Nuclear Dipole Field Quenching of Integer Spins

Abstract

For magnetic dipole-dipole coupling among integer nuclear spins in an asymmetric electric field gradient, the coupling is partially reduced by the asymmetry, and the coupling between integer spins and any nonresonant spins is highly reduced in first order. This "spin-quenching" mechanism is analogous to the quenching of electron orbital angular momentum of paramagnetic ions by low-symmetry crystal fields. These reductions in coupling are demonstrated by an examination of expectation values for the dipole-moment operator and, more formally, by calculating the Van Vleck second moment for a collection of identical spins $I=1\mathrm{}$ in both axially symmetric and non-axially symmetric electric field gradients, with and without applied magnetic fields. The contribution to the second moment of an unlike set of half-integer spins by spins $I=1\mathrm{}$, and its converse, is calculated as a function of applied magnetic field. The normal Van Vleck result is obtained, except that it is multiplied by a factor $\frac{z^2}{(1+z^2)}$, where $z$ is proportional to the applied magnetic field, and is inversely proportional to the amount of asymmetry. The quenching effect is confirmed from ${\mathrm{Cl}}^{35}$ spin-echo double-resonance measurements of BaCl${\mathrm{O}}_3$·${\mathrm{D}}_2$O, where the deuterium spins have $I=1\mathrm{}$, and couple to the ${\mathrm{Cl}}^{35}$ spins which serve as a probe to measure the interspecies coupling.