Combinatorics

Physics

Topology (electrical circuits)

Mathematics

Topological order

Topological insulator

Semimetal

Band gap

Condensed matter physics

Quantum mechanics

Quantum

Nature

The discoveries of intrinsically magnetic topological materials, including semimetals with a large anomalous Hall effect and axion insulators1–3, have directed fundamental research in solid-state materials. Topological quantum chemistry4 has enabled the understanding of and the search for paramagnetic topological materials5,6. Using magnetic topological indices obtained from magnetic topological quantum chemistry (MTQC)7, here we perform a high-throughput search for magnetic topological materials&nbsp;based on first-principles calculations. We use as our starting point the Magnetic Materials Database on the Bilbao Crystallographic Server, which contains more than 549 magnetic compounds with magnetic structures deduced from neutron-scattering experiments, and identify 130 enforced semimetals (for which the band crossings are implied by symmetry eigenvalues), and topological insulators. For each compound, we perform complete electronic structure calculations, which include complete topological phase diagrams using different values of the Hubbard potential. Using a custom code to find the magnetic co-representations of all bands in all magnetic space groups, we generate data to be fed into the algorithm of MTQC to determine the topology of each magnetic material. Several of these materials display previously unknown topological phases, including symmetry-indicated magnetic semimetals, three-dimensional anomalous Hall insulators and higher-order magnetic semimetals. We analyse topological trends in the materials under varying interactions: 60 per cent of the 130 topological materials have topologies sensitive to interactions, and the others have stable topologies under varying interactions.&nbsp;We provide a materials database for future&nbsp;experimental studies&nbsp;and open-source code for diagnosing topologies of magnetic&nbsp;materials. High-throughput calculations are performed to predict approximately 130 magnetic topological materials, with complete electronic structure calculations and topological phase diagrams.

High-throughput calculations of magnetic topological materials