Exchange coupling in magnetic heterostructures can be modified via introduction of additional magnetic spacer layers at the interfaces. The magnetic characteristics and the spacer layer thickness determine the functional properties of the whole system. We show that the hysteresis loop area of trilayer spring magnets with two different soft magnetic layers (s1, s2) and one hard magnetic layer (h) with the sequence s1/s2/h can be increased as compared to both bilayer structures s1/h and s2/h with the same total thickness of the soft layers and for definite thickness ratios of the soft layers and their sequences. For ferrimagnetic spin valves, the perpendicular exchange bias effect can be tuned via the thickness of non-magnetic spacer layers at the interface, which determine the exchange coupling between ferrimagnets. A simple quasi one-dimensional phenomenological model is able to describe the magnetic hysteresis of even complex layered structures and to predict optimal geometrical and magnetic parameters of such heterostructures.
The temperature dependence of the response of a magnetic system to an applied field can be understood qualitatively by considering variations in the energy surface characterizing the system and estimated quantitatively with rate theory. In the system analysed here, Fe/Sm-Co spring magnet, the width of the hysteresis loop is reduced to a half when temperature is raised from 25 K to 300 K. This narrowing can be explained and reproduced quantitatively without invoking temperature dependence of model parameters as has typically been done in previous data analysis. The applied magnetic field lowers the energy barrier for reorientation of the magnetization but thermal activation brings the system over the barrier. A 2-dimensional representation of the energy surface is developed and used to gain insight into the transition mechanism and to demonstrate how the applied field alters the transition path. Our results show the importance of explicitly including the effect of thermal activation when interpreting experiments involving the manipulation of magnetic systems at finite temperature.
A method for calculating the magnetic dipole-dipole interaction in topological magnetic systems has been developed. It can be used to calculate stable states and minimum energy paths that determine the magnetic transition in chiral magnetic structures. Instead of directly summing the dipole interactions between magnetic moments/magnetic elements, we solve a local equation for demagnetizing fields. The states corresponding to the local energy minimum can be found using the Lagrange method for the conditional extrema. The efficiency of the algorithm has been demonstrated by calculating the dependence of the size and shape of magnetic skyrmions and anti-skyrmions on the magnitude of magnetization.
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