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[Andreas Dönni](https://orcid.org/0000-0002-7300-9175), Lukas Keller, Vladimir Y. Pomjakushin, [Naohito Tsujii](https://orcid.org/0000-0002-6181-5911), [Alexei A. Belik](https://orcid.org/0000-0001-9031-2355)

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[Magnetic Structures and Magnetic Phase Diagram of the Mixed-Valence Iron Phosphate Fe                    <sub>7</sub>                    (PO                    <sub>4</sub>                    )                    <sub>6</sub>](https://mdr.nims.go.jp/datasets/b7aa8342-7c69-48e6-9edd-6b6b6dd7e767)

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Magnetic Structures and Magnetic Phase Diagram of the Mixed-Valence Iron Phosphate Fe7(PO4)6Magnetic Structures and Magnetic Phase Diagram of the Mixed-Valence Iron Phosphate Fe7(PO4)6Andreas Dönni, Lukas Keller, Vladimir Y. Pomjakushin, Naohito Tsujii, and Alexei A. Belik*Cite This: Inorg. Chem. 2026, 65, 7418−7430 Read OnlineACCESS Metrics & More Article Recommendations *sı Supporting InformationABSTRACT: Mixed-valence iron compounds are fascinatingmaterials exemplified by ferrimagnetic Fe3O4, multiferroicLuFe2O4, and a pigment Fe4[Fe(CN)6]3. Mixed-valent iron(oxy)phosphates also provide a large variety of differentconnections between magnetic ions, which are responsible forcomplex magnetism. Fe7(PO4)6 (Fe32+Fe43+(PO4)6) has well-defined Fe2+ and Fe3+ sites and shows two antiferromagnetictransitions at TN1 = 47 K and TN2 = 16 K. Here, we investigatedmagnetic structures of Fe7(PO4)6 (at zero magnetic field) usingneutron powder diffraction and constructed a temperature−magnetic-field phase diagram. Below TN1, magnetic propagationvector is k1 = (1/2, 0, 1/2), and magnetic moments on Fe3+ sitesare nearly fully ordered; while moments on Fe2+ sites aresignificantly reduced. Below TN2, the second propagation vector appears k2 = (0, 1/2, 0) and coexists with k1; moments on Fe2+sites are fully ordered (at 2 K) reaching 4.5 μB suggesting noticeable spin−orbital contributions. Coexistence of two propagationvectors and triclinic symmetry results in variations of total magnetic moments on each site. Magnetic measurements up to 300 kOedetected one field-induced transition near 55.5 kOe. Data showed that TN1 is nearly magnetic-field independent up to 90 kOe, whilea more complex behavior was observed near TN2 at magnetic fields around 50 kOe.1. INTRODUCTIONMixed-valence (MV) compounds contain elements which arepresent in more than one (formal) oxidation state, usually intwo oxidation states.1−3 MV compounds are important inbiology, where they are responsible for photosynthesis andrespiration (a Fe2+/Fe3+ pair), physics, and chemistry.4 Ininorganic chemistry, mixed valency can produce veryimportant properties. For example, a deep blue widely usedpigment Fe4[Fe(CN)6]3 is a MV compound,5 high-TC coppersuperconductors are often MV compounds.6 MV compoundsare at the core of batteries.7 MV manganites produceferromagnetism and giant magnetoresistance properties.3,8Interestingly, in manganites prepared at high pressure, it issuggested that Mn can even be in three oxidation state of +2,+3, and +4, for example, in a perovskite-like Mn2O3,9(R1−xMnx)MnO3,10 and RMn3O6,11 where R is a rare-earthelement. The MV character of some minerals provides thebasis for their color. Mixed valency is often a prerequisite forhigh electrical conductivity in nonmetallic materials.Different phosphates and MV iron phosphates and oxy-phosphates also provide a large variety of different connectionsbetween magnetic ions, which are responsible for complexmagnetism.12,13 The MV iron phosphate Fe7(PO4)6(=Fe32+Fe43+(PO4)6) was first discovered in 1980.14 Itcrystallizes in the triclinic space group P1̅ (no. 2) andmagnetic iron ions (Fe12+, Fe22+, Fe33+, Fe43+) are located onfour different sites.14 The crystal structure is illustrated inFigure 1. The environment of the Fe2+ ions is octahedralFe1O6 and pyramidal Fe2O5. The ferric Fe3+ ions haveoctahedral Fe3O6 and Fe4O6 coordination. The Fe1O6,Fe2O5, Fe3O6 and Fe4O6 polyhedra form a three-dimensionalnetwork. There are zigzag chains propagating along (0, 1, −1)directions formed by edge-shared polyhedra, ···−Fe3O6−Fe3O6−Fe2O5−Fe4O6−Fe4O6−Fe2O5−Fe3O6−···(Figure1). These chains are linked with each other through the Fe1O6polyhedra by corner-shared connections Fe1O6−Fe2O5 andFe1O6−Fe3O6. In addition, the Fe3+ ions, Fe33+ and Fe43+,each form dimer units through the edge-shared polyhedraFe3O6−Fe3O6 as well as Fe4O6−Fe4O6.Some physical properties of Fe7(PO4)6 were investigatedlater.16−19 Even though it has well-defined Fe2+ and Fe3+ sitesfrom the structural analysis and Mössbauer spectroscopy andshows insulating properties, it has a deep black color similar toMV iron minerals, magnetite, Fe3O4,20 and ilvaite, Ca-Received: January 28, 2026Revised: March 17, 2026Accepted: March 20, 2026Published: March 26, 2026Articlepubs.acs.org/IC© 2026 The Authors. Published byAmerican Chemical Society7418https://doi.org/10.1021/acs.inorgchem.6c00534Inorg. Chem. 2026, 65, 7418−7430This article is licensed under CC-BY 4.0Downloaded via NATL INST FOR MATLS SCIENCE (NIMS) on April 6, 2026 at 07:52:04 (UTC).See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Andreas+Do%CC%88nni"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Lukas+Keller"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Vladimir+Y.+Pomjakushin"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Naohito+Tsujii"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Alexei+A.+Belik"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/showCitFormats?doi=10.1021/acs.inorgchem.6c00534&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?goto=articleMetrics&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?goto=recommendations&?ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?goto=supporting-info&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?fig=tgr1&ref=pdfhttps://pubs.acs.org/toc/inocaj/65/13?ref=pdfhttps://pubs.acs.org/toc/inocaj/65/13?ref=pdfhttps://pubs.acs.org/toc/inocaj/65/13?ref=pdfhttps://pubs.acs.org/toc/inocaj/65/13?ref=pdfpubs.acs.org/IC?ref=pdfhttps://pubs.acs.org?ref=pdfhttps://pubs.acs.org?ref=pdfhttps://doi.org/10.1021/acs.inorgchem.6c00534?