Magnetic Hyperfine Interactions in the Mixed-Valence Compound Fe7

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C: Plasmonics; Optical, Magnetic, and Hybrid Materials

Magnetic Hyperfine Interactions in the Mixed-Valence Compound Fe(PO) from Mössbauer Experiments 7

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Alexey V. Sobolev, Alena A Akulenko, Iana S Glazkova, Alexei A. Belik, Takao Furubayashi, Larisa Victorovna Shvanskaya, Olga V. Dimitrova, and Igor A. Presniakov J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b05516 • Publication Date (Web): 24 Jul 2018 Downloaded from http://pubs.acs.org on July 26, 2018

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The Journal of Physical Chemistry

Magnetic Hyperfine Interactions in the Mixed-Valence Compound Fe7(PO4)6 from Mössbauer Experiments Alexey V. Sobolev1,*, Alena A. Akulenko1, Iana S. Glazkova1, Alexei A. Belik2, Takao Furubayashi3, Larisa V. Shvanskaya1,4, Olga V. Dimitrova1, Igor A. Presniakov1 1

Lomonosov Moscow State University, 119991 Moscow, Russia

2

Research Center for Functional Materials, National Institute for Materials Science (NIMS),

Namiki 1-1, Tsukuba, Ibaraki 305-0044, Japan 3

Research Center for Magnetic and Spintronic Materials, National Institute for Materials

Science (NIMS), Sengen 1-2-1, Tsukuba, Ibaraki 305-0047, Japan 4

National University of Science and Technology “MISiS”, 119049 Moscow, Russia

*

corresponding author, e-mail: [email protected], [email protected] ABSTRACT

Hyperfine parameters of Fe7(PO4)6 phosphate were examined using

57

Fe Mössbauer

spectroscopy in a wide temperature range of 4.2 ≤ T ≤ 300 K. Four different iron sites were successfully detected: two for the high-spin Fe2+ and two for Fe3+ ions. Mössbauer spectra below TN1 ≈ 47 K were analyzed by diagonalization of the full nuclear-interaction Hamiltonian. The noticeable difference between the saturated hyperfine fields (Bhf) for the 5-fold-coordinated site (~ 5.0 T) and the octahedral site (~ 10.1 T) was related to the symmetry of the local crystal field. Using crystal field calculations of the energy levels based on the point symmetry of the (Fe2+O5) and (Fe2+O6) sites, we estimated the intra-atomic magnetic dipolar and electron orbital current contributions to the Bhf field. The observed line broadening below the second magnetic phase transition at TN2 ≈ 16 K is approximated by the bimodal distribution of the hyperfine fields p(Bhf) that is characteristic of spin-modulated magnetic systems.

INTRODUCTION Transition metal phosphates offer a considerable number of structures, which can give rise to unusual physical and chemical properties. Iron phosphates demonstrate rich crystal chemistry and numerous practical applications, for example, as heterogeneous catalysts.1-3 Many “mixedvalence” compounds, which contain iron ions in formal oxidation states of +2 and +3, are interesting because they can show intervalence charge transfer. These compounds have been extensively investigated in connection with the increased interest in new functional materials (superconductors, colossal magnetoresistance materials, iron-based Li-ion rechargeable batteries)4 and biological systems.5

