TY - JOUR

T1 - Magnetization in narrow ribbons

T2 - curvature effects

AU - Gaididei, Yuri

AU - Goussev, Arseni

AU - Kravchuk, Volodymyr P.

AU - Pylypovskyi, Oleksandr V.

AU - Robbins, J. M.

AU - Sheka, Denis D.

AU - Slastikov, Valeriy

AU - Vasylkevych, Sergiy

PY - 2017/9/1

Y1 - 2017/9/1

N2 - A ribbon is a surface swept out by a line segment turning as it moves along a central curve. For narrow magnetic ribbons, for which the length of the line segment is much less than the length of the curve, the anisotropy induced by the magnetostatic interaction is biaxial, with a hard axis normal to the ribbon and an easy axis along the central curve. The micromagnetic energy of a narrow ribbon reduces to that of a one-dimensional ferromagnetic wire, but with curvature, torsion and local anisotropy modified by the rate of turning. These general results are applied to two examples, namely a helicoid ribbon, for which the central curve is a straight line, and a Mbius ribbon, for which the central curve is a circle about which the line segment executes a 180° twist. In both examples, for large positive tangential anisotropy, the ground state magnetization lies tangent to the central curve. As the tangential anisotropy is decreased, the ground state magnetization undergoes a transition, acquiring an in-surface component perpendicular to the central curve. For the helicoid ribbon, the transition occurs at vanishing anisotropy, below which the ground state is uniformly perpendicular to the central curve. The transition for the Mobius ribbon is more subtle; it occurs at a positive critical value of the anisotropy, below which the ground state is nonuniform. For the helicoid ribbon, the dispersion law for spin wave excitations about the tangential state is found to exhibit an asymmetry determined by the geometric and magnetic chiralities.

AB - A ribbon is a surface swept out by a line segment turning as it moves along a central curve. For narrow magnetic ribbons, for which the length of the line segment is much less than the length of the curve, the anisotropy induced by the magnetostatic interaction is biaxial, with a hard axis normal to the ribbon and an easy axis along the central curve. The micromagnetic energy of a narrow ribbon reduces to that of a one-dimensional ferromagnetic wire, but with curvature, torsion and local anisotropy modified by the rate of turning. These general results are applied to two examples, namely a helicoid ribbon, for which the central curve is a straight line, and a Mbius ribbon, for which the central curve is a circle about which the line segment executes a 180° twist. In both examples, for large positive tangential anisotropy, the ground state magnetization lies tangent to the central curve. As the tangential anisotropy is decreased, the ground state magnetization undergoes a transition, acquiring an in-surface component perpendicular to the central curve. For the helicoid ribbon, the transition occurs at vanishing anisotropy, below which the ground state is uniformly perpendicular to the central curve. The transition for the Mobius ribbon is more subtle; it occurs at a positive critical value of the anisotropy, below which the ground state is nonuniform. For the helicoid ribbon, the dispersion law for spin wave excitations about the tangential state is found to exhibit an asymmetry determined by the geometric and magnetic chiralities.

KW - curved magnets

KW - exchange energy

KW - magnetic ribbon

KW - nanoshell

KW - nanowire

KW - RCUK

KW - EPSRC

KW - EP/K024116/1

KW - EP/K02390X/1

UR - http://www.scopus.com/inward/record.url?scp=85028768710&partnerID=8YFLogxK

U2 - 10.1088/1751-8121/aa8179

DO - 10.1088/1751-8121/aa8179

M3 - Article

AN - SCOPUS:85028768710

SN - 1751-8113

VL - 50

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 38

M1 - 385401

ER -