The square cupola antiferromagnet $\mathrm{Pb}\left(\mathrm{TiO}\right){\mathrm{Cu}}_4{\left({\mathrm{PO}}_4\right)}_4$ exhibits the intriguing magnetoelectric responses arising from the consecutive change in the magnetic quadrupolar-type configuration of magnetic moments under external magnetic fields higher than 15 T. To clarify the high-field magnetic structures in $\mathrm{Pb}\left(\mathrm{TiO}\right){\mathrm{Cu}}_4{\left({\mathrm{PO}}_4\right)}_4$, an NMR measurement was performed in pulsed fields up to 32.2 T significantly extending the field range accessible by superconducting magnets. The double-peak structure of NMR spectra emerging above 29 T applied along the [001] direction evidences the successive magnetic transitions. The field dependence of NMR spectra was analyzed on the basis of cluster mean-field theory, which allows us to propose possible magnetic structures for the high-field magnetic states.

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• High magnetic fields
• Magnetoelectric effect
• Antiferromagnets
• Multiferroics
• Nuclear magnetic resonance