Welcome to this instructional site. Following are several examples of the motion of domain walls under the
application of external magnetic field.
The images were taken by using magnetic force microscopy (MFM) in the presence of external applied fields. [1] The "field lapse" animation consists of about
35 MFM images in one complete cycle. The data start at remanence, and taken in succession in progressively varying field --- first ascending to about 120 Oe, descending
through zero to -120 Oe and back again to zero.
Special MFM probes were selected[2] which had very low moments in order to reduce tip-induced image perturbation.
The caveat however, is that the small field from the tip may induce profound changes, specially when the external
field is close to some critical value which causes drastic
magnetization changes. The samples were furnished by K.J. Kirk and J.N. Chapman of the Dept. of Physics and
Astronomy, University of Glasgow, Scotland.
The films were thermally evaporated on silicon substrates and patterned
using e-beam lithography.
It takes approximately to load the animation
sequences at 20KPS, and the best results are obtained with the latest
version of Navigator. If some animations stall, try clearing or
increasing the memory
cache of Navigator (Edit/Preferences/Advanced(2x)/Cache) and reloading.
A special welcome is extended to conference attendees of the
MMM'98
Conference, and to my numerical micromagnetic modeling colleagues.
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Domain wall motion of a 3 micron x 3 micron x 26 nm thick Permalloy element in one
magnetization cycle. At remanence (H=0), the configuration is a 7 domain closure pattern with eight 90 degree
walls and two horizontal near 180 degree walls. The right 180 degree wall is itself divided
into 2 Bloch lines and 1 crosstie, thus giving the appearance that the rightmost segment
is divided into 2 subsections. (SEE General comments below for a description of Bloch lines and crossties and
how they are indentified in MFM.)
With increasing field along the vertical axis, the right
and left segments (which are parallel to the field) expand at the expense of the middle
segment. Note that the left segment, perhaps due to the absence of a crosstie, expands more
rapidly than the left. Technical saturation is achieved as soon as the
domains have coalesced.
Reduction of the field back to zero generates a complex domain structure with curved and discontinuous domain
walls, but a slight negative field (immediately after remanence) induces a transition into the familiar (classic textbook)
4 domain closure pattern.
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Domain wall motion of a 4 micron x 3 micron by 26 nm thick Permalloy
element in one magnetization cycle. At remanence (H=0), the configuration
is a 4 domain closure pattern with 90 degree strained walls. Note the
motion of the central vortex, and the formation of complex edge structures
prior to near saturation. The formation of a crosstie on the left edge
near saturation is particularly interesting. The
mechanical defect (circular protrusion) appears to induce a slight bending
of the moving "90 degree" wall.
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Domain wall motion of a 3 micron x 2 micron by 26 nm thick Permalloy
element in one magnetization cycle. At remanence (H=0), the configuration
is a 4 domain closure pattern with four 90 degree walls and one horizontal
180 degree wall. Note the creation and motion of
a Bloch line at intermediate fields (+/- 30 Oe). The mechanical defect
(diagonal strip across the lower right corner) appears to induce the
slight motion of the vortex near saturation.
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Domain wall motion of a 4 micron x 2 micron by 26 nm thick Permalloy
element in one
magnetization cycle.
At remanence (H=0), the configuration is a 4 domain closure pattern with 90 degree
walls, a 180 degree wall with 2 Bloch lines and a crosstie at the center. During the
ascending branch of the magnetization, the right domain increases in size and accompanied
by the corresponding reduction of the left. Note that prior to coalescence with the growing right domain, the crosstie at the center remains
stationary, albeit, the intensity diminishes and cants towards the growing right domain.
The crosstie was observed only during the initial remanent state and in the ascending
branch, but not during the descending branch and negative field. The sudden contrast flip of the 180 degree wall (near coercivity) indicates the reversal of the charges on the 180 degree wall. This is enigmatic.
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General comments:
Net moment at remanenence. All samples have zero or close to zero
total magnetization at remanence. These are so called "solenoidal"
domain configurations.
Magnetization orientation. Since the films are only 26 nm thick, it
can be assumed that the magnetization lies entirely in the plane of the
film.
Image interpretation. In interpreting MFM images, the contrast can be
qualitatively related to the magnetic charges (north or south poles), arising from either the -(div*M) or M*n, n being the unit outward normal to a surface plane. Since the surface charges
are non-existent in these patterns, then the contrast is due primarily to the divergence term occuring at the domain wall boundaries.
Differentiation between a Bloch line and a crosstie. Bloch lines and crossties occur as the sense of
rotation of the moments in the interior
of a 180 degree wall is reversed. The moment reversal appears as an alternation of the bright/dark contrast along the 180 degree wall. In Bloch lines,
the sense of rotation of the moment is in phase with the direction of the magnetization in the main
domains, whereas in the crossties, it is out-of phase. As a result, a strong divergence of M exists in the main domains whenever
a crosstie exists. Thus in the MFM image, a crosstie can be identified as a reversal of the contrast in a 180 wall and
accompanied by strong contrast variations transverse to the wall and extending into the main domains. A Bloch
line is a mere contrast reversal of the 180 degree wall.
Reversibility. Reversible behavior was found in all the patterns as long as the field had not caused to collapse of the domains at remanence.
Hysteretic phenomenon near technical saturation. The magnetization increases abruptly as soon as the domains coallesce (technical saturation) This is happens at some field, H1.
After technical saturation, the reverse field required for the system to revertback into a solenoidal configuration, H2 is much lower than H1.
Hysteretic property with aspect ratio. H1 increases with aspect ratio. H2 decreases with aspect ratio.
Crossties appear as the length of the 180 degree walls increases. Bloch lines appear almost as soon 180
degree walls are formed.
Crossties require a higher field (energy) to move and extinguish.
More details can be found in the following articles:
R.D. Gomez, et al., "Domain configurations of submicron Permalloy elements" and "Domain wall motion of nanostructured Permalloy Islands",
J. of Applied Physics 1999, in press.
The above analyses are solely due to the author and the viewer is welcome to offer other insights. Send
comments or preprint requests to rdgomez@eng.umd.edu.
Check out a similar animation for single
domain Cobalt islands.
REFERENCES:
[1] R.D. Gomez, E.R. Burke, I.D. Mayergoyz, "Magnetic Imaging in the Presence of an
External Field: Technique and Applications", J. Applied Physics 79, 6441-6446 (1996).
[2] R.D. Gomez, Quantification of magnetic force microscopy images by using combined
electrostatic and magnetostatic imaging", J. Applied Physics 83, 6226-6228 (1998).
Follow this link to
AIP to download the papers.
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