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 ...

Using the ultra low damping NiMnSb half-Heusler alloy patterned into vortex-state magnetic nano-dots, we demonstrate a new concept of non-volatile memory controlled by the frequency. A perpendicular bias magnetic field is used to split the frequency of the vortex core gyrotropic rotation into two distinct frequencies, depending on the sign of the vortex core polarity p = ±1 inside the dot. A magnetic resonance force microscope and microwave pulses applied at one of these two resonant frequencies allow for local and deterministic addressing of binary information (core polarity).

In a vortex-state magnetic nanodisc [1][2][3] , the static magnetization curls in the plane, except in the core region, where it points out of plane 4,5 , either up or down, leading to two possible stable states of opposite core polarity p. Dynamical reversal of p by large-amplitude motion of the vortex core [6][7][8][9] has recently been demonstrated experimentally [10][11][12][13][14] , raising the prospect of practical applications, in particular in magnetic-storage devices 15. Here we demonstrate coherent control of p by singleand double-microwave-pulse sequences, taking advantage of the resonant vortex dynamics in a perpendicular-bias magnetic field 16 . Experimental optimization of the microwave-pulse duration required for switching p also yields information about the characteristic decay time of the vortex core in the largeoscillation regime. This time is found to be less than half the length seen in the small-oscillation regime, suggesting a nonlinear behaviour of magnetic dissipation.Magnetic vortices are topological solitons with rich dynamical properties. The lowest-energy excitation of the vortex ground state is the so-called gyrotropic mode 3 , corresponding to the gyration of the vortex core around its equilibrium position with a frequency in the sub-gigahertz range 17,18 . It is now established experimentally 14 that the excitation of this gyrotropic motion leads to a dynamical distortion of the vortex-core profile, as predicted by micromagnetic simulations and theoretical analysis 8 . This distortion increases with the linear velocity of the vortex core and opposes the core polarity, until the critical velocity V c 1.66γ √ A ex (γ is the gyromagnetic ratio of the magnetic material and A ex its exchange constant) is reached and the vortex-core polarity is reversed 9 . In zero magnetic field, dynamical control of the polarity is difficult owing to the degeneracy of the gyrotropic frequencies associated with opposite polarities p = ±1, which can lead to multiple core switching 7,11 . Still, selective core-polarity reversal is possible using a circularly polarized microwave magnetic field because the sense of the core rotation is linked by a right-hand rule to its polarity 12 . Control of polarity switching can also be achieved by precise timing of non-resonant magnetic-field pulses 13,19 , in a similar fashion as domain-wall propagation in magnetic nanowires 20 . Resonant amplification 21 of the vortex gyrotropic motion enables us to reverse the core polarity with minimum excitation power 12,14,15 , as it enables us to concentrate the energy in a narrow frequency band. In this scheme, the damping ratio is an important parameter because it controls the minimum amplitude of the resonant excitation required to switch the core 9 . Here, it is shown that the damping ratio close to the reversal threshold is significantly larger than that measured in the small-oscillation regime. We associate this with the nonlinear nature of the reversal process 6,8 .