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Since the publication of the crystal structure of a mixed-valence (Fe3+/2+) phosphate Fe7(PO4)6,6 many compounds isotypic with Fe7(PO4)6 have been reported.1-9 Among them are iron-based phosphates: Na0.1Fe7(PO4)6,7 Ni3Fe4(PO4)6,8 Co3Fe4(PO4)6,9,10 Mn2Fe5(PO4)6,9 Cu2Fe5(PO4)6.11 Actually the Fe7(PO4)6-type structure allows wide iso- and alio-valent substitutions in cation and anion sublattices. Number of cations can change from 6.5 to 8 per unit cell. The structure of Fe7(PO4)6 itself has four iron sites: Fe1 and Fe2 are occupied by Fe2+ ions in mostly regular pyramidal Fe1O5 and octahedral Fe2O6 environments, and Fe3 and Fe4 sites are occupied by ferric Fe3+ ions in the octahedral Fe3O6 and Fe4O6 coordination (Fig.1). The Fe1O5, Fe2O6, Fe3O6, and Fe4O6 polyhedra form a three-dimensional network. The Fe4O6 and Fe3O6 octahedra share a common edge, forming dimer units; two Fe4O6 octahedra also share a common edge (Fig.1). There are also one-dimensional zig-zag chains formed by edge-shared polyhedra, …-Fe3O6 -Fe3O6 –Fe1O5 -Fe4O6 -Fe4O6 –Fe1O5-… . These 1D chains are linked with each other through Fe2O6 polyhedra. Despite interesting features in the crystal and electronic structure of the parent Fe7(PO4)6 compound and a large number of the Fe7(PO4)6-type compounds, magnetic properties were studied only in a few cases. In Co7H4(PO4)6,12 a metamagnetic phase transition was observed in the antiferromagnetic state below 11.8 K. Antiferromagnetic ordering was found in Mn7H4(PO4)6 11

at 6.0 K and Mn7H4(AsO4)6

13

at 9.5 K. β-Cu3Fe4(VO4)6

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was suggested to order

antiferromagnetically at 15 K, but the magnetic structure could not be determined because of a very limited number of the observed magnetic reflections on neutron powder diffraction patterns. Magnetic and dielectric properties of the parent Fe7(PO4)6 compound have been reported just recently; Fe7(PO4)6 exhibits two successive magnetic phase transitions at TN1 = 45 K and TN2 = 16 K.15 It was shown that dielectric permittivity of Fe7(PO4)6 demonstrates a kink at TN2, while no anomalies were found at TN1.15 Using the Goodenough-Anderson-Kanamori rules, the authors speculated that Fe7(PO4)6 has a collinear magnetic structure below TN1, while it shows a transformation into a non-collinear state below TN2 due to the competition of various exchange couplings.15 It is obvious that the sign and strength of exchange interactions depend on the features of iron electronic states. However, the authors did not give any information on electronic states of mixed-valence iron ions in the Fe7(PO4)4 structure. The experimental electron spin resonance (ESR) spectra of this compound demonstrated only the three different resonance modes, which can be assigned to Fe2+ in the two non-equivalent Fe1 and Fe2 sites and Fe3+ in an octahedral oxygen coordination (Fe3/Fe4 sites).15 The deviation of the effective g-factors for the both Fe2+ sites from 2 reflects essential effects of the orbital contribution due to the nonquenched orbital moment. It should be noted that the ESR measurements failed to distinguish between the two Fe3 and Fe4 states occupied by Fe3+ ions.15 Thus, it would be desirable to use ACS Paragon Plus Environment

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other local methods, which are very sensitive to electronic states of iron ions and can provide detailed insights into the nature of the two-phase transitions detected by the heat capacity and magnetic susceptibility. Mössbauer spectroscopy is a powerful tool for studying magnetic solids with complicated magnetic structures as this method offers the possibility of observation of the local spin configurations of different types as well as providing a quantitative estimation of different spin parameters. In addition, this local method is especially suitable to distinguish ferric (Fe3+) and ferrous (Fe2+) ions because of the large difference in isomer shifts, quadrupole splitting, and hyperfine fields on the 57Fe nuclei. However, 57Fe Mössbauer data reported in the literature about Fe7(PO4)6-type compounds are very limited: Mössbauer studies were performed for the parent Fe7(PO4)6 compound

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and related substituted phases such as Cu3-xFe4+x(PO4)6,11

Co3Fe4(PO4)6,9 and Na0.1Fe7(PO4)6,7 only in the paramagnetic temperature range (T > TN). In this work, we present our results of the detailed 57Fe Mössbauer study of Fe7(PO4)6 in a wide temperature range from 4.2 K to 300 K. The low-temperature spectra were analyzed using the full Hamiltonian of hyperfine interactions. We carried out a thorough analysis of temperature dependences of hyperfine parameters for the mixed-valence iron sites.

