Polymorphs, phase transitions and stability in BaM₂(PO₄)₂ M = Mn, Fe, Co systems

Abstract

BaM₂(PO₄)₂ (M²⁺ transition metals) compounds display a variety of polymorphs; among those, the well-known rhombohedral γ-form stands at the origin of a series of (quasi)2D-magnetic behaviors intensively studied in the last few decades. We have prepared original α-variants for M = Fe²⁺ and Mn²⁺ and investigated their stabilities and sequence of phase transitions by analogy to the already reported M = Co²⁺ case. Heating the α-phases leads to a variety of structural rearrangements between α, α′ and β variants, according to unified 1st order reconstructive transitions. However, spontaneous long-time transformations under ambient conditions α → γ (Fe case) versus γ → α (Co case) denote a contrasted hierarchy of stable compounds verified by DFT calculations. Interestingly, in α-BaFe₂(PO₄)₂ the quasi triangular Fe²⁺O₃₊₂ coordination is rarely observed and relies on one very short Fe–O distance of ca. 1.78 Å, destabilizing the edifice in favor of the most stable FeO₆ in the γ-type, as verified by Crystal Orbital Hamilton Population (COHP) analysis.

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1. Introduction

We have recently investigated the BaCo₂(PO₄)₂ (BCoPO) phase diagram which highlights the efficient role of large Ba²⁺ cations and phosphate groups as spacers, templating a number of bi-dimensional (2D) crystal structures.¹ Among the phases present, the so-called γ-BCoPO belongs to the well-known series of layered honeycomb lattice compounds with quasi 2D-magnetic properties such as a quasi 2D-XY behavior with a competition between two magnetic structures below Tc₁ = 7 K and Tc₂ = 3.8 K with distinct spin arrangements between in-plane ferromagnetic chains.² Other metastable α, β, β′, β′′ and ε-BCoPO polymorphs are obtained among various thermal treatments, through phase transitions. Generally speaking, most α, β, and ε phases are in competition and show a rearrangement between corner-sharing Co²⁺O₅ inside labile layers. One intriguing feature concerns the spontaneous transformation of the metastable rhombohedral γ-BCoPO with its honeycomb lattice of octahedral Co²⁺O₆ into its monoclinic stable α-variant with Co²⁺O₅ trigonal bipyramids (TBP) under ambient conditions.³ This “puzzling phase diagram” motivated us to investigate and rationalize similar phase diagrams with various M²⁺ transition metals M = Mn, Fe, Co, Ni. For M = Ni²⁺, the situation is rather simple due to the stabilization of Ni²⁺ (d⁸, S = 1) cations in octahedral crystal fields, leading to stable γ-BaNi₂(XO₄)₂ (X = P, V and As) only.^3,4 In contrast, the Fe²⁺ case deserves special attention, dealing with γ-BaFe₂(PO₄)₂ (BFePO), a unique case of a S = 2 2D-ising ferromagnet⁵ assorted with a magnetically driven re-entrant transition at low temperature.⁶ This compound was solely prepared under hydrothermal conditions which questions the existence of other polymorphs. Such compounds could pave the way to an “easy” solid state route to single phase BFePO but also to mixed Fe/M compounds (M = Ni, Co), so far fastidiously prepared under solvothermal conditions with a poor control on the Fe/M ratio.^7–9 Finally, for M = Mn²⁺ only two stoichiometric compounds are reported in the BaO–MnO–P₂O₅ system, i.e. Ba₂Mn(PO₄)₂ and BaMn(P₂O₇) with 3D lattices and disconnected MnO₅₊₁ polyhedra.¹⁰ Here the large Mn²⁺ ionic radius (0.83 Å) plays against a honeycomb lattice compatible with the PO₄ and Ba²⁺ interlayer. For instance, in triangular brucite-Mn(OH)₂, the edge-sharing Mn²⁺–Mn²⁺ distance is 3.32 Å, poorly compatible with the M–M distance in γ-BMPO phases, e.g. Fe²⁺–Fe²⁺, Co²⁺–Co²⁺ = 2.81 Å and Ni²⁺–Ni²⁺ = 2.77 Å. Here we prepared high temperature BaM₂(PO₄)₂ (M = Fe, Mn) polymorphs by a solid state route and investigated their thermal behaviors, phase transitions and preliminary high pressure transformations and DFT calculations leading to the establishment of antagonist phase stabilities in this complex family.

