Noise spectroscopy of insulating and itinerant altermagnets

One of the central goals in the emergent field of altermagnetism is the unambiguous experimental identification and characterization of altermagnetic order across a variety of compounds. This motivates exploring tools that can clearly distinguish altermagnets from antiferromagnets, based on symmetry signatures, and offer access to the dominant orbital character (e.g., $d$-wave vs. $g$-wave) of the magnetic order parameter. In this work, we theoretically explore the potential of noise magnetometry for this task, studying contributions from both magnons and itinerant electrons in different regimes and scenarios. While altermagnetism and antiferromagnetism also lead to different noise spectra for magnons, we find the most striking and symmetry-sensitive signatures in the charge fluctuations of itinerant altermagnets. Both for the homogeneous bulk case and in the presence of strain and/or around domain walls, we identify noise contributions that are only permitted by symmetry in the altermagnet and, thus, provide a unique signature of altermagnetism. Furthermore, the angular dependence of noise around domain walls also offers access to the orbital character of the altermagnet. On a more technical note, we discuss the role and relevance of lattice effects related to the dipole tensor. We hope that our work will help pave the way towards the clear experimental identification of altermagnetism across a wide range of candidate materials.