Occurrence of the vortex state for magnetic phase plates

Abstract

Occurrence of the vortex state for magnetic phase plates Abstract. Tunable magnetic phase plates may be realized as nanorings magnetized in the vortex state, where tunability would be granted by the temperature dependence of the saturation magnetization. Here, we study the statistical occurrence of the magnetic vortex state in circular and pentagonal rings within their magnetic phase diagram. We outline the useful operational range of parameters that may be utilized in practice. IntroductionIn addition to a large number of promising applications in the field of magnetic memories [1] and spintronics [2], nanorings may be utilized as magnetic phase plates in electron microscopy to achieve Zernike-type phase contrast [3,4]. In fact, thanks to the Aharonov-Bohm effect experienced by the electrons traveling through a nanoring in the vortex state, a phase shift is induced between the transmitted and scattered beams. The main benefit is visible in-focus contrast associated with weak (or strong) phase objects such as biological samples [5]. Furthermore, it was hinted in [6] that employing Zernike mode may also result in a substantial decrease of the electron dose necessary to image single atoms or molecules, so that imaging radiation sensitive materials becomes more practical. Aiming at the development of magnetic phase plates we focus here on the stability region of the vortex state in rings within a suitable parameter space. This is a necessary preliminary step to ascertain the range of dimensions and shapes that are compatible with an operational phase plate. Furthermore, we analyze with micromagnetic simulations the statistics of obtaining a vortex from a random initial configuration, and how the statistics varies with shape and size. This is useful to select the appropriate parameters that results in more frequent vortex states and, hence, reliable operability.

Characteristics and controllability of vortices in ferromagnetics, ferroelectrics, and multiferroics

“…The third class of systems is those with polygon geometries (e.g. triangles, squares, rectangles, …) [257,[294][295][296][297] or polyhedron geometries (e.g. cubes, pyramids, …) [268,269,[298][299][300][301].…”

“…Due to the polygonal or polyhedral shape anisotropy, the magnetic vortex in these systems is more likely to be formed with the formation of domains and domain walls compared with the disk or ring-shaped systems. The presence of corners can act as pinning sites for domain wall motion [297]. The stability of vortex states is enhanced by the pinning of domain walls.…”