Domain Wall Motion of Small Permalloy Elements

Laboratory for Physical Sciences, College Park, MD 20740
and Dept. of Electrical Engineering, University of Maryland, College Park, MD 20742

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.

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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.
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.
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.
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.
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
    Check out a similar animation for single domain Cobalt islands.
    [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.