Effects of Radiation Damping on Spin Dynamics

When a two-state quantum system, capable of making radiative transitions, is driven by a high-frequency field, there occur damping effects due to the reaction of the sample to its own radiated field. This damping, which becomes important for high-Q rf structures and for samples of large dc susceptibilities, is here analyzed classically for a simple prototype system—a magnetic spin system obeying the Bloch equations. These equations are augmented to include the radiation-damping torques and are then solved for the four cases of usual interest. Firstly, for steady-state slow passage, radiation damping broadens and lowers the absorption and dispersion signals. Secondly, for adiabatic fast passage, damping causes the dispersion signal to dip at the line center and causes the otherwise absent absorption signal to become finite. However, if the radiation damping field becomes larger than the rf driving field a complete adiabatic inversion is shown to be no longer possible. Thirdly, the conditions for the occurrence of delayed power peaks of the free-precession signal are discussed. Fourthly, for the case of the driven nonsteady state, the stimulated emission may, for large radiation damping, become quite large if the system is driven from an initially ``negative temperature'' condition.