
Magnetic Modes in Permalloy ElementsDecrease of Entropy in MicrowaveExcited Magnetic StructuresA. Krasyuk, F. Wegelin, S. A. Nepijko, H. J. Elmers,G. Schönhense These experiments have been performed by stroboscopic illumination of the sample by Xray pulses produced by electron bunches in the synchrotron ring. In this case, the special bunch compression mode (lowalpha mode) was utilized. It is characterized by tFWHM = 3 ps, with a repetition rate of 500 MHz. Snapshots of the time evolution of the magnetization M in the permalloy platelet are shown in Fig. 1 (top row) for the smallest field pulse. Micromagnetic simulations (bottom row) were used to verify the experimental findings, the centre row denotes the precessional motion of M. Fig. 2 shows the full series and the corresponding profiles of the field pulse and the magnetization response (in terms of the rotation angle). With increasing field amplitude the Néel wall is more and more displaced and finally driven out of the particle, see Fig. 3. This means that the order has increased. In a closed system entropy maximization tends to decrease order. An open system with a constant throughput of energy, however, allows for an increase of local order. Exciting micronsized permalloy particles with an oscillating external field we found an example for this phenomenon that relies on the nonlinear character of magnetization dynamics. The external oscillating field is the energy source while the internal damping plays the role of the sink. In the rectangular platelet shown below the equilibrium magnetization state is formed by a symmetric fluxclosure domain pattern comprising two equallysized domains separated by a 180 degree domain wall (see Fig. 1). The external field is applied along the short side of the platelet, thus exciting a precessional motion of the magnetization with a frequency of 1 GHz slightly offresonance, see full series in Fig. 2. The system reacts by increasing one magnetic domain at the expense of the others. This corresponds to a movement of the domain wall to the right. If the field amplitude is enhanced, the domain wall is shifted more and more off centre and finally is driven out of the particle, see Fig.3. At maximum field amplitude, the final state has uniform magnetization and is thus completely ordered. The basic driving mechanism, revealed by both stroboscopic imaging and computer simulation, is the decrease of the resonance frequency in the larger domain. This leads to larger energy dissipation in the system, allowing increasing order with increasing entropy. Fig. 3 shows a model calculation and a mechanical analog of the phenomenon.
Fig. 1 Top row: Selected XMCD images showing the time evolution of the xcomponent of the magnetization (bright areas are magnetized to the right, dark areas to the left) in a permalloy platelet (16 µm x 32 µm) for delay times t = 0 ps (a), 600 ps (b), 1100 ps (c) and 1400 ps (d) between the onset of the field pulse and the probe pulse (synchrotron radiation). The orientations of the exciting AC field H and the photon polarization P are both in xdirection. Centre row: Sketches of the corresponding domain patterns, the arrows denote the local magnetization directions. Bottom row: Corresponding results of micromagnetic simulations for a permalloy platelet with linearly reduced dimensions (8 µm x 16µm x 5 nm, cell size 10 nm).
Fig. 2: Full series of XMCDPEEM images; field pulse profile and magnetic response (rotation angle of the magnetisation vector).
Fig. 3 Top: Shift of the Néel wall with increasing field amplitude. Bottom: Result of a model calculation and mechanical analog. A vibrating string (first overtone) will shift its node off centre, when it is excited below its resonance frequency. Thus it can absorb more energy out of the exciting field.
Model calculations (Figs. 1 and 4) verify the observed behavior, but only if an initially nonsymmetric wall position is assumed. In the experiment, the asymmetry is induced by structural imperfections.
Fig. 4 Left panel: Snapshot of a simulated dynamical domain pattern; the colors indicate the direction of the local magnetization. Right panel: Fourier power map of the horizontal magnetization component at the excitation frequency. (figure courtesy M. Bolte, Univ. Hamburg)
Funded by BMBF (03 N 6500 „Nanocentre“) and by Stiftung RheinlandPfalz für Innovation (project 535). The early stage of the experiment was funded via Verbundforschung Synchrotronstrahlung (BMBF 05KS1 UM1/5). We thank the staff of BESSY and in particular D. Schmitz for excellent support. Special thanks are due M. Bolte (Institut für Angewandte Physik, Universität Hamburg) for performing part of the simulations.
Results were published in: Selftrapping of Magnetic Oscillation Modes in Landau FluxClosure Structures
For the description of the method, see: Timeresolved photoemission electron microscopy of magnetic field and magnetisation changes; 
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