All diffraction data were analyzed using the Rietveld package FullProf Suite (50). The structural refinements for the REBaCuFeO5 series were carried out by combining both HRPT and D2B datasets recorded at RT and 10 K. For YBa1−xSrxCuFeO5 samples, HRPT data recorded at RT and 10 K were used for the fits of the crystal structure (fig. S6). The magnetic refinements were performed on DMC data recorded at 10 K by fixing the structural parameters as determined from the refinements of the HRPT and D2B patterns (fig. S5). We used the noncentrosymmetric space group P4mm for the description of the crystal structure. The choice was motivated by the fact that, contrary to the centrosymmetric space group P4/mmm, P4mm enables the refinement of the occupation of the split Cu and Fe sites.

The Cu/Fe disorder was described by splitting the atomic position (1/2, 1/2, z) inside the two pyramidal sites of the unit cell, as shown in tables S2 and S3. In the fully disordered case, both positions are equally occupied in all pyramids (i.e., nFe = nCu = 50%), whereas full Cu/Fe order corresponds to nCu = 100% and nFe = 0 (or nCu = 0 and nFe = 100%). As shown in tables S2 and S3, the samples investigated in this work are very close to the first scenario, i.e., of |nCunFe| very close to zero. Note that Rietveld fits are not sensible to occupational correlations. The Cu/Fe disorder is thus assumed to be random, and the refined nCu and nFe values represent the average values over the full sample.

Anisotropic Debye-Waller factors were used for all atoms with the exception of Y/RE (nearly isotropic) [see (21)], Cu, and Fe. The z coordinates of the two basal oxygen sites O2 and O2′ were refined separately, but their mean-square displacements were restricted to have the same value (tables S2 and S3). No signature of interstitial oxygen at the (1/2, 1/2, z) atomic position could be observed, indicating that deviations from the sample’s formula stoichiometry, if any, were within the detection limit of PND in all the samples investigated. For the YBa1−xSrxCuFeO5 sample with x = 0.5, we could not find any evidence of alternating Ba/Sr layers, recently predicted for x ≥ 0.5 (26) and easy to identify because of the associated doubling of the c lattice parameter.

The collinear and spiral magnetic structures were described according to the models reported in (18). The best fits obtained at 10 K for all samples are shown in fig. S5. The ratio between the Fe3+(3d5 HS) and Cu2+(3d9) magnetic moments was restricted to be the same as their free-ion, spin-only values (5:1). In the temperature regions where the collinear and spiral phases coexist, the Fe and Cu magnetic moments were restricted to have the same value and the same inclination with respect to the ab plane in the two magnetic phases.

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