Microscopic Magnetism of A(TiO)Cu4(PO4)4 (A = Ba, Pb, Sr): 31P and 63,65Cu NMR Study

TL;DR

This NMR study investigates the microscopic magnetic properties of Pb(TiO)Cu4(PO4)4, comparing it with Ba and Sr analogues, revealing differences in hyperfine interactions and internal fields related to local covalency and stacking effects.

Contribution

The paper provides detailed NMR analysis of the A(TiO)Cu4(PO4)4 family, highlighting how hyperfine couplings and internal fields vary across different A-site cations, and elucidates the microscopic origins of these differences.

Findings

Above T_N, the Knight shift correlates with susceptibility and hyperfine couplings.

Below T_N, the spectrum splits into three lines, indicating static internal fields.

PbTCPO exhibits a higher internal field than BaTCPO and SrTCPO, influenced by transferred hyperfine effects.

Abstract

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 analogues in the $A$(TiO)Cu$_4$(PO$_4$)$_4$ family. Above $T_{\rm N}\simeq 6.7$ K, the $^{31}$P Knight shift tracks the bulk susceptibility and yields nearly isotropic transferred hyperfine couplings $H_{\rm hf}^{[010]}=6.77(3)$ and $H_{\rm hf}^{[001]}=6.19(3)$ kOe/$\mu_{\rm B}$. Below $T_{\rm N}$, the frequency-swept $^{31}$P spectrum splits into three lines, in contrast to the four-line pattern reported for BaTCPO. The line separation tracks the onset of the static $^{31}$P internal field with a power-law exponent $\beta\simeq 0.23$, consistent with quasi-two-dimensional criticality. Crystal-rotation $^{31}$P NMR in the ordered state resolves all eight symmetry-related P sites and their site-dependent anisotropy. In the ordered state, zero-field $^{63,65}$Cu NMR gives a Cu-site internal field $B_{\rm int}=14.50(6)$ T and a quadrupole frequency $\nu_Q=32.72(5)$ MHz, while point-charge electric-field-gradient calculations including Sternheimer corrections yield an on-site Cu hole occupancy $n_d=0.20(4)$, consistent with a ligand-hole-dominated charge-transfer character. Comparing PbTCPO with BaTCPO and SrTCPO, we find that the transferred hyperfine coupling $H_{\rm hf}$ varies across the series, reflecting changes in local Cu-O-P covalency, whereas the ordered-state $^{31}$P internal field in PbTCPO is $69.5$ mT, considerably higher than in BaTCPO ($35.6$ mT) and SrTCPO ($34.6$ mT). This enhancement is not captured by dipolar terms alone and points to the combined effects of transferred contributions and stacking-dependent cancellation.