal of the angle detector.
Application of a ferromagnetic intermediate layer would
establish exchange interaction between the Permalloy lay
ers and would further reduce
(cp

6
)
(cp).
However, the
actual advantage is negligible, because the maximum an
gle between the magnetization directions in neighboring
films is small for the field strengths used in the angle de
tector. Consequently, the domain wall between subse
quent Permalloy layers, having a width of a few nano
meters, is restricted to the intermediate layer,
so
the
exchange interaction has no influence on the magnetiza
tion orientation in the Permalloy layers. In order to obtain
a symmetrical structure, extra Cr bottom and top layers
are needed (Fig.
3).
Otherwise, the values
of
Hk,[
and
coercivity
H,,
of separate Permalloy layers differ consid
erably.
In practice, three technological problems remain: The
accuracy of the angle between the easy axes is determined
by both the inhomogeneity of the bias field and the man
ual rotation of the wafer. Thickness variations within one
layer up to 10 percent occur in our sputtering system due
to the inhomogeneous sputter process, causing thickness
differences between the layers of a multilayer film. This
is a consequence of the small sputter target and the influ
ence of the bias field on the plasma distribution.
CHARACTERIZATION
An Inductive Hysteresis Meter (IHM) is used to deter
mine the
H,,;, Hk,;,
and saturation magnetic moment
312,,;
of both layers
(i
=
1, 2) of a doublelayer. The layer
thickness
ti
is assumed to be proportional to
3n,,;.
The
32H
curve of a doublelayer is a superposition of the two
3nH
curves of the separate layers.
If
the IHM measures
Cr
NiFe layer
2
Cr
NiFe
layer
1
Fig.
3.
A doublelayer structure.
(b)
Fig.
4.
32N
curve EA1
+
HA2 (a) and EA2
+
HA1 (b)
of
a double
layer.
Fig.
5.
A sample with point contacts in pseudoHall configuration.
the easyaxis curve of layer 1 (EAl), it also measures the
hardaxis curve of layer
2
(HA2), because EA1 coincides
with HA2 in a doublelayer. Fig. 4(a) shows the
32H
curve EA1
+
HA2 from which
Hc,l,
3ns,1,
and
Hk,*
are
determined. After rotating the film
90°,
EA2
+
HA1,
with
H,,*,
3ns,2,
and
Hk,
I,
is measured (Fig. 4(b)). A four
layer cannot be characterized with the IHM.
The Crowther method
[8]
is normally used to measure
the angular dispersion in the easyaxis orientation. We
used it to determine the exact angle between the different
easy axes of a multilayer.
A third characterization method measures the Permal
loy film in a pseudoHall configuration (Fig.
5).
The film
with voltage and current point contacts is rotated over
0"
I
cp
I
180"
in a magnetic field
H
I
6
kA/m and
the pseudoHall voltage
Veh
(
cp
)
is measured
[9].
A com
puter program calculates
8
(
cp)
and determines the Fou
rier components of
(
cp

6
(
cp
).
WIEBERDINK AND EIJKEL: REDUCTION
OF
THE EFFECTS
OF
UNIAXIAL ANISOTROPY
RESULTS
AND
DISCUSSION
I
4281
We sputtered several doublelayer films, with different
Cr thickness
tcr,
and one fourlayer film. The sputtered
wafers were broken into samples of
1
x
1 cm'. The coer
civity
H,
of a doublelayer is reduced
(H,
=
25
A/m at
tcr
=
3
nm) and our results concerning
H,
as a function
of
tcr
agree with Herd and Ahn
[lo].
The differences be
tween the
Hk,i
and
t,
(i
=
l,
2)
of a doublelayer sample
vary up to
10
percent. The maximum deviation of the
easyaxis orientation with regard to the ideal orientation
is found to be
7".
Each wafer contains some samples with
a deviation of less than
1
O.
In general, the best samples
are positioned at the center of a wafer and the relation
between the technological success of a sample and
(cp

0
)
(cp)
is always very obvious. We present the re
sults of a successful doublelayer and fourlayer sample.
The systematic error
(cp

