Two-phonon spin-lattice relaxation of rigid atomic clusters

Spin-phonon relaxation due to two-phonon processes of a spin cluster embedded in an elastic medium has been studied. For the case of uniaxial anisotropy, relaxation rates due to Raman processes and processes involving the emission of two phonons have been obtained. For a biaxial spin Hamiltonian, the rates of transitions between tunnel-split levels have been computed. By comparison with the rates of corresponding direct processes, we have established temperature ranges where the Raman mechanism dominates over the one-phonon decay mechanism.

Figure 1

(Color online) Transition between adjacent spin-energy levels of Hamiltonian (23) mediated by Raman processes.

Figure 2

(Color online) Transition between the spin-energy levels of Hamiltonian (23) $m\to m+2$ due to Raman scattering.

Figure 3

(Color online) Transition between tunnel-split states due to Raman scattering.