Evolution and stability of a magnetic vortex in a small cylindrical ferromagnetic particle under applied field

Abstract

The energy of a displaced magnetic vortex in a cylindrical particle made of isotropic ferromagnetic material (magnetic dot) is calculated taking into account the magnetic dipolar and the exchange interactions. Under the simplifying assumption of small dot thickness the closed-form expressions for the dot energy is written in a non-perturbative way as a function of the coordinate of the vortex center. Then, the process of losing the stability of the vortex under the influence of the externally applied magnetic field is considered. The field destabilizing the vortex as well as the field when the vortex energy is equal to the energy of a uniformly magnetized state are calculated and presented as a function of dot geometry. The results (containing no adjustable parameters) are compared to the recent experiment and are in good agreement. 75.75.+a, 75.25.+z, 75.60.-d Introduction. The unusual magnetic properties of sub-micron cylindrical magnetic particles and their periodical two-dimensional arrays drawn much attention because of their possible potential as a magnetic storage as well as an interesting model system for studying of the magnetization reversal 1-4 . The applications of such patterned magnetic films for magnetic information storage (MRAM, for instance) are promising.In this work the isolated magnetic particles made of isotropic (soft) magnetic material shaped as circular cylinders (referred hereafter as "dots") are considered. The magnetic properties of the dots are governed by the magnetic dipolar and the exchange interactions. When the external magnetic field is absent, three parameters of the dimension of length define completely the magnetic structure of a dot. These parameters are: the dot radius R, the dot thickness L and the exchange length L E = C/M 2 S , where C is the exchange constant and M S is the saturation magnetization of the material. The phase diagram of small L/L E 4, R/L E 4 dots in no applied magnetic field showing the range of dot parameters where the magnetic vortex (curl) is the ground state was calculated by Usov and co-workers 5,6 . Vortex states were indeed observed in polycrystalline Co 7 and F eN i 4,8-11 cylindrical dots.So far there is no theory of magnetization reversal of a dot in a vortex state when the magnetic field h = H/4πM S applied in the direction perpendicular to the cylinder axis. This process taking place via nucleation, displacement and annihilation of a single magnetic vortex 11 is considered in this work. There are three characteristic fields describing this process: the "vortex" nu-

Possibility of a long-range proximity effect in a ferromagnetic nanoparticle

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Dynamic transformations of the internal structure of a moving domain wall in magnetic nanostripes

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Stability of magnetic vortex in soft magnetic nano-sized circular cylinder

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