Project supervisors: Julie Staunton; Albert Bartok-Partay

Student: Laura Cairns

The project is closely connected to ongoing research being conducted in collaboration with HetSys partner Forschungszentrum Jülich. The project will also enhance the collaboration which has just begun with materials scientists at Northeastern University in Boston in the USA on developing novel materials processing for magneto-functional materials. There will be opportunities for the student to visit both partner institutes.

Summary: Magnetic materials are technologically indispensable - used in motors, generators, solid state cooling, electronic devices, data storage, medical treatment, toys etc. Although the effects of magnetism are easily understood on the macroscopic scale, it has its origins in the complex collective behaviour of the electronic glue, simultaneously binding the nuclei of the material together and generating magnetic moments. In this project we will identify atomistic, classical spin models by using machine learning tools on data from calculations of the fundamental quantum mechanics of the electrons. From their study we will discover ways to design new magnets with reduced amounts of critical elements such as rare earth metals. The work will relate directly to theoretical work and experimental measurements by International Partners.

Background: With the drive towards more energy efficient technologies, renewable energy supplies and further miniaturisation of devices, there is an urgent demand for stronger and cheaper magnetic materials. This project will be part of ongoing development of computational modelling to understand intrinsic magnetic properties, to refine design principles and to aid the search for new functional magnets. A magnetic material comprises a crystalline lattice of nuclei surrounded by a glue of septillions of interacting electrons. Moreover, the same electrons which underpin the magnetism of a material are also responsible for determining the arrangements of its atoms. The complexity of this electron fluid presents a fundamental challenge for theory and computational modelling - the magnetism it can lead to comes from composite spins coalescing around atomic sites as a result of the cooperative behaviour of many electrons. There are interactions between pairs of such classical spins and among clusters of them. In principle these multi-spin parameters can be determined from calculations of the fundamental quantum mechanics of the electrons. To date we have developed a cluster expansion of the free energy of the system in terms of the quantities which describe the average order of the spins around the atomic sites, i.e. local magnetic order parameters, and we can describe accurately many magnetic properties and how they vary with temperature, composition and applied fields.

The extraction and investigation of an accurate model classical spin-Hamiltonian, however, from such ab initio data is a challenging task and it is at the heart of this project. To take the work to the next level and enable it to describe multicomponent magnetic materials for the
design of new magnets with reduced levels of critical elements as well as materials with intriguing topological magnetic structures (skyrmions) we need to develop machine learning tools to determine the form of the free energy rather than our current ad hoc approach.

This work will also enhance our modelling of how arrangements of atoms in multi-component alloys can be affected by the application of strain and magnetic fields and hence have an impact on novel materials processing being developed by collaborators.

References: Nakamura, H., Scr. Mater. 154, 273 (2018); Mendive-Tapia, E. and Staunton, J. B., Physical Review B 101, 144424 (2019); Patrick, C. E., and Staunton, J. B., Phys. Rev. Mat. 3, 101401(R), (2019); Marchant, G.A. et al., Physical Review B 103, 094414, (2021).