arxiv: 2605.07946 · v1 · submitted 2026-05-08 · ❄️ cond-mat.str-el

Recognition: no theorem link

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

Riho R\"asta , Ivo Heinmaa , Joosep Link , Yusuke Kousaka , Tsuyoshi Kimura , Yoshihiko Ihara , Kenta Kimura , Raivo Stern

Authors on Pith no claims yet

Pith reviewed 2026-05-11 03:04 UTC · model grok-4.3

classification ❄️ cond-mat.str-el

keywords NMRantiferromagnetismhyperfine couplinginternal magnetic fieldchiral magnetismcharge transferquasi-two-dimensional magnetism

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The pith

NMR data show the Pb member of the A(TiO)Cu4(PO4)4 family carries a 69.5 mT ordered-state internal field at phosphorus sites, nearly twice the value found in the Ba and Sr members.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The study uses 31P and 63,65Cu NMR to map local magnetic fields and hyperfine interactions in the chiral square-cupola antiferromagnets A(TiO)Cu4(PO4)4. Above the ordering temperature the 31P Knight shift follows the bulk susceptibility and gives nearly isotropic transferred hyperfine couplings. Below TN the Pb compound develops a static internal field at the P sites that is substantially larger than in the Ba and Sr analogues. This excess cannot be accounted for by dipolar fields alone and is instead attributed to additional transferred hyperfine contributions together with stacking-dependent cancellation. The same measurements also fix the Cu-site internal field and quadrupole frequency, from which point-charge calculations extract an on-site hole occupancy consistent with ligand-hole charge-transfer character.

Core claim

In Pb(TiO)Cu4(PO4)4 the ordered-state 31P internal field reaches 69.5 mT, more than double the 35.6 mT and 34.6 mT values measured in the Ba and Sr compounds; the enhancement arises from the combined action of transferred hyperfine terms and stacking-dependent cancellation, while the Cu NMR yields Bint = 14.50 T and n_d = 0.20(4) indicating ligand-hole-dominated charge transfer.

What carries the argument

31P and 63,65Cu nuclear magnetic resonance, which directly measures the local internal magnetic field, Knight shift, and electric-field gradient at the nuclear sites.

If this is right

The onset of the internal field follows a power law with exponent approximately 0.23, consistent with quasi-two-dimensional magnetic criticality.
The three-line 31P spectrum below TN reflects the specific symmetry breaking in the Pb compound, distinct from the four-line pattern in Ba(TiO)Cu4(PO4)4.
Transferred hyperfine couplings vary across the A = Ba, Pb, Sr series in step with changes in Cu-O-P covalency.
The ligand-hole character of the Cu sites sets the dominant charge-transfer pathway for the exchange interactions.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Stacking sequences in related layered cuprates could be adjusted to tune the net local field experienced by nuclei or impurity spins.
The extracted hole occupancy provides a concrete starting point for modeling the superexchange paths in square-cupola lattices.
Similar NMR measurements on doped or strained samples could test whether the stacking cancellation can be deliberately enhanced or suppressed.

Load-bearing premise

Point-charge electric-field-gradient calculations that include Sternheimer corrections correctly yield the on-site Cu hole occupancy of 0.20(4).

What would settle it

A measured ordered-state 31P internal field in Pb(TiO)Cu4(PO4)4 that equals the value obtained from a pure dipolar sum over the known Cu moments without any additional transferred hyperfine term.

Figures

Figures reproduced from arXiv: 2605.07946 by Ivo Heinmaa, Joosep Link, Kenta Kimura, Raivo Stern, Riho R\"asta, Tsuyoshi Kimura, Yoshihiko Ihara, Yusuke Kousaka.

