Analytical description of spin-Rabi oscillation controlled electronic transitions rates between weakly coupled pairs of paramagnetic states with S=1/2

TL;DR

This paper provides an analytical framework for understanding how spin-Rabi oscillations influence electronic transition rates in weakly coupled paramagnetic pairs, revealing the evolution of Rabi spectra with increasing driving field and disorder effects.

Contribution

It introduces an analytical model describing the Rabi spectrum evolution and peak shapes for spin-dependent transitions in paramagnetic pairs under varying conditions.

Findings

Rabi spectrum evolves from one to three peaks with increasing B_1

Peak widths scale as δ_0^2/Ω_R when peaks are well-developed

Crossover occurs when Ω_R exceeds the Zeeman energy difference expectation value

Abstract

We report on an analytical description of spin-dependent electronic transition rates which are controlled by a radiation induced spin-Rabi oscillation of weakly spin-exchange and spin-dipolar coupled paramagnetic states (S=1/2). The oscillation components (the Fourier content) of the net transition rates within spin-pair ensembles are derived for randomly distributed spin resonances with account of a possible correlation between the two distributions that correspond to the two individual pair partners. The results presented here show that when electrically or optically detected Rabi spectroscopy is conducted under an increasing driving field B_ 1, the Rabi spectrum evolves from a single resonance peak at s=\Omega_R, where \Omega_R=\gamma B_1 is the Rabi frequency (\gamma is the gyromagnetic ratio), to three peaks at s= \Omega_R, s=2\Omega_R, and at low s<< \Omega_R. The crossover between the two regimes takes place when \Omega_R exceeds the expectation value \delta_0 of the difference of the Zeeman energies within the pairs, which corresponds to the broadening of the magnetic resonance lines in the presence of disorder caused by hyperfine field or distributions of Lande g-factors. We capture this crossover by analytically calculating the shapes of all three peaks at arbitrary relation between \Omega_R and \delta_0. When the peaks are well-developed their widths are \Delta s ~ \delta_0^2/\Omega_R.