  Experimental determination of the magnetic moment of the Cooper pairs can
shed light on the pairing symmetry in cuprates. We argue that the intrinsic
magnetic moments of the Cooper pairs can be detected in experiments with
superconducting thin-film rings. At sufficiently low temperatures the magnetic
field generated by the supercurrent, can cause the ordering of these magnetic
moments that produces changes in the supercurrent and magnetic induction
distributions, the heat capacity and magnetic moment of the ring. It is shown
that the intrinsic magnetic moment of the Cooper pairs can be extracted from
low-temperature behaviours of these measurable quantities of the
current-carrying rings made of the cuprate superconductors.