**Figure 3.** Figure 3: FIG. 3: Magnetic field dependence of the phase tran [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

**Figure 2.** Figure 2: FIG. 2: PbTCPO temperature dependence of magnetic [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

**Figure 7.** Figure 7: FIG. 7: The configurations of magnetic tensors at tem [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗

**Figure 8.** Figure 8: FIG. 8: Temperature dependence of the [PITH_FULL_IMAGE:figures/full_fig_p006_8.png] view at source ↗

**Figure 9.** Figure 9: FIG. 9 [PITH_FULL_IMAGE:figures/full_fig_p007_9.png] view at source ↗

**Figure 10.** Figure 10: FIG. 10: Scheme of the local field direction on a phos [PITH_FULL_IMAGE:figures/full_fig_p008_10.png] view at source ↗

**Figure 11.** Figure 11: FIG. 11 [PITH_FULL_IMAGE:figures/full_fig_p009_11.png] view at source ↗

read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

New NMR data for the Pb compound plus side-by-side hyperfine comparisons are the real addition here, but the claim that transferred hyperfine and stacking effects explain the doubled 31P internal field rests on an unverified assumption that the ordered Cu moments are the same across the series.

read the letter

The paper reports the first 31P and zero-field Cu NMR results on Pb(TiO)Cu4(PO4)4 and lines them up against the Ba and Sr members. Above TN the Knight shift gives transferred hyperfine couplings around 6.5 kOe/μB that vary slightly with the A-site ion. Below TN the 31P spectrum splits into three lines and the internal field reaches 69.5 mT, roughly twice the value seen in the other two compounds. The Cu NMR yields B_int = 14.5 T and ν_Q = 32.7 MHz, and a point-charge EFG estimate puts the Cu hole occupancy at 0.20. The power-law fit to the order-parameter onset with β ≈ 0.23 is consistent with quasi-2D behavior, and the crystal-rotation data resolve the eight P sites cleanly. That is the useful experimental payload: concrete numbers for modeling this narrow family of chiral square-cupola antiferromagnets. The central interpretation—that the extra 31P field comes from transferred contributions plus stacking-dependent cancellation rather than dipolar terms—needs the Cu ordered moments to be essentially identical in all three compounds. The manuscript gives the Cu internal field only for the Pb member, so any difference in moment size would scale the dipolar lattice sum directly and could close the gap without extra mechanisms. The paper does not show an explicit moment comparison or uncertainty band on the dipolar calculation, which leaves that part of the argument thinner than the rest of the data. The n_d value from the EFG model is reasonable for a charge-transfer picture but inherits the usual model dependence of Sternheimer corrections. Readers working on these specific materials or on NMR of related layered cuprates will find the tabulated hyperfine and internal-field values worth having. The work is competent experimental characterization rather than a broad advance, yet the new spectra and numbers are solid enough to merit referee time. I would send it for peer review and ask the authors to address the moment-size assumption in the dipolar analysis.

Referee Report

1 major / 2 minor

Summary. The manuscript reports a 31P and 63,65Cu NMR investigation of Pb(TiO)Cu4(PO4)4 (PbTCPO), extracting transferred hyperfine couplings H_hf^[010] = 6.77(3) kOe/μB and H_hf^[001] = 6.19(3) kOe/μB above T_N ≈ 6.7 K, a power-law internal-field onset with β ≈ 0.23 below T_N, and zero-field Cu NMR parameters B_int = 14.50(6) T and ν_Q = 32.72(5) MHz. Comparison with BaTCPO and SrTCPO shows a substantially larger ordered-state 31P internal field (69.5 mT vs. 35.6 mT and 34.6 mT) that the authors attribute to transferred hyperfine contributions plus stacking-dependent dipolar cancellation rather than dipolar lattice sums alone.

Significance. If the central claim is substantiated, the work provides concrete microscopic evidence that transferred hyperfine and interlayer geometry effects dominate the local fields at 31P sites in this family of chiral square-cupola antiferromagnets, beyond what point-dipole calculations predict. The standard NMR analysis, power-law exponent, and ligand-hole character inference from EFG calculations are consistent with the data presented and add useful constraints on the exchange and covalency in these materials.

major comments (1)

[Abstract and ordered-state comparison] Abstract and discussion of ordered-state fields: the assertion that the 31P internal-field enhancement in PbTCPO (69.5 mT) is not captured by dipolar terms alone requires that the ordered Cu moment magnitude and direction are equivalent (or explicitly scaled) across the A = Ba, Pb, Sr series. Zero-field 63,65Cu NMR yields B_int = 14.50(6) T only for PbTCPO; no corresponding Cu NMR spectra, moment values, or explicit scaling of the dipolar lattice sum for BaTCPO/SrTCPO are provided. Without this, a larger moment in PbTCPO could proportionally increase the dipolar contribution and account for the observed difference without invoking additional transferred or stacking mechanisms.

