Electron-Spin-Echo Envelope Modulation

Abstract

If an electron-spin moment is reoriented by a pulse of microwave power at magnetic resonance in a time short compared to the Larmor periods of neighboring nuclear moments in a solid, the nuclei suffer non-adiabatic changes in local dipolar field produced by the electron spin. After the pulse, a given nucleus will precess about a new axis of quantization which is appreciably tilted from its original axis if the electron dipolar field at the nuclear site has an appreciable component perpendicular to an applied external magnetic field. Consequently, a coherent oscillating nuclear dipolar field at the electron site modulates the electron Larmor frequency at the lower nuclear resonance frequencies of the nuclear neighbor. The depth of the beat modulation, as it affects the electron free-precession signal, is determined by the magnitude of electron-nuclear magnetic coupling and the extent to which the new axis of nuclear quantization is tilted from its original axis after the microwave pulse. The electron free-precession beats are measured conveniently in terms of the electron-spin-echo envelope modulation pattern obtained from the two-pulse echo experiment. The theory of the effect is developed for purely magnetically coupled nuclei and is confirmed by electron-spin-echo measurements of paramagnetic ${\mathrm{Ce}}^{3+}$ in CaW${\mathrm{O}}_{4}$, where the 14%-abundant ${\mathrm{W}}^{183}$ nuclear isotope is coupled to ${\mathrm{Ce}}^{3+}$. The electron-nuclear ligand tensor dipole-dipole interaction is estimated from experiment to be as much as four times greater than that expected from the point dipole-dipole interaction, and the ligand hyperfine interaction appears to be small.