Direct Spatial-temporal Observation of Barkhausen Avalanche in Low Dimensional Ferromagnetic System

Abstract

We report our direct observation of the Barkhausen avalanche in ferromagnetic thin film systems, where a collective spin behavior produces nontrivial fluctuations in magnetization change under an external magnetic field. For this study, we develop and use two direct full-field magnetic imaging techniques: magneto-optical microscope magnetometer (MOMM) and magnetic transmission X-ray microscopy (MTXM). From a direct visualization and a statistical analysis of the fluctuating domain images for Co thin films, we investigate the scaling behavior of the Barkhausen avalanche both on spatial and temporal scales using MOMM. We also investigate the reproducibility of the Barkhausen avalanche process. Interestingly, the partially stochastic nucleation behavior is observed for CoCrPt alloy films by means of MTXM on a nanometer scale comparable to the fundamental length scales such as the Barkhausen volume and the grain size of the polycrystalline films. Via these direct full-field observation techniques, dynamic details of Barkhausen avalanche are revealed.

Full text

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Direct Spatial-temporal Observation of Barkhausen
Avalanche in Low Dimensional Ferromagnetic System
Dong-Hyun Kima, Bosun Kanga, Weilun Chaoa, Peter Fischera, Erik Andersona,
Sug-Bong Choeb, Mi-Young Imc, and Sung-Chul Shinc
aCenter for X-ray Optics, Lawrence Berkeley National Laboratory, Berkeley CA, USA;
bDepartment of Physics, Seoul National University, Seoul, Korea;
cDepartment of Physics, Korea Advanced Institute of Science and Technology, Daejeon, Korea
ABSTRACT
We report our direct observation of the Barkhausen avalanche in ferromagnetic thin film systems, where a
collective spin behavior produces nontrivial fluctuations in magnetization change under an external magnetic field.
For this study, we develop and use two direct full-field magnetic imaging techniques: magneto-optical microscope
magnetometer (MOMM) and magnetic transmission X-ray microscopy (MTXM). From a direct visualization and
a statistical analysis of the fluctuating domain images for Co thin films, we investigate the scaling behavior of the
Barkhausen avalanche both on spatial and temporal scales using MOMM. We also investigate the reproducibility
of the Barkhausen avalanche process. Interestingly, the partially stochastic nucleation behavior is observed for
CoCrPt alloy films by means of MTXM on a nanometer scale comparable to the fundamental length scales such
as the Barkhausen volume and the grain size of the polycrystalline films. Via these direct full-field observation
techniques, dynamic details of Barkhausen avalanche are revealed.
Keywords: Barkhausen avalanche, magnetic domain, scaling behavior
1. INTRODUCTION
The magnetic domain dynamics in a ferromagnetic system has for long been a fundamental issue in magnetism.
Formation and evolution of magnetic domain is a result of relevant energy minimization in collective spin behavior
under a certain external magnetic field. When the domain is formed, each spin in the ferromagnetic system
cannot behave independently and it shares its spin information with neighboring spins via exchange interaction,
coupling with a lattice, and magnetostatic dipolar interaction. Therefore, macroscopic domain dynamics can be
interpreted as a subsequent microscopic spin behavior. Any question related to the domain dynamics and to the
magnetism is basically the question on how the domain wall moves and how the large number of spins behaves
microscopically during the wall motion process.
