Within this paper we show the importance of accurate implementations of the Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions for antiferromagnetically coupled ferromagnetic layers with thicknesses exceeding the exchange length. In order to evaluate the performance of different implementations of RKKY interaction, we develop a benchmark problem by deriving the analytical formula for the saturation field of two infinitely thick magnetic layers that are antiparallelly coupled. This benchmark problem shows that state of the art implementations in commonly used finite-difference codes lead to errors of the saturation field that amount to more than 20% for mesh sizes of 2 nm which is well below the exchange length of the material. In order to improve the accuracy, we develop higher order cell-based and nodal-based finite-difference codes that significantly reduce the error compared to state of the art implementations. For the second order cell-based approach and first order nodal-based approach the error of the saturation field is reduced by about a factor of 10 (2% error) for the same mesh size of 2 nm.

This manuscript discusses the difficulties with magnetic position and orientation (MPO) system design and proposes a general method for finding optimal layouts. The formalism introduces a system quality measure through state separation and reduces the question “How to design an MPO system?” to a global optimization problem. The latter is then solved by combining differential evolution algorithms with magnet shape variation based on analytical computations of the field. The proposed formalism is then applied to study possible realizations of continuous three-axis joystick motion tracking, realized with just a single magnet and a single 3D magnetic field sensor. The computations show that this is possible when a specific design condition is fulfilled and that large state separations as high as $1\mathrm{mT}{/}^{\circ }$ can be achieved under realistic conditions. Finally, a comparison to state-of-the-art design methods is drawn, computation accuracy is reviewed critically, and an experimental validation is presented.

We present a simple atomistic model for the description of noncollinear coupling in magnetic multilayers with hybrid spacer layers made of Ru alloyed to ferromagnetic atoms such as Fe. In contrast to previous analytical and micromagnetic models that explain the noncollinear coupling by means of lateral fluctuations in the coupling constant, the presented model accounts for atom-atom coupling in all three spatial dimensions within the spacer layer. The model is able to accurately predict the dependence of the macroscopic bilinear and biquadratic coupling constants on the spacer-layer composition and thickness, showing much better quantitative agreement than lateral-fluctuation models. Moreover, it predicts that the noncollinear coupling is virtually independent of the exchange stiffness in the ferromagnetic layers, which goes beyond the predictions of previous models. This prediction is validated by experimental measurements.

In this work, it is demonstrated that straightforward implementations of the well-known textbook expressions of the off-axis magnetic field of a current loop are numerically unstable in a large region of interest. Specifically, close to the axis of symmetry and at large distances from the loop, complete loss of accuracy happens surprisingly fast. The origin of the instability is catastrophic numerical cancellation, which cannot be avoided with algebraic transformations. All exact expressions found in the literature exhibit similar instabilities. We propose a novel exact analytic expression, based on Bulirsch’s complete elliptic integral, which is numerically stable (15–16 significant figures in 64 bit floating point arithmetic) everywhere. Several field approximation methods (dipole, Taylor expansions, Binomial series) are studied in comparison with respect to accuracy, numerical stability and computation performance. In addition to its accuracy and global validity, the proposed method outperforms the classical solution, and even most approximation schemes in terms of computational efficiency.

The signal-to-noise ratio (SNR) of a bit series written with heat-assisted magnetic recording on granular media depends on a large number of different parameters. The choice of material properties is essential for the obtained switching probabilities of single grains and, therefore, for the written bits’ quality in terms of SNR. Studies where the effects of different material compositions on transition jitter and the switching probability are evaluated were done, but it is not obvious, how significant those improvements will finally change the received SNR. To investigate that influence, we developed an analytical model of the switching probability phase diagram, which contains independent parameters for, inter alia, transition width, switching probability, and curvature. Different values lead to corresponding bit patterns on granular media, where a reader model detects the resulting signal, which is finally converted to a parameter dependent SNR value. For grain diameters between 4 and 8 nm, we show an increase of $\sim 10\mathrm{dB}$ for bit lengths between 4 and 12 nm, an increase of $\sim 9\mathrm{dB}$ for maximum switching probabilities between 0.64 and 1.00, a decrease of $\sim 5\mathrm{dB}$ for down-track-jitter parameters between 0 and 4 nm, a decrease of 1–3 dB for off-track-jitter parameters between 0 and 50 K, and an increase of $\sim 0.5\mathrm{dB}$ for the reduced bit curvature. Those results are furthermore compared to the theoretical formulas for the SNR. We obtain a good agreement, even though we show slight deviations.