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.

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