2. Methods

2.1 Powder XRD data

Room-temperature powder X-ray diffraction (XRD) was carried out on a Bruker D8 Advance diffractometer with a Bragg–Brentano geometry using monochromatic CuKα radiation in the range 2θ = (5–80)° with 0.02° steps and 0.5 seconds per step. Sample purity was checked on the resulting scan using Diffrac.Eva software.

Synchrotron measurements were performed at room temperature in the I11 beamline (λ = 0.824899 Å) at Diamond in the range 2θ = (2–92) ° with 0.004° steps on BaFe₂P₂O₈ and BaMn₂P₂O₈ powder placed into a 0.5 mm glass capillary. Structures were solved and refined from these data using the FULLPROF suite¹¹ and JANA 2006 software.¹²

2.2 Magnetic measurements

Magnetic data and heat capacities were measured on a physical property measurement system (PPMS) Dynacool (9T) system from Quantum Design, using ground powder of BaFe₂P₂O₈ and BaMn₂P₂O₈. We performed typical measurements using zero field cooling (ZFC) and field cooling (FC) procedures under various fields (0.05 T, 0.1 T). Magnetization versus H was measured between −9 and 9T at various temperatures. Specific heat was measured without a magnetic field using BaMn₂P₂O₈ and BaFe₂P₂O₈ materials pressed into pellets.

2.3 Thermal analysis

Thermogravimetric analysis (TGA) was carried out on a thermoanalyzer Setsys Evolution SETARAM device upon heating and cooling under an air or flowing argon atmosphere at a ramp rate of 5 K min⁻¹ up to 1273 K on ground powder. XRD was performed on the resulting products. High temperature X-ray diffraction (HTXRD) was performed using a D8 Advance Bruker instrument equipped with an XRK900 chamber under flowing air or argon, on ground powder. Each powder pattern was recorded in the range of 10–80° (2θ) (step ΔT = 50 K, 30 min per scan) from room temperature up to 1273 K. Reversibility was checked for each experiment upon cooling.

2.4 Density functional theory (DFT) calculations – computational methods

DFT calculations were carried out using the Vienna ab initio simulation package (VASP)¹³ by employing the projector augmented wave (PAW)^14,15 method and the generalized gradient approximation of Perdew, Burke and Ernzerhof (PBE) for the exchange–correlation functionals.¹⁶ GGA+U calculations were employed with U = 4 in the case of BaCo₂P₂O₈ and BaMn₂P₂O₈ and U = 6 eV in the case of BaFe₂P₂O₈ following the previous work.⁵ For the structural optimizations, a plane wave cutoff energy of 550 eV (400 eV for the total energy calculations) was used. For accurate total energies, the threshold of self-consistent-field energy convergence was set to 10⁻⁶ eV. See Table S11a† for details.

2.5 IR and UV-visible spectroscopy

Infrared spectroscopy measurements were performed on a PerkinElmer Spectrum 2 device, equipped with a diamond attenuated total reflectance (ATR) accessory. Samples (ground powder) were measured between 4000 and 400 cm⁻¹. No ATR corrections were applied on the spectrum. UV-visible measurement was performed on a PerkinElmer Precisely Lambda 650 Spectrometer device, using an STD Detector module and a HARRICK Praying Mantis Sampling Kit. The measurement was performed between 900 and 250 nm.

2.6 SEM and TEM microscopy

Energy dispersive X-Ray spectrometry (EDS) analysis was performed on powder pressed onto a pellet placed on a carbon tape and introduced in a field-emission gun scanning electron microscope (SEM) HITACHI S4700 device equipped with an Energy-dispersive X-Ray detector, operating at 20 kV electron beam energy. The EDS analysis is given from the average of several different point acquisitions. An electron diffraction study was performed on an FEI Tecnai G2-20 twin Transmission Electron Microscope (TEM). The powder was crushed and dropped in the form of an alcohol suspension on carbon supported copper grids followed by evaporation under ambient conditions.

2.7 Solid state synthesis

The original α-BFePO and α-BMnPO have been prepared by a solid state route under a controlled atmosphere, from mixtures of BaCO₃, Fe, Fe₂O₃, NH₄H₂PO₄ (3 : 2 : 2 : 6 ratio, total mass = 7 g) and BaCO₃, MnO and NH₄H₂PO₄ (1 : 1 : 2 ratio, total mass = 7 g) at 1190 K either in an evacuated silica tube or under flowing argon for Fe²⁺ and under argon for Mn²⁺.

