Remanence Increase in SrFe12O19/Fe Exchange-Decoupled Hard-Soft Composite Magnets Owing to Dipolar Interactions.

In the search for improved permanent magnets, fueled by the geostrategic and environmental issues associated with rare-earth-based magnets, magnetically hard (high anisotropy)-soft (high magnetization) composite magnets hold promise as alternative magnets that could replace modern permanent magnets, such as rare-earth-based and ceramic magnets, in certain applications. However, so far, the magnetic properties reported for hard-soft composites have been underwhelming. Here, an attempt to further understand the correlation between magnetic and microstructural properties in strontium ferrite-based composites, hard SrFe12O19 (SFO) ceramics with different contents of Fe particles as soft phase, both in powder and in dense injection molded magnets, is presented. In addition, the influence of soft phase particle dimension, in the nano- and micron-sized regimes, on these properties is studied. While Fe and SFO are not exchange-coupled in our magnets, a remanence that is higher than expected is measured. In fact, in composite injection molded anisotropic (magnetically oriented) magnets, remanence is improved by 2.4% with respect to a pure ferrite identical magnet. The analysis of the experimental results in combination with micromagnetic simulations allows us to establish that the type of interaction between hard and soft phases is of a dipolar nature, and is responsible for the alignment of a fraction of the soft spins with the magnetization of the hard. The mechanism unraveled in this work has implications for the development of novel hard-soft permanent magnets.

Using small-angle scattering to guide functional magnetic nanoparticle design.

Magnetic nanoparticles offer unique potential for various technological, biomedical, or environmental applications thanks to the size-, shape- and material-dependent tunability of their magnetic properties. To optimize particles for a specific application, it is crucial to interrelate their performance with their structural and magnetic properties. This review presents the advantages of small-angle X-ray and neutron scattering techniques for achieving a detailed multiscale characterization of magnetic nanoparticles and their ensembles in a mesoscopic size range from 1 to a few hundred nanometers with nanometer resolution. Both X-rays and neutrons allow the ensemble-averaged determination of structural properties, such as particle morphology or particle arrangement in multilayers and 3D assemblies. Additionally, the magnetic scattering contributions enable retrieving the internal magnetization profile of the nanoparticles as well as the inter-particle moment correlations caused by interactions within dense assemblies. Most measurements are used to determine the time-averaged ensemble properties, in addition advanced small-angle scattering techniques exist that allow accessing particle and spin dynamics on various timescales. In this review, we focus on conventional small-angle X-ray and neutron scattering (SAXS and SANS), X-ray and neutron reflectometry, gracing-incidence SAXS and SANS, X-ray resonant magnetic scattering, and neutron spin-echo spectroscopy techniques. For each technique, we provide a general overview, present the latest scientific results, and discuss its strengths as well as sample requirements. Finally, we give our perspectives on how future small-angle scattering experiments, especially in combination with micromagnetic simulations, could help to optimize the performance of magnetic nanoparticles for specific applications.

Concept of the Energy-Dependent Temperature for Direct Langevin Dynamics Simulations of Rare Events in Systems with Arbitrary High Energy Barriers.

We suggest an algorithm which allows single-stage direct Langevin dynamics simulations of transitions over arbitrarily high energy barriers. For this purpose, we propose a concept of the energy-dependent temperature (EDT): near the energy minima this temperature is high, but it tends toward room temperature for energies approaching the barrier value. In the resulting algorithm simulation time required for the computation of the escape rate over the barrier does not increase with barrier height. Switching times computed via our EDT algorithm agree very well with those obtained with the forward flux sampling (FFS). As the simulation time required by our method does not increase with the energy barrier, we achieve a very large speed-up compared even to our strongly optimized version of FFS (and all other multistage algorithms). In addition, our approach is free from the instability occurring in all multistage "climbing" methods where a product of a large number of transition probabilities between the interfaces must be computed.

Optimal Control of Magnetization Reversal in a Monodomain Particle by Means of Applied Magnetic Field.

A complete analytical solution to the optimal reversal of a macrospin with easy-axis anisotropy is presented. An optimal control path minimizing the energy cost of the reversal is identified and used to derive the time-dependent direction and amplitude of the optimal switching field. The minimum energy cost of the reversal scales inversely with the switching time for fast switching, follows exponential asymptotics for slow switching, and reaches the lower limit proportional to the energy barrier between the target states and to the damping parameter at infinitely long switching time. For a given switching time, the energy cost is never smaller than that for a free macrospin. This limitation can be bypassed by adding a hard anisotropy axis that activates the internal torque in the desired switching direction, thereby significantly reducing the energy cost. A comparison between the calculated optimal control path and minimum energy path reveals that optimal control does not translate to the minimization of the energy barrier but signifies effective use of the system's internal dynamics to aid the desired magnetic transition.

