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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>>Ω_R), the frequency components of the Rabi oscillation do not depend on J, rather they are determined by the relation between Ω_R and D. We derive analytical expressions for the frequencies and the intensities of all three Rabi oscillation components as functions of Ω_R/D and δ/D, where δis detuning of the driving ac field from the Larmor frequency. When Ω_R>>D, the two lower frequencies approach s=Ω_R, while the upper line approaches s=2Ω_R. Disorder of the local Larmor frequencies leads to a Gaussian broadening of the spectral lines. We calculate corresponding widths for different Ω_R/D and δ/D. Unexpectedly, we find that one of the frequency components exhibits an unusual evolution with Ω_R: its frequency decreases with Ω_R at Ω_R<D. Upon further increase of Ω_R this frequency then passes through a minimum and, eventually, approaches s=Ω_R. Nonmonotonic behavior of the frequencies is accompanied by nonmonotonic behavior of the respective oscillation intensity.