Bistability of Vortex Core Dynamics in a Single Perpendicularly Magnetized Nanodisk

Abstract

Microwave spectroscopy of individual vortex-state magnetic nano-disks in a perpendicular bias magnetic field, H, is performed using a magnetic resonance force microscope (MRFM). It reveals the splitting induced by H on the gyrotropic frequency of the vortex core rotation related to the existence of the two stable polarities of the core. This splitting enables spectroscopic detection of the core polarity. The bistability extends up to a large negative (antiparallel to the core) value of the bias magnetic field Hr, at which the core polarity is reversed. The difference between the frequencies of the two stable rotational modes corresponding to each core polarity is proportional to H and to the ratio of the disk thickness to its radius. Simple analytic theory in combination with micromagnetic simulations give quantitative description of the observed bistable dynamics.Magnetic vortices are singular topological states found in the equilibrium magnetic configuration of sub-micron size ferromagnetic dots [1,2]. In a certain range of dot aspect ratios (ratio β = t/R of the dot thickness t to its radius R) the equilibrium ground state of the static magnetization consists of the curling in-plane magnetization and a nanometer size core of the out-of-plane magnetization at the dot center. The magnetization of the vortex core can point either up or down, both polarities p = ±1 being degenerate at zero field. This bi-stable property of magnetic vortices, as well as the switching from one polarity to the other, have been intensively studied in the past few years because of their possible applications in magnetic storage devices [3,4,5,6]. It has already been established : (i) that the lowest excitation mode of the vortex state is the gyrotropic mode corresponding to a rotation of the vortex core about the dot center, (ii) that the frequency of this mode is linearly proportional the dot aspect ratio β [7], and (iii) that the sense of gyration of the vortex core is determined by a right-hand rule to the core polarity [4].In this Letter, we report that by using the exquisitely sensitive method of magnetic resonance force microscopy (MRFM) [8], we were able to observe bistability of the vortex core dynamics in a single magnetic disk subjected to a perpendicular bias magnetic field, that was varied in a wide range from positive (parallel to the vortex core) to negative (antiparallel to the vortex core) values. We demonstrate that in a certain range of the bias field magnitudes there are two stable gyrotropic modes of the vortex core rotation having different frequencies and opposite circular polarizations, and corresponding to opposite orientations of the vortex core relative to the direction of the bias magnetic field. The difference in frequencies of these two stable gyrotropic modes is proportional to the magnitude of the applied bias field, H, and, also, to the dot aspect ratio β. We believe that this effect might be important for the development of novel magnetic memory elements. It allows one to determine the polarity of the ...

Perpendicular-bias-field-dependent vortex-gyration eigenfrequency

“…2 (closed circles) cannot be understood. Recently Loubens et al 15 reported an experimental result of the linear response, describing the result as an explicit expression of x 0 ðH p Þ ¼ x 0 ð0Þ½1 þ pðH p =H s Þ, where H s is the field to saturate the dot along the normal (see solid line in Fig. 2).…”

“…Very recently, Loubens et al 15 reported an experimental observation of the dependence of x 0 on the strength of a static magnetic field H p applied perpendicularly to the nanodot plane. However, the underlying physics have yet to be quantitatively unraveled.…”

Optically induced magnetization dynamics and variation of damping parameter in epitaxialCo2MnSiHeusler alloy films

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Limits for the vortex state spin torque oscillator in magnetic nanopillars: Micromagnetic simulations for a thin free layer

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