Magnetic properties of a long, thin-walled ferromagnetic nanotube

TL;DR

This paper analyzes the magnetic states, stability, and field interactions of long, thin-walled ferromagnetic nanotubes, identifying conditions for different stable magnetization configurations and their responses to external fields.

Contribution

It introduces a theoretical model for magnetic states in ferromagnetic nanotubes, determining stability criteria based on geometric and material parameters, and explores their magnetic field interactions.

Findings

Parallel and vortex states depend on the parameter b3.

The vortex state is stable when b3>1.

Half-domain structures are energetically favorable at tube ends.

Abstract

We consider magnetic properties of a long, thin-walled ferromagnetic nanotube. We assume that the tube consists of isotropic homogeneous magnet whose spins interact via the exchange energy, the dipole-dipole interaction energy, and also interact with an external field via Zeeman energy. Possible stable states are the parallel state with the magnetization along the axis of the tube, and the vortex state with the magnetization along azimuthal direction. For a given material, which of them has lower energy depends on the value \gamma=R^2d/(L \lambda_x^2), where R is the radius of the tube, d is its thickness, L is its length and \lambda_x is an intrinsic scale of length characterizing the ration of exchange and dipolar interaction. At \gamma<1 the parallel state wins, otherwise the vortex state is stable. A domain wall in the middle of the tube is always energy unfavorable, but it can exist as a metastable structure. Near the ends of a tube magnetized parallel to the axis a half-domain structure transforming gradually the parallel magnetization to a vortex just at the edge of the tube is energy favorable. We also consider the equilibrium magnetization textures in an external magnetic field either parallel or perpendicular to the tube. Finally, magnetic fields produced by a nanotube and an array of tubes is analyzed.