3. Results

3.1 Crystal structures of α-variants

Here the so-called α-form refers to the high temperature route, by analogy to the BCoPO case,¹ see Fig. 2. We also used the same analogy for β and γ labels of the Fe and Mn variants. α′ and β′ polytypes were identified in situ and verified by DTA, but have not been structurally characterized. Their crystal structures have been refined using room temperature synchrotron data collected at Diamond (see Fig. 1a), l11 beamline, λ = 0.824899 Å, see Tables S1 and S2† for refinement data for both structures (including atomic positions and equivalent thermal displacement).

Fig. 1 (a) Synchrotron XRD patterns for α-BaFe₂P₂O₈, crystallizing in the P3121 trigonal space group. (b) SXRD for α-BaMn₂P₂O₈ clearly showing the splitting of the diffraction maxima due to the reduction in symmetry to C2. Low purple tick marks are coming from a secondary minority phase Ba₂Mn(PO₄)₂.

Fig. 2 (a) α-BaFe₂P₂O₈ crystal structure and (b) the infinite zigzag chains of TBP sharing corners. (c) α-BaMn₂P₂O₈ crystal structure and (d) selected zigzag chains of MnO₅ square pyramids. (e and f) show the β- and γ-BaM₂P₂O₈ variants respectively based on the cobalt case (ref. 1).

3.1.1 α-BFePO. For α-BFePO (R_Bragg = 6.63%), very weak peaks of a second phase were excluded from the refinement. α-BFePO crystallizes in the P3₁21 space group with a = 5.1141(1) Å and c = 25.1108(1) Å which involves three stacked layers _∞[FePO₄]⁻ per unit cell (see Fig. 2a). It displays strongly distorted TBPs sharing their O1 corners along zigzag chains, see Fig. 2b. The Fe–O4 distance of 1.784(6) Å is particularly short due to the mainly triangular coordination in Fe²⁺O₃₊₂ TBPs and balances the bonding scheme towards a bond valence sum calculated to be 1.99 for Fe²⁺ ions, see Table 1. This short value was confirmed using powder neutron diffraction (3T2 diffractometer, LLB, CEA, Saclay, France λ = 2.42 Å) data at 80 K (d(Fe–O4) = 1.776 Å), see Fig. S15b.† The influence of this short bond will be discussed later in the frame of the α-BFePO phase stability. The refinement results and atomic positions are given in ESI S1(a and b).† The formula is in good agreement with the scanning electron microscopy energy dispersive X-ray spectroscopy (SEM EDS) analysis from which the Ba/Fe/P averaged ratio of 2.09/4.01/3.90 was determined (see Fig. S3a†). One should note the similitude between α-BFePO and α-BCoPO due to MO₅ chelated by PO₄ polyhedra.¹ This edge-sharing structural situation is known to increase the operating potential during the discharge (Li-extraction) of LiFe(PO₄) by the inductive effect, which suggests a rather “high” redox stability for α-BFePO.¹⁷ We checked by TGA in air and by high-temperature X-ray diffraction (HTXRD) that our Fe²⁺ compound is stable until 773 K and then transforms into a mixture of FePO₄ and other unidentified phases. The mass uptake accompanying the Fe²⁺ → Fe³⁺ oxidation was observed after 673 K by TGA, see SI5a.† This rather high stability is comparable to the oxidation along with Fe₂O₃ exsolution of γ-BFePO above 250 °C.⁷

Table 1 Bond distances and BVS for α-BFePO obtained from SXRD and refined in the P3212 space group

Ba		Fe		P
Ba1–O2	2.421(5)	Fe1–O1	2.057(4)	P1–O1	1.530(4)
Ba1–O2	2.421(5)	Fe1–O1	2.524(6)	P1–O2	1.476(6)
Ba1–O3	2.972(4)	Fe1–O1	2.911(7)	P1–O3	1.559(5)
Ba1–O3	2.972(4)	Fe1–O2	2.589(6)	P1–O4	1.578(7)
Ba1–O4	2.633(5)	Fe1–O3	2.072(4)
Ba1–O4	2.633(5)	Fe1–O4	1.767(4)
BVS Ba1	2.48(2)	BVS Fe1	1.99(2)	BVS P1	4.84(3)
BVS O1	1.80(1)	BVS O2	2.21(2)	BVS O3	1.69(2)
		BVS O4	2.38(2)

