2019 # Spontaneous deformation of flexible ferromagnetic ribbons induced by Dzyaloshinskii-Moriya interaction

**Abstract:** Here, we predict the effect of the spontaneous deformation of a flexible ferromagnetic ribbon induced by Dzyaloshinskii-Moriya interaction (DMI). The geometrical form of the deformation is determined both by the type of DMI and by the equilibrium magnetization of the stripe. We found three different geometrical phases, namely (i) the DNA-like deformation with the stripe central line in the form of a helix, (ii) the helicoid deformation with the straight central line and (iii) cylindrical deformation. In the ma…

Help me understand this report

View preprint versions

Search citation statements

Paper Sections

Select...

2

1

1

1

Citation Types

0

12

0

Year Published

2020

2022

Publication Types

Select...

3

3

1

Relationship

1

6

Authors

Journals

(14 citation statements)

0

12

0

“…The last term ${\mathrm{scriptE}}_{\text{rib}}^{\mathrm{normalD}}$ describes the intrinsic DMI. Using the explicit form of the Bloch type DMI [ 68 ] and Néel type DMI, [ 98 ] one can get the DMI for the ribbon $$\begin{array}{ll}left\hfill & {\mathrm{scriptE}}_{\text{rib}}^{\mathrm{D}(B)}={D}^{(B)}{\mathrm{sin}}^{2}\mathrm{\Theta}\left(2\mathrm{sin}\mathrm{normal\Phi}\text{}{\mathrm{\Theta}}^{\prime}-{\mathrm{\Gamma}}_{1}\mathrm{sin}\mathrm{normal\Phi}+{\mathrm{\Gamma}}_{2}\mathrm{cos}\epsilon \mathrm{cos}\mathrm{normal\Phi}\right)\hfill \\ left\hfill & {\mathrm{scriptE}}_{\text{rib}}^{\mathrm{D}(N)}={D}^{(N)}\left(2{\mathrm{sin}}^{2}\mathrm{normal\Theta}\mathrm{cos}\mathrm{normal\Phi}\text{}{\mathrm{\Theta}}^{\prime}+\kappa \mathrm{sin}\epsilon {\mathrm{cos}}^{2}\mathrm{normal\Theta}\right)\hfill \end{array}$$ …”

confidence: 99%

“…The last term ${\mathrm{scriptE}}_{\text{rib}}^{\mathrm{normalD}}$ describes the intrinsic DMI. Using the explicit form of the Bloch type DMI [ 68 ] and Néel type DMI, [ 98 ] one can get the DMI for the ribbon $$\begin{array}{ll}left\hfill & {\mathrm{scriptE}}_{\text{rib}}^{\mathrm{D}(B)}={D}^{(B)}{\mathrm{sin}}^{2}\mathrm{\Theta}\left(2\mathrm{sin}\mathrm{normal\Phi}\text{}{\mathrm{\Theta}}^{\prime}-{\mathrm{\Gamma}}_{1}\mathrm{sin}\mathrm{normal\Phi}+{\mathrm{\Gamma}}_{2}\mathrm{cos}\epsilon \mathrm{cos}\mathrm{normal\Phi}\right)\hfill \\ left\hfill & {\mathrm{scriptE}}_{\text{rib}}^{\mathrm{D}(N)}={D}^{(N)}\left(2{\mathrm{sin}}^{2}\mathrm{normal\Theta}\mathrm{cos}\mathrm{normal\Phi}\text{}{\mathrm{\Theta}}^{\prime}+\kappa \mathrm{sin}\epsilon {\mathrm{cos}}^{2}\mathrm{normal\Theta}\right)\hfill \end{array}$$ …”

confidence: 99%

“…In brief, we will systematically describe in the micromagnetic theory of curvilinear wires [60] and ribbons [61] and then proceed with the description of curved helimagnetic wires, [62] curvilinear spintronics, [63] curvilinear spin-orbirtonics, [64] curvilinear magnonics, [65,66] and mechanically flexible (helimagnetic) wires. [67,68] Methodologically, we put efforts to unify the terminology and mathematical notation to simplify the understanding of the topic and make it accessible as well for the young generation of scientists, who only considers joining this new field of research in modern magnetism.…”

confidence: 99%

“…Namely, the magnetostriction interaction through even a small tensile deformation could change the equilibrium magnetization distribution in torsional spring nanowires. [335] Contrary, a magnetization change could mediate the shape transformation of a flexible magnetic object, [336,337] for example, the transition from vortex to the onion state in a ferromagnetic elastic ring will cause elliptic-shape deformations. (ii) Curvilinear spintronics and spinorbitronics is yet to be developed.…”

confidence: 99%

“…Using a curvilinear reference frame we parametrize the magnetization in the following way m = sin θ cos φ e 1 + sin θ sin φ e 2 + cos θ n. Expressions for E X , E B D , and E N D for a general case of a local curvilinear basis were previously obtained in Refs. [49], [50], and [45], respectively (also see Appendix A). In the following we look for the equilibrium magnetization states.…”

confidence: 99%