Collective spin behavior on a submicron scale during the motion of domain wall has been investigated for
the last decade by means of various experimental techniques,1
information storage and magnetoelectric devices2as well as by the fundamental interest issued above. Much
effort has been devoted to reveal the microscopic nature of spin behavior even down on an atomic scale during the
domain wall motion. Very recently, it has been experimentally reported that the domain wall actually trapped
between crystalline planes and it propagates by discrete jumps matching with the lattice periodicity.3And the
effective mass of the single domain wall in its motion has been experimentally determined when it is coupled to
the spin-polarized current.4
motivated by the applications for magnetic
While the physical properties of domain wall have been intensively studied in microscopic details, little
attention has been paid to the fundamental question on how the collective spin behavior will be affected when
the moving domain wall meets disorders such as structural irregularities and defects inevitably distributed over
the ferromagnetic system. Disorders generate pinning potentials and they usually pin the domain wall until the
pinned wall is activated by the thermal fluctuation and released from being pinned. In this case, small amount
Further author information: (Send correspondence to Dong-Hyun Kim)
E-mail: dhkim@lbl.gov, Telephone: 1 510 486 5288
Invited Paper
Fluctuations and Noise in Materials II, edited by Peter Svedlindh, Dragana Popovic,
Michael B. Weissman, Proceedings of SPIE Vol. 5843 (SPIE, Bellingham, WA, 2005)
0277-786X/05/$15 · doi: 10.1117/12.609637
40

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of local spin fluctuation may lead to totally different domain wall configurations over the entire ferromagnetic
system.5
One of the most beautiful features among these fluctuation-dominated phenomena is the critical
scaling behavior, where the characteristic length disappears and the scale-free behavior appears. Specifically, if
one measures the magnetization change induced by the domain wall movement under an external magnetic field,
the measured magnetization change exhibits nontrivial fluctuation. Considering that the domain wall moves with
a sequential jerky jumps in most of ferromagnetic systems, which is well known as the Barkhausen avalanche, the
nontrivial fluctuation of intermittent magnetization change corresponds to each Barkhausen jump. It has been
reported that the distribution of the Barkhausen jump size follows a power-law behavior and that the distribution
can be fitted with a single value of the slope on log-log scale over several orders of magnitude, where the value
of the slope allows us to determine the corresponding scaling exponent.6,7
the moving domain wall through disordered medium via Barkhausen jumps have great number of analogies in
wide variety of physical systems having any driven interface and correlated fluctuation,8such as surface growth,
fluid invasion in porous media, dynamics of superconductor and superfluid, microfracture, and earthquakes.
Interestingly, phenomena related to
So far, several models have been proposed to explain the scaling behavior of the Barkhausen effect. Classical
criticality tuneable by amplitude and distribution of disorder was proposed by Sethna et al. within the context
of a random-field Ising model.9
On the other hand, self-organized criticality (SOC), achieved by self-organized
evolution among barely stable states in a complex dynamic system was first introduced by Bak et al.10and
then, applied to the Barkhausen avalanche by Cote and Meisel.6With an appropriate assumption of long-range
dipolar interaction known to be essential in describing a ferromagnetic system,7,11Cizeau et al.12, 13proposed
a phenomenological model (CZDS) of domain wall dynamics in disordered system, which could explain more
general situations than the previous models14and has been later investigated within more generalized scheme.15
From an experimental point of view, it should be noted that most experimental studies have been carried out
on bulk samples using a classical inductive technique dated back to Barkhausen’s pioneering work,16which is
difficult to apply to low dimensional ferromagnetic system due to the low signal intensity. For this reason, very
few experiments have been done on ferromagnetic thin films.17
there exists a critical nature in ferromagnetic thin films by means of magnetooptical Kerr effect (MOKE)?and
magnetic X-ray scattering,19where both techniques provide enough sensitivity even for the ferromagnetic thin
film system, but still not sufficiently informative in describing real-space domain configuration. Based on MOKE
measurement, the first reliable experiment reporting scaling behavior of Barkhausen effect has been carried out
for Fe thin films,18although the experimental value of the scaling exponent is quite different from the values
predicted by the existing models.10,15,20
Magnetic X-ray scattering technique has been utilized to statistically
investigate the correlation among repeated microscopic domain evolutions, where the statistical analysis has been
carried for the scattered patterns in a momentum space, not in a real space.19
Only very recently, it has been reported that
Clarification of the reason for this disagreement of the scaling exponent values and better understanding of
the phenomenon require direct observation of the Barkhausen avalanche phenomenon in a real space. Direct
visualization capability enables us to investigate the motion of domain wall in full details during the Barkhausen
avalanche and offers a better understanding of this interesting physical phenomenon. In the present study,
we report the use of novel magnetic imaging techniques for observation of domain wall fluctuation during the
Barkhausen avalanche. We could directly visualize and analyze domain wall motions in various ferromagnetic
films such as Co and CoCrPt by means of these full-field imaging techniques.
