353 research outputs found

    Dissipation characteristics of quantized spin waves in nano-scaled magnetic ring structures

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    The spatial profiles and the dissipation characteristics of spin-wave quasi-eigenmodes are investigated in small magnetic Ni81_{81}Fe19_{19} ring structures using Brillouin light scattering microscopy. It is found, that the decay constant of a mode decreases with increasing mode frequency. Indications for a contribution of three-magnon processes to the dissipation of higher-order spin-wave quasi-eigenmodes are found

    Direct current control of three magnon scattering processes in spin-valve nanocontacts

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    We have investigated the generation of spin waves in the free layer of an extended spin-valve structure with a nano-scaled point contact driven by both microwave and direct electric current using Brillouin light scattering microscopy. Simultaneously with the directly excited spin waves, strong nonlinear effects are observed, namely the generation of eigenmodes with integer multiple frequencies (2 \emph{f}, 3 \emph{f}, 4 \emph{f}) and modes with non-integer factors (0.5 \emph{f}, 1.5 \emph{f}) with respect to the excitation frequency \emph{f}. The origin of these nonlinear modes is traced back to three magnon scattering processes. The direct current influence on the generation of the fundamental mode at frequency \emph{f} can be related to the spin-transfer torque, while the efficiency of three-magnon-scattering processes is controlled by the Oersted field as an additional effect of the direct current

    Direct observation of domain wall structures in curved permalloy wires containing an antinotch

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    The formation and field response of head-to-head domain walls in curved permalloy wires, fabricated to contain a single antinotch, have been investigated using Lorentz microscopy. High spatial resolution maps of the vector induction distribution in domain walls close to the antinotch have been derived and compared with micromagnetic simulations. In wires of 10 nm thickness the walls are typically of a modified asymmetric transverse wall type. Their response to applied fields tangential to the wire at the antinotch location was studied. The way the wall structure changes depends on whether the field moves the wall away from or further into the notch. Higher fields are needed and much more distorted wall structures are observed in the latter case, indicating that the antinotch acts as an energy barrier for the domain wal

    Realization of XNOR and NAND spin-wave logic gates

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    We demonstrate the functionality of spin-wave logic XNOR and NAND gates based on a Mach-Zehnder type interferometer which has arms implemented as sections of ferrite film spin-wave waveguides. Logical input signals are applied to the gates by varying either the phase or the amplitude of the spin waves in the interferometer arms. This phase or amplitude variation is produced by Oersted fields of dc current pulses through conductors placed on the surface of the magnetic films.Comment: 5 pages, 2 figure

    Complexity of Coloring Graphs without Paths and Cycles

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    Let PtP_t and CℓC_\ell denote a path on tt vertices and a cycle on ℓ\ell vertices, respectively. In this paper we study the kk-coloring problem for (Pt,Cℓ)(P_t,C_\ell)-free graphs. Maffray and Morel, and Bruce, Hoang and Sawada, have proved that 3-colorability of P5P_5-free graphs has a finite forbidden induced subgraphs characterization, while Hoang, Moore, Recoskie, Sawada, and Vatshelle have shown that kk-colorability of P5P_5-free graphs for k≥4k \geq 4 does not. These authors have also shown, aided by a computer search, that 4-colorability of (P5,C5)(P_5,C_5)-free graphs does have a finite forbidden induced subgraph characterization. We prove that for any kk, the kk-colorability of (P6,C4)(P_6,C_4)-free graphs has a finite forbidden induced subgraph characterization. We provide the full lists of forbidden induced subgraphs for k=3k=3 and k=4k=4. As an application, we obtain certifying polynomial time algorithms for 3-coloring and 4-coloring (P6,C4)(P_6,C_4)-free graphs. (Polynomial time algorithms have been previously obtained by Golovach, Paulusma, and Song, but those algorithms are not certifying); To complement these results we show that in most other cases the kk-coloring problem for (Pt,Cℓ)(P_t,C_\ell)-free graphs is NP-complete. Specifically, for ℓ=5\ell=5 we show that kk-coloring is NP-complete for (Pt,C5)(P_t,C_5)-free graphs when k≥4k \ge 4 and t≥7t \ge 7; for ℓ≥6\ell \ge 6 we show that kk-coloring is NP-complete for (Pt,Cℓ)(P_t,C_\ell)-free graphs when k≥5k \ge 5, t≥6t \ge 6; and additionally, for ℓ=7\ell=7, we show that kk-coloring is also NP-complete for (Pt,C7)(P_t,C_7)-free graphs if k=4k = 4 and t≥9t\ge 9. This is the first systematic study of the complexity of the kk-coloring problem for (Pt,Cℓ)(P_t,C_\ell)-free graphs. We almost completely classify the complexity for the cases when k≥4,ℓ≥4k \geq 4, \ell \geq 4, and identify the last three open cases

    Exhaustive generation of kk-critical H\mathcal H-free graphs

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    We describe an algorithm for generating all kk-critical H\mathcal H-free graphs, based on a method of Ho\`{a}ng et al. Using this algorithm, we prove that there are only finitely many 44-critical (P7,Ck)(P_7,C_k)-free graphs, for both k=4k=4 and k=5k=5. We also show that there are only finitely many 44-critical graphs (P8,C4)(P_8,C_4)-free graphs. For each case of these cases we also give the complete lists of critical graphs and vertex-critical graphs. These results generalize previous work by Hell and Huang, and yield certifying algorithms for the 33-colorability problem in the respective classes. Moreover, we prove that for every tt, the class of 4-critical planar PtP_t-free graphs is finite. We also determine all 27 4-critical planar (P7,C6)(P_7,C_6)-free graphs. We also prove that every P10P_{10}-free graph of girth at least five is 3-colorable, and determine the smallest 4-chromatic P12P_{12}-free graph of girth five. Moreover, we show that every P13P_{13}-free graph of girth at least six and every P16P_{16}-free graph of girth at least seven is 3-colorable. This strengthens results of Golovach et al.Comment: 17 pages, improved girth results. arXiv admin note: text overlap with arXiv:1504.0697
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