First order reversal curve (FORC) diagrams are a powerful method of investigating the physical mechanisms giving rise to hysteresis in magnetic systems. We have acquired FORC diagrams for an array of submicron-scale Co dots fabricated by interference lithography. These dots reverse magnetization through the nucleation and annihilation of a single-vortex state. Using FORC diagrams, we are able to obtain precise values for the nucleation and annihilation fields involved in magnetic reversal. Our results indicate, however, that there are actually two distinct paths for vortex annihilation: When a complete magnetic reversal takes place, a vortex enters on one side of a dot and exits out the opposite side. But if the magnetization is returned to its original orientation before a complete reversal has occurred, then the vortex will exit on the same side from which it has entered. We are unable to obtain a precise field value for this later path of annihilation; however, it is shown that, statistically, the vortex annihilates with greater ease when it exits out the same side from which it has entered.
We describe experiments on arrays of polycrystalline Co structures fabricated by interference lithography. The dots are thin (15–40 nm), submicron in size, and are patterned with a uniaxial, in-plane, shape anisotropy axis. We use magnetic force microscopy (MFM) in the presence of an applied field to directly observe magnetic reversal in the dots. These experiments reveal that reversal occurs predominantly through the nucleation and annihilation of a single magnetic vortex in each dot. Hysteresis loop measurements indicate that the vortices are stable over a wide range of applied fields and that the limits of this range depend on the size and thickness of the dots. Using the MFM data, we determine the statistical distribution of the single-vortex nucleation field for several different arrays. We attribute the observed variance to the random orientation of the polycrystalline grains. Finally, we show that the average vortex nucleation and annihilations fields are linearly correlated to the demagnetization field of a uniformly magnetized structure.
We present a magnetic force microscopy @IF&i) analysis of arrays of submicron-scale Co dots fabricated by interference lithography. The dots are thin (I%--300 A) and elliptical in shape. MFiM reveals that these structures relax into highly ordered remanent states whose symmetry and configuration are governed by their shape anisotropy. In particular, when the dots are saturated alon g their long-axis, a uniformly magnetized state persists at remanence. However, when the dots are saturated along their short-axis, they relax into a single-vortex state in which the circulation can have either sign. Both states are characterized by smoothly varying magnetization patterns and a high degree of uniformity across the array. We attribute the ordered behavior of these.structures to the film microstructure, which allows the shape anisotropy to dominate over magnetocrystalline anjsotropy. By imaging a series of minor-loop remanent states, we show that magnetization reversal in these structures occurs via the nucleation and annihilation of a single vortex. Magnetic hysteresis loop measurements are consistent with these observations and provide additional details. Furthexnore. we present the results ofmicromagneticsimulations.which are in excellent agreement with both the klFiL1 images and the hysteresis loop measurements. G
An analysis of the effects of relative phase changes on the interference pattern formed by the coherent addition of four plane waves is presented. We focus on the configuration in which four plane waves converge at equal angles along two orthogonal planes, an arrangement that is potentially useful for printing arrays of microstructures in resist. We show that, depending on the set of polarization vectors chosen, the shape of the interference pattern is a strong function of the phase difference between each pair of beams. If all the beams have the same phase constant, an intensity distribution that is perfectly modulated and that exhibits strong contrast is produced. However, if the phase constant of any one of the beams is shifted by pi from this condition, a pattern with degraded modulation and significantly weaker contrast is formed. We discuss the implication of these results on lithographic applications of multiple-beam patterns. Further, we show that the sensitivity to phase is a general property of all interference patterns formed by four or more intersecting coherent wave fronts that have collinear electric-field components.
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