Ferromagnetic resonance and magnetooptic study of submicron epitaxial Fe(001) stripes

We present a combined magnetooptic and ferromagnetic resonance study of a series of arrays of single-crystalline Fe stripes fabricated by electron beam lithography on epitaxial Au(001)/Fe(001)/MgO(001) films grown by pulsed laser deposition. The analysis of the films revealed a clear fourfold magnetocrystalline anisotropy, with no significant presence of other anisotropy sources. The use of a large series of arrays, with stripe widths between 140 and 1000 nm and separation between them of either 200 nm or 500 nm, allowed studying their magnetization processes and resonance modes as well as the effects of the dipolar interactions on both. The magnetization processes of the stripes were interpreted in terms of a macrospin approximation, with a good agreement between experiments and calculations and negligible influence of the dipolar interactions. The ferromagnetic resonance spectra evidenced two types of resonances linked to bulk oscillation modes, essentially insensitive to the dipolar interactions, and a third one associated with edge-localized oscillations, whose resonance field is strongly dependent on the dipolar interactions. The ability to produce a high quality, controlled series of stripes provided a good opportunity to achieve an agreement between the experiments and calculations, carried out by taking into account just the Fe intrinsic properties and the morphology of the arrays, thus evidencing the relatively small role of other extrinsic factors.

A Semi-Lagrangian Particle Level Set Finite Element Method for Interface Problems

We present a quasi-monotone semi-Lagrangian particle level set (QMSL-PLS) method for moving interfaces. The QMSL method is a blend of first order monotone and second order semi-Lagrangian methods. The QMSL-PLS method is easy to implement, efficient, and well adapted for unstructured, either simplicial or hexahedral, meshes. We prove that it is unconditionally stable in the maximum discrete norm, � · �h,∞, and the error analysis shows that when the level set solution u(t) is in the Sobolev space Wr+1,∞(D), r ≥ 0, the convergence in the maximum norm is of the form (KT/Δt)min(1,Δt � v �h,∞ /h)((1 − α)hp + hq), p = min(2, r + 1), and q = min(3, r + 1),where v is a velocity. This means that at high CFL numbers, that is, when Δt > h, the error is O( (1−α)hp+hq) Δt ), whereas at CFL numbers less than 1, the error is O((1 − α)hp−1 + hq−1)). We have tested our method with satisfactory results in benchmark problems such as the Zalesak’s slotted disk, the single vortex flow, and the rising bubble.