Electric Quadrupole-Quadrupole Interaction in Cerium Ethyl Sulfate

Abstract

Electron paramagnetic resonance (EPR) of cerium ethyl sulfate (CeES) below 2\ifmmode^\circ\else\textdegree\fi{}K gives evidence of a large nondipolar interaction between nearest-neighbor cerium ions. Writing the spin Hamiltonian for the interaction of two spins ${S}_{i}$ and ${S}_{j}$ as ${\mathcal{H}}_{\mathrm{ij}}=({\ensuremath{\alpha}}_{\mathrm{ij}}+{A}_{\mathrm{ij}}){S}_{\mathrm{iz}}{S}_{\mathrm{jz}}+\frac{1}{2}({\ensuremath{\beta}}_{\mathrm{ij}}+{B}_{\mathrm{ij}})({S}_{i+}{S}_{j\ensuremath{-}}+{S}_{i\ensuremath{-}}{S}_{j+}),$ where ${\ensuremath{\alpha}}_{\mathrm{ij}}$ and ${\ensuremath{\beta}}_{\mathrm{ij}}$ are the known contributions from dipole-dipole interaction, the experiments suggest that ${A}_{\mathrm{ij}}=0.105\ifmmode\pm\else\textpm\fi{}0.003$ ${\mathrm{cm}}^{\ensuremath{-}1}$ and ${B}_{\mathrm{ij}}=0.073\ifmmode\pm\else\textpm\fi{}0.003$ ${\mathrm{cm}}^{\ensuremath{-}1}$. Although there is no proof, there are four pieces of evidence which strongly support the hypothesis that the interaction is due to electric quadrupole-quadrupole (QQ) interaction. Firstly, the order of magnitude of ${A}_{\mathrm{ij}}$ and ${B}_{\mathrm{ij}}$ are reasonable. Secondly, QQ interaction affords an explanation of the differences between the temperature dependence of the EPR spectra of diluted and undiluted CeES. Thirdly, the spectra of rare-earth impurities in CeES, and fourthly, the spectra of pairs of interacting cerium ions in dilute specimens, are consistent with QQ interaction. Finally, it is shown that superexchange and exchange of virtual phonons probably contribute very little to the observed interaction.