NUCLEAR MODULATION EFFECTS IN HIGH-SPIN ELECTRON-SYSTEMS WITH SMALL ZERO-FIELD SPLITTINGS

An analytic theory has been developed to simulate the nuclear modulations arising from the application of the two-pulse electron-spin-echo envelope modulation (ESEEM) technique to a high-spin-electron system with S = 5/2, coupled both to its own nuclear spin, I'= 5/2, and a distant nuclear spin, I = 1/2. This theory differs from that previously used by Mims [Electron Paramagnetic Resonance, edited by S. Geschwind (Plenum, New York, 1972), pp. 263-35 1] to describe the ESEEM results of a simpler system (S= 1/2, I= 1/2) by the inclusion of a zero-field splitting (ZFS) term in the spin Hamiltonian. The major assumption made in the derivation is that only transitions that do not share a common electron energy level are excited. This and other assumptions are discussed. The resulting analytic form suggests that each of the five possible single-quantum electron transitions in the S = 5/2 system make a contribution to the ESEEM spectrum. The contribution from each electron transition is similar to that described by Mims for the simpler system, i.e., two nuclear frequencies, a sum frequency and a difference frequency. The frequencies and intensities, however, differ from those predicted for the simpler spin system. The nuclear frequencies are shown to be a function of the particular electron transition excited by the microwave field. Whether or not a specific electron transition makes a contribution to the ESEEM spectrum is shown to be a function of the magnitudes and relative orientations of the ZFS and superhyperfine tensors. This results in an orientation selective property of the ESEEM experiment imparted by the anisotropy of the ZFS term. This is shown to affect the predicted powder-pattern-averaged spectra. Although there is a specific application to the case of Mn(II), the result is general and is applicable to all-electron high-spin systems with S greater-than-or-equal-to 1/2.