Conservation of the total angular momentum, spin + mechanical, requires coupling between mechanical rotation of a body and magnetic moments inside the body, known as the Einstein – de Haas effect. Microscopic mechanisms of this effect vary for different systems. Motion of domain walls dominates the magneto-mechanical coupling in microcantilevers [1,2]. Spins provide universal damping mechanism for the mechanical motion of a nanocantilever [3]. Non-trivial quantum mechanics of the angular momentum exists in magnetic molecules that have full or partial mechanical freedom [4]. Coupled quantum dynamics of a spin and a mechanical resonator explains recent experiments with single magnetic molecules grafted onto a carbon nanotube [5]. The concept of the phonon spin becomes useful in the analysis of the conservation of angular momentum in spin-phonon processes [6]. A solid containing two-state systems, magnetic molecules in particular, may exhibit measurable forces of quantum origin [7]. Spin mechanics problems of practical interest include switching of the magnetic moment in a nanoresonator by the combined effect of the spin-polarized current and mechanical kick [8], possibility of the electromechanical magnetization switching in multiferroics [9], and switching of the magnetization by surface acoustic waves [10]. This research has been supported by grants from the U.S. National Science Foundation.

References: [1] R. Jaafar, E. M. Chudnovsky, and D. A. Garanin, Dynamics of Einstein - de Haas Effect: Application to Magnetic Cantilever, Phys. Rev. B 79, 104410 (2009). [2] S-H. Lim, A. Imtiaz, T. M. Wallis, S. Russek, P. Kabos, L. Cai, and E. M. Chudnovsky, Magneto-Mechanical Investigation of Spin Dynamics in Magnetic Multilayers, Europhys. Lett. 105, 37009 (2014). [3] E. M. Chudnovsky and D. A. Garanin, Damping of a Nanocantilever by Paramagnetic Spins, Phys. Rev. B 89, 174420 (2014). [4] E. M. Chudnovsky, Spin Tunneling in Magnetic Molecules that Have Full or Partial Mechanical Freedom (Ch. 3 in “Molecular Magnets: Physics and Applications”, Springer 2014). [5] M. F. O’Keeffe, E. M. Chudnovsky, and D. A. Garanin, Landau-Zener Dynamics of a Nanoresonator Containing a Tunneling Spin, Phys. Rev. B 87, 174418 (2013). [6] D. A. Garanin and E. M. Chudnovsky, Angular Momentum in Spin-Phonon Processes, Phys. Rev. B 92, 024421 (2015). [7] E. M. Chudnovsky, J. Tejada, and R. Zarzuela, Quantum Forces in Solids with Two-State Systems: An Example of a Molecular Magnet, Phys. Rev. B 88, 220409(R) (2013). [8] L. Cai, R. Jaafar, and E. M. Chudnovsky, Mechanically-Assisted Current-Induced Switching of the Magnetic Moment in a Torsional Oscillator, Phys. Rev. Appl. 1, 054001 (2014). [9] E. M. Chudnovsky and R. Jaafar, Electromechanical Magnetization Switching, J. Appl. Phys. 117, 103910 (2015). [10] E. M. Chudnovsky and R. Jaafar, Magnetization Reversal by Surface Acoustic Waves, to be published.