Multiple Quantum Transitions in Paramagnetic Resonance

Abstract

At high rf fields the normal paramagnetic resonance spectrum of ${\mathrm{Mn}}^{++}$ in cubic MgO is found to be modified by the appearance of additional absorption lines which occur at the frequencies: $\frac{({E}_{k}\ensuremath{-}{E}_{k\ensuremath{-}2})}{2h}$. These are interpreted as double quantum transitions ($\ensuremath{\Delta}M=2$) which occur between nearly equally spaced energy levels at high rf power. The transitions $M=\ensuremath{-}\frac{3}{2}\ensuremath{\rightarrow}+\frac{1}{2}$ and $M=\ensuremath{-}\frac{1}{2}\ensuremath{\rightarrow}\frac{3}{2}$ have been observed at both room and liquid nitrogen temperatures for a number of orientations of the crystal with respect to a dc magnetic field of 3400 oersteds. At 77\ifmmode^\circ\else\textdegree\fi{}K evidence of the triple quantum transitions $\ensuremath{-}\frac{1}{2}\ensuremath{\rightarrow}\frac{5}{2}$, $\ensuremath{-}\frac{5}{2}\ensuremath{\rightarrow}\frac{1}{2}$ was observed.Second order time-dependent perturbation theory yields a formula for the ratio of the absorption intensity of the double quantum transition to the absorption intensity for a first order transition. The predicted ratio agrees with the experimentally observed ratio.