Analytical study of spin-dependent transition rates within pairs of dipolar and strongly exchange coupled spins with (S = 1/2) during magnetic resonant excitation

We study theoretically the spectrum, F(s), of spin-dependent transition rates within dipolar D and exchange J coupled pairs of two spins with S=1/2 undergoing Rabi oscillations due to a coherent magnetic resonant excitation. We show that the Rabi oscillation controlled rates exhibit a spectrum with three frequency components. When exchange is stronger than the Rabi frequency (J>>\Omega_R), the frequency components of the Rabi oscillation do not depend on J, rather they are determined by the relation between \Omega_R and D. We derive analytical expressions for the frequencies and the intensities of all three Rabi oscillation components as functions of \Omega_R/D and \delta/D, where \delta is detuning of the driving ac field from the Larmor frequency. When \Omega_R>>D, the two lower frequencies approach s=\Omega_R, while the upper line approaches s=2\Omega_R. Disorder of the local Larmor frequencies leads to a Gaussian broadening of the spectral lines. We calculate corresponding widths for different \Omega_R/D and \delta/D. Unexpectedly, we find that one of the frequency components exhibits an unusual evolution with \Omega_R: its frequency decreases with \Omega_R at \Omega_R<D. Upon further increase of \Omega_R this frequency then passes through a minimum and, eventually, approaches s=\Omega_R. Nonmonotonic behavior of the frequencies is accompanied by nonmonotonic behavior of the respective oscillation intensity.