Direct and two-phonon Orbach-Aminov type spin-lattice relaxation in molecular magnet V₁₅

In this article we propose a model of spin-phonon relaxation in K ₆[V^IV ₁₅As₆O₄₂(H ₂O)]-8H₂O, the so called V₁₅ cluster exhibiting the unique layered magnetic structure. The work is motivated by the recent observation of the Rabi oscillation [1] in this system and aimed to elucidate the role of spin-phonon interaction as a source of decoherence. The spin-phonon coupling is assumed to appear as a result of the modulation of the isotropic and antisymmetric (Dzyaloshinsky-Moriya) exchange interactions in the central triangular layer of vanadium ions by the acoustic lattice vibrations. The relaxation rates are estimated within the Debye model for the lattice vibrations. Within the pseudo-angular momentum representation the selection rules for the direct (one-phonon) transitions between Zeeman levels are derived and a special role of the antisymmetric exchange is underlined. The probabilities of the two-phonon Orbach-Aminov type processes are evaluated as well, while the Raman type relaxation is shown to have a negligible importance at low temperatures at which the Rabi oscillations have been detected.