arXiv subjects

Frederik Laust Durhuus

Publications and source records attributed to Frederik Laust Durhuus.

4 recordsLinked to original sources

arXiv2026

Exact demagnetisation field for periodic one-dimensional array of rectangular prisms

The magnetic field from a uniformly magnetised, rectangular prism is known exactly, which is the basis for a large number of micromagnetic simulations. Here we derive an analytical solution for the field from a periodically repeating infinite array of prisms aligned end-to-end, which becomes exact on the center axis in the limit of infinitesimally thin prisms. Using the same method we derive the on-axis field for a one-dimensional array of point dipoles. We validate the obtained results numerically and furthermore compare with the common macrogeometry approach and more recent uniform magnetisation method, demonstrating an excellent convergence rate for the novel method.

cond-mat.mtrl-sci↗

arXiv2026

Including sample shape in micromagnetics with 3D periodic boundary conditions

Periodic boundary conditions (PBCs) for computing magnetic fields in repeating magnetic structures, e.g. in micromagnetic simulations, are typically imposed using the quasi periodic macrogeometry approach, where many copies of the simulated domain are introduced. This can be computationally problematic, especially if the simulated domain is incommensurate with the desired sample shape. In this work, we present a formal proof that for sufficiently large magnetic samples, only the average magnetisation gives non-negligible shape effects. Using this insight, we develop a simple, computationally efficient modification of existing implementations which incorporates shape effects in PBC methods.

cond-mat.mtrl-sci↗

arXiv2025

Magnetic levitation at low rotation frequencies using an on-axis magnetic field

The Ucar effect is a simple yet astonishing phenomenon where a permanent magnet can be levitated by placing it in the vicinity of another permanent magnet that rotates sufficiently fast. The few previous works on this type of magnetic levitation all required magnets rotating on the order of 200 Hz. Here we investigate the influence of applying a static magnetic field on the rotation axis and show that this can lower the needed rotation frequency to below 50 Hz. We explain this by a detailed analysis of the force producing levitation, which is a superposition of a repelling force caused by the off-axis (rotating) magnetic field and an attractive force due to the on-axis field. We study this force and resulting levitation experimentally, analytically and numerically for three different rotor magnet configurations, showing that trends in the levitation distance and frequency range can be accurately predicted from both the numerical and analytical models.

physics.class-ph↗

arXiv2023

Magnetic levitation by rotation

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.

physics.app-ph↗