EXPERIMENT The Fe7(PO4)6 compound was synthesized by a solid-state method from a stoichiometric mixture of FePO4 and Fe by annealing at 1173 K for 130 h in evacuated sealed quartz tubes with several intermediate grindings. The synthesized Fe7(PO4)6 sample was black powder. The powder X-diffraction analysis was performed using Ultima-IV Rigaku diffractometer (CuKα1 radiation, λ = 1.54056 Å). The experimental and calculated patterns were in very good agreement; the Fe7(PO4)6 sample synthesized by the solid-state method was single-phase. The chemical composition of the sample was determined using a Tuscan Vega II XMU scanning electron microscope equipped with an INCA Energy 450 energy-dispersive spectrometer; the accelerating voltage was 20 kV. Magnetic and thermodynamic measurements were performed on a SQUID magnetometer (Quantum Design, MPMS-XL-7T) between 2 and 350 K in different applied fields under both zero-field-cooled (ZFC) and field-cooled on cooling (FCC) conditions. Isothermal magnetization measurements were performed between -7 and 7 T at different temperatures and between 0 and 9 T at 5 K on a PPMS. Specific heat, Cp, at magnetic fields of 0 and 7 T was recorded between 2 and 70 K on cooling by a pulse relaxation method using a commercial calorimeter (Quantum Design PPMS).



Mössbauer experiments were performed in transmission geometry with a 1.1 GBq γ-source of 57Co(Rh) mounted on a conventional constant acceleration drive. The spectra were fitted using the SpectrRelax program.18,19 The isomer shift values are referred to that of α-Fe at 300 K.

RESULTS AND DISCUSSION A. X-ray Diffraction data X-ray powder diffraction patterns of the synthesized samples showed the formation of the triclinic Fe7(PO4)6 phase (space group P1) without any traces of impurity phases. The refined lattice parameters of Fe7(PO4)6 (a = 7.9694(9) Å, b = 9.3128(9) Å, c = 6.3545(8) Å, α = 108.300(9)°, β = 101.614(9)°, and γ = 105.185(9)°) synthesized by the solid-state method are in good agreement with literature data.16

B. Thermodynamic and magnetic data Specific heat Cp(T) measurements clearly showed two magnetic transitions at TN2 = 16(1) K and TN1 = 47(2) K (Fig. 2a). Magnetic susceptibility χ(T) measurements showed a kink at TN1 (Fig. 2b), but χ(T) continues to increase with decreasing temperature and only below TN2, a sharp drop was observed typical for antiferromagnetic (AFM) transitions. In addition, isothermal magnetic measurements (M vs H) showed no hysteresis at all temperatures indicating the AFM nature of the transitions. The M vs H curves were also linear between -7 and 7 T at 25 and 55 K and between about -5 and 5 T at 5 K (see Supporting Information). Above about 5.5 T at 5 K, a field-induced transition was observed. These results are in good agreement with previously published data of thermodynamic and magnetic measurements of Fe7(PO4)6.15 Such reproducibility demonstrated good quality of our samples.

C. Mössbauer spectroscopy Paramagnetic temperature range, T > TN1 The 57Fe Mössbauer spectra of Fe7(PO4)6 measured in the paramagnetic temperature range (T > TN1) (Fig. 3) represent very asymmetric paramagnetic doublets with broadened lines, thus indicating a superposition of several partial subspectra with different hyperfine parameters. We described the spectra as a superposition of four quadrupole doublets Fe(i) (Fig. 3). The high values of isomer shifts , δ1 and δ2, for the Fe(1) and Fe(2) doublets (Table 1) correspond to the high-spin ferrous ions Fe2+(d6).20 The values of δ3 and δ4 are characteristic of ferric ions Fe3+(d5) in octahedral oxygen environments.20 Taking into account the crystallographic ratio of two Fe2+ sites, (Fe2+)P:(Fe2+)O = 2:1, we can assign the most intense quadrupole doublet Fe(1) to the Fe2+


