The vortex state, characterized by a curling magnetization, is one of the equilibrium configurations of soft magnetic materials and occurs in thin ferromagnetic square and disk-shaped elements of micrometre size and below. The interplay between the magnetostatic and the exchange energy favours an in-plane, closed flux domain structure. This curling magnetization turns out of the plane at the centre of the vortex structure, in an area with a radius of about 10 nanometres--the vortex core. The vortex state has a specific excitation mode: the in-plane gyration of the vortex structure about its equilibrium position. The sense of gyration is determined by the vortex core polarization. Here we report on the controlled manipulation of the vortex core polarization by excitation with small bursts of an alternating magnetic field. The vortex motion was imaged by time-resolved scanning transmission X-ray microscopy. We demonstrate that the sense of gyration of the vortex structure can be reversed by applying short bursts of the sinusoidal excitation field with amplitude of about 1.5 mT. This reversal unambiguously indicates a switching of the out-of-plane core polarization. The observed switching mechanism, which can be understood in the framework of micromagnetic theory, gives insights into basic magnetization dynamics and their possible application in data storage.

Magnetic nanostructures are being developed for use in many aspects of our daily life, spanning areas such as data storage, sensing and biomedicine. Whereas patterned nanomagnets are traditionally two-dimensional planar structures, recent work is expanding nanomagnetism into three dimensions; a move triggered by the advance of unconventional synthesis methods and the discovery of new magnetic effects. In three-dimensional nanomagnets more complex magnetic configurations become possible, many with unprecedented properties. Here we review the creation of these structures and their implications for the emergence of new physics, the development of instrumentation and computational methods, and exploitation in numerous applications.

We present an ultrafast route for a controlled, toggle switching of magnetic vortex cores with ultrashort unipolar magnetic field pulses. The switching process is found to be largely insensitive to extrinsic parameters, like sample size and shape, and it is faster than any field-driven magnetization reversal process previously known from micromagnetic theory. Micromagnetic simulations demonstrate that the vortex core reversal is mediated by a rapid sequence of vortex-antivortex pair creation and annihilation subprocesses. Specific combinations of field-pulse strength and duration are required to obtain a controlled vortex core reversal. The operational range of this reversal mechanism is summarized in a switching diagram for a 200 nm Permalloy disk.

We study the interaction between two important features of ferromagnetic nanoparticles: magnetic domain walls and spin waves. Micromagnetic simulations reveal that magnetostatic spin waves change their phase as they pass through domain walls. Similar to an Aharonov-Bohm experiment, we suggest to probe this effect by splitting the waves on different branches of a ring. The interference of merging waves depends on the domain walls in the branches. A controlled manipulation of spin-wave phases could be the first step towards nanoscaled ferromagnetic devices performing logical operations based on spin-wave propagation.

We present a micromagnetic study on the current-induced domain-wall motion in cylindrical Permalloy nanowires with diameters below 50 nm. The transverse domain walls forming in such thin, round wires are found to differ significantly from those known from flat nanostrips. In particular, we show that these domain walls are zero-mass micromagnetic objects. As a consequence, they display outstanding dynamic properties, most importantly the absence of a breakdown velocity generally known as the Walker limit. Our simulation data are confirmed by an analytic model which provides a detailed physical understanding. We further predict that a particular effect of the current-induced dynamics of these domain walls could be exploited to measure the nonadiabatic spin-transfer torque coefficient.

We report on a micromagnetic study on domain wall (DW) propagation in ferromagnetic nanotubes. It is found that DWs in a tubular geometry are much more robust than ones in flat strips. This is explained by topological considerations. Our simulations show that the Walker breakdown of the DW can be completely suppressed. Constant DW velocities above 1000 m/s are achieved by small fields. A different velocity barrier of the DW propagation is encountered, which significantly reduces the DW mobility. This effect occurs as the DW reaches the phase velocity of spin waves (SWs), thereby triggering a Cherenkov-like emission of SWs.

A magnetic vortex and an antivortex can annihilate, resulting in a homogeneous magnetization. A detailed description of the magnetization dynamics of such annihilation processes is obtained by micromagnetic simulations based on the Landau-Lifshitz-Gilbert equation. We show that, depending on the relative polarization of the vortex-antivortex pair, the annihilation process is either a continuous transformation of the magnetic structure or it involves the propagation of a micromagnetic singularity (Bloch point) causing a burstlike emission of spin waves. These results provide new insight into a fundamental micromagnetic process that has recently been proposed for a controlled generation of spin waves. DOI: 10.1103/PhysRevLett.97.177202 PACS numbers: 75.40.Gb, 75.40.Mg, 75.75.+a Magnetic vortices in ferromagnets are regions of typically just a few nanometers size, with a core around which the magnetization circulates. Up to a few years ago, such magnetic vortices were considered mainly as a topological detail of magnetic flux-closure patterns [1]. It was found that vortices inevitably occur in singly connected samples with magnetic flux-closure patterns and that they may be located, e.g., at the junctions of magnetic domains [2]. In the wake of the recent dramatic progress in nanomagnetism, static and dynamic properties of submicrometer-sized particles have been extensively studied, and the tiny magnetic vortices and particularly their dynamic properties have moved into the focus of interest [3][4][5][6][7] The counterpart of a magnetic vortex is a magnetic structure with similar properties, known as an antivortex. Both vortex and antivortex have a magnetic core which is magnetized perpendicular to the plane. A vortex and an antivortex can annihilate when they meet [8,9]. Besides the fact that the annihilation is connected with an emission of spin waves [10], not much is known about the magnetization dynamics of a vortex-antivortex annihilation process. We have studied the annihilation of a vortex and an antivortex with finite-element micromagnetic simulations based on the Landau-Lifshitz-Gilbert equation. These simulations yield a detailed description of this previously unexplored fundamental magnetization process. The results reveal the process to strongly depend on the relative orientation of the core magnetization of both the vortex and the antivortex. Particularly, if the vortex and antivortex cores are antiparallel to each other, the annihilation process involves the propagation of a Bloch point, which causes a burstlike dissipation of exchange energy (''exchange explosion'') via spin waves. Considering the proposed use of magnetic vortices in data storage and magnetologic approaches [5,11,12], a good control of the dynamic behavior will be mandatory. Understanding the annihilation dynamics of vortices and antivortices is, therefore, an important step towards a precise description of the complicated dynamic magnetization processes involving the temporary formation of vortices.The similarities and differen...

Arrays of suitably patterned and arranged magnetic elements may display artificial spin-ice structures with topological defects in the magnetization, such as Dirac monopoles and Dirac strings. It is known that these defects strongly influence the quasistatic and equilibrium behavior of the spin-ice lattice. Here, we study the eigenmode dynamics of such defects in a square lattice consisting of stadiumlike thin film elements using micromagnetic simulations. We find that the topological defects display distinct signatures in the mode spectrum, providing a means to qualitatively and quantitatively analyze monopoles and strings that can be measured experimentally.