Ferromagnetic filament shapes in a rotating field reveal their magnetoelastic properties

Dynamic response of a ferromagnetic nanofilament under rotating fields: effects of flexibility, thermal fluctuations and hydrodynamics

“…These profiles are also compared to the predictions of a model for the S 1 structures that was deduced very recently from the continuum representation of rather rigid microfilaments. 57 In such approach, small deviations of the filament profile from a reference straight rod configuration, from which one can define a parallel reference axis x , are given by the parametric equationwhere y is the distance to the reference axis, l ∈ [− L /2, L /2] is the archlength parameter along the filament, C m is the aforementioned magnetoelastic dimensionless number and Δ y /Δ x is the ratio of the filament contour lengths measured, respectively, in perpendicular and parallel directions to the reference axis while assuming that the free ends remain parallel to the latter. In order to compare our results to this model, we set Δ y /Δ x directly from the shapes obtained in our simulations.…”

“…As length scale we take the contour length of the filament, L , which corresponds to its end-to-end distance for an ideal, perfectly straight configuration: L = ( N − 1) b ,where b is the center-to-center distance between first nearest neighbours along the chain. Finally, as time scale we will take a factor relating the characteristic strength of the viscous and elastic forces in the system, equivalent to the prefactor of the so-called elasto-viscous number, 56 frequently used in continuum MF models: 47,57 t s = 8π ηL 4 / B 0 where B 0 is an arbitrary reference value of the filament bending rigidity, B . Note that, in general, the bending rigidity of a polymer-like chain is related to its persistence length, l p , by the well known relationship 58 B = l p kT .…”

“…where b is the center-to-center distance between first nearest neighbours along the chain. Finally, as time scale we will take a factor relating the characteristic strength of the viscous and elastic forces in the system, equivalent to the prefactor of the so-called elasto-viscous number, 56 frequently used in continuum MF models: 47,57…”

“…These profiles are also compared to the predictions of a model for the S 1 structures that was deduced very recently from the continuum representation of rather rigid microfilaments. 57 In such approach, small deviations of the filament profile from a reference straight rod configuration, from which one can define a parallel reference axis x, are given by the parametric equation…”