2. EXPERIMENT
We directly investigate domain wall motion in real time during the Barkhausen avalanche by means of a mag-
netooptical microscope magnetometer (MOMM), capable of time-resolved domain observation.5,?
consists of a polarizing optical microscope set to observe magnetic contrast via MOKE. The optical illumination
path was tilted to provide an incident angle of 20ofrom the film normal by shifting the position of the objective
lens as well as adjusting the relevant optics. Therefore, we could visualize in-plane magnetic domains utilizing
longitudinal MOKE. The spatial resolution is 2 µm and the Kerr angle resolution is 0.1oin this setup. To
store domain images, the system is equipped with advanced video processing having an image grabbing rate of
30 frames/s in real time. The time-resolved sequential domain images on a 400 × 320 µm2sample area were
initially grabbed on a 256 gray scale and then, intensified by image processing technique such as background
It basically
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Figure
[http://www.cxro.lbl.gov]
1.
(a) Schematic diagram of MOMM setup.[Ref.5] (b) Schematic diagram of XM-1 setup.
subtraction, noise filtering, and black-and-white image extraction. The Barkhausen avalanche was triggered by
applying a constant magnetic field to an initially saturated sample. The strength of an applied field was about
99 % of the coercive field to eliminate the influence caused by the difference in the field-sweeping rates.13
Barkhausen jumps were directly visualized and characterized from serial time-resolved domain images. The
schematic diagram of MOMM is illustrated in Fig. 1(a).
The
For additional understand of the scaling behavior of Barkhausen avalanche, extensions are needed for direct
observations in both temporal and spatial dimensions. To this end, we are exploring the use an ultrahigh
resolution full field magnetic transmission X-ray microscope (MTXM) developed by the Center for X-Ray Optics
at beamline 6.1.2 in the Advanced Light Source Synchrotron, which uses XMCD contrast to enable us to observe
the Barkhausen avalanche with full details on an ultra-fine spatial scale (∼ 20 nm) and potentially, ultra-
fast temporal scale (∼70 ps).22,23
To record the images, circularly polarized radiation passing through the
ferromagnetic sample was projected through the micro zone plate onto a 2048 × 2048 pixel array of a CCD
camera. Since the magnetic contrast is given by the projection of the magnetization onto the photon propagation
direction, the CoCrPt sample with a perpendicular magnetic anisotropy was mounted with its surface normal
parallel to the photon beam direction. To study the magnetization reversal in the CoCrPt films, the images have
been recorded with varying external magnetic fields perpendicular to the film plane. The schematic diagram of
MTXM is illustrated in Fig. 1(b).
We prepared several Co and CoCrPt films on glass substrates for MOMM study and membrane substrates for
MTXM study by dc-magnetron sputtering. For simple Co films, an in situ magnetic field of 300 Oe was applied
along a certain orientation in the film plane during deposition to induce magnetic anisotropy in this orientation,
what was the same for all samples. Polycrystalline granular morphology with a cobalt grain size of a few tens of
nanometers was confirmed by transmission electron microscopy (TEM). All the Co samples exhibit an in-plane
magnetic anisotropy having uniaxial easy axis along the applied field orientation during the sample preparation.
For CoCrPt alloy films, 40-nm Ti buffer layer was first deposited on a 200-nm SiN membrane. The membrane
substrate was used to allow sufficiently high transmittance of soft X-ray and thus, enough illumination intensity.
All the CoCrPt alloy films exhibit a strong perpendicular magnetic anisotropy due to the good hcp(002) crys-
tallographic alignment. The average grain size was determined from TEM images and was about several tens of
nanometers.
3. RESULTS
3.1. Spatial fluctuation during Barkhausen avalanche
In Fig. 2(a), we illustrate a series of six representative domain-evolution patterns successively observed for 25-
nm single Co film by means of the MOMM, where the colors code represents an elapsed time during 4 seconds
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Figure 2. (a) A series of six domain images showing the avalanches of the domain structure captured successively on
the same 400 × 320 µm2area of a 25-nm Co film. The color code represents the elapsed time from 0 to 4 seconds when
magnetization reversal occurs. The sample was saturated downward first and then, a constant field was applied upward,
denoted by the solid arrow. (b) Magnetization reversal curves obtained from the corresponding domain patterns of (a).
[Ref. 5]
after applying an external field to trigger Barkhausen avalanche. Domain evolution patterns in each picture
clearly exhibit typical avalanche-like features such as sudden and abrupt jumps during the reversal process. As
we repeatedly carry out an observation at the same area keeping the same field of view, each magnetization
reversal proceeds with quite different jumps with clearly different domain wall configuration. From the direct
visualization, we conclude that the occurrence of each Barkhausen jump seems to be not reproducible with
respect to interval, size, and location of the jump. And we can pinpoint the position of the domain wall in a real
time and in a real space at each observation. Domains have a simple 180otype walls throughout the avalanche
process, which is expected from the uniaxial anisotropy induced during the sample preparation process. The
observed avalanche-like characteristics prevails also for the other Co samples having different thickness of down
to 5 nm.