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cations in the trigonal bipyramidal oxygen coordination (P). Thus, the doublet Fe(2) with a larger isomer shift δ2 and quadrupole splitting ∆2 can be related to the Fe2+ cations in an octahedral (O) oxygen coordination. Such assignment is well correlated with the general trend: compounds with four- and five-coordinated iron sites exhibit lower isomer shifts than compounds with sixcoordinated iron sites (iron-ligand bond lengths are shorter and more covalent when the coordination number is smaller).20 The observed disagreement between the experimental area ratio I1:I2 = 1.94(6) for the Fe(1) and Fe(2) partial spectra (Table 1) and the expected ratio 2:1 for the populations of two ferrous sites in Fe7(PO4)6 can be explained by the difference in the Lamb-Mössbauer factors (fP > fO) for the 5-fold (fP) and 6-fold (fO) coordinated iron ions.21 At the same time, a minor deviation the experimental ratio (I3 + I4):(I1 + I2) = 1.33(1) from the expected value of [Fe3+]:[Fe2+] = 4:3 should be related with a partial oxidation Fe2+→Fe3+ upon introducing excess phosphate groups (PO43-): 3Fe2+ ↔ 3Fe3+ + PO43-. Using the experimental ratio [Fe3+]:[Fe2+] ≈ 1.33, we estimated the composition as Fe7(PO4)6.002 (hereinafter, this almost stoichiometric phase will be referred as “Fe7(PO4)6”). To assign the partial spectra Fe(3) and Fe(4) to the corresponding positions of Fe3+ cations in Fe7(PO4)6, we calculated a lattice contribution {Vijlat}i,j = x,y,z to the electric field gradient (EFG) tensor at

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Fe nuclei in the different iron sites. Calculations have been realized within “ionic

model” taking monopole contribution (V% mon ) from ions occupied non-equivalent positions and dipole contribution ( V% dip ), arising from the induced electric dipole moments (pO) of oxygen O2ions (see Supporting Information).22 Our calculations of the EFG tensor, using crystal data for Fe7(PO4)6,12 have shown that in addition to the lattice V% mon and V% dip contributions large weight has an electronic contribution V% el related to overlapping of 2s/2p orbitals of the O2- anions with the iron cations np orbitals ( V% ov ).23,24 The tensor operator V% tot of the “total” EFG tensor is conveniently expressed as

V% tot = (1 − γ∞ ){V% mon + V% dip }lat + (1 − R)V% el ,

(1)

where V% el ≡ V% ov , γ∞ = -9.14 and R = 0.32 are Sternheimer’s antishielding and shielding factors.21 The principal components {Viitot}i = X,Y,Z of the EFG tensor were used to estimate the theoretical quadrupole splitting after diagonalization procedure: ∆theor = eQVZZtot (1 + 13 η 2 )1/2 ,

(2)

where eQ = 0.15 barn 21 is the nucleus quadrupole moment for 57Fe in its excited state, η ≡ (VYY VXX)/VZZ is the parameter of asymmetry with VZZ≥VYY≥VXX. The Viitot values and



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quadrupole splittings ∆theor calculated by Eq. (2) are represented in Table 2. The best agreement between the theoretical and experimental values of quadrupole splitting at 300 K (Table 1) was found for the polarizability value αО ≈ 1.7 Å3 and nominal charges ZO = −2, ZFe = +2/+3, ZP = +5 (Supporting Information). The obtained high value of αО agrees well with the data for other iron compounds.25 According to the EFG calculation, the Fe(3) quadrupole doublet can be related to the ferric Fe3O6 octahedron with the largest bond length distortion parameter ∆d3 = 113.1⋅10-4 Å2 and the average bond length ≈ 2.014 Å.7 Thus, the Fe(4) doublet can be assign to the ferric Fe4 sites with the average bond length ≈ 2.031 Å and parameter ∆d4 = 54.4⋅10-4 Å2, that is closer to the geometry of an ideal octahedron FeO6 than the Fe(3) sites (Fig. 1). At the same time, our calculations of the V% tot tensor for the ferrous Fe1 and Fe2 sites showed that it is impossible to reach any quantitative agreement between the experimental and theoretical values, underlying that the symmetry of the crystal environment in these sites cannot cause such high values of the EFG at

