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We establish a general Langevin Dynamics model of interacting, single-domain magnetic nanoparticles in liquid suspension at finite temperature. The model couples the LLG equation for the moment dynamics with the mechanical rotation and translation of the particles. Within this model, we derive expressions for the instantaneous transfer of energy, linear and angular momentum between the particles and with the environment. We demonstrate by numerical tests that all conserved quantities are fully accounted for, thus validating the model and the transfer expressions. The energy transfer expressions derived here are also useful analysis tools to decompose the instantaneous, non-equilibrium power loss at each MNP into different loss channels. To demonstrate the model capabilities, we analyse simulations of MNP collisions and high-frequency hysteresis in terms of power and energy contributions.

According to the laws of magnetism, the shape of magnetically soft objects limits the effective susceptibility. For example, spherical soft magnets cannot display an effective susceptibility larger than 3. Although true for macroscopic multi-domain magnetic materials, we show that magnetic nanoparticles in a single-domain state do not suffer from this limitation. This is a consequence of the particle moment being forced to saturation by the predominance of exchange forces, and only allowed to rotate coherently in response to thermal and/or applied fields. We apply statistical mechanics to determine the static and dynamic susceptibility of single-domain particles as a function of size, temperature and material parameters. Our calculations reveal that spherical single-domain particles with large saturation magnetisation and small magneto-crystalline anisotropy, e.g. FeNi particles, can have very a large susceptibility of 200 or more. We further show that susceptibility and losses can be tuned by particle easy axis alignment with the applied field in case of uniaxial anisotropy, but not for particles with cubic anisotropy. Our model is validated experimentally by comparison with measurements on nanocomposites containing spherical 11$\pm$3 nm $\gamma$-Fe$_2$O$_3$ particles up to 45 vol% finely dispersed in a polymer matrix. In agreement with the calculations for this specific material, the measured susceptibility of the composites is up to 17 ($\gg$3) and depends linearly on the volume fraction of particles. Based on these results, we predict that nanocomposites of 30 vol% of superparamagnetic FeNi particles in an insulating non-magnetic matrix can have a sufficiently large susceptibility to be used as micro-inductor core materials in the MHz frequency range, while maintaining losses below state-of-the-art ferrites., Comment: 10 pages, 5 figures, 1 table, 20 numbered equations

A permanent magnet can be levitated simply by placing it in the vicinity of another permanent magnet that rotates in the order of 200 Hz. This surprising effect can be easily reproduced in the lab with off-the-shelf components. Here we investigate this novel type of magnetic levitation experimentally and clarify the underlying physics. Using a 19 mm diameter spherical NdFeB magnet as rotor magnet, we capture the detailed motion of levitating, spherical NdFeB magnets, denoted floater magnets. We find that as levitation occurs, the floater magnet frequency-locks with the rotor magnet, and, noticeably, that the magnetization of the floater is oriented close to the axis of rotation and towards the like pole of the rotor magnet. This is in contrast to what might be expected by the laws of magnetostatics as the floater is observed to align its magnetization essentially perpendicular to the magnetic field of the rotor. Moreover, we find that the size of the floater has a clear influence on the levitation: the smaller the floater, the higher the rotor speed necessary to achieve levitation, and the further away the levitation point shifts. We verify that magnetostatic interactions between the rotating magnets are responsible for creating the equilibrium position of the floater. Hence, this type of magnetic levitation does not rely on gravity as a balancing force to achieve an equilibrium position. Based on theoretical arguments and a numerical model, we show that a constant, vertical field and eddy-current enhanced damping is sufficient to produce levitation from rest. This enables a gyroscopically stabilised counter-intuitive steady-state moment orientation, and the resulting magnetostatically stable, mid-air equilibrium point. The numerical model display the same trends with respect to rotation speed and the floater magnet size as seen in the experiments., Comment: 15 pages, 6 figures, 10 videos + 8 pages supplementary material. Videos available at https://youtube.com/playlist?list=PLOfbFSFa_WoK4PgYQXhuNucS_WcIxXDET

A novel device that can be used as a tunable support-free phase plate for transmission electron microscopy of weakly scattering specimens is described. The device relies on the generation of a controlled phase shift by the magnetic field of a segment of current-carrying wire that is oriented parallel or antiparallel to the electron beam. The validity of the concept is established using both experimental electron holographic measurements and a theoretical model based on Ampere's law. Computer simulations are used to illustrate the resulting contrast enhancement for studies of biological cells and macromolecules.