Since we are dealing with digitized information of the time-resolved domain wall images captured at CCD,
we can quantitatively determine the time-dependent magnetization reversal curve from the time-resolved domain
image in Fig. 2(a). For ferromagnetic thin films having thickness comparable to the exchange length, we can
assume that there is negligible change of spin direction along the thickness direction and the net magnetization
parallel to an applied field direction is simply proportional to the reversed domain area. In Fig. 2(b), we plot
the magnetization reversal curves corresponding to the six domain-evolution patterns in Fig. 2(a), where a
stepwise feature is vividly witnessed. Each step in the curve corresponds to the area swept by a Barkhausen
jump visualized in Fig. 2(a). The interesting characteristic of the curves in Fig. 2(b) is the presence of steps
whose time interval and amplitude randomly fluctuate among the curves.
In our experiment, the Barkhausen jump size is determined from the direct measurement of abrupt areal
change of real-time domain patterns observed using the MOMM, while all the other experiments up to now have
determined the jump size via indirect methods such as inductive coil7,13,14,24or MOKE technique.18Through
a statistical analysis of the fluctuating size of Barkhausen jump from more than 1000 repetitive experiments
for each sample, the distribution of Barkhausen jump size was obtained. In this analysis any Barkhausen jump
which started or ended outside the observation area was not counted. In principle, counting only the jumps fully
inside the frame provides us more reliable value of the scaling exponent.25However, most of domain walls have
their two ends outside the field of view due to their uniaxial 180otype domain wall structure. Number of images
having the domain wall with both ends inside the field of view is less than one hundred, even though we have
carried out more than several thousands of repeated observations. Practically, it is very difficult to achieve an
enough number of statistical ensembles with images having both ends inside the field of view.
The distribution is found to exhibit a power law behavior and fitted as P(s) ∼ s−τwith scaling exponent
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Figure 3. Distribution of Barkhausen jump size in 25-nm Co samples. Distributions in 5, 10, and 50-nm Co samples are
shown in the insets. Fitting curve with ( = 4/3 is denoted at each graph. [Ref. 5]
τ ∼ 4/3 as plotted in Fig. 3, where s is the Barkhausen jump size, normalized by the total area of observation. The
most striking feature of Fig. 3 is the fact that the τ values are the same for both samples within the measurement
error despite of the difference in their thickness. We may expect that the 50-nm film has about ten times number
of defects compared with the 5-nm film, since two samples were prepared with the same preparation conditions
except the thickness. Our experimental result implies an invariance of the scaling exponent τ irrespective of
the number of defects in the Co thin films, within a thickness range comparable to the exchange length. This
result reminds us the recent theoretical studies predicting that the variation of the number of defects does not
affect the critical exponent, but only changes the cut-off of the power-law scaling in the distribution of the
avalanche size.8,20
However, the difference in the cut-off values of various Co films is not apparent enough to
be quantitatively analyzed. The origin of the cut-off in scaling distribution is still controversial: the variation
of disorder distribution,8,20the demagnetization effect,13,24or the finite size effect6,10has been suggested to
explain the origin of the cut-off. The cut-off in Fig. 3 originated from the finite size effect since it accordingly
varies with respect to the magnification and thus, with respect to the size of field of view.
Since the scaling exponent is the key parameter in description of the Barkhausen avalanche, we need to
compare the value of τ with theoretical prediction. As discussed above, several models which adopt different
assumptions and predict different values of scaling exponent, have been proposed. The prediction of τ for a two-
dimensional system is diversely given as 1.5 for classical plain-old criticality,20∼1.0 for SOC.10,26Moreover, it
is well known that difference may exist even among experimentally obtained scaling exponents due to different
magnetization reversal mechanism, different domain type, or different driving field rate.13,14,27Therefore, before
comparing the experimental and theoretical values it is necessary to carefully examine the assumptions of the
models as well as to clearly define the experimental configurations by direct domain observation and driving-field
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rate control.