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3.1.2 α-BMnPO. Due to the large ionic radius of Mn²⁺ the XRD-pattern shows a related but distorted structure for α-BMnPO with splitting of most of the diffraction peaks; they can be fully indexed and refined in the monoclinic subcell given by a_M = √3·a_T, b_M = b_T, c_M = c_T, β_M ∼ 90° where T and M subscripts refer to the monoclinic and parent trigonal phases, respectively. The space group C2 was selected as the most symmetrical monoclinic subgroup of P3₁21 (R_Bragg = 10.9%, minor Ba₂Mn(PO₄)₂ impurity), see Fig. 1b. Three independent Mn²⁺ ions result from this symmetry reduction; these are arranged in two kinds of layers containing mixed Mn1/Mn2 or Mn3 metals, see Fig. 2c. Both show strongly distorted MnO₅ square pyramids connected by corners in the layers, and each was chelated by phosphate groups, similarly to the α-BFePO case, see Fig. 2d. Besides the structural distortion into two individual layers, the structure remains essentially the same between the Fe²⁺ and Mn²⁺ cases. However, all three MnO₅ coordination polyhedra tend to square pyramids due to PO₄ re-orientations. The calculated BVS are 2.06(2), 1.64(2) and 1.60(2) for Mn1, Mn2 and Mn3 respectively due to short Mn–O distances taking into account the Mn²⁺ radius, e.g. Mn1–O4_2 = 1.96(1) Å, see Table 2. It pictures a rather stressed crystal structure and our attempts to restrain longer Mn–O distances considerably damaged the quality of the refinement. Pertinent interatomic distances are given in Table 2, and refinement data and atomic coordinates in ESI Table S2(a and b).† These results are supported by powder neutron diffraction (3T2 diffractometer, LLB, CEA, Saclay, France λ = 2.42 Å) data at 80 K, see Fig. S15b.† The formula is in good agreement with the averaged SEM EDS analysis of 2.01/3.95/4.04 for Ba/Mn/P (see S3b†). The IR and UV spectra are given in S4 showing vibrational bands typical of phosphate oxo-anions. The experimental optical bandgaps are 4.1 eV for α-BFePO and 4.6 eV for α-BMnPO in good agreement with their pale colors. However the weak/broad absorption band around 550 nm is responsible for the pale-pink shade in α-BMnPO.

Table 2 Bond distances and BVS for α-BMnPO obtained from SXRD and refined in the C2 space group

Ba		Mn		P
Ba1–O2_2	2.994(6)	Mn1–O1_1	2.055(5)	P1–O1_1	1.544(5)
Ba1–O2_2	2.719(6)	Mn1–O1_2	2.301(8)	P1–O2_1	1.512(5)
Ba1–O3_2	2.996(7)	Mn1–O2_2	2.448(7)	P1–O3_1	1.539(6)
Ba1–O4_2	2.780(5)	Mn1–O3_2	2.032(5)	P1–O4_1	1.530(6)
Ba1–O2_3	3.057(8)	Mn1–O4_2	1.958(6)
Ba1–O2_3	2.766(7)			P2–O1_2	1.546(6)
Ba1–O3_3	2.732(7)	Mn2–O1_1	2.233(7)	P2–O2_2	1.528(7)
Ba1–O4_3	2.531(5)	Mn2–O2_1	2.229(8)	P2–O3_2	1.543(5)
		Mn2–O3_1	2.217(9)	P2–O4_2	1.485(5)
Ba2–O2_1	2.692(7)	Mn2–O4_1	2.133(6)
Ba2–O2_1	2.692(7)	Mn2–O1_2	2.212(6)	P3–O1_3	1.523(5)
Ba2–O3_1	2.822(6)			P3–O2_3	1.524(6)
Ba2–O3_1	2.822(6)	Mn3–O1_3	2.463(8)	P3–O3_3	1.528(5)
Ba2–O4_1	2.518(7)	Mn3–O1_3	2.184(6)	P3–O4_3	1.546(6)
Ba2–O4_1	2.518(7)	Mn3–O2_3	2.422(7)
		Mn3–O3_3	2.144(7)
		Mn3–O4_3	2.050(7)
BVS Ba1	2.08(2)	BVS Ba2	2.20(2)
BVS Mn1	2.06(2)	BVS Mn2	1.64(2)	BVS Mn3	1.60(2)
BVS P1	5.04(4)	BVS P2	5.13(4)	BVS P3	5.06(4)
BVS O1_1	2.01(2)	BVS O1_2	1.78(2)	BVS O1_3	1.82(2)
BVS O2_1	1.97(2)	BVS O2_2	1.90(2)	BVS O2_3	1.86(2)
BVS O3_1	1.78(2)	BVS O3_2	1.89(2)	BVS O3_3	1.96(2)
BVS O4_1	2.19(2)	BVS O4_2	2.33(2)	BVS O4_3	2.22(2)