6
)
(cp)
of a doublelayer
(Fig.
6)
is a sin
(4~)
function with an amplitude approx
imately proportional to
(&/2H)*.
For higher values
of the magnetic field strength (not shown in Fig.
6),
the
sin
(2cp)
term with amplitude
qlHk/2H
dominates in
(cp

0
)
(cp).
The factor
q1
indicates the suppression of
the sin
(2cp)
term and should be zero for an ideal double
layer. The amplitude of
(cp

e)(cp)
is slightly higher
than expected from the model. Therefore, the
Hk
of a dou
blelayer, calculated using
(7),
is increased in comparison
with the
Hk,,
of the separate layers.
Hk
is found to depend
on the magnetic field strength and increases up to
600
A/m at
H
=
6
kA/m. This is not predicted by the model.
The systematic error
(cp

6)
(cp)
of a fourlayer (Fig.
7)
is, in an ideal case, a sin
(8p)
function with an ampli
tude proportional
to
(Hk/2H)4.
The sin
(8~)
term in the
film of Fig.
7
is only recognizable for the lowest magnetic
field strength
(500
A/m) because the sin
(2cp)
term dom
inates for
H
I
1
kA/m. The influence of the sin
(4p)
term with amplitude
q2
(
Hk/2
H
)'
is negligible because
Hk/H
<<
1.
Good fourlayers
(qI
=
q2
=
0.01)
can
achieve
(cp

8)(p)
I
0.05"
forH
=
5
kA/m.
Again, the behavior of the film deviates from the model:
The
Hk
of the fourlayer, calculated using
(7),
depends
strongly on the magnetic field strength and varies from
350
A/m at
H
=
500
A/m to
1
kA/m at
H
=
6
kA/m.
The unexpected dependence oft& on
H
does not occur
in singlelayer films. Therefore, the observed deviation
from the model is ascribed to the existence of magnetic
coupling between the layers, which is neglected in the
model. To explain the observed effects, this coupling
should tend to increase the angle between the magneti
zation in two neighboring layers. Such a coupling can be
either magnetostatic, viz. dipolar coupling via planar de
magnetization, or of an exchange type. Computer simu
lations show that the demagnetizing field of our films is
orders of magnitude too small to account for the observed
behavior. Therefore, the existence of an antiferromag
netic exchange coupling between the Permalloy layers is
regarded as a candidate for the observed deviations. Such
an interaction between Fe thin films across a Cr interme
diate layer has recently been reported by Griinberg
[l
11.
T
4
E
3
Fig.
6.
Measured
(q

6
)
(q)
of a doublelayer.
(
fCr
=
3
nm,
t,,,,
=
50
nm,
Hk,,
=
400
A/m,
q,
=
0.02.)
Fig.
7.
Measured
(q

6
)(q)
of a fourdayer.
(tCr
=
3
nm,
tNIFe
=
25
nm,
q,
=
0.1,
q2
=
0.1.)
His experiments concern epitaxially grown Fe and Cr lay
ers, which seems to be of crucial importance for the ob
served pronounced antiferromagnetic coupling between
the Fe layers. The question whether a weak antiferro
magnetic exchange coupling between polycrystalline
Permalloy layers across a thin polycrystalline Cr inter
mediate layer is the cause of the observed dependence of
fik
on
H
is
a very interesting one. Further experiments
will be necessary to provide an insight into this problem.
CONCLUSIONS
The effect of the uniaxial anisotropy on the perfor
mance of the angle detector can be reduced by using mul
tilayers of Permalloy with different easyaxis orientation.
The anisotropy field strength
Hk
and the thickness of each
layer must be equal and the angle between their easy axes
must be exactly
7r/2
(doublelayer) or
7r/4
(fourlayer).
In this ideal situation, the systematic error
(cp

