Edge saturation fields and dynamic edge modes in ideal and nonideal magnetic film edges

Abstract

This paper describes modeling of the micromagnetic behavior near edges of ferromagnetic thin films when uniform fields are applied in plane and perpendicular to the edge. For ideal film edges with vertical edge surfaces, the field required to saturate the magnetization perpendicular to the edge, H sat , and the frequency of precession in the localized edge mode are calculated using numerical micromagnetics for a wide range of film thicknesses. Analysis of the critical state at the saturation field and the full micromagnetic results are used to develop a simple macrospin model for the edge magnetization. This model predicts both H sat and edge mode precession frequency values that agree well with the micromagnetic results. Three classes of nonideal edges are also modeled: tilted edge surfaces, diluted magnetization near the edge, and surface anisotropy on the edge surface. Despite their different physical mechanisms, all three of these defects produce similar reductions in H sat and similar dynamic properties of the edge magnetization.

Spin wave eigenmodes in transversely magnetized thin film ferromagnetic wires

“…As a result, the equilibrium magnetization is stabilized by the exchange interaction close to edges, as also noted in Ref. 50. In non-ideal wires, extrinsic parameters such as the edge surface anisotropy also play a stabilizing role for the equilibrium magnetization.…”

“…The spin wave eigenmodes of in-plane transversely magnetized thin film ferromagnetic wires can be treated as width eigenmodes 23,24,34,49,50 due to the geometric confinement of the spin wave spectrum in the wire width direction. One particular mode that displays its maximum amplitude at the wire edges is called the edge mode (EM).…”

“…The value of the pinning parameter is determined by a number of factors, including the magnitude of magnetic surface anisotropy at the wire edge, edge roughness, edge surface profile, and the direction of magnetization with respect to the edge normal 50 . For λ = 0, these boundary conditions reduce to the so called free boundary conditions, which correspond to null normal derivatives of the magnetization at the edge surfaces.…”

Nanowire spin torque oscillator driven by spin orbit torques

“…It is well-known that spin wave eigenmodes of a transversely magnetized thin-film ferromagnetic nanowire can be classified as bulk and edge eigenmodes 34,[41][42][43] . These eigenmodes have spatially inhomogeneous profiles along the wire width with reduced (enhanced) amplitude near the wire edges for the bulk (edge) eigenmodes.…”

Influence of spin-transfer torque on thermally activated ferromagnetic resonance excitations in magnetic tunnel junctions

“…This peak indexation is consistent with the fact that a slower magnetization dynamics is expected at the edges. 20 Following the Kittel formula the slope of the frequency square dependence on applied field gives the saturation magnetization M s . In fact FMR measurements on full sheet samples lead to an extracted value of M s corresponding to the bulk value.…”