Tracking three-dimensional magnetization trajectories by the radiation damping feedback field for differential spin control

In solution magnetic resonance (MR), manipulating the spin system in real time is difficult to implement in part due to the challenge of measuring the longitudinal magnetization within the constraints of MR detection hardware. Here we exploit the dynamical frequency shift induced by the radiation damping feedback field to estimate the longitudinal magnetization of individual spin species in one-, two-, and three-component spin systems. The calculated longitudinal magnetization is found to be in excellent agreement with that measured through independent experiments. Targeting the goal of differential spin control, extensions of this approach to real-time tracking of magnetization trajectories are discussed.