Angular momentum and pseudo angular momentum in magnetic materials

In condensed matter systems it is necessary to distinguish between two kinds of momenta: the momentum of the constituents of the material, such as nuclei and electrons, and the pseudomomentum of the emergent fields (or quasiparticles) that are present in the material, e.g., phonons and magnons. The same distinction is also valid for angular momentum and pseudo angular momentum. The latter is conserved when the system is invariant under rotations of the emergent fields. Based on Noether's theorem, I demonstrate that the recently discussed orbital angular momenta of phonons [1,2] and magnons [3,4] are pseudo angular momenta. The conceptual difference between angular momentum and pseudo angular momentum is important for a proper understanding of the transfer of angular momentum in condensed matter systems, for example in spintronics applications.

[1] J. J. Nakane et al., Phys. Rev. B 97 , 174403 (2018).
[2] J. H. Mentink et al., Phys. Rev. B 99 , 064428 (2019).
[3] C. Jia et al., Nat. Commun. 10 , 2077 (2019).
[4] Y. Jiang et al., Phys. Rev. Lett. 124, 217204 (2020).