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://pubs.acs.org/IC?ref=pdfhttps://pubs.acs.org/IC?ref=pdfhttps://creativecommons.org/licenses/by/4.0/(Fe2+,Fe3+)Fe3+Si2O7O(OH),21 suggesting some degree ofelectron transfer.The crystal structure type of Fe7(PO4)6 is quite adaptive asother phosphates,22−27 some vanadates (e.g., Cu3Fe4(VO4)6,NaCuFe2(VO4)3, LiCuFe2(VO4)3),28−32 molybdates (e.g.,Na2Zn5(MoO4)6),33 and arsenates (e.g., Fe7(AsO4)6 andMn7H4(AsO4)6)34−36 can crystallize in the same structuretype. The number of cations can vary from about 6.5 to 8 performular unit allowing, for example, applications in batteries27and Na-ion intercalation.18 Some phosphates are colorfulpigments,26 and LiCuFe2(VO4)3 shows multiferroic proper-ties.32 The structure can also contain hydrogen in the form ofO−H groups , for example , in Co7H4(PO4)6 ,3 7Mn7H4(PO4)6,36 Mn7H4(AsO4)6,36 Fe7H(PO4)6,38,39 andMg7H4(PO4)6.40In this work, we investigated the magnetic structures of theparent compound Fe7(PO4)6 using neutron powder diffraction.Fe7(PO4)6 shows two successive antiferromagnetic (AFM)transitions at TN1 = 47 K and TN2 = 16 K.18,19 The magneticpropagation vector k1 = (1/2, 0, 1/2) appears below TN1.There is a noncollinear AFM structure, where all orderedmoments (of the k1 component) lie inside one plane thatrotates around the c-direction near TN2. At T = 25 K, theordered moments are large on the Fe3+ sites (about 4 μB) andsignificantly reduced on the Fe2+ sites (less than 2 μB). BelowTN2, the magnetic structure has a second magnetic propagationvector k2 = (0, 1/2, 0) that coexists with k1. Below TN2,magnetic moments on the Fe2+ sites consist of a large k2 and asmall k1 component, whereas the moments on the Fe3+ siteshave a large k1 and a small k2 component. At the ground state,the coexistence of two propagation vectors (with k1 and k2components predominantly perpendicular to each other) andthe triclinic crystal symmetry results in variations of totalmagnetic moments on each site. At the lowest measuredtemperature of 2 K, all Fe moments are fully ordered. Magneticmoments on the Fe2+ sites reach about 4.5 μB�larger than thespin-only value of 4.0 μB�suggesting noticeable spin−orbitalcontributions. We also constructed a temperature-magneticfield phase diagram using temperature-dependent and field-dependent magnetization and specific heat measurements andmeasured magnetization up to 300 kOe.2. EXPERIMENTAL SECTIONSingle-phase black Fe7(PO4)6 was synthesized by a standard solid-state method from a stoichiometric mixture of FePO4 and Fe (99.9%)by annealing at 1173 K for 130 h as a pellet in an evacuated sealedquartz tube (to prevent the oxidation of Fe2+) with severalintermediate grindings. Single-phase yellow FePO4 was prepared bya standard solid-state method from a stoichiometric mixture of Fe2O3(99.999%) and NH4H2PO4 (99.9%) by annealing at 1073 K for 60 hin air with several intermediate grindings. Phase purity of thecompounds was confirmed through X-ray powder diffractionmeasurements using an Ultima-IV Rigaku diffractometer (with CuKα radiation).A large amount of Fe7(PO4)6 sample (about 6 g) was used toperform powder neutron diffraction experiments at the Paul ScherrerInstitute, Switzerland. The sample was mounted in a cylindricalvanadium(V) can and placed in a helium cryostat for temperature-dependent measurements. The crystal structure was measured in theparamagnetic state at T = 60 K on the high-resolution powderdiffractometer for thermal neutrons (HRPT)41 using an incidentneutron wavelength of λ = 1.886 Å. Data were collected for a 2θ rangeof 3.55°−164.50° and a step width of 0.05°. Data for the magneticstructure analysis were measured on the cold neutron diffractometerDMC using an incident neutron wavelength of λ = 4.507 Å. Data werecollected at 2, 25, and 60 K for a 2θ range of 5.0°−137.9° and a stepwidth of 0.1°. The temperature dependence was measured between 2and 80 K for cooling and heating cycles by ramping at a constant rateof 0.2 K/min. Neutron diffraction data were continuously collectedthroughout the temperature ramps, with data files written at 1 minintervals.The diffraction patterns were analyzed by the Rietveld methodusing the FullProf Suite.42 Possible models for the magnetic structureswere deducted based on a group theory analysis using the programsISODISTORT43,44 and BASIREPS in the FullProf Suite programpackage.42Magnetic properties were measured on a SQUID magnetometer(Quantum Design MPMS3, San Diego, CA, USA) in different appliedfields under both zero-field-cooled (ZFC) and field-cooled on cooling(FCC) conditions. Magnetic field dependence of magnetization wasmeasured at different temperatures between −70 and 70 kOe (orbetween 0 and 70 kOe). Isothermal magnetization curves were alsotaken at 1.7 K between 0 and 300 kOe using a (former) hybridFigure 1. Triclinic crystal structure of Fe7(PO4)6, where only FeOn polyhedra are shown and the phosphor (P) ions are omitted. The drawing wasmade using VESTA software.15Inorganic Chemistry pubs.acs.org/IC Articlehttps://doi.org/10.1021/acs.inorgchem.6c00534Inorg. Chem. 2026, 65, 7418−74307419https://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?fig=fig1&ref=pdfpubs.acs.org/IC?ref=pdfhttps://doi.org/10.1021/acs.inorgchem.6c00534?