Two-photon NMR on spins with I=1 in solids

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Abstract
The NMR excitation of the double quantum (DQ) transition of a spin system with I=1 in a solid by double-frequency irradiation fields is studied. The efficiency of the DQ excitation by the two irradiation fields applied simultaneously at the two sides of the single quantum frequency spectrum of this system is calculated. The theory of Shirley for periodical time-dependent Hamiltonians is extended to describe these NMR experiments. The two-photon character of the DQ excitation is discussed and the two-photon resonance conditions are derived. The effective rf irradiation intensity on the DQ transition is calculated to be ω1ω2{(ωQ−ωT)−1 +(ωQ+ωT)−1}, where ω1 and ω2 are the intensities of the two rf irradiation fields, 2ωT the frequency distance between these rf fields and ωQ the quadrupole frequency of the spin system. This result is valid for all ωQ values as long as ω1, ω2< ‖ ωQ−ωT ‖. Accurate computer calculations are performed to examine the exact time evolution of the density matrix of the spin systems. Experimental results from 2D-NMR measurements on an oriented single crystal of deuterated malonic acid are compared with the theory.

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