Band Topology in Quantum Magnets: From nontrivial excitations to non-Hermitian topology and spintronics

The focus workshop TOPMAX22 which took place June 13-15, 2022 brought together 88 participants (34 on-site, 54 virtual) from 17 countries working on topological excita- tions in magnetic systems. Our goal was to address the key challenges and questions in this rapidly developing field and to develop connections to the adjacent fields of quantum magnetism, spintronics, non-Hermitian topology, the dynamics of complex spin textures, and electronic topological materials coupled to magnetism.

The workshop included talks from many of the key contributors to this new and growing field. We highlight:

• Sasha Chernyshev: who kicked off the meeting with pressing questions on the effect of strong magnon interactions on topology

• Marcus Garst: who presented the first evidence for emergent Landau levels in the magnon excitations of a skyrmion crystal.

• Yuan-Ming Lu: who provided a framework for discovering topological magnon ma- terials based on Topological Quantum Chemistry

• Alexander Mook: who discussed the role of magnon bound states in enhancing the possible topological magnon states

  We structured the workshop to create opportunities for junior scientists to present their recent work as contributed presentations. These were generally excellent talks, addressing timely questions, and initiating productive discussions. In particular, we call attention to: Miska Elliot who spoke about recent work on the observation of Dirac magnons in a stacked honeycomb system and Peter Czajka who provided tantalizing evidence for topological magnons underlying the perplexing thermal Hall signal observed in α-RuCl3.

  The workshop opened a range of lively discussions on several key questions in the field of topological magnetic excitations:

  Does magnon band topology survive the presence of interactions? (such as quasi- particle decay) How can we experimentally detect topologically protected magnon surface states in real materials? Can topological magnons play a role in generating or controlling spin currents that may be useful for spintronics?

  The meeting provided the first face-to-face forum for discussing issues in this developing field and provided considerable food for thought. The organizers look forward to a further iteration of this meeting in the hopefully near future once some of the current challenges have been met.

  The organizers would like to express their appreciation to the staff at PKS, including the cafeteria and guest house staff. We also thank Ronny Börner for his technical assistance with the hybrid conference system that enabled the seamless participation of our online attendees and contributors. We would like to especially thank Mandy Lochar for her remarkable organizing skills and patience, without which this meeting would not have been possible.