Dispersion relation for kink-type solitons in one-dimensional ferromagnets

Галкина, Е. Г.; Иванов, Б. А.

doi:10.1134/1.568329

Cited by 15 publications

(11 citation statements)

References 4 publications

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“…It is important, however, that the difference of the momenta for two different states of the DW is a gauge-invariant quantity. 29 To show this, let us imagine the DW as a trajectory in spin space { S}, S = S(ξ). The trajectories emerging from one point, say, S = S( e x sin θ 0 − e z cos θ 0 ) and ending at another point S = S( e x sin θ 0 + e z cos θ 0 ) can be associated with DW's that move with different velocities but obey identical boundary conditions at infinity.…”

Section: Domain Wall Dynamics In Continuum Approximationmentioning

confidence: 99%

“…For the near Heisenberg antiferromagnets with weak anisotropy of any origin, exchange or single-ion, treated on the basis of the sigma-model, the singularities in the Lagrangian for the staggered magnetization are absent for a sufficiently general set of models (including antiferromagnets subject to strong external magnetic fields and in the presence of Dzyaloshinski-Moriya interactions of arbitrary symmetry 36 ) and a periodic DW dispersion law is not realized. 29 Another interesting feature, which is common to classical and quantum physics, is that states with finite range of motion for the coordinate, but infinite range for momentum are present for large enough pinning potential, U 0 > T 0 . Evidently such trajectories do not exist for standard mechanical systems with a parabolic dispersion law H = P 2 /2M + U (X).…”

Section: Dw Tunnelingmentioning

confidence: 99%

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Semiclassical dynamics of domain walls in the one-dimensional Ising ferromagnet in a transverse field

Иванов

Mikeska

2004

Phys. Rev. B

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We investigate analytically and numerically the dynamics of domain walls in a spin chain with ferromagnetic Ising interaction and subject to an external magnetic field perpendicular to the easy magnetization axis (transverse field Ising model). The analytical results obtained within the continuum approximation and numerical simulations performed for discrete classical model are used to analyze the quantum properties of domain walls using the semiclassical approximation. We show that the domain wall spectrum shows a band structure consisting of 2S non-intersecting zones.

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Section: Domain Wall Dynamics In Continuum Approximationmentioning

confidence: 99%

Section: Dw Tunnelingmentioning

confidence: 99%

Semiclassical dynamics of domain walls in the one-dimensional Ising ferromagnet in a transverse field

Иванов

Mikeska

2004

Phys. Rev. B

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“…preserves b = ∇ m × a. It is known that the linear momentum p derived from Noether's theorem is gauge-dependent [8,11]. This is a cause for concern: physical quantities should be gauge-invariant.…”

Section: Introductionmentioning

confidence: 99%

“…Tretiakov et al [16] obtain it by translating the Landau-Lifshitz equation of motion for the magnetization field m(r, t) into the language of collective coordinates q(t). Here we obtain it directly from the definition of the gauge potential (8) and magnetic field (9):…”

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confidence: 99%

Conserved momenta of a ferromagnetic soliton

Tchernyshyov

2015

Annals of Physics

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Linear and angular momenta of a soliton in a ferromagnet are commonly derived through the application of Noether's theorem. We show that these quantities exhibit unphysical behavior: they depend on the choice of a gauge potential in the spin Lagrangian and can be made arbitrary. To resolve this problem, we exploit a similarity between the dynamics of a ferromagnetic soliton and that of a charged particle in a magnetic field. For the latter, canonical momentum is also gauge-dependent and thus unphysical; the physical momentum is the generator of magnetic translations, a symmetry combining physical translations with gauge transformations. We use this analogy to unambiguously define conserved momenta for ferromagnetic solitons. General considerations are illustrated on simple models of a domain wall in a ferromagnetic chain and of a vortex in a thin film.

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“…It can be written through a surface integral of the type of dS rot m A and it is equal to S/a, multiplied by the area, on the sphere m 2 = 1, inside two trajectories, corresponding to these pairs of kinks. 33 It is clear that for a biaxial ferromagnet there are pairs of diametrically opposite trajectories (e.g., the trajectories B+ and B− in Fig. 2) corresponding to energetically equivalent but physically different kinks.…”

Section: B Topological Analysis Of Domain Wall Structurementioning

confidence: 98%

Chirality tunneling and quantum dynamics for domain walls in mesoscopic ferromagnets

et al. 2008

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We studied the quantum dynamics of ferromagnetic domain walls (topological kink-type solitons) in one dimensional ferromagnetic spin chains. We show that the tunneling probability does not depend on the number of spins in a domain wall; thus, this probability can be large even for a domain wall containing a large number of spins. We also predict that there is a strong interplay between the tunneling of a wall from one lattice site to another (tunneling of the kink coordinate) and the tunneling of the kink topological charge (so-called chirality). Both of these elementary processes are suppressed for kinks in one-dimensional ferromagnets with half-integer spin. The dispersion law (i.e., the domain wall energy versus momentum) is essentially different for chains with either integer or half-integer spins. The predicted quantum effects could be observed for mesoscopic magnetic structures, e.g., chains of magnetic clusters, large-spin molecules, or nanosize magnetic dots.

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Dispersion relation for kink-type solitons in one-dimensional ferromagnets

Cited by 15 publications

References 4 publications

Semiclassical dynamics of domain walls in the one-dimensional Ising ferromagnet in a transverse field

Semiclassical dynamics of domain walls in the one-dimensional Ising ferromagnet in a transverse field

Conserved momenta of a ferromagnetic soliton

Chirality tunneling and quantum dynamics for domain walls in mesoscopic ferromagnets

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