Undulation instabilities in laterally structured magnetic multilayers

JOURNAL OF APPLIED PHYSICS VOLUME 91, NUMBER 10 15 MAY 2002
Undulation instabilities in laterally structured magnetic multilayers
T. Eimüller a)
MPI Für Metallforschung, Heisenbergstrasse 1, 70569 Stuttgart, Germany and Exp. Physik IV,
Universität Würzburg, Am Hubland, 97074 Würzburg, Germany
M. Scholz
Exp. und Angew. Physik, Universität Regensburg, 93040 Regensburg, Germany
P. Guttmann
Institut für Röntgenphysik, Universität Göttingen c/o BESSY, Albert-Einstein-Strasse 15,
12489 Berlin, Germany
M. Köhler and G. Bayreuther
Exp. und Angew. Physik, Universität Regensburg, 93040 Regensburg, Germany
G. Schmahl
Institut für Röntgenphysik, Universität Göttingen, Geiststrasse 11, 37073
P. Fischer and G. Schütz
MPI für Metallforschung, Heisenbergstrasse 1, 70569 Stuttgart, Germany and Exp. Physik IV,
Universität Würzburg, Am Hubland, 97074 Würzburg, Germany
Undulation instabilities of magnetic domains have been observed in nanostructured strips of a
ferromagnetic Fe/Gd multilayer. The novel technique of magnetic transmission x-ray microscopy,
which is based on the x-ray magnetic circular dichroism, was used for imaging. Below a critical
magnetic field, sinus-like modulations of the magnetic domains could be observed. At a higher rate
of field induced strain rectangular patterns occur. They seem to be characteristic for the reduced
lateral width of the magnetic system and are in contrast to chevron patterns observed in extended
systems. The domain morphologies found in different magnetic fields H, and in nanowires of
various widths L z , have been summarized in a H – L z ‘‘phase’’ diagram. An analogy with theoretical
predictions for extended systems could be found. © 2002 American Institute of Physics.
DOI: 10.1063/1.1452682
INTRODUCTION
The competition of short-range attractive and long-range
repulsive interactions gives rise to modulated domain morphologies
in a variety of condensed matter systems. A second
modulation perpendicular to the original layer normal occurs,
if these systems are triggered by mechanical, temperature,
or field induced strain. Such buckling or undulation
instabilities, forming sinusoidal or chevron patterns, could be
found in smectic liquid crystals, 1
ferromagnetic garnet
films, 2,3 magnetic fluids, 4 or in cholesteric mixtures. 5 We report
on the observation of undulation instabilities in nanostructured
strips of a ferromagnetic Fe/Gd multilayer by
magnetic transmission x-ray microscopy MTXM.
EXPERIMENTAL DETAILS
A (4 ÅFe/4 ÅGd)75 multilayer has been prepared by
dc magnetron sputtering on top of a 30-nm-thick Si 3N 4
membrane ensuring a sufficiently high transmission in the
soft x-ray range. The film was protected against corrosion by
an 8-nm-thick Al layer. Electron beam lithography was used
to structure the system. The pattern has thereby been transferred
from a polymethylmethacrylate layer to an Al 2O 3
film, serving as a mask for ion beam etching. This two-step
a Electronic mail: thomas.eimueller@physik.uni-augsburg.de
procedure enhances the sharpness of the edges. Strips of different
widths L z , between 2 m and 100 nm have been
generated. The magnetic behavior of the equivalent unstructured
system has been studied previously. 6 Measurements
with a torque magnetometer revealed an easy axis of magnetization
directing 60° out of the sample plane.
The novel technique of magnetic transmission x-ray
microscopy 7 was used to image the field dependent evolution
of magnetic domains. The method is based on transmission
x-ray microscopy TXM and utilizes the x-ray magnetic circular
dichroism, i.e., the dependence of the absorption of
circularly polarized x rays on the projection of the magnetization
onto the photon propagation direction. This effect
serves as a large and element-specific magnetic contrast that
allows imaging of magnetic domains in a quantitative way, in
varying external magnetic fields, and with a lateral resolution
down to about 25 nm. 6–9 The images presented here are
taken at the Fe L 3 edge with the full field TXM at BESSY I
in Berlin, 10 using a zone plate, able to distinguish feature
sizes of 30 nm.