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3.1.3 Structural modulations of the α-phases. Both refined structures have shown a certain degree of disorder based on the large thermal parameters refined for PO₄ groups. These may be related to the existence of a commensurate modulation characterized by (2a, b, 2c supercell, referred to the trigonal subcell) in both α-BFePO and α-BMnPO as observed by electron diffraction, see Fig. 3(b) for the α-BFePO case. In the Fe²⁺ case, the q vector is incompatible with the trigonal symmetry, which suggests for the two compounds the 4D-monoclinic C2(0, ½, ½)0 superspace group. However very weak supercell spots have been only identified in SXRD data (not in PND), see Fig. 3(a) which questions their real origin and correlation length. Our attempts to observe and refine any kind of modulated feature on all atoms using a super-space approach failed, leaving a constant electronic density along the fourth dimension, such that at this stage the refined average structure prevails. Indeed, one has to keep in mind that the “average structure” may be erroneous, due to local, medium- or long-range ordering. In particular, the DFT structural relaxation discussed below may lack the 2a, b, 2c supercell ordering, for a representative optimized structure.

Fig. 3 (a) Modulation peaks indexed in green on synchrotron data for α-BaFe₂P₂O₈; minor impurity peaks are marked with a blue star. (b) ED patterns of α-BaFe₂P₂O₈ with highlights of the modulation indexed with the vector. (c) BaM₂P₂O₈ (M = Co, Fe, Mn) diagrams vs. temperature with ideal symmetries, cell volumes and phase transformations.

3.2 Phase transitions

We have investigated the stabilities and phase transformations occurring in BMPO, keeping in mind the complex BCoPO behavior that motivated this work, see Fig. 3(c), and S8a† for more information about cell parameters.¹

3.2.1 α-BMnPO upon warming and pressure. Due to the redox stability of divalent manganese phosphates, α-BMnPO behaves similarly in air and nitrogen without any significant mass evolution, see S5b.† DTA and HTXRD for BMnPO show reversible 1st order transitions into α′ (unchanged monoclinic reflections reasonably assigned to the parent C2 or C2/m space groups) at 680 K and then into β-BMnPO at 831 K with sharp DTA endo/exothermic effects upon heating/back cooling, see Fig. 4(a) and (b). β-BMnPO is characterized by an abrupt volumic expansion leading to a trigonal unit cell (a, c/3), see Fig. 4(c) and S6b† and is reconstructive as observed in the cobalt case.¹ Finally, it is worth mentioning that preliminary high pressure syntheses starting from β-BMnPO at 2 GPa, 873 K lead to a novel polymorph, obtained in a multiphase mixture at the moment. Our preliminary Lebail indexation gives a monoclinic unit cell with a = 9.2830(12) Å, b = 4.9783(6) Å, c = 8.1326(10) Å, and β = 94.106(7)(9)°, compatible with the P2₁/a space group. This phase is under investigation but the analogy with α-BCoPO suggests TBP coordination around Mn²⁺.

Fig. 4 (a) DTA under flowing air for α-BaMn₂P₂O₈, showing the α → α′ and α′ → β transitions. (b) The two phase transitions (red to green, green to magenta) by HTXRD data for α-BaMn₂P₂O₈ upon heating. (d) DTA under flowing Ar for α-BaFe₂P₂O₈, with evidence of the transitions α → α′ and α′ → β. (e) Corresponding volume expansion upon heating under flowing N₂ from HTXRD data.

3.2.2 α-BFePO upon warming and over time. Preserving the Fe²⁺ oxidation state, α-BFePO reversibly transforms under flowing N₂ into an α′-polytype at 766 K with minor lattice evolution. Here the P3₁21 symmetry is assumed to be retained from the analysis of XRD peaks. Then it transforms into a β-polymorph with one third unit cell volume at 809 K, see Fig. 4(d) and S5a.† Sharp DTA peaks on heating broaden when on the cooling ramp. The characteristic cell evolution upon the transformation was followed by HTXRD, see Fig. 4(e) and S6a.† At 1123 K we refined a = 5.257(3) Å and c = 8.290(5) Å (V = 198.41(1) ų), very similar to the β-BCoPO case, see Fig. 2e for representation of the structure.¹ It is noteworthy that after a long-time (>1 year) in the desiccator, α-BFePO partially transforms into the rhombohedral γ-BFePO (α → γ) (see Fig. 2f for the representation of the structure) which supports the metastable character of both the α and β forms, see Fig. S7.† In contrast, an opposite γ → α long-time transformation occurs for BCoPO.^18,19 We found in the RT reaction product the evidence of a second phase indexed in a unit cell similar to the one of Ba₂Mn(PO₄)₂, for which the Fe member is non-reported, see S7.†

At this stage, within the Fe²⁺ and Mn²⁺ series, taking into account our relaxed structures detailed below, we assume that the modulated features are lost in both the α′ and β variants.

