The original period system ordered chemical elements by their chemical properties. This classification in his day led Dmitri Ivanovich Mendeleev to the prediction – and the subsequent discovery – of new elements. Similarly, non-magnetic crystalline solids have recently been classified using a “topological periodic table” based on a new theory called Topological Quantum Chemistry (TQC) and symmetry indicators. From this classification, tens of thousands of potentially topological non-magnetic materials have been identified, which has already led to the discovery of a considerable number of topological insulators.
However, unlike non-magnetic materials, so far the Magnetic compounds could not be classified using a similar methodology, mainly due to the lack of topological quantum chemistry for magnetic materials. Instead, research on topological magnetic materials was being carried out on a case-by-case basis, motivated by possible applications such as efficient thermoelectric converters, components of energy-efficient microelectronic devices that could form the core of quantum computers, or improved magnetic storage media.  Although the first theoretical studies of topological materials and their properties in the early 1980s were conceived in magnetic systems (efforts that were awarded the Nobel Prize in Physics in 2016), paradoxically the advances in the last 40 years in The discovery of topological materials has largely occurred in insulators and non-magnetic topological semimetals.
The relative absence of candidates for topological magnetic materials can be attributed to two main causes. On the one hand, to the complicated symmetries of magnetic crystals: non-magnetic structures are classified into 230 space groups, magnetic materials into 1,421. On the other, to the theoretical and experimental difficulties involved in the simulation and measurement of quantum magnets; thus, while in existing databases hundreds of thousands of crystalline compounds can be searched, in the largest ones of magnetic materials there are only a few hundred experimentally measured magnetic structures. “In addition to this, in all magnetic systems we must also take into account other interactions, which are much more difficult to simulate. This makes the task of predicting magnetic topological materials significantly more complicated, even if the numbers were more favorable, "says B. Andrei Bernevig, professor of physics at Princeton University.
Bernevig's group work, published in the journal Nature has taken a great step towards the discovery of magnetic materials with non-trivial topological electronic properties.
Previously, in 2017, this same team developed a complete and novel approach to understand the structure of bands in non-magnetic materials. “In this theory called TQC, we linked the topological characteristics of a material with its underlying chemistry. This turned the search for non-magnetic topological materials into a task that could be effectively automated, ”says Luis Elcoro, professor at the UPV / EHU Faculty of Science and Technology and co-author of both studies. TQC represents a universal framework to predict and characterize all possible band structures in crystalline materials. TQC was applied to 35,000 experimentally known non-magnetic compounds and led to the discovery of 15,000 new topological materials.
“In the last two years we have identified thousands of topological materials, while in the last two decades only a few have been identified hundreds of them. Before the application of these novel tools, the search for new materials with these amazing properties was like looking for a needle in a haystack at dusk. Now, the search for non-magnetic topological materials is almost a routine exercise ”, says Maia G. Vergniory, Ikerbasque associate researcher at DIPC, and also co-author of both studies.
To reproduce the success achieved with non-magnetic materials, the researchers They faced two main obstacles: on the one hand, the theoretical machinery that must be elucidated in order to analyze the band structure of a given magnetic material is very complex. And, on the other hand, the number of magnetic materials whose magnetic structure is reliably known in detail is quite small. "While we had 200,000 non-magnetic compounds to analyze, the largest database of experimentally measured magnetic structures has approximately 1,000 records," explains Professor Elcoro.
"Fortunately, we had the meticulous work of the people behind the Bilbao Crystallographic Server database of magnetic structures, which allowed us to introduce the correct initial parameters in our theoretical models ”, says Yuanfeng Xu, postdoctoral researcher at the Max Planck Institute in Halle, and first author of the study. The magnetic information is hosted on the Bilbao Crystallographic Server ( www.cryst.ehu.es ), which has been partially developed by Professor Elcoro.
After a selection of the best potential candidates, the The team analyzed 549 magnetic structures by first applying simulations from first principles that do not use empirical initial parameters to obtain the magnetic symmetries of electronic wave functions, and then constructing a magnetic extension of the TQC to determine which magnetic structures harbored a topology of Non-trivial electronic band.
As a result of the study, the existence of 130 topological magnetic materials is predicted. Likewise, they have found that the proportion of topological magnetic materials (130 out of 549) in nature appears to be similar to the proportion in non-magnetic compounds.
The authors are optimistic with the results, since, despite the reduced absolute number of magnetic compounds compared to the thousands of non-magnetic materials studied to date, they have found a greater diversity of fascinating characteristics that make them very interesting to design future experiments. "Now that we have predicted new topological magnetic materials, the next step is to experimentally verify their topological properties," says G. Vergniory.
Researchers have also created an online database to freely access the results of the present study: www.topologicalquantumchemistry.fr/magnetic . Using different search tools, users can explore the topological properties of the more than 500 magnetic structures analyzed. "We have laid the foundations for a catalog of topological magnetic structures," says Elcoro. It is expected that the standardization of the use of magnetic symmetry in experimental and theoretical environments, accompanied by the widespread adoption of the tools developed in this work, will lead to a great explosion of discoveries in magnetic materials in the coming years.
Yuanfeng Xu, Luis Elcoro, Zhida Song, Benjamin J. Wieder, MG Vergniory, Nicolas Regnault, Yulin Chen, Claudia Felser, and B. Andrei Bernevig (2020) High-throughput calculations of magnetic topological materials Nature doi: 10.1038 / s41586-020-2837-0
Edition produced by César Tomé López from materials supplied by UPV / EHU Komunikazioa  The article A catalog of topological magnetic structures has been written in Cuaderno de Cultura Científica .