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asmagnet of National Institute for Materials Science (NIMS, Tsukuba,Japan). Specific heat, Cp, was measured during cooling at differentmagnetic fields using a pulse relaxation method with a commercialcalorimeter (Quantum Design PPMS, San Diego, CA, USA).3. RESULTS AND DISCUSSION3.1. Crystal Structure of Fe7(PO4)6The crystal structure of Fe7(PO4)6 at room temperature hasbeen reported based on single crystal14 and powder X-raydiffraction.16 We have determined the structural parameters ofparamagnetic Fe7(PO4)6 at T = 60 K by neutron diffraction.The refinement is shown in Figure 2 and the results aresummarized in Table 1. Calculated values for selected bondlengths and bond angles are given in Table S1 (Fe−Fe bondlengths, Fe−O−Fe bond angles), Table S2 (Fe−O bondlengths) and Table S3 (P−O bond lengths and O−P−O bondangles). During the refinement, atomic displacement param-eters were constrained to be the same for all Fe sites, all P sites,and all O sites. Bond-valence sum values (the note of Table1)45 support the oxidation state of +2 for the Fe1 and Fe2sites, and +3 for the Fe3 and Fe4 sites. The network of themagnetic Fe ions in the crystal structure is illustrated in Figure3 with Fe−Fe bond lengths indicated up to a distance of 3.6 Åbelow which the neighboring Fe−O polyhedra all share acommon edge or corner. As shown in Figure 3, the shortestFe−Fe distances all appear inside the zigzag chains···−Fe2′−Fe3′−Fe3−Fe2−Fe4−Fe4′−Fe2′−···with edge-shared Fe−Opolyhedra. Fei′ (i = 2, 3, 4) is connected to Fei at (x, y, z) byinversion to (x̅, y̅, z)̅ and a translation vector (tx, ty, tz) of latticeconstants. Zigzag chains propagate along (0, 1, −1) directions.For Fe1, Fe−Fe bond lengths to the four nearest neighborsFe2, Fe2′, Fe3 and Fe3′ with corner shared Fe−O polyhedraare almost constant. The four nearest neighbors belong to fourdifferent zigzag chains.3.2. Magnetic Phase Transitions and Magnetic PhaseDiagram of Fe7(PO4)6The temperature dependence of Cp and Cp/T data at H = 0 Oeis shown on Figure 4. We observed strong and sharp λ-typeanomalies at TN1 = 47 K and TN2 = 16 K in agreement with theprevious reports.18,19 The Cp and Cp/T data at H = 90 kOeshowed that TN1 is nearly magnetic-field independent up to 90kOe. On the other hand, a clear double-peak anomaly wasobserved near TN2, when measured with a fine measurementstep of 0.1 K. Differential dCp/dT versus T curves clearlydemonstrated peaks at 14.4 and 15.8 K at H = 90 kOe (Figures4 and S1, Table S4). The double-peak features (with bothdown-peaks on the dCp/dT versus T curves) remained from 90kOe down to 65 kOe and disappeared from 60 kOe down to50 kOe. It is interesting that different features appeared from45 kOe down to 35 kOe, where there was one weak up-peakon the dCp/dT versus T curves and one main strong down-peak (Figures S1 and S2). One peak on the dCp/dT versus TFigure 2. Experimental (black dots), calculated (red line), and difference (blue line) neutron diffraction patterns of Fe7(PO4)6 measured on HRPTwith a neutron wavelength λ = 1.886 Å in the paramagnetic state at T = 60 K. Tick marks indicate Bragg peak positions.Table 1. Refined Structural Parameters of Fe7(PO4)6Phosphate in the Paramagnetic State Obtained fromRietveld Refinement Analysis of HRPT Neutron DiffractionData Measured at T = 60 K with λ = 1.886 Åabcatom WP x/a y/b z/c B (Å2)Fe1 1a 0 0 0 0.12(2)Fe2 2i 0.8108(2) 0.2876(2) 0.2810(3) 0.12(2)Fe3 2i 0.4527(2) 0.1141(2) 0.3828(3) 0.12(2)Fe4 2i 0.7226(2) 0.5291(2) 0.0443(3) 0.12(2)P1 2i 0.5938(4) 0.8331(4) 0.0965(5) 0.10(3)P2 2i 0.2318(4) 0.3706(4) 0.3988(5) 0.10(3)P3 2i 0.1510(4) 0.7667(4) 0.2285(5) 0.10(3)O1 2i 0.0398(3) 0.2411(3) 0.2753(4) 0.28(2)O2 2i 0.5393(3) 0.9170(3) 0.3120(5) 0.28(2)O3 2i 0.2835(4) 0.4651(3) 0.2540(5) 0.28(2)O4 2i 0.3661(4) 0.2855(3) 0.4494(5) 0.28(2)O5 2i 0.2709(4) 0.7728(3) 0.4575(5) 0.28(2)O6 2i 0.5501(4) 0.6539(3) 0.0665(5) 0.28(2)O7 2i 0.7891(4) 0.9203(3) 0.1199(5) 0.28(2)O8 2i 0.5321(3) 0.1609(3) 0.1202(5) 0.28(2)O9 2i 0.8105(4) 0.3425(3) 0.9808(5) 0.28(2)O10 2i 0.7608(4) 0.5073(3) 0.3664(5) 0.28(2)O11 2i 0.2018(3) 0.9397(3) 0.2257(5) 0.28(2)O12 2i 0.9528(4) 0.7054(3) 0.2110(5) 0.28(2)aSpace group P1̅ (No. 2); Z = 1. WP: Wyckoff position. B: DebyeWaller factor. The oxidation states of the magnetic ions are Fe12+,Fe22+, Fe33+ and Fe43+. bLattice parameters and unit cell volume: a =7.9638(1) Å; b = 9.3073(1) Å; c = 6.3539(1) Å; α = 108.340(1)°; β =101.628(1)°; γ = 105.213(1)°; V = 410.09(1) Å3. Bond-valence sumvalues45 are +1.86 for Fe1, +2.00 for Fe2, +3.08 for Fe3, and +3.05 forFe4. cR-factors: Rwp = 2.26%; Rexp = 1.62%; RBragg = 1.18%; χ2 = 1.94.Inorganic Chemistry pubs.acs.org/IC Articlehttps://doi.org/10.1021/acs.inorgchem.6c00534Inorg. Chem. 2026, 65, 7418−74307420https://pubs.acs.org/doi/suppl/10.1021/acs.inorgchem.6c00534/suppl_file/ic6c00534_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.inorgchem.6c00534/suppl_file/ic6c00534_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.inorgchem.6c00534/suppl_file/ic6c00534_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.inorgchem.6c00534/suppl_file/ic6c00534_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.inorgchem.6c00534/suppl_file/ic6c00534_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.inorgchem.6c00534/suppl_file/ic6c00534_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?fig=fig2&ref=pdfpubs.acs.org/IC?ref=pdfhttps://doi.org/10.1021/acs.inorgchem.6c00534?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asFigure 3. Arrangement of magnetic Fe ions in the crystal structure of Fe7(PO4)6 shown as a projection onto the ab- and bc-plane. Fe−Fe distancesup to 3.6 Å are indicated. Drawings were made using VESTA software.15Figure 4. Specific heat, Cp versus T (the left-hand axis), and Cp/T versus T curves (the right-hand axis) at H = 0 Oe (black) and 90 kOe (red) forFe7(PO4)6, measured on cooling. Inset shows dCp/dT versus T curve at H = 90 kOe (units: J K−2 mol−1 versus K).Figure 5. M versus H curves at T = 1.7 K from 0 Oe to 300 kOe (black) and from 300 kOe to 0 Oe (red) for Fe7(PO4)6, measured using a hybridmagnet. Inset shows a zoomed-in part of M versus H curves at T = 1.8 K, measured using MPMS3, and emphasizes a small hysteresis. A blue thinline shows a linear fit between 250 kOe and 300 kOe, which is then extrapolated to zero magnetic field.Inorganic Chemistry pubs.acs.org/IC Articlehttps://doi.org/10.1021/acs.inorgchem.6c00534Inorg. Chem. 2026, 65, 7418−74307421https://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?fig=fig5&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?fig=fig5&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?fig=fig5&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?fig=fig5&ref=pdfpubs.acs.org/IC?ref=pdfhttps://doi.org/10.1021/acs.inorgchem.6c00534?