We like to point out that the development of MOMM has opened a new possibility for direct full-field inves-
tigation of the Barkhausen avalanche phenomenon. However, the spatial resolution is limited by the diffraction
limit of visible light ( ∼ 400 nm). Very recently, spatial spin fluctuation during the Barkhausen avalanche has
been investigated using magnetic force microscope (MFM) with significant improvement in spatial resolution.28
Although a scanning microscope like MFM has an intrinsic disadvantage in studying fluctuation dominated
avalanche-like behavior due to the tip-sample interaction, this technique with higher spatial resolution can be a
meaningful complementary tool for this study.
3.2. Temporal fluctuation during Barkhausen avalanche
Barkhausen avalanche in ferromagnetic system is also known to exhibit a scaling behavior over wide range of
temporal scale, during which the domain wall fluctuates nontrivially with intermittent avalanche-like bursts of
magnetization jumps.?
In addition to the jump size distribution, the distribution of the duration of each jump
has been also known to follow a power-law behavior, providing another corresponding scaling exponent.24,29
Interestingly, the statistical distributions of the spatiotemporally fluctuating quantities such as jump size and
jump duration are often described based on universality. However, recent studies have been mainly devoted to
investigate the spatial scaling behavior5,18and very little has been known about the temporal scaling behavior of
the Barkhausen avalanche. It should be noted that the scaling behavior in spatial scale is closely related to that
in temporal scale and they are not mutually independent.13Therefore, experimental observation and statistical
analysis of Barkhausen avalanche in temporal scale as well as in spatial scale can extend our understanding of
the scaling phenomenon.
In this section, we report a statistical analysis of the intermittency of Barkhausen avalanche by measuring
the distribution of the separation time ∆T between adjacent two Barkhausen jumps in Co films having thickness
ranging from 5 to 50 nm. The seperation time is determined from a direct time-resolved domain observation by
means of MOMM.30The temporal resolution is about 30 ms and a series of 128 domain evolution patterns are
captured sequentially during 4 seconds. The Barkhausen avalanche is triggered by applying a constant magnetic
field to an initially saturated sample. The strength of an applied field is constant near the coercive field to
eliminate the influence caused by the difference in the field-sweeping rates.13,31
jumps are directly characterized and the seperation time ∆T is determined from serial time-resolved domain
images. A series of 1000 measurements have been repeatedly carried out at 10 random positions of each sample
to achieve reliable statistics.
Intermittency of Barkhausen
The typical time-resolved domain evolution patterns and the scaling properties of jump size distribution
have been intensively investigated in our previous section, where it has been revealed that discrete and sudden
Barkhausen jumps with simple 180odomain walls exist throughout the avalanche process. In the present section,
we will focus on the intermittency of Barkhausen avalanche and its statistical distribution. In Fig. 4(a), we
plot the magnetization reversal curve determined from a typical domain-evolution pattern observed at x200
magnification. From the magnetization curve we can easily determine when each jump has occurred and what
the elapsed time separating two successive jumps is, as demonstrated in Fig. 4(a). All measurements for each
sample are carried out during 4 seconds at x200 magnification. As the experiments are repeatedly performed at
the same area of the film, magnetization reversal proceeds with quite different jumps every time as discussed in
the previous section.
Through a statistical analysis of the fluctuating time interval ∆T between two Barkhausen jump events
from more than 1000 times repetitive experiments for each sample, distribution of ∆T has been obtained. In
determination of ∆T, there should be a threshold value in defining a jump event to identify the Barkhausen
jump from the background noise. In our experimental configuration, the noise level is less than 1 % at x200
magnification and we only consider the Barkhausen jump event occurring with the measured jump size over
than 1 % of the observed area (400×320 µm2at x200 magnification). In all samples, the distribution of ∆T
determined in this way seems to have a power-law-like distribution, as illustrated in Fig. 4(b). The power-law
form of the distribution does not vary with the slight change of threshold in counting jump events from 1 % to 2 %.
Interestingly, one can notice that the four distribution curves from four kinds of samples having different thickness
(5, 10, 25, and 50-nm) seem to fall in single universal curve within the measurement error. Unfortunately, the
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Figure 4. (a) Time-dependent magnetization reversal curve. (b) Distributions of ∆T which separates two adjacent
Barkhausen jump events. [Ref. 30]
error is not negligible here and we believe the experimental proving of the universal intermittency behavior of
Barkhausen avalanche is still an open problem. The relatively large error in case of the distribution of separation
time compared to the case of the distribution of jump size seems to be originated from the smaller temporal
measurement region (0.2 ∼ 4 seconds). However, the exact reason is not clear, since even from the same set of
time-resolved domain evolution patterns, the temporal fluctuation distribution has generally rough power-law
form while the spatial fluctuation distribution has smoother power-law form. The temporal resolution of MOMM,
in this work, is limited by 60 Hz frame grabbing and CCD operation time (∼ 30 ms), which is not enough to
fully investigate the fast dynamics of the Barkhausen avalanche. Development of faster observation technique is
required for further in-depth study of temporal scaling behavior of the Barkhausen avalanche.
