We show experimentally and by model calculations that in finite, nonellipsoidal, micrometer size magnetic thin film elements the dynamic magnetic eigenexcitations (spin waves) may exhibit strong spatial localization. This localization is due to the formation of a potential well for spin waves in the highly inhomogeneous internal magnetic field within the element.

Small-angle neutron scattering (SANS) is one of the most important techniques for microstructure determination, being utilized in a wide range of scientific disciplines, such as materials science, physics, chemistry, and biology. The reason for its great significance is that conventional SANS is probably the only method capable of probing structural inhomogeneities in the bulk of materials on a mesoscopic real-space length scale, from roughly 1 − 300 nm. Moreover, the exploitation of the spin degree of freedom of the neutron provides SANS with a unique sensitivity to study magnetism and magnetic materials at the nanoscale. As such, magnetic SANS ideally complements more real-space and surface-sensitive magnetic imaging techniques, e.g., Lorentz transmission electron microscopy, electron holography, magnetic force microscopy, Kerr microscopy, or spinpolarized scanning tunneling microscopy. In this review article we summarize the recent applications of the SANS method to study magnetism and magnetic materials. This includes a wide range of materials classes, from nanomagnetic systems such as soft magnetic Fe-based nanocomposites, hard magnetic Nd−Fe−B-based permanent magnets, magnetic steels, ferrofluids, nanoparticles, and magnetic oxides, to more fundamental open issues in contemporary condensed matter physics such as skyrmion crystals, noncollinar magnetic structures in noncentrosymmetric compounds, magnetic/electronic phase separation, and vortex lattices in type-II superconductors. Special attention is paid not only to the vast variety of magnetic materials and problems where SANS has provided direct insight, but also to the enormous progress made regarding the micromagnetic simulation of magnetic neutron scattering.

In this paper we present an overview of recent progress made in the understanding of the spintorque induced magnetization dynamics in nanodevices using mesoscopic micromagnetic simulations. We first specify how a spin-torque term may be added to the usual LandauLifshitz-Gilbert equation of magnetization motion and detail its physical meaning. After a brief description of spin-torque driven dynamics in the macrospin approximation, we discuss the validity of this approximation for various experimentally relevant geometries. Next, we perform a detailed comparison between accurate experimental data obtained from nanopillar devices and corresponding numerical modelling. We show that, on the one hand, many qualitatively important features of the observed magnetization dynamics (e.g., non-linear frequency shift and frequency jumps with increasing current) can be satisfactory explained by sophisticated micromagnetic models, but on the other hand, understanding of these experiments is still far from being complete. We proceed with the numerical analysis of pointcontact experiments, where an even more complicated magnetization dynamics is observed. Simulations reveal that such a rich behaviour is due to the formation of several strongly nonlinear oscillation modes. In the last part of the paper we emphasize the importance of sample characterization and conclude with some important remarks concerning the relation between micromagnetic modelling and real experiments.

Abstract:We present spectral measurements of spin-wave excitations driven by direct spin-

A Brillouin light scattering study and theoretical interpretation of spin-wave modes in arrays of in-plane magnetized micron-size rectangular Ni 80 Fe 20 elements are reported. It is shown that two-dimensional spinwave eigenmodes of these elements can be approximately described as products of one-dimensional spin-wave eigenmodes of longitudinally and transversely magnetized long finite-width permalloy stripes. The lowest eigenmodes of rectangular elements are of dipole-exchange nature and are localized near the element edges, while the higher eigenmodes are of a mostly dipolar nature and are weakly localized near the element center. The frequency spectra and spatial profiles of these eigenmodes are calculated both analytically and numerically, and are compared with the results of the Brillouin light scattering experiment.