Angular momentum of phonons and its application to single-spin relaxation

Angular momentum conservation and phonon spin in magnetic insulators

“…(8) as adhered to in most papers [11,15,45]. On the other hand, that definition appears similar to the field (or pseudo) angular momentum introduced independently by Nakane and Kohno [18]. The leading one-phonon/one-and two-magnon contributions to the magnetoelastic Hamiltonian (12) read in momentum space…”

Dynamic magnetoelastic boundary conditions and the pumping of phonons

“…The current-induced spin transfer by electrons [1] and magnons [2,3] can, e.g., be used for nonvolatile memories and magnetic logic devices. Electromagnetic fields [4,5] and lattice vibrations [6][7][8][9][10][11][12][13] may also carry spin. The orbital and spin angular momentum of the deformation fields of continuous isotropic acoustic media with SO(3) rotational symmetry derive from Noether's theorem [7,10].…”

“…Electromagnetic fields [4,5] and lattice vibrations [6][7][8][9][10][11][12][13] may also carry spin. The orbital and spin angular momentum of the deformation fields of continuous isotropic acoustic media with SO(3) rotational symmetry derive from Noether's theorem [7,10]. The phonon spin is the angular-momentum contribution that does not depend on the origin of the coordinate system [10,12,13].…”

Orbital magnetic moments of phonons

“…In recent years, various physical phenomena have been attributed to the effect of phonon angular momentum, such as the phonon Hall and phonon spin Hall effects [16][17][18], a contribution to the Einstein-de Haas effect [14,[19][20][21][22] and to spin relaxation [21,23], the phonon a.c. Stark effect [24], and the phonon Zeeman effect [12]. Furthermore, terahertz sources are nowadays able to coherently excite phonons to yield large vibrational amplitudes, so that the effects of phonon angular momentum become visible also on a macroscopic level, for example by interaction with the magnetic or valley degrees of freedom of a material [25,26].…”