Toward Understanding Complex Spin Textures in Nanoparticles by Magnetic Neutron Scattering.

In the quest to image the three-dimensional magnetization structure we show that the technique of magnetic small-angle neutron scattering (SANS) is highly sensitive to the details of the internal spin structure of nanoparticles. By combining SANS with numerical micromagnetic computations we study the transition from single-domain to multidomain behavior in nanoparticles and its implications for the ensuing magnetic SANS cross section. Above the critical single-domain size we find that the cross section and the related correlation function cannot be described anymore with the uniform particle model, resulting, e.g., in deviations from the well-known Guinier law. In the simulations we identify a clear signature for the occurrence of a vortexlike spin structure at remanence. The micromagnetic approach to magnetic SANS bears great potential for future investigations, since it provides fundamental insights into the mesoscale magnetization profile of nanoparticles.

Investigation of magnetically driven passage of magnetic nanoparticles through eye tissues for magnetic drug targeting.

This paper elucidates the feasibility of magnetic drug targeting to the eye by using magnetic nanoparticles (MNPs) to which pharmaceutical drugs can be linked. Numerical simulations revealed that a magnetic field gradient of 20 T m-1 seems to be promising for dragging magnetic multicore nanoparticles of about 50 nm into the eye. Thus, a targeting magnet system made of superconducting magnets with a magnetic field gradient at the eye of about 20 T m-1 was simulated. For the proof-of-concept tissue experiments presented here the required magnetic field gradient of 20 T m-1 was realized by a permanent magnet array. MNPs with an optimized multicore structure were selected for this application by evaluating their stability against agglomeration of MNPs with different coatings in water for injections, physiological sodium chloride solution and biological media such as artificial tear fluid. From these investigations, starch turned out to be the most promising coating material because of its stability in saline fluids due to its steric stabilization mechanism. To evaluate the passage of MNPs through the sclera and cornea of the eye tissues of domestic pigs (Sus scrofa domesticus), a three-dimensionally printed setup consisting of two chambers (reservoir and target chamber) separated by the eye tissue was developed. With the permanent magnet array emulating the magnetic field gradient of the superconducting setup, experiments on magnetically driven transport of the MNPs from the reservoir chamber into the target chamber via the tissue were performed. The resulting concentration of MNPs in the target chamber was determined by means of quantitative magnetic particle spectroscopy. It was found that none of the tested particles passed the cornea, but starch-coated particles could pass the sclera at a rate of about 5 ng mm-2 within 24 h. These results open the door for future magnetic drug targeting to the eye.

Towards understanding of magnetization reversal in Nd-Fe-B nanocomposites: analysis by high-throughput micromagnetic simulations.

We demonstrate how micromagnetic simulations can be employed in order to characterize and analyze the magnetic microstructure of nanocomposites. For the example of nanocrystalline Nd-Fe-B, which is a potential material for future permanent-magnet applications, we have compared three different models for the micromagnetic analysis of this material class: (i) a description of the nanocomposite microstructure in terms of Stoner-Wohlfarth particles with and without the magnetodipolar interaction; (ii) a model based on the core-shell representation of the nanograins; (iii) the latter model including a contribution of superparamagnetic clusters. The relevant parameter spaces have been systematically scanned with the aim to establish which micromagnetic approach can most adequately describe experimental data for this material. According to our results, only the last, most sophisticated model is able to provide an excellent agreement with the measured hysteresis loop. The presented methodology is generally applicable to multiphase magnetic nanocomposites and it highligths the complex interrelationship between the microstructure, magnetic interactions, and the macroscopic magnetic properties.

Nonlinear magnetic vortex dynamics in a circular nanodot excited by spin-polarized current.

We investigate analytically and numerically nonlinear vortex spin torque oscillator dynamics in a circular magnetic nanodot induced by a spin-polarized current perpendicular to the dot plane. We use a generalized nonlinear Thiele equation including spin-torque term by Slonczewski for describing the nanosize vortex core transient and steady orbit motions and analyze nonlinear contributions to all forces in this equation. Blue shift of the nano-oscillator frequency increasing the current is explained by a combination of the exchange, magnetostatic, and Zeeman energy contributions to the frequency nonlinear coefficient. Applicability and limitations of the standard nonlinear nano-oscillator model are discussed.