Magneto-optical determination of helical magnetic structure in amorphous microwires

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Physica B 403 (2008) 289–292
Magneto-optical determination of helical magnetic structure
in amorphous microwires
A. Chizhika,?, J.M. Blancob, A. Zhukova, J. Gonzaleza, C. Garciaa,
P. Gawronskic, K. Kulakowskic
aDepartamento Fı ´sica de Materiales, Facultad de Quı ´mica, UPV 1072, 20080 San Sebastia ´n, Spain
bDepartamento Fı ´sica Aplicada I, EUPDS, UPV/EHU, Plaza Europa 1, 20018 San Sebastia ´n, Spain
cFaculty of Physics and Applied Computer Science, AGH University of Science and Technology, 30-059 Cracow, Poland
Abstract
Surface magnetization reversal has been investigated in Co-rich glass-covered microwires. Difference in mechanism of the surface
magnetization reversal has been observed in the microwires with different thicknesses of glass covering. Correlation of the surface
magnetic properties and the surface helical magnetic anisotropy has been found.
r 2007 Elsevier B.V. All rights reserved.
PACS: 75.50.Kj; 75.60.Ch; 75.60.Ej
Keywords: Amorphous microwire; Kerr effect; Hysteresis loop
Giant magnetoimpedance (GMI) of glass-covered amor-
phous microwires is of special scientific interest due to the
large sensitivity of the electrical impedance of the magnetic
conductor to the dc magnetic field [1]. Taking into account
that the GMI effect is a surface effect, the investigation of
the magnetic structure in the surface area of the wire takes
special importance. The application of the magneto-optical
Kerr effect (MOKE) for the study of microwires demon-
strated the advantages of this method for the investigation
of magnetization reversal in the surface of non-plane
samples [2]. The aim of this work is to determine the type of
the magnetic structure and the degree of helical anisotropy
in the surface area of the microwires.
Glass-covered microwires (nominal composition Co69.5
Fe3.9Ni1B11.8Si10.8Mo2) have been studied with different
geometric ratio r of metallic nucleus diameter d to total
diameter D, r ¼ 0.785 and 0.930. The experiments have
been performed using the transverse MOKE in axial
magnetic field. The change of the light intensity reflected
from the surface of the microwire was proportional to the
circular projection of the magnetization in the surface area
of the wire. An axial magnetic field has been produced by a
pair of Helmholtz coils.
Fig. 1 presents the transverse Kerr effect dependencies
on the ac circular magnetic field (frequency f ¼ 60Hz) with
the dc axial magnetic field as a parameter. Fig. 1(a)–(e) and
(f)–(k) show the axial field-induced transformation of the
surface circular hysteresis loop for the microwires with
r ¼ 0.93 and 0.785, respectively. Fig. 2 presents the
transverse Kerr effect dependences on the ac axial magnetic
field (frequency f ¼ 60Hz) for the microwires with
r ¼ 0.93 (Fig. 2(a)) and 0.785 (Fig. 2(b)).
When the dc axial magnetic field is absent, the shape
of the circular hysteresis loop is perfectly rectangular
(Fig. 1(a) and (f)) that is related to the circular magnetic
bistability. For the circular magnetic field smaller than the
value of the circular coercive field the hysteresis loop is not
observed.
The dc axial magnetic field initiates the transformation of
the circular hysteresis loop and this transformation occurs
in two different ways for the two studied microwires. Let us
consider first the transformation of the hysteresis loop for
the microwire with r ¼ 0.93 (Fig. 1(a)–(e)). The application
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doi:10.1016/j.physb.2007.08.031
?Corresponding author. Fax: +34943017130.
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of the dc axial magnetic field causes the asymmetrical
change of the switching field, HSW (associated with the
switching current) (Fig. 1(b)–(d)). We can see that the value
of one of the switching field ðHþ
of another switching field ðH?
manifests as the observed ‘‘shift’’ of the hysteresis loop
along the x-axis.
The transformation of the circular hysteresis loop for the
microwire with r ¼ 0.785 occurs in another way. The
absolute values of H?
and the ‘‘shift’’ effect is not observed (Fig. 1(g)–(j)). The
application of the negative axial magnetic field (Fig. 1(k))
transforms the hysteresis loop in the same way as the
positive one.
A great difference is also seen between the hysteresis
loops obtained in the ac axial magnetic field for two
studied microwires (Fig. 2(a) and (b)). As we have seen
earlier [3], when the external axial magnetic field increases,
a monotonic increase of Kerr signal is observed. This
increase is related to the rotation of the magnetization
from the axial to the circular direction in the outer
shell of the wire. After that, a sharp jump of the signal
takes place with change in signal sign. This is related to the
jump of the circular magnetization. For the microwire
with r ¼ 0.93 this jump occurs at relatively small axial field
and the value of the jump of magnetization is high enough.
For the microwire with r ¼ 0.785 the magnetization
reversal consists mainly of the fluent rotation of the
magnetization. The jump of the circular magnetization is
small.
The calculation of the hysteresis loops has been
performed taking into account the existence of a helical
magnetic anisotropy in the surface area of the microwire.