3.3. Reproducibility of Barkhausen avalanche
A visualization capability of the MOMM enables us to directly investigate the motion of domain wall in the
Barkhausen avalanches. The repeated observation of the domain wall motion reveals that there exist some
pinning segments around which domain walls are very flexible. The flexible part of domain wall moves forward
via Barkhausen jump, while the pinned part is fixed at the same position for a relatively long time. This is
quite expected because of the role of disorders as the pinning sites. It is very interesting to determine whether
the domain wall fluctuation continues to appear even when a strong pinning site exists in the observed area.
Time-resolved images of domain walls around the strong point-like pinning site were repeatedly obtained at the
same area as illustrated in Fig. 5, where the position of point-like pinning site is indicated by the dashed arrow.
As clearly seen in Fig. 5, the domain wall is still flexible in this case.
In Fig. 6, we provide another interesting example of critical fluctuation of Barkhausen avalanche in the
case of a linear defect. From the time-resolved images illustrated in Fig. 3, we may expect that there exists a
nearly horizontal linear defect, since all the domain evolution patterns indicate a common stop of evolution at
linear line at the same location indicated by dotted line. Even in this extreme situation where the strong linear
defect is expected to exist, the detailed propagation of domain wall shows significant fluctuation with constraint
introduced by the linear defect. Barkhausen jump occurs still in a random critical way, keeping the system still
at the criticality.
For a arbitrary region without any clear sign of pinning site, we repeat our observations at the same area
with the same experimental conditions and visualize the microscopic behavior of fluctuating domain walls. By
superimposing these fluctuating domain walls of each observation, we can generate the probability map to find
domain wall at a certain position, which directly indicates how reproducible the avalanche process at a position
will be. In Fig. 7(a), we demonstrate four representative images of time-resolved domain evolution patterns
observed successively at the same area with identical experimental conditions. Note that domain evolution
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Figure 5. A series of domain evolution images captured repeatedly on the same 400x320 (m2 area with the same
experimental conditions. The pinning site is indicated by the dotted arrow at the upper left image. The field is applied
upwardly as denoted by solid arrow. [Ref. 32]
Figure 6. A series of domain evolution images captured repeatedly. The color code represents elapsed time. The dotted
line at the upper left image indicates the estimated location of the linear defect. The field is applied upwardly. [Ref. 32]
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Figure 7. (a) Time-resolved domain patterns captured successively at the same area with identical experimental con-
ditions. The sample magnetization was initially saturated downward and then, constant field was applied upward. (b)
Domain walls determined via edge-finding image processing technique. (c) Probability map indicating spatial distribution
of probability to find a domain wall at each position. Grey-level represents probability determined from 100 repeated
observation. [Ref. 33]
patterns in each picture clearly exhibit discrete and sudden Barkhausen jumps and that domain configuration is
not exactly reproducible at each observation. To quantitatively understand, we statistically analyze the domain
wall configurations from our repeated observations. As a first step, we determine the domain-wall lines from
the domain evolution patterns as illustrated in Fig. 7(b). The images of domain-wall lines in Fig. 7(b) are
determined from the corresponding images of Fig. 7(a) via edge-finding image processing technique. For 100
repeated observations, we superimpose these images of domain-wall lines, where we can generate the probability
map by counting how many times the domain wall is found at a certain position. Therefore, the map represents
the spatial distribution of probability of finding domain wall at the position as vividly shown in Fig. 7(c).
Interestingly enough, one can clearly notice that there exists a more probable region where the domain wall
statistically prefers to exist.
However, question still remains on the reproducibility of avalanche process on a smaller scale, since the spatial
resolution of MOMM is not enough to provide us any domain information of the Barkhausen avalanche on a
submicron scale. For example, most of polycrystalline ferromagnetic films have smaller grain size about several
tens of nanometers than the resolution of longitudinal MOMM (∼ 2 µm) and no experimental study has been
addressed to investigate the Barkhausen avalanche on a nanometer scale considering nanogranular structures.