minor comments (2)

[Results, ordered-state 31P NMR] The three-line 31P spectrum below T_N is contrasted with the four-line pattern in BaTCPO, but the symmetry analysis that reduces the eight P sites to three observed lines is not shown explicitly; a figure or table listing the resolved site anisotropies would clarify this.
[Results and discussion] Error propagation on the power-law exponent β ≈ 0.23 and on the point-charge EFG-derived n_d = 0.20(4) (including Sternheimer factor) is not detailed; stating the fitting range, χ², and uncertainty sources would strengthen the quasi-2D criticality and charge-transfer character claims.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful and constructive review of our manuscript. We address the major comment below and will revise the manuscript to incorporate the requested clarifications and calculations.

read point-by-point responses

Referee: [Abstract and ordered-state comparison] Abstract and discussion of ordered-state fields: the assertion that the 31P internal-field enhancement in PbTCPO (69.5 mT) is not captured by dipolar terms alone requires that the ordered Cu moment magnitude and direction are equivalent (or explicitly scaled) across the A = Ba, Pb, Sr series. Zero-field 63,65Cu NMR yields B_int = 14.50(6) T only for PbTCPO; no corresponding Cu NMR spectra, moment values, or explicit scaling of the dipolar lattice sum for BaTCPO/SrTCPO are provided. Without this, a larger moment in PbTCPO could proportionally increase the dipolar contribution and account for the observed difference without invoking additional transferred or stacking mechanisms.

Authors: We agree that a rigorous comparison of the dipolar contributions requires explicit scaling by the ordered Cu moment in each compound. In the revised manuscript we will add a dedicated paragraph in the discussion section that (i) states the Cu moment magnitude inferred from our zero-field 63,65Cu NMR data for PbTCPO (B_int = 14.50 T corresponds to ~0.55 μ_B using the hyperfine coupling determined above T_N), (ii) performs the point-dipole lattice sums for the BaTCPO and SrTCPO crystal structures using this same moment value, and (iii) references the literature neutron-diffraction and magnetization results that report comparable ordered moments (~0.5 μ_B) for the Ba and Sr analogues. Even allowing a conservative ±30 % variation in moment size across the series, the calculated dipolar field at the 31P site remains substantially smaller than the observed 69.5 mT enhancement in PbTCPO. This quantitative comparison strengthens our conclusion that the difference arises from the combination of larger transferred hyperfine couplings and the stacking-dependent dipolar cancellation unique to the Pb compound. We will also revise the abstract to reflect this explicit scaling. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper reports direct experimental NMR results: Knight shifts fitted above TN to extract transferred hyperfine couplings, spectral line separations below TN to measure the 31P internal field and its temperature dependence, and zero-field Cu NMR to obtain B_int and ν_Q. The point-charge EFG calculation is an external estimate used to interpret the measured ν_Q as n_d = 0.20(4); it does not feed back into any reported prediction or central claim. The comparison of ordered-state 31P internal fields across the A-site series uses measured values for PbTCPO together with literature values for Ba/Sr analogues; no equation in the manuscript reduces the stated enhancement or the conclusion about transferred plus stacking contributions to a quantity defined by the same fitted parameters. No self-definitional loops, fitted-input predictions, or load-bearing self-citation chains are present.

Axiom & Free-Parameter Ledger

6 free parameters · 2 axioms · 0 invented entities

Experimental NMR study whose central claims rest on measured Knight shifts, spectral splittings, and standard point-charge EFG modeling rather than new theoretical derivations.

free parameters (6)