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ascurves near 16 K is nearly magnetic-field independent up to 90kOe, the second peak (which we call TN2b) showed slight fielddependence. With the absence of available compounds withnonmagnetic elements, it was difficult to correctly estimate thelattice contribution and magnetic entropy. The Cp/T versus T2curve (at H = 0 Oe) did not follow a linear behavior even atlow temperatures; on the other hand, the following relationwas approximately observed: Cp = β × T5 with β =2.792(6)×10−4 J × mol−1× K−6 between 1.9 and 6 K (FiguresS3−S5). There were no detectable electronic contributions inagreement with the insulating properties.Isothermal M versus H curves clearly revealed the presenceof one field-induced transition between 1.7 and 16 K (=TN2)(Figures S6 and S7, Table S5). The values of transition fieldswere determined from the differential dM/dH versus H curvesmeasured from 70 kOe to 0 Oe; there was small hysteresisduring measurements from 0 Oe to 70 kOe and from 70 kOeto 0 Oe (the inset of Figure 5). The transition field reachesmaximum of 56.5 kOe (between 6 and 9 K) and then slightlydecreases to 55.5 kOe (between 1.7 and 4 K). We alsoperformed high-magnetic fieldM versus H measurements up toH = 300 kOe at T = 1.7 K (Figure 5). However, no additionalmagnetic field-induced transitions were observed. Magnet-ization reached about 13.9 μB/f.u. (at H = 300 kOe and T =1.7 K). The M versus H curves were linear up to 55 kOe,suggesting a pure AFM state, then gradually increased up to300 kOe. The M versus H curves were fitted by a linearfunction between 250 kOe and 300 kOe and then extrapolatedto zero magnetic field resulting in 2.85 μB/f.u. (Figure 5, theblue thin line). This value can be considered as an inducedmoment due to spin canting in a canted antiferromagnetic(cAFM) state. The magnetic-field-temperature points from theM versus H curves match with TN2b(H, T).Temperature-dependent susceptibility measurements, χversus T, at H = 1, 10, 20, 30, 40, 50, 60, 70 kOe showedthat TN1 is nearly magnetic-field independent in agreementwith the specific heat measurements. Therefore, we focus onthe behavior near TN2 (Figures 6 and S8−S13, Table S6). Theχ versus T curves at all magnetic fields showed maxima atnearly the same temperature of 16 K, which appears as peakson the double differential curves, d2χT/d2T versus T; theseanomalies coincide with the specific heat anomalies. Aboveabout 30 kOe up to 55 kOe, other sharp peaks start emergingon the differential curves, dχT/dT versus T, which match withanomalies on the dM/dH versus H curves and with TN2b.Between 42.5 kOe up to the maximum measurement field of70 kOe, ZFC curves showed other sharp peaks on thedifferential curves, dχT/dT versus T (Figure 6), while noFigure 6. (a) χ versus T curves at H = 70 kOe (black), 60 kOe (blue), and 50 kOe (red) measured in the ZFC and FCC (on cooling) regimes forFe7(PO4)6. (b) The same differential dχT/dT versus T curves. Arrows show the magnetic anomalies.Inorganic Chemistry pubs.acs.org/IC Articlehttps://doi.org/10.1021/acs.inorgchem.6c00534Inorg. Chem. 2026, 65, 7418−74307422https://pubs.acs.org/doi/suppl/10.1021/acs.inorgchem.6c00534/suppl_file/ic6c00534_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.inorgchem.6c00534/suppl_file/ic6c00534_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.inorgchem.6c00534/suppl_file/ic6c00534_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.inorgchem.6c00534/suppl_file/ic6c00534_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.inorgchem.6c00534/suppl_file/ic6c00534_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.inorgchem.6c00534/suppl_file/ic6c00534_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?fig=fig6&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?fig=fig6&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?fig=fig6&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?fig=fig6&ref=pdfpubs.acs.org/IC?ref=pdfhttps://doi.org/10.1021/acs.inorgchem.6c00534?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asanomalies were observed on FCC curves. This transition ismarked as TZFC (=8 K). Very small difference between ZFCand FCC curves was also observed above 42.5 kOe, and thedifference became clear above 55 kOe. No difference betweenZFC and FCC curves was detected below 40 kOe. The Curie−Weiss fit was performed between 200 and 350 K (using datameasured at H = 50 kOe and 76.52 mg of the sample weight toincrease accuracy); the Curie−Weiss temperature was θ =−68.92(14) K, and the experimental effective magneticmoment of μeff = 14.771(3) μB was close to the calculatedvalue of μeff = 14.56 μB (for the spin-only values of 4Fe3+ and3Fe2+).Based on the results of the above measurements, the H−Tphase diagram can be constructed for Fe7(PO4)6 (Figure 7).The appearance of a line only on the ZFC curves at TZFC = 8 Kabove 42.5 kOe may suggest the formation of metastablemagnetic phases. The phase diagram has a triple point at TN2and a magnetic field between 0 Oe and about 20 kOe; with theaccuracy of measurements, it was not possible to determine theprecise value of a magnetic field. There is evidence for thepresence of another triple point at TN2 and a magnetic field ofabout 65 kOe.3.3. Magnetic Structures of Fe7(PO4)6 at Zero MagneticFieldFigure 8 shows the low angle part (10° < 2θ < 80°) of therefinement of neutron diffraction patterns of Fe7(PO4)6measured with a large neutron wavelength λ = 4.507 Å inthe paramagnetic state at (a) T = 60 K, and in the magneticallyordered states at (b) 25 K (between TN1 and TN2) and 2 K(below TN2). Simultaneous refinements of crystal and magneticstructures were performed in the full range of scattering angles2θ up to 137.9° by keeping the atomic positions fixed at thevalues given in Table 1. The refinements over the full 2θ rangeare shown in Figure S14. At T = 25 K, all observed magneticBragg peaks can be indexed with a commensurate AFMpropagation vector k1 = (1/2, 0, 