Frustration and Fluctuations in Altermagnets

• Applicant: Professor Dr. Mathias Scheurer
• Subject Area: Theoretical Condensed Matter Physics
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 571588623

Altermagnetism (AM) has recently emerged as a very actively studied research area of condensed matter physics. It refers to a class of magnetic orders in which the net magnetization vanishes as a result of a combination of time-reversal and point-group symmetries. As opposed to antiferromagnetism, where translations relate the magnetic sublattices, AM leads to a momentum-dependent spin splitting of the electronic bands; this splitting is not a relativistic correction and can therefore be much larger than that of spin-orbit coupling, making altermagnets attractive for spintronics applications. Despite intense activities, there are, however, still many interesting open questions concerning altermagnets. For instance, although the consequences of static AM for quantum physics (e.g., splitting of electronic bands or superconductivity) have been studied in detail, there are comparatively few works on the impact of strong quantum fluctuations on the altermagnetic order itself. Even concerning thermal fluctuations, there are many mostly unexplored questions, such as the formation of vestigial order and the spectral function of electrons in the presence of thermally fluctuating AM. At the same time, fluctuations are expected to be rich and relevant for altermagnets as they exhibit several anti-aligned magnetic moments in their typically complex unit cells, which naturally leads to frustration. This motivates us to address, in this project, the consequences of strong fluctuations, thermal and quantum, on AM and “nearby” orders which are energetically close as a result of frustration. For both insulating and itinerant systems, we will study the resulting complex phase diagrams, including phases where part of the altermagnetic or closely related order is lost while certain vestiges survive. We will investigate the characteristic spectral signatures of strong fluctuations and consequences for superconductivity, and aim at identifying altermagnetic systems where the fluctuation-related effects are particularly prominent and interesting. Apart from being the origin of the underlying rich physics, we will also explore fluctuations as a non-trivial probe of AM; we will compute the expected signatures of the different states of the project in nitrogen-vacancy (NV) quantum sensing experiments. This is motivated by recent remarkable progress in using NV qubits to measure local field fluctuations. To achieve our goals, we will use both numerical and analytical techniques, study an exactly solvable itinerant model I constructed, collaborate with ab initio experts, and stay in close contact with an experimental group working on NV sensing. In the long term, I anticipate that the research will broaden the phenomenology of AM significantly, establish novel connections to multiple other concepts of strongly correlated matter, and establish NV sensing as a promising probe of altermagnets and fluctuations therein.

• DFG Programme: Research Grants