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Phonon-assisted spin diffusion in solids
Authors:Dolinsek   Cereghetti   Kind
Affiliation:a J. Stefan Institute, Jamova 39, SI-1000, Ljubljana, Slovenia;Institute of Quantum Electronics, ETH-Hönggerberg, CH-8093, Zürich, Switzerlandf1
Abstract:The spin flip-flop transition rate is calculated for the case of spectral spin diffusion within a system of dipolarly coupled spins in a solid where the lattice vibrations are present. Long-wavelength acoustic phonons time-modulate the interspin distance rij and enhance the transition rate via the change of the 1/r3ij term in the coupling dipolar Hamiltonian. The phonon-assisted spin diffusion rate is calculated by the golden rule in the Debye approximation of the phonon density of states. The coupling of the spins to the phonons introduces temperature dependence into the transition rate, in contrast to the spin diffusion in a rigid lattice, where the rate is temperature-independent. The direct (one-phonon absorption or emission) processes introduce a linear temperature dependence into the rate at temperatures not too close to T = 0. Two-phonon processes introduce a more complicated temperature dependence that again becomes simple analytical for temperatures higher than the Debye temperature, where the rate is proportional to T2, and in the limit T → 0, where the rate varies as T7. Raman processes (one-phonon absorption and another phonon emission) dominate by far the phonon-assisted spin flip-flop transitions.
Keywords:phonons   spin diffusion   nuclear magnetic resonance
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