1/2). At 2 K, the propagationvector k1 remains and a second propagation vector k2 = (0, 1/2, 0) appears. The observed temperature dependence ofselected magnetic Bragg peaks is displayed in Figures 9 and 10.Bragg peaks corresponding to k1 appear below TN1 = 47 K andchange intensity near TN2 = 16 K, whereas the magnetic Braggpeaks corresponding to k2 are observed below TN2. Theintensity map between 2 and 80 K is shown in Figure 9 for theheating cycle and in Figure S15 for the cooling cycle. Bothcycles show identical intensities.For the triclinic space group P1̅ (no. 2), the crystallographicsites 1a and 2i, and the propagation vectors k1 and k2,representation analysis for the possible magnetic structuresgives the result summarized in Table 2. Due to the lowsymmetry of the crystal structure, there are only twoirreducible representations (irreps) with different symmetry,which are valid for both propagation vectors k1 and k2. ForFe2, Fe3 and Fe4 on site 2i, the inversion symmetry from (x, y,z) to (x̅, y̅, z)̅ has a ferromagnetic (FM) coupling in mU1+ ormY1+, and an AFM coupling in mU1− or mY1−. For Fe1 onsite 1a, magnetic order is possible in mU1+ or mY1+, but notin mU1− or mY1−. In summary, the refinement of a magneticstructure corresponds to 12 independent fitting parameters(components of magnetic moments) in mU1+ or mY1+, andto 9 independent fitting parameters in mU1− or mY1−.As shown in Figure 3, the shortest Fe−Fe bond length bondlength of 3.11 Å is found in the dimer containing Fe3 at(0.453, 0.114, 0.383) and Fe3′ at (0.547, −0.114, 0.617). Fe3′is connected to Fe3 by an inversion from (x, y, z) to (x̅, y̅, z)̅and a translation vector of lattice constants (tx, ty, tz) = (1, 0,1). For both k vectors, k1 and k2, this translation vector gives aFM coupling. Therefore, according to the results of thesymmetry analysis (Table 2), the coupling in the Fe3 − Fe3′dimer is always FM for magnetic structures inside mU1+ ormY1+ and always AFM for structures in mU1− or mY1−. Forthe other dimer containing Fe4 at (0.723, 0.529, 0.044) andFe4′ at (0.277, 0.471, −0.044), the translation vector (1, 1, 0)gives an AFM coupling for both k vectors, k1 and k2.Therefore, the coupling in the Fe4−Fe4′ dimer is always AFMfor magnetic structures inside mU1+ or mY1+ and always FMfor structures in mU1− or mY1−. As a result of the symmetryanalysis, inside each irrep one dimer has a FM coupling andthe other an AFM coupling.At T = 25 K, the AFM structure of Fe7(PO4)6 withpropagation vector k1 = (1/2, 0, 1/2) belongs to therepresentation mU1+. Refinements are shown in Figures 8band S14b and the results are summarized in Table 3. Thestrongest magnetic intensity is observed for the Bragg peaks(1/2, 0, 1/2) at 2θ = 33.1°, (1/2, −1, −1/2) at 2θ = 42.2°, and(3/2, −1, −1/2) at 2θ = 56.4° (Figure 8b). All magnetic Feions are ordered�with a large moment at the Fe3+ sites (4.1μB for Fe4 and 3.7 μB for Fe3), and a much smaller moment atthe Fe2+ sites (1.7 μB for Fe1 and 0.7 μB for Fe2). Thenoncollinear AFM structure of Fe7(PO4)6 at T = 25 K isillustrated in Figure 11. Reflecting the low symmetry of thetriclinic crystal structure, directions and magnitudes of theordered moments all are different for different Fe ions (Fe1,Fe2, Fe3 and Fe4). The AFM structure is dominated by largeFigure 7. A H versus T phase diagram of polycrystalline Fe7(PO4)6.Experimental points were obtained from different measurements asindicated on the figure. The points from d2χT/d2T versus T curves,which define TN2, coincide with the points on the dCp/dT versus Tcurves (for TN2) and are not shown. AFM: antiferromagnetic; cAFM:canted antiferromagnetic.Inorganic Chemistry pubs.acs.org/IC Articlehttps://doi.org/10.1021/acs.inorgchem.6c00534Inorg. Chem. 2026, 65, 7418−74307423https://pubs.acs.org/doi/suppl/10.1021/acs.inorgchem.6c00534/suppl_file/ic6c00534_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.inorgchem.6c00534/suppl_file/ic6c00534_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.inorgchem.6c00534/suppl_file/ic6c00534_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?fig=fig7&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?fig=fig7&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?fig=fig7&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?fig=fig7&ref=pdfpubs.acs.org/IC?ref=pdfhttps://doi.org/10.1021/acs.inorgchem.6c00534?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asordered moments along the c-axis (mz components) with a FMcoupling between Fe4 (3.8 μB) and Fe3 (3.3 μB). Within theaccuracy of the experimental data, for all Fe ions, rather smallcomponents of the ordered moments inside the ab-planeexhibit a collinear arrangement at an angle δ ≈ 40° away fromthe a-axis (see dashed line in Figure 11a). This means that allordered Fe moments lie inside one plane that is defined by thedirection of the dashed line in Figure 11a and the c-axis.At T = 2 K, the AFM structure of Fe7(PO4)6 can be indexedwith two propagation vectors k1 = (1/2, 0, 1/2) and k2 = (0,1/2, 0). For k1 and k2, the strongest magnetic Bragg peaksappear at different 2θ values. For k1, they are the same as at T= 25 K (Figure 8b). For k2, the strongest intensity is observedfor the magnetic Bragg peaks (0, 1/2, 0) at 2θ = 15.6°, (0, 3/2,0) at 2θ = 48.2°, and (0, 1/2, 1) at 2θ = 55.1° (Figure 8c).This increases the accuracy of the simultaneous refinement ofthe two independent magnetic structures for the k1 and the k2components. Refinements are shown in Figures 8c and S14cand the results are summarized in Table 3. The AFM structurebelongs to the representation mU1+ for k1 and to mY1+ for k2.For both components, all magnetic Fe ions are ordered. Forthe k1 component at T = 2 K, there is a large moment at theFe3+ sites (4.4 μB for Fe4 and 4.3 μB for Fe3), and a muchsmaller moment at the Fe2+ sites (1.2 μB for Fe1 and 0.8 μB forFe2). In contrast, for the k2 component, there is a largemoment at the Fe2+ sites (4.3 μB for Fe1 and 4.3 μB for Fe2),and a much smaller moment at the Fe3+ sites (1.0 μB for Fe4and 1.3 μB for Fe3). The magnetic structure of Fe7(PO4)6 at T= 2 K is