3.3 Phase stability: – DFT calculation

We have performed electronic structure and total energy calculations by GGA and GGA+U for both the α and γ variants of BMPO compounds. Several results should be pointed out.

(i) Constraining the experimental unit cells for α-BMnPO and α-BFePO yields models not fully compatible with our α experimental diffraction data. Indeed, after simulation of the XRD patterns corresponding to the DFT optimized structures, we found them very similar to those observed in situ at high temperature in the α′ domain, see S10.† For instance after relaxing α-BFePO under the conditions given in S11a† using GGA+U (U = 6 eV), with the Hubbard term U used at the relaxation level since it has been reported to allow more accurate geometry optimizations in several magnetic systems, the calculated XRD pattern clearly shows misestimated reflections (015, 112, 118, 11 10 …), see S9d† compared to our experimental data (α-form), see Fig. S9(a–c).† The intensities of these specific reflexions are significantly lowered at the α → α′ transition, such that surprisingly an α′ related model is obtained after convergence. Generally speaking, more regular MO₅ polyhedra are obtained after relaxation but associated with strong BVS deviations compared to expected values for M²⁺, P⁵⁺, and O²⁻ charges, see Table S11b.† One should deduce the primary importance of the 2a, b, 2c ordering in the real α-model. Finally, the total energy was calculated using the α refined average model at room temperature. Considering ΔG = ΔE + PΔV − TΔS for a transition, the PΔV term may be neglected considering solids and TΔS = 0 since our DFT calculations are at zero kelvin. Then, ΔG = ΔE and we use the DFT total energies to evaluate the relative stability within each title system.

(ii) Comparing the total energies of experimental α and γ models and neglecting minor ΔV and entropic effects shows that for BFePO/U = 6 eV: ΔG_γ–α = −0.85 eV per FU and for BCoPO/U = 4 eV: ΔG_α–γ = −1.07 eV per FU validating the observed transformations under ambient conditions, see S11a.† We note the very strong energy differences involved compared to phosphate systems, e.g. VOPO₄.²⁰

(iii) For the hypothetical γ-BMnPO, the full-structure relaxation at U = 4 eV gives an unrealistic model, with BVS (Mn) ∼3+, and BVS (P) ∼4.5+, see Table S11b.† The most stable α-form is verified by: ΔU_α–γ = −1.01 eV per FU.

Deeper investigations have been performed combining extended Hückel tight binding calculations (EHTB) on the Fe²⁺ and Co²⁺ α and γ-polytypes. EHTB give a rough image of the crystal field and have been used in γ-BFePO compounds to explain the origin of the re-entrant transition.⁶ For the α-types, we have used an isolated MPO₇ unit to take into account the M–P vicinity, see Fig. 5b. The d splitting deduced from molecular orbitals is shown in Fig. 5a. In α-BFePO, the role of the Fe–O4 bond is rather atypical due to the particularly short distance Fe–O4 = 1.776 Å. It leads to a σ* bond calculated ∼0.5 eV above the d⁶ barycenter. This simple vision is comforted by the Fe total 3d-DOS projection using (U = 6 eV) for which the majority spin (↑) contribution has the particularity of being disrupted below E_F, see Fig. 5d.⁵ These projected DOS on 3d-Fe show also that the majority spins (↑) are fully occupied while the minority spins (↓) are partially empty in accordance with a high spin state and the expected oxidation state Fe²⁺. The highest d-based atomic orbital (EHTB) and the highest populated ↑d-states clearly correspond to a predominant d_xy contribution in reference with the crystal axes. The three in-plane oxygen ligands along the x and y axes were assigned to this d_x²−y² setting, see Fig. 5c and S12† for details about orbital representation. This configuration is plausibly strongly destabilizing compared to the standard octahedral crystal field calculated for FeO₆ in γ-BFePO. A rough calculation of the crystal field stabilization energy (CFSE) for d⁶ HS-Fe²⁺ shows similar results mostly in favor of octahedra against TBP (0.4Δ_Ovs. 0.38Δ_TBP). The same calculation for d⁷ HS-Co²⁺ phases gave the same tendency (0.79Δ_Ovs. 0.76Δ_TBP) and does not match the higher stability of α-BCoPO, which also takes into account the on-site electrostatic repulsion above all with mainly a 3D arrangement. At least, these calculations validate comparable d-manifold splitting, and the stability of the observed phases.

