Exchange Interactions in multi-correlated Spin-Orbit Systems

In condensed matter physics, we talk about spin-orbit-coupled solids when the spin-orbit coupling is comparable in energy with other relevant interactions. Spin-orbit coupling is a relativistic effect that couples the spin (magnetic) and orbital (charge) degrees of freedom. It substantially affects materials` structural, electronic, and magnetic properties. It can drastically change the physical interactions, leading to magnetic configurations never observed before. All these reasons have pushed the scientific interest toward materials where spin-orbit coupling has a strong impact. Among the recently discovered materials are notable examples of the 5d double perovskites. These are complex structures where the magnetic ions, belonging to the transition metal group of the periodic table, have a 5d electronic configuration. In these materials, exotic magnetic orderings that involve tilted magnetic structures or elusive ferromagnetic ordering of magnetic octupoles have been observed. Understanding how spin-orbit coupling activates or counteracts the other active interactions in forming the mentioned magnetic ground states poses significant challenges. However, first- principles calculations can provide a valuable solution by calculating the corresponding magnetic interactions "ab initio." The following project aims to study the interplay of spin-orbit coupling with structural effects and when magnetic ions have different valence on neighboring sites. The focus will be on pristine and chemically doped 5d1 double perovskites. We plan to extend an ab initio scheme for calculating magnetic interactions to multi-correlated structures (meaning with distinct characters of the magnetic ions) to accomplish the proposed goals. The research will be conducted in the host institution under Dr. Leonid Pourovskii at the Centre de Physique Théorique Ecole Polytechnique in Paris.

Understanding and controlling the magnetic properties of materials is an important challenge in modern condensed matter physics. The focus of this project was the study of a special class of materials known as spin-orbit-coupled materials, in which magnetism is strongly influenced by relativistic effects that arise in heavy elements. In these systems, spin-orbit coupling links the electron's spin to its orbital motion around the nucleus, giving rise to magnetic behaviors that do not occur in conventional magnets. One particularly intriguing consequence is the emergence of multipolar "hidden order" phases: magnetic orders that produce clear thermodynamic signatures, yet remain difficult to detect using standard experimental techniques. A class of materials recently proposed and shown to host such hidden multipolar phases are double perovskites containing heavy transition-metal ions, such as osmium or rhenium. The goal of the project was to understand how relativistic effects, together with other key interactions such as electronic correlations, crystal-field effects, and magnetic superexchange, combine to determine the magnetic properties of these materials. To address this challenge, we developed advanced computational methods that allow for the calculation of magnetic properties directly from fundamental physical principles, or "ab initio". A major achievement of the project was the extension of one of these methods, known as the Force-Theorem in the Hubbard-I method, to materials containing several interacting magnetic sites. This advance made it possible to study distorted crystal structures, the interplay between lattice effects and magnetic interactions, and the role of electrons that become locally trapped due to small lattice distortions. These trapped electrons, known as small polarons, naturally form when the material is chemically doped. Using this framework, we uncovered a strong interplay between lattice distortions and magnetism, showing that even small structural or electronic changes can significantly modify magnetic interactions and stabilize previously unknown hidden magnetic phases. Overall, this work provides new insight into how complex magnetic states emerge in strongly interacting materials and offers guiding principles for designing materials with novel magnetic properties, with potential relevance for future quantum technologies.