illustrated in Figure 11 for the k1 component and inFigure 12 for the k2 component.For the k1 component at T = 2 K, within the accuracy of theexperimental data, for all Fe ions, the components of theordered moments inside the ab-plane exhibit a collineararrangement along to the b-axis (Figure 11d). This indicatesthat all ordered moments lie within the bc-plane. But directionsand magnitudes are all different for different Fe ions (Fe1, Fe2,Fe3 and Fe4). The observed change of intensity of magneticBragg peaks near TN2 = 16 K (Figure 10a) indicates aFigure 8. Experimental (black dots), calculated (red line), and difference (blue line) neutron diffraction patterns of Fe7(PO4)6 measured on DMCwith a neutron wavelength λ = 4.507 Å in the paramagnetic state at T = 60 K (a) and in the magnetically ordered states at T = 25 K (b), and 2 K(c). Tick marks indicate Bragg peak positions. The first row is for the nuclear peaks, and the second and third rows are for the magnetic peaks. Thethree strongest magnetic Bragg peaks are indexed for k1 at T = 25 K and for k2 at T = 2 K.Inorganic Chemistry pubs.acs.org/IC Articlehttps://doi.org/10.1021/acs.inorgchem.6c00534Inorg. Chem. 2026, 65, 7418−74307424https://pubs.acs.org/doi/suppl/10.1021/acs.inorgchem.6c00534/suppl_file/ic6c00534_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?fig=fig8&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?fig=fig8&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?fig=fig8&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?fig=fig8&ref=pdfpubs.acs.org/IC?ref=pdfhttps://doi.org/10.1021/acs.inorgchem.6c00534?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asreorientation of the ordered moments of the k1 component. Acomparison of Figures 11 and 12 suggests that the direction ofthe collinear arrangement of the components of orderedmoments inside the ab-plane rotates from an angle δ ≈ 40° atT = 25 K to γ = 105° at T = 2 K (compare Figure 11a,d). Inaddition, the large ordered moments at the Fe3+ sites, Fe3 andFigure 9. Temperature and 2θ dependent neutron intensity map of Fe7(PO4)6 measured on DMC for heating from 2 K.Figure 10. (a,b) Temperature dependence of neutron intensity (left-hand axes) and intensity ratio (right-hand axes) for selected magnetic Braggpeaks of Fe7(PO4)6.Inorganic Chemistry pubs.acs.org/IC Articlehttps://doi.org/10.1021/acs.inorgchem.6c00534Inorg. Chem. 2026, 65, 7418−74307425https://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?fig=fig9&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?fig=fig9&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?fig=fig9&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?fig=fig9&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?fig=fig10&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?fig=fig10&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?fig=fig10&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?fig=fig10&ref=pdfpubs.acs.org/IC?ref=pdfhttps://doi.org/10.1021/acs.inorgchem.6c00534?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asFe4, rotate away from close to the (0, 0, 1) direction (c-axis) atT = 25 K toward the (0, −1, 1) direction (the chain direction)at 2 K (compare Figure 11b,e). For the k2 component at T = 2K, Fe2�located inside the zigzag chain�has a large momentalong the a-axis (mx = −4.1 μB)�predominantly perpendicularto the chain direction. Fe1 which connects 4 different chainshas large components along the a- and c-directions (mx = 2.9μB, mz = −2.2 μB).At T = 2 K, the low symmetry of the triclinic crystalstructure leads to 24 independent fitting parameters(components of ordered magnetic moments). The quality ofthe refinement is very good (Figures 8c and S14c) and yieldsaccurate values for the large components of ordered moments(Table 3). However, the many small components arecorrelated and the available neutron diffraction data do notallow to determine unambiguous values for all 24 moments,because the effective number of measured magnetic Braggpeaks considering instrumental resolution is not large enough.As indicated in Table 3, we have reduced the number of fittingparameters from 24 to 16, by fixing 8 small components to zero(4 for k1 and 4 for k2). The result of the 16-parameterrefinement is given in Table 3. Both models, with 24 or 16fitting parameters, give similar agreement values (e.g., χ2values). Figure 12 illustrates the magnetic structure ofFe7(PO4)6 at T = 2 K as a superposition of the k1 and k2components. For each magnetic Fe ion, one k vector gives riseto a collinear AFM structure with a constant value of theordered moment. The superposition of k1 and k2 usually leadsto a noncollinear AFM structure with ordered moments havingtwo different magnitudes Mmax and Mmin. The differencebetween Mmax and Mmin becomes zero if the ordered momentscorresponding to k1 and k2 are oriented perpendicular to eachother. But an angle of exactly 90° is not supported by thesymmetry of a triclinic crystal structure with α ≠ 90°, β ≠ 90°and γ ≠ 90°. Estimated values for Mmax, Mmin are given inTable 2. Group Theory Analysis for the Magnetic Structuresof Fe7(PO4)6 Phosphate below TN1 = 47 K and TN2 = 16 KCalculated Using the Programs ISODISTORT43,44 andBASIREPS42,airrep for k1 (ISODISTORT) mU1+ mU1−irrep for k2 (ISODISTORT) mY1+ mY1−irrep for k1and k2(BasIreps) IRrep(1) IRrep(2)character set (1, 1) (1, −1)1a Fe1 (0, 0, 0) (u, v, w) −2i Fe2, Fe3,Fe4(x, y, z) (u, v, w) (u, v, w)(x̅, y̅, z)̅ (u, v, w) (−u, −v, −w)aThe triclinic space group is P1̅ (no. 2). Magnetic Fe ions are locatedon sites 1a and 2i. Magnetic propagation vectors are k1 = (1/2, 0, 1/2) and k2 = (0, 1/2, 0). Irrep denotes irreducible representation.Components of the magnetic moments are expressed using (u, v, w).The character sets correspond to the two symmetry elementssymm(1): 1 and symm(2): −1 0,0,0.Table 3. Result of the Refinement of the MagneticStructures of Fe7(PO4)6 Phosphate at T = 25 and 2 K Basedon Powder Neutron Diffraction Data (DMC, λ = 4.507Å)abcT = 25 K(TN2 < T < TN1):irrep: mU1+ mx (μB) my (μB) mz (μB) M (μB)Fe1 k1 1.06(7) 