Curvature effects in statics and dynamics of low dimensional magnets

Abstract

Abstract. We develop an approach to treat magnetic energy of a ferromagnet for arbitrary curved wires and shells on the assumption that the anisotropy contribution much exceeds the dipolar and other weak interactions. We show that the curvature induces two effective magnetic interactions: effective magnetic anisotropy and effective Dzyaloshinskii-like interaction. We derive an equation of magnetisation dynamics and propose a general static solution for the limit case of strong anisotropy. To illustrate our approach we consider the magnetisation structure in a ring wire and a cone surface: ground states in both systems essentially depend on the curvature excluding strictly tangential solutions even in the case of strong anisotropy. We derive also the spectrum of spin waves in such systems.

Oscillatory behavior of the domain wall dynamics in a curved cylindrical magnetic nanowire

“…However, because of the considered dimensions, this difference is small, and we will adopt λ = 1/4 to describe magnetostatic contributions to the energy [8,17,20]. In terms of the adopted parametrization, the exchange energy density is given by [17,27] …”

The stability of a skyrmion in a nanotube

“…either external or internal field. Recent theoretical and experimental analyzes reveal that in addition to exchange interaction the 3D curved and torsional magnets can induce two effective magnetic interactions: curvatureinduced effective anisotropy and effective DMI [30][31][32]. So the adjunction of these two energies will have a significant impact on the stability and dynamical properties of skyrmions.…”

Spontaneous deformation of flexible ferromagnetic ribbons induced by Dzyaloshinskii-Moriya interaction

“…The first term in (A4a) is the exchange density E ex = i=x,y,z (∂ i m) 2 with A being exchange constant. In the curvilinear reference frame exchange energy can be written as [50][51][52]…”