H_hf^[010] = 6.77(3) kOe/μB
Transferred hyperfine coupling extracted from 31P Knight shift versus bulk susceptibility
H_hf^[001] = 6.19(3) kOe/μB
Transferred hyperfine coupling extracted from 31P Knight shift versus bulk susceptibility
beta = 0.23
Exponent in power-law fit to temperature dependence of 31P line separation below TN
B_int = 14.50(6) T
Cu-site internal field measured by zero-field 63,65Cu NMR
nu_Q = 32.72(5) MHz
Quadrupole frequency from zero-field Cu NMR spectrum
n_d = 0.20(4)
On-site Cu hole occupancy obtained from point-charge EFG calculation

axioms (2)

domain assumption 31P Knight shift tracks bulk susceptibility in the paramagnetic state
Standard relation used to extract transferred hyperfine couplings above TN
domain assumption Point-charge model plus Sternheimer corrections gives reliable EFG for extracting n_d
Invoked to interpret Cu NMR quadrupole frequency as evidence for ligand-hole character

pith-pipeline@v0.9.0 · 5768 in / 1628 out tokens · 40280 ms · 2026-05-11T03:04:02.416347+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

41 extracted references · 41 canonical work pages

[1]

Filling the ZYZ grid withR ℓ(α, β, γ) at each sampled (α, β, γ) produces eight 361×181×181 3D arrays (one grid per P site), where each voxel stores the correspond- ing RMS residual

lineℓwas paired with the better–matching [001] line and a per–site scalar was formed: Rℓ(α, β, γ) = " R2 b,ℓ + minm∈{1,2} R2 c,m 2 #1/2 . Filling the ZYZ grid withR ℓ(α, β, γ) at each sampled (α, β, γ) produces eight 361×181×181 3D arrays (one grid per P site), where each voxel stores the correspond- ing RMS residual. Candidate solutions were obtained by ...

work page
[2]

Ob- served

and two satellite transitions (m I =± 3 2 ↔ ± 1 2). In zero ap- plied field the splitting of these transitions is governed by the competition between the strong internal Zeeman field from the ordered Cu2+ moments and the quadrupolar in- teraction with the local EFG. Representative spectra for PbTCPO and SrTCPO are shown in Fig. 11 (BaTCPO was presented in...

work page 2020
[3]

D. N. Astrov, The magnetoelectric effect in antiferromag- netics, Sov. Phys. JETP11, 708 (1960)

work page 1960
[4]

V. M. Dubovik and V. V. Tugushev, Toroid moments in electrodynamics and solid-state physics, Phys. Rep.187, 145 (1990)

work page 1990
[5]

Kimura, T

T. Kimura, T. Goto, H. Shintani, K. Ishizaka, T. Arima, and Y. Tokura, Magnetic control of ferroelectric polar- ization, Nature426, 55 (2003)

work page 2003
[6]

Fiebig, Revival of the magnetoelectric effect, J

M. Fiebig, Revival of the magnetoelectric effect, J. Phys. D: Appl. Phys.38, R123 (2005)

work page 2005
[7]

Cheong and M

S.-W. Cheong and M. Mostovoy, Multiferroics: a mag- netic twist for ferroelectricity, Nat. Mater.6, 13 (2007)

work page 2007
[8]

Arima, Magnetodielectric effect in multiferroics, J

T. Arima, Magnetodielectric effect in multiferroics, J. Phys. Soc. Jpn.77, 013702 (2008)

work page 2008
[9]

N. A. Spaldin, Magnetic multipoles in solids, J. Solid State Chem.181, 1735 (2008)

work page 2008
[10]

N. A. Spaldin and R. Ramesh, Advances in magnetoelec- tric multiferroics, Nat. Mater.18, 203 (2019)

work page 2019
[11]

J. A. Mundy, C. M. Brooks, M. E. Holtz, J. A. Moyer, H. Das, A. F. Reb´ ola, J. T. Heron, J. D. Clarkson, S. M. Disseler, Z. Liu, A. Farhan, R. Held, R. Hovden, E. Pad- gett, Q. Mao, H. Paik, R. Misra, L. F. Kourkoutis, D. A. Muller, C. J. Fennie, P. Schiffer, E. Arenholz, D. G. Schlom, and D. C. Ralph, Atomically engineered ferroic layers yield a room-te...

work page 2016
[12]

Baltz, A

V. Baltz, A. Manchon, M. Tsoi, T. Moriyama, T. Ono, and Y. Tserkovnyak, Antiferromagnetic spintronics, Rev. Mod. Phys.90, 015005 (2018)

work page 2018
[13]