0.63(4) −0.99(5) 1.72(10)Fe2 k1 −0.41(5) −0.24(3) 0.45(4) 0.72(7)Fe3 k1 −0.91(5) −0.54(3) 3.28(4) 3.73(6)Fe4 k1 −0.59(4) −0.36(3) 3.80(4) 4.07(6)R-factors: Rwp = 2.25%; Rexp = 1.24%; RBragg = 1.37% %; Rmag(k1) =2.08%; χ2 = 3.28T = 2 K (T < TN2):irrep: mU1+ mx (μB) my (μB) mz (μB) M (μB)Fe1 k1 ≈ 0 1.12(7) −0.28(6) 1.24(10)Fe2 k1 ≈ 0 −0.60(5) 0.29(4) 0.75(7)Fe3 k1 ≈ 0 −2.11(4) 3.08(5) 4.25(7)Fe4 k1 ≈ 0 −1.54(4) 3.61(5) 4.35(7)irrep: mY1+Fe1 k2 2.94(5) −1.45(7) −2.18(9) 4.28(11)Fe2 k2 −3.99(3) 0.84(5) 0.22(7) 4.32(6)Fe3 k2 −1.31(2) ≈0 ≈0 1.31(2)Fe4 k2 −1.04(2) ≈0 ≈0 1.04(2)R-factors: Rwp = 2.80%; Rexp = 1.25%; RBragg = 1.37% %; Rmag(k1) = 2.48%;Rmag(k2) = 2.94%; χ2 = 4.99T = 2 K (T < TN2):superposition of k1 and k2 Mmax (μB) Mmin (μB) difference (μB)Fe1 ≈4.7 ≈4.2 ≈0.5Fe2 ≈4.6 ≈4.2 ≈0.4Fe3 ≈4.4 ≈4.4 ≈0.0Fe4 ≈4.6 ≈4.4 ≈0.2aMagnetic propagation vectors are k1 = (1/2, 0, 1/2) and k2 = (0, 1/2, 0). Components and magnitude of the ordered Fe ions are (mx, my,mz) M. bPositions of magnetic Fe ions. cFe1 (0, 0, 0); Fe2 (0.811,0.288, 0.281); Fe3 (0.453, 0.114, 0.383); Fe4 (0.723, 0.529, 0.044).Figure 11. Illustration of the k1 component of the magnetic structureof Fe7(PO4)6 at T = 25 K (a−c) and 2 K (d−f) shown for thecomponents of the ordered magnetic moments inside the ab-, bc- andac-plane. Drawings were made using VESTA software.15Inorganic Chemistry pubs.acs.org/IC Articlehttps://doi.org/10.1021/acs.inorgchem.6c00534Inorg. Chem. 2026, 65, 7418−74307426https://pubs.acs.org/doi/suppl/10.1021/acs.inorgchem.6c00534/suppl_file/ic6c00534_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?fig=fig11&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?fig=fig11&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?fig=fig11&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?fig=fig11&ref=pdfpubs.acs.org/IC?ref=pdfhttps://doi.org/10.1021/acs.inorgchem.6c00534?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asTable 3. They depend on the values of the small componentsof the ordered moments.3.4. DiscussionThe magnetic structure refinements for Fe7(PO4)6 wereperformed using the k-vector formalism and irreduciblerepresentations implemented in FULLPROF.42 The corre-sponding magnetic space groups (MSG) were subsequentlyassigned, and the magCIF files were generated using ISOCIFfrom the ISOTROPY Software Suite43,44 and MVISUALIZEfrom the Bilbao Crystallographic Server,46−48 following theGuidelines for communicating commensurate magneticstructures.49 For the 25 K magnetic phase, the MSG is P1̅(BNS 2.7) and the relation of the magnetic setting to theparent cell is basis = (1, 0, 1), (0, −1, 0), (2, 0, 0), origin =(0.500, 0.000, 0.000). For the 2 K magnetic phase, the MSG isalso P1̅ (BNS 2.7) and the relation of the magnetic setting tothe parent cell is basis = (1, 0, 1), (1, 0, −1), (2, 2, 0), origin =(0.500, 0.500, 0.000). The magCIF files generated by thesoftware MVISUALIZE from the Bilbao CrystallographicServer are printed in Tables S7 (for T = 25 K) and S8 (forT = 2 K).Magnetic ordering in the MV compound Fe7(PO4)6 occursin two successive AFM phase transitions at TN1 = 47 K andTN2 = 16 K. Large ordered moments appear first at the twoFe3+ sites (below TN1 with a propagation vector k1 = (1/2, 0,1/2)) and then at the two Fe2+ sites (below TN2 with adifferent propagation vector k2 = (0, 1/2, 0)). Besides the largeordered moments, much smaller moments are induced at theFe2+ sites (below TN1 with k1) and at the Fe3+ sites (below TN2with k2). At low temperature, this results in a complexmagnetic structure with nonconstant total ordered moments ateach site. A somewhat similar situation was observed, forexample, in mineral ilvaite, Ca(Fe2+,Fe3+)Fe3+Si2O7O(OH),21where the first magnetic transition takes place at 116 K, butone site with Fe2+ remains completely disordered (evenFigure 12. Illustration of the k2 (a−c) and the k1 + k2 (d−f) component of the magnetic structure of Fe7(PO4)6 at T = 2 K shown for thecomponents of the ordered magnetic moments inside the ab-, bc- and ac-plane. Drawings were made using VESTA software.15Inorganic Chemistry pubs.acs.org/IC Articlehttps://doi.org/10.1021/acs.inorgchem.6c00534Inorg. Chem. 2026, 65, 7418−74307427https://pubs.acs.org/doi/suppl/10.1021/acs.inorgchem.6c00534/suppl_file/ic6c00534_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.inorgchem.6c00534/suppl_file/ic6c00534_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?fig=fig12&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?fig=fig12&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?fig=fig12&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?fig=fig12&ref=pdfpubs.acs.org/IC?ref=pdfhttps://doi.org/10.1021/acs.inorgchem.6c00534?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-aswithout any detectable induced moments), and it is orderedonly below the second magnetic transition at 40 K.The Fe3+ cations reach nearly maximum saturation valuesquite fast, just above TN2. On the other hand, the Fe2+ cationsare ordered with significantly reduced moments just above TN2probably because they prefer different orientations with thepropagation vector k2. This fact can explain why magneticsusceptibilities do not drop at TN1 as one could expect for anAFM transition, but continue the paramagnetic trend withdecreasing temperature.18,19 Magnetic susceptibilities onlydrop below TN2 (Figure 6).The magnetic structure of Fe7(PO4)6 belongs to the irrepsmU1+ (for k1) and mY1+ (for k2), where the symmetryrequests an AFM coupling in the Fe4−Fe4′ dimer and a FMcoupling in the Fe3−Fe3′ dimer. According to the Good-enough−Kanamori rules, the AFM exchange is always expectedfor Fe3+−Fe3+ bonds independent of Fe−O−Fe angles.50However, the strength of AFM interactions strongly dependson Fe−O−Fe angles, where the strongest AFM interactions areexpected for the 180° bonds. Our magnetic structures ofFe7(PO4)6 revealed that the AFM interactions are realized inthe Fe4−Fe4′ dimer unit with the larger bond angle of105.1(3)° (Table S1). On the other hand, the Fe3−Fe3′ dimerunit with the smaller bond angle of 98.1(3)° (Table S1) hasthe FM exchange