Microscopic magnetism of A ( TiO ) Cu 4 ( PO 4 ) 4 ( A = Ba, Pb, Sr): P 31 and Cu 63 , 65 NMR study

We report a comprehensive NMR study of the chiral square-cupola antiferromagnet Pb ( TiO ) Cu 4 ( PO 4 ) 4 and compare its microscopic hyperfine and local-field parameters with the Ba/Sr analogs in the A ( TiO ) Cu 4 ( PO 4 ) 4 family. Above T N ≃ 6.7 K , the P 31 Knight shift tracks the bulk susceptibility and yields nearly isotropic transferred hyperfine couplings H hf [ 010 ] = 6.77 ( 3 ) and H hf [ 001 ] = 6.19 ( 3 ) kOe/ μ B . Below T N , the frequency-swept P 31 spectrum splits into three lines, in contrast to the four-line pattern reported for BaTCPO. The line separation tracks the onset of the static P 31 internal field with a power-law exponent β ≃ 0.23 , consistent with quasi-two-dimensional criticality. Crystal-rotation P 31 NMR in the ordered state resolves all eight symmetry-related P sites and their site-dependent anisotropy. In the ordered state, zero-field Cu 63 , 65 NMR gives a Cu-site internal field B int = 14.50 ( 6 ) T and a quadrupole frequency ν Q = 32.72 ( 5 ) MHz , while point-charge electric-field-gradient calculations including Sternheimer corrections yield an on-site Cu hole occupancy n d = 0.20