In our experiments, the part of the surface of the wire from
which the light goes to the detector is almost plane one.
Therefore, in our calculations we treat the wire surface as a
two-dimensional system. The magnetic field can be
presented as a superposition of two mutually perpendicular
fields (haxialand hcirc) and the direction of the anisotropy
was changed from axial to circular direction.
SWÞ decreases when the value
SWÞ increases. This effect
SWand Hþ
SWdecrease symmetrically
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Fig. 1. Transverse Kerr effect dependences on circular magnetic field with
axial bias field as a parameter: (a–e) wire with r ¼ 0.93; (f–k) wire with
r ¼ 0.785.
Fig. 2. Transverse Kerr effect dependencies on axial magnetic field for two
wires with different geometric ratios r.
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The expression of the energy of the system has the form
U ¼ ? KUcos2ðy ? jÞ ? h ? m
¼ ? KUcos2ðy ? jÞ ? haxialcosðyÞ ? hcircmsinðyÞ,
ð1Þ
where KU is the uniaxial anisotropy constant, m is
the saturation magnetization, y is the angle between
the magnetic moment and the microwire axis and j is the
angle between the anisotropy axis and the microwire axis.
We obtain calculated hysteresis curves of two types: the
dependencies of the circular magnetization on the circular
magnetic field in the presence of the axial bias field and the
dependences of the circular magnetization on the axial
magnetic field.
The results of the numerical analysis of Eq. (1) are
presented in Figs. 3 and 4. There are hysteresis loops for
two configurations: when the direction of the uniaxial
anisotropy is close to the circular direction in the micro-
wire (Figs. 3(d)–(f) and 4(b)) and when this direction
isnoticeablyinclinedfrom
(Figs. 3(a)–(c) and 4(a)).
The results on the calculated hysteresis loops allow us to
conclude as follows. The presence of the anisotropy
inclined from the circular direction causes an asymmetric
transformation of the hysteresis loop. The shift of the
curve takes place in the presence of the axial bias field
(Fig. 3(a)–(c)). The direction of the shift depends on the
sign of the bias field. When the anisotropy direction is
directed exactly along the circular direction, the bias field
induced shift is not observed and the value of the switching
field decreases symmetrically. For the case when the
angle of anisotropy j is close to 901, the shift is very small
(Fig. 3(d)–(f)).
The calculated loops presented in Fig. 4 demonstrate
how the direction of the anisotropy influences on the
dependence of the circular magnetization on the axial
magnetic field. When the direction of the anisotropy is
close to the circular direction (Fig. 4(b)), the magnetization
reversal consists mainly of the rotation of the magnetiza-
tion. The sharp jump of the magnetization is related to the
overcoming of the hard axis close to the axial direction.
(When the anisotropy is directed exactly along the circular
direction, the jump is not observed and only the rotation of
the magnetization takes place.) The inclination of the
direction of the magnetization towards the axial direction
causes an increase of the jump of the circular magnetiza-
tion and a decrease of the part of hysteresis related to the
rotation of the magnetization. Therefore, the observed
features of the calculated hysteresis curves are very similar
to the features observed in the experimental Kerr effect
curves (Figs. 1 and 2) and, consequently, we can conclude
that these experimentally observed properties are related to
the different direction of the anisotropy axis in the surface
area of the wire or, in another words, to the degree of the
thecirculardirection
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Fig. 3. Calculated dependences of circular magnetization on normalized
circular magnetic field with normalized axial bias field as a parameter for
two different angles of anisotropy direction j: (a–c) j ¼ 541; (d–f)
j ¼ 881.
Fig. 4. Calculated dependences of circular magnetization on normalized
axial magnetic field for two different angles of anisotropy direction j:
(a) j ¼ 541; (b) j ¼ 881.
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helical anisotropy: for the wire with r ¼ 0.785 the direction
of the surface anisotropy is very close to the circular
direction and for the wire with r ¼ 0.93 this direction is
inclined toward the axial direction.
Considering the studied glass-covered microwires as a
model, we do not discuss in this paper the reason for the
influence of the glass covering on the surface magnetic
properties. Generally, the surface magnetic structure in the
glass-covered microwires originates from the magnetoelas-
tic anisotropy associated with the internal stresses. The
main source of these internal stresses is the glass covering.
In conclusion, the surface magnetization reversal has
been studied in the Co-rich microwires with different
thicknesses of glass covering. The calculation of the surface
hysteresis loops has been performed taking into account
the existence of a helical magnetic anisotropy. Based on the
comparative analysis of the results of the experiments and
the calculation, the value of the angle of the surface helical
anisotropy has been determined for the studied microwires.
It was found that the different direction of the helical
anisotropy causes the great difference in the surface
magnetic behaviour.
Acknowledgment
This work was supported by MEyC under project
PCI2005-A7-0230.
References
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[2] A. Chizhik, A. Zhukov, J. Gonzalez, J.M. Blanco, J. Appl. Phys. 97
(2005) 073912.
[3] A. Chizhik, J. Gonzalez, A. Zhukov, J.M. Blanco, Appl. Phys. Lett. 82
(2003) 610.
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