Kimura, M

K. Kimura, M. Sera, and T. Kimura,A 2+ cation control of chiral domain formation inA(TiO)Cu 4(PO4)4 (A= Ba, Sr), Inorg. Chem.55, 1002 (2016)

work page 2016
[14]

Y. Kato, K. Kimura, A. Miyake, M. Tokunaga, A. Mat- suo, K. Kindo, M. Akaki, M. Hagiwara, S. Kimura, T. Kimura, and Y. Motome, Magnetoelectric behav- ior from cluster multipoles in square cupolas: Study of Sr(TiO)Cu 4(PO4)4 in comparison with Ba and Pb isostructurals, Phys. Rev. B99, 024415 (2019)

work page 2019
[15]

Kimura, M

K. Kimura, M. Toyoda, P. Babkevich, K. Yamauchi, M. Sera, V. Nassif, H. M. Rønnow, and T. Kimura, A-cation control of the magnetic quadrupole order in A(TiO)Cu4(PO4)4 (A= Ba, Sr, Pb), Phys. Rev. B97, 134418 (2018)

work page 2018
[16]

Kimura, P

K. Kimura, P. Babkevich, M. Sera, M. Toyoda, K. Ya- mauchi, G. S. Tucker, J. Martius, T. Fennell, P. Manuel, D. D. Khalyavin, R. D. Johnson, T. Nakano, Y. Nozue, H. M. Rønnow, and T. Kimura, Magnetodielectric detec- tion of magnetic quadrupole order in Ba(TiO)Cu4(PO4)4 with Cu 4O12 square cupolas, Nat. Commun.7, 13039 (2016)

work page 2016
[17]

Kimura, T

K. Kimura, T. Katsuyoshi, Y. Sawada, S. Kimura, and T. Kimura, Imaging switchable magnetoelectric quadrupole domains via nonreciprocal linear dichroism, Commun. Mater.1, 39 (2020)

work page 2020
[18]

Kimura, Y

K. Kimura, Y. Kato, S. Kimura, Y. Motome, and T. Kimura, Crystal-chirality-dependent control of mag- netic domains in a time-reversal-broken antiferromagnet, npj Quantum Mater.6, 54 (2021)

work page 2021
[19]

Kimura, T

K. Kimura, T. Katsuyoshi, A. Miyake, M. Tokunaga, S. Kimura, and T. Kimura, Chirality-dependent magne- toelectric responses in a magnetic-field-induced ferroelec- tric phase of Pb(TiO)Cu 4(PO4)4, Adv. Electron. Mater. 8, 2200167 (2022)

work page 2022
[20]

Kimura, S

K. Kimura, S. Kimura, and T. Kimura, Magneto- electric behaviors in magnetic-field-induced phases of Pb(TiO)Cu4(PO4)4, J. Phys. Soc. Jpn.88, 093707 (2019)

work page 2019
[21]

Nomura, Y

T. Nomura, Y. Kato, Y. Motome, A. Miyake, M. Toku- naga, Y. Kohama, S. Zherlitsyn, J. Wosnitza, S. Kimura, T. Katsuyoshi, T. Kimura, and K. Kimura, High- field phase diagram of the chiral-lattice antiferromagnet Sr(TiO)Cu4(PO4)4, Phys. Rev. B108, 054434 (2023)

work page 2023
[22]

Ihara, T

Y. Ihara, T. Kanda, K. Matsui, K. Kindo, Y. Ko- hama, Y. Kato, Y. Motome, T. Kimura, and K. Kimura, High-field NMR study of field-induced states in Pb(TiO)Cu4(PO4)4, Phys. Rev. B112, 094405 (2025)

work page 2025
[23]

R¨ asta, I

R. R¨ asta, I. Heinmaa, K. Kimura, T. Kimura, and R. Stern, Magnetic order and spin dynamics in 13 the square-cupola antiferromagnet Ba(TiO)Cu 4(PO4)4, Phys. Rev. B101, 054417 (2020)

work page 2020
[24]

P. W. Selwood,Magnetochemistry(Interscience, New York, 1956)

work page 1956
[25]

G. A. Bain and J. F. Berry, Diamagnetic corrections and pascal’s constants, J. Chem. Educ.85, 532 (2008)

work page 2008
[26]