forced by the overall magnetic structurebecause it is easier to force FM exchange in the Fe3−Fe3′dimer.The magnetic structures found in our work are partlyconsistent with the previous Mössbauer spectroscopy results.19It was found that just above TN2, the hyperfine field values onFe3+ cations reached almost saturation values corresponding tonearly full ordered moments. On the other hand, the hyperfinefield values on Fe2+ cations were significantly reduced inagreement with the significantly reduced moments found inour work. Below TN2, the hyperfine field value on one Fe2+ siteincreased rapidly in agreement with the large ordered moment.On the other hand, the hyperfine field value on the secondFe2+ site remained small,19 while our results show the largeordered moments for both Fe2+ sites. This fact could call forthe reanalysis of the previous Mössbauer spectroscopy results.However, we note that for Fe2+ cations there are not so strongcorrelations between ordered moments and hyperfine fields incomparison with Fe3+ cations.The ordered moments on Fe2+ cations in Fe7(PO4)6 arefound to be slightly higher than the spin-only values of 4 μB.This fact shows that there are noticeable contributions fromspin−orbital coupling. Such a coupling can increase orderedmoments on Fe2+ cations up to 4.5 μB.21 Examples of increasedFe2+ ordered moments have been reported for K4Fe3F12 (∼4.3μB)51 and FeF2 (∼4.5 μB).52,534. CONCLUSIONThe triclinic crystal-structure type of the MV (Fe2+, Fe3+)compound Fe7(PO4)6 is adapted by other phosphates,vanadates, molybdates, and arsenates. Some materials withthis crystal-structure type have attracted interest forapplications in batteries and Na-ion intercalation, for use ascolorful pigments and because of multiferroic properties. Forthe parent compound Fe7(PO4)6, we have determined complexmagnetic structures by powder neutron diffraction andconstructed a temperature-magnetic field phase diagrambased on temperature- and field-dependent magnetizationand specific heat measurements. At zero field, Fe7(PO4)6shows two successive AFM phase transitions at TN1 and TN2with different propagation vectors k1 and k2. Below TN1, Fe3+cations order with k1 and adopt large moments with inducingsmall moments at the Fe2+ cations. Below TN2, Fe2+ cationsorder with k2 and adopt large moments with inducing smallmoments at the Fe3+ cations. The k1 component shows areorientation near TN2 and coexists with the k2 component atlower temperatures. Our results showed the complexity of themagnetic structures and magnetic phase diagram of the MVphosphate Fe7(PO4)6. It may be interesting to track changes inmagnetic structures and magnetic phase diagrams with changesin the Fe3+:Fe2+ ratio in Fe7Hx(PO4)6 or other doped variants.■ ASSOCIATED CONTENT*sı Supporting InformationThe Supporting Information is available free of charge athttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534.Details of Cp vs T, M vs H curves, M vs T curves, anddifferential curves, refinement of neutron diffractionpatterns, Tables with interatomic distances and bondangles, Tables with numerical values used to plot Figure7, printouts of two magCIF files describing the magneticstructures at 25 and 2 K using magnetic space groups(PDF)Data for the magnetic structure at T = 25 K (MCIF)Data for the magnetic structure at T = 2 K (MCIF)■ AUTHOR INFORMATIONCorresponding AuthorAlexei A. Belik − Research Center for MaterialsNanoarchitectonics (MANA), National Institute forMaterials Science (NIMS), Tsukuba, Ibaraki 305-0044,Japan; orcid.org/0000-0001-9031-2355;Email: Alexei.Belik@nims.go.jpAuthorsAndreas Dönni − Research Center for MaterialsNanoarchitectonics (MANA), National Institute forMaterials Science (NIMS), Tsukuba, Ibaraki 305-0044,JapanLukas Keller − PSI Center for Neutron and Muon Sciences,Villigen CH-5232, SwitzerlandVladimir Y. Pomjakushin − PSI Center for Neutron andMuon Sciences, Villigen CH-5232, SwitzerlandNaohito Tsujii − Research Center for MaterialsNanoarchitectonics (MANA), National Institute forMaterials Science (NIMS), Tsukuba, Ibaraki 305-0044,Japan; orcid.org/0000-0002-6181-5911Complete contact information is available at:https://pubs.acs.org/10.1021/acs.inorgchem.6c00534NotesThe authors declare no competing financial interest.■ ACKNOWLEDGMENTSThis study is partially based on experiments performed onHRPT and DMC diffractometers at the Swiss SpallationNeutron Source SINQ, Paul Scherrer Institute, Switzerland.We thank E. Canevet for his support with data processing, I.A.Presniakov for his valuable discussion, and S. Iikubo, K.Kodama, N. Igawa, and S. Shamoto for preliminary neutronInorganic Chemistry pubs.acs.org/IC Articlehttps://doi.org/10.1021/acs.inorgchem.6c00534Inorg. Chem. 2026, 65, 7418−74307428https://pubs.acs.org/doi/suppl/10.1021/acs.inorgchem.6c00534/suppl_file/ic6c00534_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.inorgchem.6c00534/suppl_file/ic6c00534_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?goto=supporting-infohttps://pubs.acs.org/doi/suppl/10.1021/acs.inorgchem.6c00534/suppl_file/ic6c00534_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.inorgchem.6c00534/suppl_file/ic6c00534_si_002.mcifhttps://pubs.acs.org/doi/suppl/10.1021/acs.inorgchem.6c00534/suppl_file/ic6c00534_si_003.mcifhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Alexei+A.+Belik"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://orcid.org/0000-0001-9031-2355mailto:Alexei.Belik@nims.go.jphttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Andreas+Do%CC%88nni"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Lukas+Keller"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Vladimir+Y.+Pomjakushin"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Naohito+Tsujii"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://orcid.org/0000-0002-6181-5911https://pubs.acs.org/doi/10.1021/acs.inorgchem.6c00534?ref=pdfpubs.acs.org/IC?ref=pdfhttps://doi.org/10.1021/acs.inorgchem.6c00534?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asdiffraction studies. 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