RESULTS AND DISCUSSION
Four typical states of the magnetization reversal are presented
in Fig. 1. Each image Figs. 1a–1d shows two adjacent
nanowires, each L z670 nm wide. Before imaging
the sample was saturated in a magnetic field of H
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© 2002 American Institute of Physics
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J. Appl. Phys., Vol. 91, No. 10, 15 May 2002 Eimüller et al.
FIG. 1. Undulation instability in nanowires of 670 nm width. With decreasing
magnetic field, straight stripe domains, visible as dark and light zones in
both strips a accumulate strain and undergo a buckling instability. Thereby
the ‘‘dark’’ stripe breaks open marked in b and forms a wavelike pattern
c, which transforms into a rectangular modulation in d.
1.75 kOe, applied perpendicular to the film plane. Lowering
the field, three nearly parallel stripe domains with an
initial periodicity P 0 appear at H nuc , as can be seen in Fig.
1a. With decreasing external field, H, the equilibrium periodicity,
P(H), is expected to decrease. 11 Thus, new stripes
should nucleate to minimize the total free energy of the system.
Indeed, a second ‘‘dark’’ band can be observed, e.g., in
the upper part of Figs. 1c and 1d. However, in areas
where the injection of new stripes is hampered by energy
barriers, e.g., by pinning centers, 8 the pattern accumulates a
dilative strain 1P(H)/P 0. Theories for extended
systems use this strain to explain undulation
instabilities. 12–14 Beyond that, a buckling pattern can also be
generated by compressive strain, 14 e.g., induced by dipolar
repulsions.
As shown in the tagged part of Fig. 1b, the dark stripe
breaks open at H750 Oe, marking the onset of undulation
instability: Below a critical field H u a wavelike pattern can
be observed. With a further decreasing field the amplitude of
this pattern increases continuously, while simultaneously its
wavelength decreases. Fig. 1c presents the system at H
565 Oe, which is well below H u . Finally, if H falls below
H sr , a rectangular modulation can be observed, as shown in
Fig. 1d. Concomitantly, in more and more areas the system
can realize the equilibrium state, showing two parallel dark
stripe domains. Whereas sinusoidal undulations could previously
be observed in continuous magnetic garnet films, 2,3 the
rectangular pattern seems to be characteristic for the reduced
width L z of the structured system.
The undulation amplitude, u 0 , measured as an average
of the maximum excursions of the center of the reversed
stripe domains on different parts of the sample, is presented
in Fig. 2 as a function of the external magnetic field, H. The
field axis is plotted in reverse order to show the rise of strain
from left to right. In the field range of the straight stripe
domains the amplitude is zero. It starts to increase at the
undulation instability field H u800 Oe. In the whole region
of sinus-like undulation the amplitude rises continuously
with decreasing magnetic field. However, at the transition
from sinus-like to rectangular modulation the slope of the
u 0(H) curve decreases to nearly zero. The kink in the slope
has been used to define the transition field H sr . Reversibility
7335
FIG. 2. Amplitude of the undulating domains in strips of 670 nm width as a
function of the applied magnetic field. Squares mark values taken with decreasing
field, triangles correspond to values taken with increasing field. A
reversible behavior can be observed.
of buckling has been studied in a field cycle 1005 Oe
→625 Oe→765 Oe. Values taken with increasing field, i.e.,
decreasing strain, are plotted as open triangles. They follow
the curve, taken with decreasing field, thus showing that the
rise of the undulation amplitude is completely reversible up
to a certain value of strain.
