To locally control the position and the motion of a domain wall, it is common to introduce artificial topological imperfections, such as notches or antinotches, into the wire. The potential created around such a notch is sufficient to trap and release the domain wall in a controlled way. Although a wealth of information has already been experimentally and theoretically obtained, the fundamental question of under what conditions, if any, the domain-wall dynamics in the vicinity of artificial notches can be fully deterministic has not been addressed so far.

The Berkeley–Hamburg group used the soft x-ray microscope at ALS Beamline 6.1.2 for an in-depth investigation of the statistical behavior of the domain wall depinning field at a single notch in permalloy nanowires with different wire widths (w), notch depths (N_d), and film thicknesses (t). Magnetic images based on magnetic circular dichroism contrast with a spatial resolution of better than 25 nm were recorded as an applied magnetic field was gradually increased in steps. In a magnetically saturated wire (only one domain in the wire), increasing the field successively nucleates a second domain (and hence a domain wall) at one end of the wire, propagates the wall down the wire until it becomes pinned at a notch, depins the wall, and drives the wall to the other end of the wire.

Top: Typical SEM image of a 50-nm thick nanowire with a width of 150 nm together with enlarged notch patterns with notch depths of about 30% and 50% of the wire width. Bottom: Three representative image sequences of magnetic-domain wall evolution as an applied magnetic field was gradually increased in steps for wire widths of w = 150 nm (left), 250 nm (center), and 450 nm (right). The images illustrate the nucleation of the domain wall in the bulb at the left end of the wire and its subsequent motion toward the right end. The magnetic field at each step of the domain-wall evolution pattern is indicated.

The stochastic nature of the domain-wall depinning field for different notch depths and wire widths was systematically investigated by determination of the field distribution from depinning events in experiments repeated at least 40 times for each wire. For the first time, these results clearly showed that the domain-wall depinning field exhibits stochastic behavior and the stochastic nature depends considerably on the wire width and the notch depth. A thorough analysis of the data allowed the researchers to conclude that it is the multiplicity of domain-wall types (transverse, vortex, etc.) generated in the vicinity of a notch that is responsible for the observed dependence of the stochastic nature of the domain-wall depinning field on the wire width and the notch depth.

Domain-wall evolution patterns taken from three consecutive experiments under identical measurement conditions for wires of width w = 150, 250, and 450 nm. The color scale represents the field when a domain wall reaches the notch and is pinned and when the wall is depinned at a notch. A hint of the width dependence of the variation in the depinning field is already evident. Analysis of 40 measurements for each of several wires with different wire widths and notch depths demonstrates the domain wall motion does have a stochastic nature but that it depends on the width and depth, thereby providing a path to minimizing this behavior.

While at first glance these findings seem to discourage a successful implementation of devices driven by domain walls, it also shows that a proper geometrical design of the wires could limit the domain-wall types and hence minimize the stochastic behavior of the domain-wall-depinning process, which should be easy to achieve with state-of-the-art patterning and fabrication tools.

Mi-Young Im and Peter Fischer of Berkeley Lab’s Center for X-Ray Optics at the XM-1 full-field soft x-ray transmission microscope at ALS Beamline 6.1.2.

Research conducted by M.-Y. Im and P. Fischer (Center for X-Ray Optics, Berkeley Lab); L. Bocklage and G. Meier (University of Hamburg, Germany).

Research funding: U.S. Department of Energy, Office of Basic Energy Sciences (BES) and the Deutsche Forschungsgemeinschaft. Operation of the ALS is supported by BES.

Publication about this research: M.-Y. Im, L. Bocklage, P. Fischer, and G. Meier, “Direct Observation of Stochastic Domain-Wall Depinning in Magnetic Nanowires,” Phys. Rev. Lett. 102, 147204 (2009).