Theory of nonlinear spin response: Rapid passage for very slow molecular reorientation

Abstract

Electron-spin-resonance (ESR) spectra, detected 90\ifmmode^\circ\else\textdegree\fi{} out of phase with respect to the Zeeman modulation and using a saturating microwave field, are sensitive to molecular motion several orders of magnitude slower than are ordinary ESR spectra observed in phase with the modulation. A comprehensive theory of electron magnetic resonance based on an extension of the stochastic Liouville equation, explicitly including the effects of electromagnetic radiation and Zeeman modulation fields, of Markoffian motion modulating the magnetic anisotropy, and of relaxation and Heisenberg spin exchange, is presented. The theory is quite general and capable of explaining a large body of "modulation effects" in both single- and double-resonance experiments. Application to $^{15}\mathrm{N}$-labeled nitroxides is studied in detail, and a number of experimental spectra for the model system 2,2,6,6-tetramethyl-4-piperidone-1-oxyl (TANONE) in supercooled sec -butylbenzene are presented for comparison with theoretical results. When the eigenfunctions of the time-independent Hamiltonian are used as a basis set for computing spin matrix elements, pseudosecular transitions (simultaneous electron and nuclear spin flips) are found to make an important contribution to the computed spectrum in the slow tumbling region. While the out-of-phase dispersion at the first harmonic of the Zeeman modulation and the out-of-phase absorption at the second harmonic are both sensitive to slow motion, arguments based on saturation and modulation behavior favor the former as the more sensitive; greater signal-to-noise sensitivity should in fact be possible than for the ordinary ESR signal for the study of very slowly tumbling molecules.