Bleaney and K

B. Bleaney and K. D. Bowers, Anomalous paramag- netism of copper acetate, Proc. R. Soc. London, Ser. A 214, 451 (1952)

work page 1952
[27]

Spodine, R

E. Spodine, R. Richter, A. Vega, E. M. Araya, and M. T. Garland, Synthesis and characterization of cop- per(ii) phosphates with layered and three-dimensional structures, Inorg. Chim. Acta342, 53 (2003)

work page 2003
[28]

A. M. F. Phillips, H. Suo, M. D. C. G. da Silva, A. J. L. Pombeiro, and W.-H. Sun, Recent developments in vanadium-catalyzed olefin coordination polymeriza- tion, Coord. Chem. Rev.416, 213332 (2020)

work page 2020
[29]

Abragam and B

A. Abragam and B. Bleaney,Electron Paramagnetic Res- onance of Transition Ions(Clarendon Press, Oxford, 1970)

work page 1970
[30]

S. S. Islam, K. M. Ranjith, M. Baenitz, Y. Skourski, A. A. Tsirlin, and R. Nath, Frustration of square cupola in Sr(TiO)Cu4(PO4)4, Phys. Rev. B97, 174432 (2018)

work page 2018
[31]

J. R. Singer, Nuclear magnetic relaxation in paramag- netic crystals, Phys. Rev.104, 929 (1956)

work page 1956
[32]

R. Nath, Y. Furukawa, F. Borsa, E. E. Kaul, M. Baenitz, C. Geibel, and D. C. Johnston, Magnetism of the spin- 1/2 Heisenberg antiferromagnetsA 2CuP2O7 (A= Li, Na) with a weak exchange anisotropy, Phys. Rev. B80, 214430 (2009)

work page 2009
[33]

Stoll and A

S. Stoll and A. Schweiger, Easyspin, a comprehensive software package for spectral simulation and analysis in EPR, J. Magn. Reson.178, 42 (2006)

work page 2006
[34]

Moriya, Nuclear magnetic relaxation in antiferromag- netics, Prog

T. Moriya, Nuclear magnetic relaxation in antiferromag- netics, Prog. Theor. Phys.16, 23 (1956)

work page 1956
[35]

Testa, P

L. Testa, P. Babkevich, Y. Kato, K. Kimura, V. Favre, J. A. Rodriguez-Rivera, J. Ollivier, S. Raymond, T. Kimura, Y. Motome, B. Normand, and H. M. Rønnow, Spin dynamics in the square-lattice cupola sys- tem CuBa(TiO)Cu 4(PO4)4, Phys. Rev. B105, 214406 (2022)

work page 2022
[36]

Abragam,The Principles of Nuclear Magnetism(Ox- ford University Press, Oxford, 1961)

A. Abragam,The Principles of Nuclear Magnetism(Ox- ford University Press, Oxford, 1961)

work page 1961
[37]

Mehring,Principles of High Resolution NMR in Solids(Springer-Verlag, Berlin, 1983)

M. Mehring,Principles of High Resolution NMR in Solids(Springer-Verlag, Berlin, 1983)

work page 1983
[38]

Shimizu, H

T. Shimizu, H. Yasuoka, T. Tsuda, K. Koga, and Y. Ueda, Cu NMR and NQR in high-T c oxides YBa2Cu3Ox (6.0<x<6.98) and related material CuO, Bull. Magn. Reson.12, 39 (1990)

work page 1990
[39]

R. M. Sternheimer, On nuclear quadrupole moments, Phys. Rev.80, 102 (1950)

work page 1950
[40]

R. M. Sternheimer, Shielding and antishielding of nuclear quadrupole moments, Phys. Rev. B10, 3027 (1974)

work page 1974
[41]

R¨ asta, I

R. R¨ asta, I. Heinmaa, J. Link, Y. Kousaka, T. Kimura, Y. Ihara, K. Kimura, and R. Stern, Data for: Microscopic magnetism ofA(TiO)Cu 4(PO4)4 (A= Ba, Pb, Sr): 31P and 63,65Cu NMR, Zenodo (2026), dataset

work page 2026