2,114 research outputs found
Hilbert's 16th Problem for Quadratic Systems. New Methods Based on a Transformation to the Lienard Equation
Fractionally-quadratic transformations which reduce any two-dimensional
quadratic system to the special Lienard equation are introduced. Existence
criteria of cycles are obtained
Skyrmion robustness in non-centrosymmetric magnets with axial symmetry: The role of anisotropy and tilted magnetic fields
We investigate the stability of N\'eel skyrmions against tilted magnetic
fields, in polar magnets with uniaxial anisotropy ranging from easy-plane to
easy-axis type. We construct the corresponding phase diagrams and investigate
the internal structure of skewed skyrmions with displaced cores. We find that
moderate easy-plane anisotropy increases the stability range of N\'eel
skyrmions for fields along the symmetry axis, while moderate easy-axis
anisotropy enhances their robustness against tilted magnetic fields. We stress
that the direction, along which the skyrmion cores are shifted, depends on the
symmetry of the underlying crystal lattice. The cores of N\'eel skyrmions,
realized in polar magnets with C symmetry, are displaced either along or
opposite to the off-axis (in-plane) component of the magnetic field depending
on the rotation sense of the magnetization, dictated by the sign of the
Dzyaloshinskii constant. The core shift of antiskyrmions, present in chiral
magnets with D symmetry, depends on the in-plane orientation of the
magnetic field and can be parallel, anti-parallel, or perpendicular to it. We
argue that the role of anisotropy in magnets with axially symmetric crystal
structure is different from that in cubic helimagnets. Our results can be
applied to address recent experiments on polar magnets with C symmetry,
GaVS and GaVSe
Multiply periodic states and isolated skyrmions in an anisotropic frustrated magnet
Multiply periodic states appear in a wide variety of physical contexts, such
as the Rayleigh-Benard convection, Faraday waves, liquid crystals, domain
patterns in ferromagnetic films and skyrmion crystals recently observed in
chiral magnets. Here we study a simple model of an anisotropic frustrated
magnet and show that its zero-temperature phase diagram contains numerous
multi-q states including the skyrmion crystal. We clarify the mechanism for
stabilization of these states, discuss their multiferroic properties and
formulate rules for finding new skyrmion materials. In addition to skyrmion
crystal, we find stable isolated skyrmions with topological charge 1 and 2.
Physics of isolated skyrmions in frustrated magnets is very rich. Their
statical and dynamical properties are strongly affected by the new zero mode -
skyrmion helicity.Comment: 9 pages, 6 figure
Asymmetric isolated skyrmions in polar magnets with easy-plane anisotropy
We introduce a new class of isolated magnetic skyrmions emerging within
tilted ferromagnetic phases of polar magnets with easy-plane anisotropy. The
asymmetric magnetic structure of these skyrmions is associated with an
intricate pattern of the energy density, which exhibits positive and negative
asymptotics with respect to the surrounding state with a ferromagnetic moment
tilted away from the polar axis. Correspondingly, the skyrmion-skyrmion
interaction has an anisotropic character and can be either attractive or
repulsive depending on the relative orientation of the skyrmion pair. We
investigate the stability of these novel asymmetric skyrmions against the
elliptical cone state and follow their transformation into axisymmetric
skyrmions, when the tilted ferromagnetic moment of the host phase is reduced.
Our theory gives clear directions for experimental studies of isolated
asymmetric skyrmions and their clusters embedded in tilted ferromagnetic
phases
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