High-field NMR study of field-induced states in Pb(TiO)Cu${}_4$(PO${}_4$)${}_4$

The square cupola antiferromagnet Pb(TiO)Cu${}_4$(PO${}_4$)${}_4$ 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 Pb(TiO)Cu${}_4$(PO${}_4$)${}_4$, 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.