Abstract
In condensed matter systems it is necessary to distinguish between the momentum of the constituents of the system and the pseudomomentum of quasiparticles. The same distinction is also valid for angular momentum and pseudoangular momentum. Based on Noether's theorem, we demonstrate that the recently discussed orbital angular momenta of phonons and magnons are pseudoangular momenta. This conceptual difference is important for a proper understanding of the transfer of angular momentum in condensed matter systems, especially in spintronics applications.
Highlights
In 1915, Einstein, de Haas, and Barnett demonstrated experimentally that magnetism is fundamentally related to angular momentum
The transfer of angular momentum between lattice and magnetization has been investigated in several recent works, for example, the dynamics of a single spin embedded in an elastic solid [20,21,22] and the transfer of angular momentum in magnetic insulators [23,24,25,26,27]
While in the case of pseudomomentum we can identify the pseudomomentum with the wave-vector k of a plane wave, in the case of pseudoangular momentum, we can identify the pseudoangular momentum projection along the z axis with the angular momentum quantum number m of an expansion of the field in terms of spherical harmonics Ylm for spherical geometries [22], or in terms of Bessel functions for cylindrical geometries [34]
Summary
Based on Noether’s theorem, we demonstrate that the recently discussed orbital angular momenta of phonons and magnons are pseudoangular momenta. This conceptual difference is important for a proper understanding of the transfer of angular momentum in condensed matter systems, especially in spintronics applications. In 1915, Einstein, de Haas, and Barnett demonstrated experimentally that magnetism is fundamentally related to angular momentum. Condensed matter systems support closely related conservation laws: the conservation of the pseudomomentum and pseudoangular momentum of quasiparticles, such as magnons and phonons. There is a conceptual issue related to these recent advances: neither phonons nor magnons carry an orbital angular momentum.
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