This grain volume is now comparable to the fundamental elementary unit volume in magnetization reversal
mechanism with an assistance of thermal fluctuation, known as the Barkhausen volume. For investigation of
the avalanche-like behavior on this fundamental length scale, magnetic imaging technique with better spatial
resolution is required.
Recently, magnetization reversal behavior of CoCrPt alloy films has been investigated using MTXM developed
by the Center for X-Ray Optics at beamline 6.1.2 in the Advanced Light Source Synchrotron.34MTXM basically
uses X-ray magnetic circular dichroism (XMCD) contrast to enable us to observe domain dynamics with spatial
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Figure 8. Typical nucleation dominant domain evolution image of CoCrPt alloy films and Hysteresis loop determined
from quantitative analysis of XMCD contrast in field-dependent images.
resolution of ∼ 20 nm comparable to the grain size of most ferromagnetic polycrystalline films such as CoCrPt
alloy films. Typical domain wall configuration of CoCrPt alloy films is shown in Figure 8. Unlike the case of an
in-plane magnetic anisotropy sample having simple 180o-type domain wall, reversed domains are first nucleated
and then expanded by the wall motion.35
Interestingly, the observed nucleation size is ∼ 80 nm or smaller,
which is roughly corresponding to two grains of CoCrPt films or less. It is concluded that the nucleation starts
with the reversal of individual grains in the sample.34
If we quantitatively analyze the field-dependent images, we can determine the magnetic hysteresis loop, as
demonstrated in Fig. 8. If each grain is magnetically isolated and the thermal fluctuation of grain magnetization
is negligible, the entire hysterectic magnetic cycles will be exactly reproducible since the energy landscape of the
system is simply a sum of each grain contribution. In this case, the moving path of domain wall is predetermined
and it finds its own path minimizing energy cost referring the fluctuation-tolerant energy landscape. However,
the observed nucleation process in the present study seems to be at least partially stochastic, as depicted in Fig.
9. Many different nucleation sites appear, as we repeat our observation at the same experimental configuration,
implying the possibility of intergranular magnetic interaction leading to the partially stochastic behavior in
nucleation process. If we pay attention to the very recent experimental report on the Barkhausen avalanche
using MFM, where it has been found that the scaling behavior exists in a wall expansion from the initially
nucleated domain, not in a nucleation process, 28 it is considered that systematic study for clarifying an existence
of the scaling behavior in nucleation process is required. To determine the origin of partial stochastic behavior of
nucleation as demonstrated in Fig. 9, investigation with temperature-dependent and field-dependent magnetic
imaging is essential to examine the statistical nature of thermal noise contributing to the magnetization reversal
of nanogranular CoCrPt alloy films, which is being developed and integrated in MTXM.
4. CONCLUSIONS
We report our direct observation of the Barkhausen avalanche in ferromagnetic thin film systems. For this study
we have used full-field magnetic imaging techniques: magneto-optical microscope magnetometer (MOMM) and
magnetic transmission X-ray microscopy (MTXM). For example, by means of MOMM, we directly visualize and
analyze domain wall fluctuation patterns in simple Co films, where a statistical analysis of the fluctuating size
of Barkhausen jump from numerous repetitive observations has been carried out and the distribution of jump
size is found to exhibit a universal power-law scaling behavior within the measurement error, irrespective of
the film thickness ranging from 5 to 50 nm. On the other hand, we explore the use of an ultrahigh resolution
full-field magnetic transmission X-ray microscope (MTXM) to visualize the Barkhausen avalanche process on
nanometer scale comparable to the fundamental spatial scales such as Barkhausen volume and grain size of
polycrystalline CoCrPt alloy films. Repeated observation using MTXM reveals that initial nucleation process
is neither completely reproducible nor completely stochastic. Further investigation using MTXM is required to
understand the underlying physical origin of the partially stochastic nucleation behavior on such a fundamental
length scale.
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Figure 9. Coordinates of nucleation sites in two successive observations represented by red square and blue triangle.
ACKNOWLEDGMENTS
This work was supported by the Korea Research Foundation Grant (M01-2004-000-20348-0). This work was also
supported by U.S. Department of Energy office of science under contract No. DE-AC03-76SF00098.
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