Recent interest in topological semimetals has led to the proposal ofmany newtopological phases that can be realized in real materials. Next to Dirac and Weyl systems, these include more exotic phases based on manifold band degeneracies in the bulk electronic structure. The exotic states in topological semimetals are usually protected by some sort of crystal symmetry, and the introduction of magnetic order can influence these states by breaking time-reversal symmetry. We show that we can realize a rich variety of different topological semimetal states in a single material, CeSbTe. This compound can exhibit different types ofmagnetic order that can be accessed easily by applying a small field. Therefore, it allows for tuning the electronic structure and can drive it through a manifold of topologically distinct phases, such as the first nonsymmorphic magnetic topological phase with an eightfold band crossing at a high-symmetry point. Our experimental results are backed by a full magnetic group theory analysis and ab initio calculations. This discovery introduces a realistic and promising platform for studying the interplay of magnetism and topology. We also show that we can generally expand the numbers of space groups that allow for high-order band degeneracies by introducing antiferromagnetic order.
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