New magnetostatic modes in small nonellipsoidal magnetic particles

TL;DR

This paper investigates new types of magnetostatic modes in small nonellipsoidal magnetic particles, revealing bulk-extended, subsurface localized, and a novel comb mode with unique oscillation profiles, through numerical analysis of dipolar fields and Landau-Lifshitz dynamics.

Contribution

It introduces the discovery of a new class of magnetostatic modes, called comb modes, in small nonellipsoidal particles, expanding understanding of magnetic excitations.

Findings

Bulk-extended modes dominate high-energy spectrum.

Subsurface localized modes form the lower spectrum.

Comb modes exhibit distinct internal and border oscillation regions.

Abstract

Magnetostatic normal modes are investigated here in elongated rods. The dipolar field resulting from the dipole-dipole interactions is calculated numerically in points of the axis connecting opposite rod face centers (\emph{central axis}) by collecting individual contributions to this field coming from each of the atomic planes perpendicular to the central axis. The applied magnetic field is assumed to be oriented along the central axis, and the magnetization to be uniform throughout the sample. The \emph{frequency} spectrum of magnetostatic waves propagating in the direction of the applied field is found numerically by solving the Landau-Lifshith equation of motion with the spatially \emph{nonhomogeneous} dipolar field taken into account; the mode amplitude \emph{profiles} are depicted as well. While energetically highest modes have \emph{bulk-extended} character, the modes forming the lower part of the spectrum are localized in the subsurface region (\emph{bulk-dead modes}). Between these two mode types, magnetostatic modes of a new type (\emph{comb modes}) are found to occur, characterized by two clearly discernible regions: a zone of fast amplitude oscillations inside the rod, and narrow slow-oscillation regions at the borders. Absorbing virtually no energy from an applied alternating field, comb modes will have no significant contribution to the magnetic noise.