Conserved momenta of a ferromagnetic soliton

Tchernyshyov, Oleg

doi:10.1016/j.aop.2015.09.004

Cited by 43 publications

(62 citation statements)

References 28 publications

(77 reference statements)

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“…The translational motion of a rigid structure can be described in terms of a position r s (t) = (X(t), Y (t)) where X and Y are collective coordinates describing a soft mode. 43,59,60 The following discussion does not require a specific definition of r s (t). To obtain the Poisson bracket structure from Eq.…”

Section: A Translational Modes Of Rigid Topological Texturesmentioning

confidence: 99%

Characterizing breathing dynamics of magnetic skyrmions and antiskyrmions within the Hamiltonian formalism

et al. 2019

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We derive an effective Hamiltonian system describing the low energy dynamics of circular magnetic skyrmions and antiskyrmions. Using scaling and symmetry arguments we model (anti-)skyrmion dynamics through a finite set of coupled, canonically conjugated, collective coordinates. The resulting theoretical description is independent of both micromagnetic details as well as any specificity in the ansatz of the skyrmion profile. Based on the Hamiltonian structure we derive a general description for breathing dynamics of (anti-)skyrmions in the limit of radius much larger than the domain wall width. The effective energy landscape reveals two qualitatively different types of breathing behavior. For small energy perturbations we reproduce the well-known small breathing mode excitations, where the magnetic moments of the skyrmion oscillate around their equilibrium solution. At higher energies we find a breathing behavior where the in-plane angle of the skyrmion continuously precesses, transforming Néel to Bloch skyrmions and vice versa. For a damped system we observe the transition from the continuously rotating and breathing skyrmion into the oscillatory one. We analyze the characteristic frequencies of both breathing types, as well as their amplitudes and distinct energy dissipation rates. For rotational (oscillatory) breathing modes we predict on average a linear (exponential) decay in energy. We argue that this stark difference in dissipative behavior should be observable in the frequency spectrum of excited (anti-)skyrmions.

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Section: A Translational Modes Of Rigid Topological Texturesmentioning

confidence: 99%

Characterizing breathing dynamics of magnetic skyrmions and antiskyrmions within the Hamiltonian formalism

et al. 2019

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“…As discussed in detail in Ref. 17, the canonical momentum (18) is a poorly defined quantity for a domain wall. Under a gauge transformation (7),…”

Section: A Domain Wall In One Spatial Dimensionmentioning

confidence: 99%

“…Doing so would eliminate the unphysical energy flux far away from the domain wall. Canonical momentum is [17]…”

Section: A Domain Wall In One Spatial Dimensionmentioning

confidence: 99%

“…Our attempts to find such a transformation for the stress-energy tensor of a ferromagnet (9) were unsuccessful. Instead, we relied on our previous work [17], which resolved a similar problem for a related global quantity: the linear momentum P i of a ferromagnetic soliton. Because it is directly related to the T 0 i component of the energy-momentum tensor, we have been able to extend the recipe for constructing gauge-invariant conserved momenta to the components of the stress-energy tensor T β α .…”

Section: Introductionmentioning

confidence: 99%

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Energy-momentum tensor of a ferromagnet

Dasgupta

Tchernyshyov

2018

Phys. Rev. B

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The energy-momentum tensor of a ferromagnet derived according to the standard prescription of Noether's theorem has a major flaw: the term originating from the spin Berry phase is gaugedependent. As a consequence, some physical quantities computed from the tensor show unphysical behavior. For example, the presence of a spin-polarized current does not affect the energy of the domain wall in the commonly accepted gauge, which implies-incorrectly-the absence of the adiabatic spin torque. In other gauges, the spin torque shows unphysical glitches occurring when the plane of magnetization crosses the Dirac string associated with a magnetic monopole in spin space. We derive a gauge-invariant energy-momentum tensor that is free from these artifacts but requires the addition of an extra spatial dimension, with the ferromagnet living on its boundary. It can be obtained most directly from the Wess-Zumino action for spins, which relies on the same extra dimension.

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“…This DW motion is in analogy to the motion of a charged particle in a magnetic field, which exhibits both translational and rotational motion. 16) One can solve Eqs. (3) and (4) for the case of CIDWM with V(q) = 0, H = 0 to obtain…”

Section: Progress In Study Of Current-induced Domain Wall Motionmentioning

confidence: 99%

Current-driven magnetic domain wall motion and its real-time detection

Kim

Yoshimura

Ono

2017

Jpn. J. Appl. Phys.

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Current-controlled magnetic domain wall motion has opened the possibility of a novel type of shift register memory device, which has been optimistically predicted to replace existing magnetic memories. Owing to this promising prospect, intensive work has been carried out during the last few decades. In this article, we first review the progress in the study of current-induced magnetic domain wall motion. Underlying mechanisms behind the domain wall motion, which have been discovered during last few decades, as well as technological achievements are presented. We then present our recent experimental results on the real-time detection of current-driven multiple magnetic domain wall motion, which directly demonstrates the operation of a magnetic domain wall shift register.

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Conserved momenta of a ferromagnetic soliton

Cited by 43 publications

References 28 publications

Characterizing breathing dynamics of magnetic skyrmions and antiskyrmions within the Hamiltonian formalism

Characterizing breathing dynamics of magnetic skyrmions and antiskyrmions within the Hamiltonian formalism

Energy-momentum tensor of a ferromagnet

Current-driven magnetic domain wall motion and its real-time detection

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