Magnetism at interfaces: from quantum to reality

Permanent magnets are a key technology for modern society with applications in air conditioning, mobility or power generation. The quality of a permanent magnet is given by the strength to withstand an external applied field. At a certain external field, the coercive field, the magnet loses its magnetic state. The measured coercive fields in modern permanent magnets reach only a small fraction of theoretical values. A series of experimental studies have shown that discontinuities and misalignment at the at omic scale significantly affect the coercivity. Understanding defects at the atomic scale, and their relation to the quality of the magnet, helps to modify and improve the production process of permanent magnets and to obtain stronger permanent magnets. Since fabrication and experiments are expensive and time consuming, the best way to investigate magnets is modelling and simulation. In this project, we develop a quantitative model of coercivity, taking into account the local atomic structure, the spatial variation of the magnetic properties close to the atomic defects, and the physical microstructure of the magnet. To achieve this goal we bridge different length scales, from sub-nanometer features up to a few micrometers. Usually it is difficult to pass information between different length scales. With the help of modern computer systems and sophisticated algorithms we bridge the different length scales to obtain the coercivity of a permanent magnet based on its smallest entity, the atomic structure. The developed model is guided by well described magnetic materials to validate the system throughout the progress of the project. There are material systems, which are examined experimentally and theoretically for many years, like for example Iron-Nickel (FeNi) and Iron- Platinum (FePt). Here we start to develop and validate our multiscale approach. Afterwards we use the developed model to analyse and understand more complex material systems. We invite international experts for each material system to cooperate closely between experiments and our developed model. Throughout the project we gather information from experiments and from simulations. We apply data assimilation, which is a machine learning model, to adjust the simulation model according to coercivity measurements by correcting systematic errors. Using the developed multiscale model and the machine leaning model, we will be able to describe magnetic material systems based on its atomistic structure and to develop stronger permanent magnets.

In this project, we explored how thin interfaces between metals influence magnetic behavior in structured magnetic materials. Our focus was on multilayer systems made of cobalt (Co), ruthenium (Ru), iron (Fe), platinum (Pt), and nickel (Ni), where magnetic layers are separated by only a few atomic layers. At the smallest scale, we used quantum-mechanical (ab initio) calculations to understand the effect of atomic structures at these interfaces. In particular, we studied how neighboring magnetic layers can either align in the same direction (ferromagnetic) or opposite directions (antiferromagnetic), depending on the thickness and composition of the spacer layer between them. We found that even slight mixing of atoms at the interfaces, common in real materials, strongly affects this coupling and can explain experimental observations very well. We also showed that the magnetic anisotropy (the preferred direction of magnetization) and more complex interaction terms depend sensitively on the exact interface structure. To connect these atomic-scale insights to realistic materials, we developed a multiscale modeling approach that links atomistic calculations to micromagnetic simulations. These larger-scale simulations describe magnetization behavior over nanometer to micrometer scales allowing to study realistic material structures. A key achievement was the development of a computational method that uses adaptive meshes to efficiently simulate magnetic fields. This approach automatically increases resolution only where needed, such as near interfaces or domain walls, enabling much larger and more detailed simulations. Using these tools, we investigated how microscopic material features such as grain size, crystal orientation, and interface roughness affect magnetic behavior. We found that irregularities in the material create strong pinning sites that hinder the movement of magnetic domain walls. When applied to multilayer systems like Co/Ru/Co, we showed that the strength of the coupling between layers determines whether the system forms simple, uniform magnetization patterns or more complex domain structures. Importantly, by incorporating results from atomistic calculations, we were able to simulate how magnetic coupling changes with temperature and how magnetization can abruptly change at interfaces, an effect not captured by simpler models. We also demonstrated that modifying the interface, for example by adding atoms or introducing controlled roughness, can enhance the coupling strength. Finally, the developed methods were applied to other material systems such as Fe/Pt and Fe/Ni multilayers, providing a consistent picture of how interface structure controls magnetic properties. Overall, this project provides a powerful framework for designing magnetic multilayers with tailored properties by linking atomic-scale physics to real-world material behavior.