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

TL;DR

This theoretical study analyzes the spectrum of spin-dependent transition rates in dipolar and exchange coupled spin pairs during magnetic resonance, revealing complex frequency behaviors and broadening effects.

Contribution

It provides analytical expressions for Rabi oscillation components in coupled spins, highlighting the influence of exchange, dipolar interactions, and detuning on the spectral features.

Findings

Three frequency components in Rabi oscillations with specific dependencies

Nonmonotonic evolution of frequency components with Rabi frequency

Gaussian broadening of spectral lines due to disorder

Abstract

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.