6
)(cp)
of the angle detector is in good approximation propor
tional to
(Hk/2H)"
sin
(2ncp),
where
n
is the number of
layers
(n
=
2,
4).
In order to induce a new easyaxis orientation during
deposition of a Permalloy layer on top of another Perm
alloy layer in a weak bias field, an intermediate layer is
necessary to interrupt the continuity of the Permalloy, be
cause otherwise the easyaxis orientation of the previous
layer is continued. Chromium proved to be successful and
has the advantage of not disturbing the
AMR
signal of the
angle detector.
We realized doublelayers that meet the requirements
for application in an angle detector:
(
cp

8
)
(cp)
<
0.1
"
for
H
=
10
kA/m. The model predicts an even better
performance of fourlayers but they require a more accu
4282
IEEE TRANSACTIONS
ON
MAGNETICS,
VOL.
25.
NO.
5.
SEPTEMBER
1989
rate technology. Our laboratory conditions are insufficient
to realize good fourlayers. The amplitude of
(
p

8
)
(
p)
of double and fourlayers is higher than predicted by the
model. As a consequence, calculations based on the model
yield an average anisotropy field strength
Hk
of a multi
layer that is higher than the
Hk,i
of
the separate layers.
This is probably due to the neglect
of
magnetic coupling
between the layers. Antiferromagnetic exchange coupling
between the Permalloy and chromium layers is a possible
candidate
for
such a coupling. Further experiments have
to be performed to solve this question.
ACKNOWLEDGMENT
This work is part
of
the research on Permalloy sensors
in the Transducers and Materials Science group of the
Faculty of Electrical Engineering, University of Twente,
under the supervision
of
prof. dr. Th.
J.
A.
Popma and
prof, dr.
J.
H.
J.
Fluitman. The authors would like to
thank ir.
P.
de Haan and dr. R. M. de Ridder for helpful
discussions.
REFERENCES
K.
J.
Eijkel and
J.
H.
J.
Fluitman, “Angle detection based
on
the
resistance anisotropy of permalloy,”
IEEE
Trans. Magn.,
vol. MAG
J.
W.
Wieberdink, M. Sc. thesis, University of Twente, UT/EL/TDM
070.2386, 1988
(in Dutch).
K.
J.
Eijkel and R. Rijk, “Contactless angle detection using permal
loy,”
IEEE
Trans. Magn.,
vol.
24,
pp.
17611763, 1988.
22,
pp.
955957, 1986.
[4]
M. Prutton,
Thin Ferromagnetic Films.
London, UK: Butterworth,
1964,
p.
55.
[SI
W. Metzdorf, “Die Beeinflussbarkeit der uniaxialen Anisotropie auf
gedampfter Permalloyschichten durch Tempern im Magnetfeld,”
Zeirschrij2
Ang.
Phys.,
vol.
18,
pp.
534540, 1965
(in German).
[6]
K.
J.
Eijkel,
“A
thin film magnetoresistive angle detector,” Ph.D.
dissertation, University of Twente,
1988.
171
P. Swiatek, F. Saurenbach, Y. Pang, P. Griinberg, and
W.
Zinn,
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61,
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37533755, 1987.
[8]
T.
S.
Crowther, “Angular and magnitude dispersion of the anisotropy
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vol.
18,
pp.
580586, 1963.
[9]
K.
J.
Eijkel, “Measurement of the anisotropy in permalloy,”
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[lo]
S.
R. Herd and K. Y. Ahn, “Magnetic domain structures in multi
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pp.
23842386, 1979.
[I
11
P. Griinberg, in R. F.
C.
Fallow
et
al., Thin Film Growrh Techniques
for
Low
Dimensional
Siructures
(NATO AS1 Series,
Series
B
Physics
Vol.
163).
New York,
NY:
Plenum,
1987,
pp.
487505.
Johan
W. Wieberdink
was born in Apeldoorn, The Netherlands, in
1963.
He
received the M.Sc. degree in electrical engineering
from
the University
of Twente, Enschede, The Netherlands, in
1988.
Kees
J.
M.
Eijkel
was born
in
Heiloo, The Netherlands, in
1959.
He
re
ceived the M.Sc. degree in mathematics from the University of Amster
dam, Amsterdam, The Netherlands, in
1983
and the Ph.D. degree from the
University of Twente, Enschede, The Netherlands, in
1988.