Quantum many-body dynamics of the Einstein–de Haas effect

Abstract

In 1915, Einstein and de Haas and Barnett demonstrated that changing the magnetization of a magnetic material results in mechanical rotation, and vice versa. At the microscopic level, this effect governs the transfer between electron spin and orbital angular momentum, and lattice degrees of freedom, understanding which is key for molecular magnets, nano-magneto-mechanics, spintronics, and ultrafast magnetism. Until now, the timescales of electron-to-lattice angular momentum transfer remain unclear, since modeling this process on a microscopic level requires addition of an infinite amount of quantum angular momenta. We show that this problem can be solved by reformulating it in terms of the recently discovered angulon quasiparticles, which results in a rotationally invariant quantum many-body theory. In particular, we demonstrate that non-perturbative effects take place even if the electron-phonon coupling is weak and give rise to angular momentum transfer on femtosecond timescales. J λl − ω k ω + iε + ∆E JM J λl − ω k (C9) K2 M J λl (ω) = k |U λ (k) Q λl | 2 ∆E JM 0 J λl − ω k 2 ω + iε + ∆E JM J λl − ω k (C10) with ∆E JM J = E − E JM J and ∆E JM J λl = E − E JM J λl , where E is the variational ground-state energy. The integrals are computed numerically with ε 1 until convergence is achieved. Explicit expressions for the energy of the bare impurity, E JM J , and the energy of the bare impurity with phonons excited, E JM J λl , as well as for Q λl , are given in Appendix B.

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].…”

The ultrafast Einstein–de Haas effect

“…From this it appears that although spin transport can contribute to ultrafast demagnetisation, there must also be sizeable contributions from spin-flip scattering.If indeed some fraction of angular momentum is transferred to the crystal lattice on ultrafast time scales, it should be possible to quantitatively measure the resulting structural dynamics. The dynamics of the Einstein-de Haas effect have been previously considered in other contexts 16,17 .Here we consider specifically the case where bulk, magnetised iron is uniformly demagnetised by a homogeneous femtosecond pump excitation. The idea is sketched in Fig.…”

“…If indeed some fraction of angular momentum is transferred to the crystal lattice on ultrafast time scales, it should be possible to quantitatively measure the resulting structural dynamics. The dynamics of the Einstein-de Haas effect have been previously considered in other contexts 16,17 .…”

Magnetoelastic hybrid excitations in CeAuAl 3

“…Paramagnetic rare-earth intermetallics with weak ME coupling are particularly suited to resolve these questions, as both spin and orbital angular contributions generate the ME coupling, and the well-defined multiplet structure of the f shells makes the ME coupling tractable (18). For instance, formation of a vibronic bound state (VBS) between phonons and CEF excitations has been reported in normalCnormalenormalAnormall2 (19–22).…”