Fig. 5 DOS (a) Molecular orbital diagrams from EHTB calculations for the α- and γ-forms with indication of the Δo or ΔTBP energies. (b) Details of a FeO_3-O₄P dimer used for the crystal field estimation of α-BFPO/P3₁21. (c) Corresponding molecular orbitals (MO) and MO diagram with indication of the dominant d orbital contribution. (d) DFT-calculated DOS projected on the 3d orbitals of Fe in α-BFePO. The inset shows a zoom around the Fermi level (dashed vertical line).

More insights into the bonding situation are given by the COHP (Crystal Orbital Hamilton Population) analysis carried out using the LOBSTER^21–23 software and the results are shown for the shortest Fe–O4 bond and for a longer “standard” Fe–O1 bond for comparison. The majority spin (↑) COHP is bonding in the lower VB part while it is antibonding close to the Fermi level, with a much larger antibonding contribution at E_F for Fe–O4. It highlights the instability suggested above compared to “standard” Fe–O bonds. The minority spin (↓) COHP however is mostly bonding in the all VB range for both Fe–O bonds stabilizing for the edifice. We note that very close to E_F this contribution is nonbonding. This is also obvious from the Fe–O integral COHPs (ICOHP) (see Table S11c†) which are all of net bonding character with significantly higher values for the minority spin population. However, this is much more pronounced in the case of the short Fe–O bond with ICOHP (↑) = −1.044 eV and the stronger bonding character of ICOHP (↓) = −1.627 eV then giving a strong covalent bond with electronic instability to the Fermi level (Fig. 6).

Fig. 6 Fe–O projected COHP (pCOHP) for (a) the short Fe–O4 and (b) for next longer Fe–O1 distances Å. The bonding (antibonding) interactions are set positive (negative) by convention.

3.4 Magnetic characterisation

3.4.1 α-BFePO. The magnetic susceptibility of α-BFePO was measured at H = 0.1 T after a preliminary alignment at room temperature of magnetite domains present as a minor impurity, not detected by XRD, see Fig. 7a. This latter is responsible for the weak ferromagnetic evidence at room temperature (see Fig. 7b) and the anomaly at the Verwey transition (T = 125 K), see Fig. 7b. The Curie Weiss law between 400 and 125 K was fitted taking into account the impurity contribution leading to θ_CW = −7.9 K and μ_eff = 6.16μ_B/Fe²⁺ (very similar to what has been reported for γ-BFePO,⁶ 6.16μ_B/Fe²⁺) well above the calculated spin-only moment (S = 2) of 4.89μ_B/Fe²⁺ due to orbital contribution, see Fig. S13.† Below T_N ≈ 15 K the compound orders antiferromagnetically with the appearance of a significant ferromagnetic contribution assigned to a canted spin, similarly to α-BCoPO (T_N = 17 K). We found the remanent moment at 2 K to be M_2K = 0.03μ_B per FU. The Fe connectivity creates zigzag chains separated by PO₄ groups and Ba²⁺ in and between the layers, respectively. Both the in-layer super-exchange path (Fe–O–Fe angle = 120.2°, Fe–O1 = 2.55 Å) and the very long between-layer distances Fe–Fe > 6.25 Å contribute to the low magnetic ordering temperature, although dealing with large local magnetic moments. For instance, it is drastically lower when compared to the honeycomb γ-BFePO which orders ferromagnetically at T_c = 65 K due to its Ising ferromagnetism independent of the interlayer coupling.⁵ These results are also supported by specific heat measurement, see Fig. S14.†

Fig. 7 (a) χ(T) and χ⁻¹(T) plots for α-BFePO recorded at H = 0.1 T in ZFC and FC modes. The inset shows the weak FM observed below T_N. Curie–Weiss fit above 130 K. (b) M(H) for α-BFePO at different temperatures opening an hysteresis at 2 K. (c) χ(T) and χ⁻¹(T) plots for α-BMnPO measured at H = 0.1 T in ZFC and FC modes. The inset shows that the weak FM occurs below T_N. Curie–Weiss fit above 80 K. (d) Cp(T) t for α-BMnPO at H = 0 T.

