353 research outputs found
Dissipation characteristics of quantized spin waves in nano-scaled magnetic ring structures
The spatial profiles and the dissipation characteristics of spin-wave
quasi-eigenmodes are investigated in small magnetic NiFe 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
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
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
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
Let and denote a path on vertices and a cycle on
vertices, respectively. In this paper we study the -coloring problem for
-free graphs. Maffray and Morel, and Bruce, Hoang and Sawada,
have proved that 3-colorability of -free graphs has a finite forbidden
induced subgraphs characterization, while Hoang, Moore, Recoskie, Sawada, and
Vatshelle have shown that -colorability of -free graphs for
does not. These authors have also shown, aided by a computer search, that
4-colorability of -free graphs does have a finite forbidden induced
subgraph characterization. We prove that for any , the -colorability of
-free graphs has a finite forbidden induced subgraph
characterization. We provide the full lists of forbidden induced subgraphs for
and . As an application, we obtain certifying polynomial time
algorithms for 3-coloring and 4-coloring -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 -coloring problem for -free
graphs is NP-complete. Specifically, for we show that -coloring is
NP-complete for -free graphs when and ; for we show that -coloring is NP-complete for -free graphs
when , ; and additionally, for , we show that
-coloring is also NP-complete for -free graphs if and
. This is the first systematic study of the complexity of the
-coloring problem for -free graphs. We almost completely
classify the complexity for the cases when , and
identify the last three open cases
Exhaustive generation of -critical -free graphs
We describe an algorithm for generating all -critical -free
graphs, based on a method of Ho\`{a}ng et al. Using this algorithm, we prove
that there are only finitely many -critical -free graphs, for
both and . We also show that there are only finitely many
-critical graphs -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 -colorability problem in the respective classes.
Moreover, we prove that for every , the class of 4-critical planar
-free graphs is finite. We also determine all 27 4-critical planar
-free graphs.
We also prove that every -free graph of girth at least five is
3-colorable, and determine the smallest 4-chromatic -free graph of
girth five. Moreover, we show that every -free graph of girth at least
six and every -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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