Nuclear ordering and superconductivity in lithium

Lithium metal constitutes a unique system of nuclear spins and conduction electrons, where the energy scales of the collective behavior among the two distinct, though interpenetrating, subsystems are of the same order of magnitude. We have demonstrated experimentally the onset of magnetic ordering of the nuclear spins in lithium below 0.3 μK in zero magnetic field as well as the transition to the superconducting state of electrons below 0.4 mK. So far, these two ordering phenomena have been observed only in different samples in different experimental arrangements due to the conflicting requirements of large polarizing magnetic field for one and careful magnetic shielding for the other. In this paper we consider the possibility to perform an experiment combining both aspects and discuss upon plausible outcome of such experiments.