The transition from sinus-like to rectangular modulation
is further visible in the magnetic field dependence of the
buckling wavelength . As shown in Fig. 3, for strips with
L z670 nm triangular data points and for strips with L z
600 nm rectangular data points, the undulation period
decreases with decreasing magnetic field. In the field range
of rectangular modulations reaches a shallow minimum at
about zero magnetic field and increases with further decreasing
field.
Undulation instabilities with an analogous behavior
could also be observed in strips of L z600 nm, 460 nm, and
400 nm width. The dependence of the domain morphology
on the external magnetic field and the width of the strips L z
is summarized in a H – L z ‘‘phase’’ diagram, shown in Fig. 4.
The decrease of the nucleation field H nuc with decreasing L z
can be explained by the reduced stray magnetic field of the
smaller elements. The undulation instability field H u and the
FIG. 3. Undulation wavelength as a function of the applied magnetic field
observed in nanowires of 670 nm width squares and 600 nm width triangles.
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7336 J. Appl. Phys., Vol. 91, No. 10, 15 May 2002 Eimüller et al.
FIG. 4. ‘‘Phase’’ diagram showing different domain morphologies in strips
of various widths, separated by the nucleation field H nuc , the undulation
field H u , and the transition field between sinus-like and rectangular modulation,
H sr .
transition field H sr follow this trend. Nanowires of 300 nm
width and smaller show mere single and lamellar domain
states but no undulating pattern.
Large strips of 2 m width reverse by nucleation of
several straight stripe domains, not necessarily oriented parallel
to the long axis of the nanowire. With decreasing field
wavelike and finally maze patterns occur. However, rectangularly
modulated domains could not be observed, which
indicates that the constraint of finite width of the strips plays
a decisive role in generating this pattern.
The experimental results have been compared with theoretical
models. Sornette used the analogy to smectic liquid
crystals to develop an effective elastic theory for ferromagnetic
systems. 13 A more extensive analysis has been given by
Singer. 12,14 Thereby, systems with an extension L z large compared
with the domain periodicity P 0 exhibit an undulation
amplitude that is maximal at the center of the system and is
zero at the borders. In contrast to such ‘‘bulk’’ systems, in
our nanostructured system the dimension L z is nearly equal
to the domain periodicity P 0 . For this marginal case theories
do not exist thus far. Nevertheless, an analogy to buckling
instabilities in extended systems could be found. Near H u the
theories 12–14 predict a linear relation between the undulation
period 0 and the size L z of the extended system: 0
(P 0L) 1/2 N 0 1/2 Lz , where N 0 is the number of domain
periods counted along L z . Likewise, between the width L z of
the structured strips and the initial undulation periodicity
0 , a linear relation could be found, as shown in Fig. 5.
Notable is the fact that the experimental data follow exactly
the predicted slope for the extended system. Whereas for
dilation-induced buckling is expected to increase with increasing
strain, for compressed-induced buckling a decrease
of L has been predicted, 14 in qualitative agreement with the
observation. Beyond that, a comparison of the buckling profiles
calculated for dilative and for compressive strain 14 reveals
that the compressed-induced profile is closer to the
observed rounded sinus-like shape.
FIG. 5. The undulation period 0 depends linearly on the width of the
strips, L z . A linear least squares fit of the data upper line shows exactly the
slope of the function predicted by theory for extended systems lower line.
To summarize, undulating domain pattern of sinus-like
shape could be observed by MTXM in nanowires of a ferromagnetic
Fe/Gd multilayer. For a large rate of strain in the
strips of reduced dimension Lz rectangular domains occur, in
contrast to chevron structures observed 1–5
in and
predicted 12–14 for extended systems. The undulation period
behaves analogously to theoretical predictions, 12–14 and hints
of a compressed induced buckling could be found. However,
an extension of the theory to the limit L z→P 0 is required to
provide a comprehensive description of the observations.
ACKNOWLEDGMENTS
Valuable discussions with Sherwin Singer from the Ohio
State University, the technical support by BESSY, and the
financial support by the German Federal Ministry of Research
and Technology BMBF are gratefully acknowledged.
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