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Micron-sized ferromagnetic permalloy disks having an in-plane vortexlike configuration are excited by a fast-rise-time magnetic-field pulse perpendicular to the plane. The excited modes are imaged using timeresolved magneto-optic Kerr microscopy and Fourier transformation. Two types of modes are observed: modes with circular nodes and modes with diametric nodes. The frequency of the modes with circular nodes increases with the number of nodes. In contrast, the frequency of the modes with diametric nodes decreases with the number of nodes. This behavior is explained accurately by an analytical model.

Thin-circular lithographically defined magnetic elements with a spin vortex configuration are excited with a short perpendicular magnetic field pulse. We report the first images of excited magnetic eigenmodes up to third order, obtained by means of a phase sensitive Fourier transform imaging technique. Both axially symmetric and symmetry breaking azimuthal eigenmodes are observed. We observe strong oscillations of the magnetization in the central part of the magnetic elements. The experimental data are in good agreement with micromagnetic simulations.

Within the framework of the Landau-Lifshitz-Gilbert equation, using permalloy parameters, we study the statics and dynamics of flat circular magnetic nano-structures with an in-plane magnetic vortex configuration, putting particular emphasis on the vorticity of the magnetic state and on the (perpendicular) polarisation of the vortex center, which may be shifted with respect to the center of the circle. These binary degrees of freedom can in principle be used to manipulate two independent bits of information.Studying switching processes induced by in-plane and out-of plane field pulses we find that it is possible to switch the vorticity of the magnetic dot on a time scale of 40 ps in strong enough and short enough perpendicular external field pulses (B ext z ≈ 0.5 T, duration ≈ 40 ps). But for realistically small values of the Gilbert damping, only the vorticity can be switched this fast, and it turns out that it is better to dismiss the center of the circle totally, concentrating on flat 'nano-rings' with an inner radius R 1 and an outer radius R 2 . On these 'nano-rings' the vortex state is more stable, and with respect to the switching of the vorticity these structures have similar properties as circular dots.

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Oscillations of the giant magnetoresistance (GMR) and thermo-electric power (TEP) vs. both the thickness of the non-magnetic spacer and also that of the ferromagnetic slabs are studied in the current-perpendicular-to-plane (CPP) geometry of magnetic trilayer systems, in terms of a singleband tight-binding model without impurities. The spin-dependent conductance has been calculated from the Kubo formula by means of a recursion Green's function method and the semi-infinite ideal-lead wires trick. Additionally the TEP is obtained directly from Mott's formula. In general, the thickness oscillations of the GMR and the TEP may have just one or two (short and long) oscillations. The long period, related to spectacular beats, is apparently of non-RKKY type. The TEP oscillations are strongly enhanced with respect to those of the GMR, have the same periods, but different phases and a negative bias.The phenomenon of giant magnetoresistance (GMR) in magnetic multilayers has been intensively studied both experimentally [1,2] and theoretically [3][4][5][6][7] for more than five years now. After the paper [5] was published it has become clear that one can expect a large magnetoresistance even in systems which have no impurities and no structural defects. As pointed out in [7], the GMRoscillations have not only RKKY-type components, but may additionally reveal large particular non-RKKY oscillations (see below). For the case of semi-infinite ferromagnetic slabs, a period of those extra oscillations with the spacer thickness in the CPP (current perpendicularto-plane) geometry has been shown in [7] to originate from values of the in-plane wavenumber k at which at least one spectral density vanishes at the ferromagnetic interface.In the present letter we study the CPP-GMR (currentperpendicular-to-plane) behaviour of layered systems of the type W/F 1 /S/F 2 /W , where W stands for a semiinfite ideal lead wire, F 1 and F 2 for different ferromagnets, generally with different thicknesses, and S for the non-magnetic spacer. Thus, apart from the leads, we are dealing with the usual magnetic trilayer systems. Our aim is to show that very pronounced beats may also, under some circumstances, appear as a function of the thicknesses of the ferromagnetic slabs. Besides the giant magneto-resistance effect, we also calculate the corresponding effect for the thermo-electric power (TEP).The calculation technique, we have developed, is based on the Green's function recursion method [8,6]; it is close to that of [6] with one essential exception, namely instead of working with finite systems in the in-plane space (x, y directions), we have reduced the whole problem to one dimension by performing the Fourier transform in the infinite x-y plane. Hence, our Green's functions fulfil the following equation:where for the simple cubic lattice t z,z ′ = t δ z ′ ,z±1 andIn eqn. (2), E F is the Fermi energy; t (< 0) is the nearest-neighbour hopping integral; a is the lattice constant, and V σ (z) is the spin-dependent atomic potential, which we assume to be c...

By ab initio LMTO calculations in the atomic sphere approximation we study the oscillatory thickness dependence of the exchange coupling between ferromagnetic CO slabs grown epitaxially on the (001) surface of a f.c.c. Cu spacer in a d,-Co/&-Cu multilayer structure and find not only the well-known oscillations with the spacer thickness 4 , but-as a new result-also a pronounced oscillation with the magnetic thickness dl . Thus, the experimentalist should not only vary, as usual, the spacer thickness 4 , but also the magnetic thickness dl , when trying to optimize the exchange coupling of the system for applications.

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