3.4.2 α-BMnPO. α-BMnPO orders antiferromagnetically at T_N ≈ 8 K and it follows a Curie–Weiss law above T = 75 K resulting in θ_CW = −43.52 K and μ_eff = 5.9μ_B/Mn²⁺ (see Fig. 7c), which matches with the expected value for S = 5/2 and shows a moderate frustration of T_N/θ_CW ≈ 5. This transition is also observed in heat capacity measurements at around 9 K as shown in Fig. 7d.

4. Conclusion

In conclusion, the BaM₂(PO₄)₂ system phase diagram was investigated in this work, as well as the magnetic properties of the novel α form dealing with M = Mn²⁺ and Fe²⁺. They show particularly complex phase diagrams with α, β, and γ variants all based on layered architectures, and weak ferromagnetism. This specificity arises from the strong tendency of large Ba²⁺ to favor 2D-structures while associated with oxo-anions. The α → α′ → β transitions are order disorder ones, suggesting a diversity of related structural polymorphs already well characterized in the M = Co²⁺ case. They consist of MO₅ polyhedra that vary from TBP to square-pyramids depending on M. The TBP Fe²⁺O₅ in α-BFePO is not common, especially dealing with a particularly short Fe–O bond of 1.77 Å. Similarly we found rather short Mn–O distances in α-BMnPO which suggest stressed α-types likely for high temperature transitions, comforting the experimental lattice expansion across the α → α′ → β transitions. The internal constraints evidenced from interatomic distances and bond valence sums are probably relaxed locally by commensurate modulations, evidenced as k = (½, 0, ½) by electron microscopy, but possibly associated with short/medium correlation lengths. This feature is important since, in the absence of a “supercell-box”, our structural optimizations did not converge to the stable α models but rather to the α′ ones. For Co²⁺ and Fe²⁺, a strong competition exists between these variants and the so-called γ one characterized by isolated Honeycomb octahedral layers. Dealing with quasi-2D magnetic compounds, they are of strategical importance in the field of low-D magnets, but prepared under different conditions compared to the α-variants, i.e. solvothermal conditions for γ-BFePO and melting/quenching for γ-BCoPO. In fact, the relative stabilities of the α/γ tandem under ambient conditions are reversed between the Co²⁺ and Fe²⁺ cases such that after a long-time stay (>1 year) in the desiccator, α-BFePO partially transforms into the rhombohedral γ-BFePO (α → γ) while, an opposite γ → α long-time transformation occurs for BCoPO. These transformations verified the energies calculated for each compound. In the case of γ-BFePO we propose that the short Fe–O distance mentioned above destabilizes the α type for the γ one. Finally, one could consider these room temperature transformations as opportunities to prepare mixed γ-BaFe/MPO phases using a solid state route with a strict control of the Fe/M ratio. We recall that so far, these phases are prepared under hydrothermal conditions with a poor stoichiometric control.

Conflicts of interest

The authors declare no competing financial interest.

Acknowledgements

This work was carried out under the framework of the LOVE-ME project supported by the ANR (Grant ANR ANR-16-CE08-0023). The Fonds Européen de Développement Régional (FEDER), CNRS, Région Hauts-de-France and Ministère de l'Education Nationale, de l'Enseignement Supérieur et de la Recherche are acknowledged for funding the X-ray diffractometers and PPMS equipment. Chevreul Institute (FR 2638), Ministère de l'Education Nationale, de l'Enseignement Supérieur et de la Recherche, Région Hauts-de-France, FEDER are acknowledged for supporting this work. We thank Laurence Burylo, Nora Djelal and Claire Minaud at the UCCS for their technical help.

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Footnote

† Electronic supplementary information (ESI) available: More detailed crystallographic information (with powder refinement datas, atomic positions and equivalent anisotropic thermal displacement) EDS analysis, UV visible and IR spectroscopy, thermal analysis (HTXRD, and DTA/TGA), cell parameter evolution and phase transition upon heating, synchrotron refineùent, DFT calculations, density-of-states calculations, magnetic measurement and specific heat measurement; X-ray crystallographic data. CCDC 1942484 for α-BaFe₂(PO₄)₂ and 1942500 for α-BaMn₂(PO₄)₂. For ESI and crystallographic data in CIF or other electronic format see DOI: 10.1039/c9qi00934e

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