Dipolar order under fast magic-angle spinning

The thermodynamics of systems of nuclear spins coupled by dipolar interactions is investigated under fast magic-angle spinning. It is shown experimentally and theoretically that, although the two-spin quasi-invariant – the dipolar Hamiltonian – is averaged out, a dipolar quasi-invariant exists, resulting from `three-spinʹ terms in the series development of the effective Hamiltonian which rules the spin system evolution. The related nuclear spin order, here called the pseudo-dipolar order, is studied as well as its saturation by the sample rotation and its thermal mixing with the Zeeman order by weak radio-frequency irradiation.