The theoretical foundation for a nonvolatile memory device based on magnetic vortices is presented. We propose a realization of a vortex random-access memory (VRAM) containing vortex cells that are controlled by alternating currents only. The proposed scheme allows to transfer the vortex into an unambiguous binary state regardless of its initial state within a subnanosecond time scale. The vortex handedness defined as the product of chirality and polarization as a bit representation allows direct mechanisms for reading and writing the bit information. The VRAM is stable at room temperature.

In experiments the distinction between spin-torque and Oersted-field driven magnetization dynamics is still an open problem. Here, the gyroscopic motion of current-and field-driven magnetic vortices in small thinfilm elements is investigated by analytical calculations and by numerical simulations. It is found that for small harmonic excitations the vortex core performs an elliptical rotation around its equilibrium position. The global phase of the rotation and the ratio between the semi-axes are determined by the frequency and the amplitude of the Oersted field and the spin torque. PACS numbers: 75.60.Ch, 72.25.Ba Recently it has been found that a spin-polarized current flowing through a magnetic sample interacts with the magnetization and exerts a torque on the local magnetization. 1,2 A promising system for the investigation of the spin-torque effect is a vortex in a micro-or nanostructured magnetic thinfilm element. Vortices are formed when the in-plane magnetization curls around a center region. In this few nanometer large center region 3 , called the vortex core, the magnetization turns out-of-plane to minimize the exchange energy. 4 It is known that these vortices precess around their equilibrium position when excited by magnetic field pulses 5,6 and it was predicted that spin-polarized electric currents can do the same. 7 The spacial restriction of the vortex core as well as its periodic motion around its ground state yield an especially accessible system for space-and time-resolved measurements with scanning probe and time-integrative techniques such as soft X-ray microscopy or X-ray photoemission electron microscopy. 5,6,8,9,10 Magnetic vortices also occur in vortex domain walls. The motion of such walls has recently been investigated intensively. 11,12 Understanding the dynamics of confined vortices can give deeper insight in the mechanism of vortex-wall motion. 13 An in-plane Oersted field accompanying the current flow also influences the motion of the vortex core. For the interpretation of experimental data it is crucial to distinguish between the influence of the spin torque and of the Oersted field. 14 (a) l X (b) FIG. 1: (a) Scheme of the magnetization in a square magnetic thinfilm element with a vortex that is deflected to the right. (b) Magnetization of a vortex in its static ground state. The height denotes the z-component while the gray scale corresponds to the direction of the in-plane magnetization.In this paper we investigate the current-and field-driven gyroscopic motion of magnetic vortices in square thin-film elements of size l and thickness t as shown in Fig. 1 and present a method to distinguish between spin torque and Oersted field driven magnetization dynamics. In the presence of a spinpolarized current the time evolution of the magnetization is given by the extended Landau-Lifshitz-Gilbert equationwith the coupling constant b j = P µ B /[eM s (1 + ξ 2 )] between the current and the magnetization where P is the spin polarization, M S the saturation magnetization, and ξ the degree o...

Time-resolved X-ray microscopy is used to image the influence of alternating high-density currents on the magnetization dynamics of ferromagnetic vortices. Spin-torque induced vortex gyration is observed in micrometer-sized permalloy squares. The phases of the gyration in structures with different chirality are compared to an analytical model and micromagnetic simulations, considering both alternating spin-polarized currents and the current's Oersted field. In our case the driving force due to spin-transfer torque is about 70% of the total excitation while the remainder originates from the current's Oersted field. This finding has implications to magnetic storage devices using spin-torque driven magnetization switching and domain-wall motion.PACS numbers: 68.37. Yz, 72.25.Ba , 75.25.+z, 75.40.Mg, The discovery that spin-polarized electrons traveling through ferromagnets apply a torque on the local magnetization 1 opened up a new field of research in solid state physics that could potentially result in new magnetic storage media. It is now understood that the spin-transfer torque acts on inhomogeneities in the magnetization, e.g., on interfaces between magnetic layers, 2 on domain walls, 3,4 i.e., interfaces between regions of uniform magnetization, or on magnetic vortices. 5,6,7,8 Magnetic domain walls, usually vortex walls, can be driven by spin-polarized currents to store information in bit registers. 10Vortices appear in laterally confined thin films when it is energetically favorable for the magnetization to point in-plane and parallel to the edges. In the center the magnetization is forced out-of-plane to avoid large angles between magnetic moments that would drastically increase the exchange energy. The region with a strong out-of-plane magnetization component is called the vortex core and is only a few nanometers in diameter. 11,12 The direction of the magnetization in the vortex core, also called the core polarization p, can only point out-ofor into-the-plane (p=+1 or p=−1, respectively). Hence ferromagnetic thin films containing vortex cores have been suggested as data storage elements. The chirality c = +1(−1) denotes the counterclockwise (clockwise) in-plane curling direction of the magnetization. It is known that vortices can be excited to gyrate around their equilibrium position by magnetic fields. 13,14 Recently it has been shown that field excitation can also switch the core polarization. 15,16,17,18,19,20 Micromagnetic simulations predict that spin-polarized currents can cause vortices both to gyrate 5,7 and to switch their polarization. 8,21,22 Both for field-and spin-torque-driven excitation, the direction of gyration is governed by the vortex polarization according to the right-hand rule (see Fig. 2 of Ref.14 ). The phase of field-driven gyration depends also on the chirality, while spin-torque driven gyration is independent of the chirality as the spin-transfer torque is proportional to the spatial derivative of the magnetization.7 Time-and spatially averaging experimental techniques indicate...

The influence of the magnetostatic interaction on vortex dynamics in arrays of ferromagnetic disks is investigated by means of a broadband ferromagnetic-resonance setup. Transmission spectra reveal a strong dependence of the resonance frequency of vortex-core motion on the ratio between the center-to-center distance and the element size. For a decreasing ratio, a considerable broadening of the absorption peak is observed following an inverse sixth power law. An analogy between the vortex system and rotating dipoles is confirmed by micromagnetic simulations.

Different numerical approaches for the stray-field calculation in the context of micromagnetic simulations are investigated. We compare finite difference based fast Fourier transform methods, tensor grid methods and the finite-element method with shell transformation in terms of computational complexity, storage requirements and accuracy tested on several benchmark problems. These methods can be subdivided into integral methods (fast Fourier transform methods, tensor-grid method) which solve the stray field directly and in differential equation methods (finite-element method), which compute the stray field as the solution of a partial differential equation. It turns out that for cuboid structures the integral methods, which work on cuboid grids (fast Fourier transform methods and tensor grid methods) outperform the finite-element method in terms of the ratio of computational effort to accuracy. Among these three methods the tensor grid method is the fastest. However, the use * of the tensor grid method in the context of full micromagnetic codes is not well investigated yet. The finite-element method performs best for computations on curved structures. Stray-Field ProblemConsider a magnetization configuration M that is defined on a finite region Ω = {r : M (r) = 0}. In order to perform minimization of the full micromagnetic energy functional or solve the Landau-Lifshitz-Gilbert (LLG) equation it is necessary to compute the stray field within the finite region Ω. The stray-field energy is given by(1)