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We present an analytical solution for the magnetic field of a homogeneously magnetized cylinder tile and by extension solutions for full cylinders, rings, cylinder sectors and ring segments. The derivation is done by direct integration in the magnetic surface charge picture. Results are closed-form expressions and elliptic integrals. All special cases are treated individually, which enables the field computation for all possible position arguments. An implementation is provided in Python together with a performance analysis. The implementation is tested against numerical solutions and applied to compute the magnetic field in a discrete Halbach cylinder., Comment: 29 pages, 6 Figures

Conjugate gradient methods for energy minimization in micromagnetics are compared. When the step length in the line search is controlled, conjugate gradient techniques are a fast and reliable way to compute the hysteresis properties of permanent magnets. The method is applied to investigate demagnetizing effects in NdFe12 based permanent magnets. The reduction of the coercive field by demagnetizing effects is 1.4 T at 450 K.

We investigate the effect of curvature on the energy and stability of domain wall configurations in curved cylindrical nanotubes and nanowires. We use micromagnetic simulations to calculate the phase diagram for the transverse wall (TW) and vortex wall (VW) states in tubes, finding the ground state configuration and the metastability region where both types of walls can exist. The introduction of curvature shifts the range for which the TW is the ground state domain wall to higher diameters, and increases the range of metastability. We interpret this behavior to be primarily due to the curvature-induced effective Dzyaloshinskii-Moriya term in the exchange energy. Furthermore, we demonstrate qualitatively the same behavior in solid cylindrical nanowires. Comparing both tubes and wires, we observe how while in tubes curvature tends to suppress the transformation from the TW to VW, in wires it promotes the transformation of the VW containing the Bloch point into the TW. These findings have important implications in the fundamental understanding of domain walls in 3D geometries, and the design of future domain wall devices., This work was supported by the EPSRC Cambridge NanoDTC EP/L015978/1, and the Winton Program for the Physics of Sustainability. L. Skoric acknowledges support from St Johns College of the University of Cambridge. C. Donnelly was supported by the Leverhulme Trust (ECF-2018-016), the Isaac Newton Trust (18-08) and the L'Or\'eal-UNESCO UK and Ireland Fellowship For Women In Science. A. Hierro-Rodriguez acknowledges support from Spanish AEI under project reference PID2019–104604RB/AEI/10.13039/501100011033. The authors acknowledge the University of Vienna research platform MMM Mathematics - Magnetism - Materials, and the FWF project I 4917.

A uniform mode theory is used to find the parameter range for realizing fast switching below the Stoner–Wohlfarth limit in weakly coupled granular tilted media. The theory is used to estimate the field amplitudes and directions for simultaneous switching of a family of uniformly magnetized and noninteracting grains with dispersion in the easy axis and initial magnetization directions. The effect of interactions is then studied numerically by using a 3D finite element micromagnetic simulations. The numerical results shows that the theory provides rather accurate estimate. In addition, it is verified that in an appropriate range of applied field amplitudes the switching time decreases by decreasing the external field.