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Fe nuclei. This result indicates the necessity of considering additional

electronic contribution (V% val ) to the EFG related with different electronic population of iron 3dorbitals (see below).21 Most importantly, our experiments reveal that Fe7(PO4)6 can be assigned to Robin-Day Class I mixed-valence systems,26 where the time scale of the electron hopping Fe3+ ↔ Fe2+ is much longer than the precession time (τQ ≈ 10-8 s) of the exposed, then different static patterns Fe

3+

and Fe

2+

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Fe nucleus in EFG to which it is

are observed. Additional energy would be

required to remove the structural distortion and hence average the two mixed-valence sites to single “Fe2.5+” state. It should be noted that the effects of the structural distortion and iron valence ordering do not preclude electron hopping between neighboring Fe2+/Fe3+ sites which may occur at a slower rate than the Mössbauer time scale measurements.

Magnetic “intermediate” temperature range TN2 < T < TN1 A complex Zeeman structure appears in the spectra of Fe7(PO4)6 upon moving into the lowtemperature region TN2 < T < TN1 (Fig. 4), indicating the hyperfine magnetic fields Bhf induced at 57

Fe nuclei. Taking into account the above results in the paramagnetic temperature range (T >>

TN1), the spectra have been approximated as a superposition of four hyperfine Zeeman patterns. Since the maximum value of the hyperfine magnetic field Bhf for the Fe(1) and Fe(2) subspectra, corresponding to the ferrous ions, does not exceed ∼11 T even at the lowest temperatures, and the quadrupole coupling constant reaches the values |eQVZZ| ≥ ~5 mm/s (Table 3), we used in all


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subsequent fitting the full Hamiltonian of hyperfine interactions having the simplest form in the coordinate system of the principal axes of the EFG tensor:21

[

]

eQVZZ Hˆ µQ = 3IˆZ2 − Iˆ + η( IˆX2 − IˆY2 ) − g N µ N Bhf [( IˆX cos ϕ + IˆY sin ϕ) sin θ + IˆZ cos θ], 4 I (2 I - 1)

(3)

where IˆX ,IˆY ,IˆZ are the angular momentum operators of the 57Fe nucleus in its exited state; gN is nuclear g-factor; µN is the nuclear Bohr magneton. The eigenvalues ĤµQ depend not only on the hyperfine parameters of the system (δ, eQVZZ, Bhf, η), but also on spherical angles (θ, ϕ) that determine the orientation of the Bhf hyperfine field in the system defined by the principal axes Ô(X,Y,Z) of the EFG tensor. The linewidths (Wi) of the peaks were restricted to be the same for the all four Fe(i) subspectra to reduce the number of variables in the fitting. Since these Zeeman patterns originate from the same crystal lattice this restriction must be reasonable approximation at least to the first order. The application of the above model allowed us to describe satisfactorily the entire series of experimental spectra (Fig. 4). The best-fit hyperfine parameters and relative intensities (Ii) of the Fe(i) spectra at T = 20 K are given in Table 3. The linewidth (W) for all Zeeman patterns is close to that (∼0.35 mm/s) obtained from the paramagnetic temperature range (T > TN1), thus underlying that in each crystalline position iron ions have a uniform magnetic surrounding. The small line broadening ∆W (= WT - W300K) ≈ 0.09 mm/s can be attributed to relaxation processes usually observed in the vicinity of the magnetic ordering temperature.27,28 We observed a development of paramagnetic components (lower panel of Fig. 4) with hyperfine parameters corresponding to the four quadrupole doublets Fe(i) at T > TN1 (Fig. 3), whose partial contribution increases with temperature as the magnetic ordering temperature is approached (T ≈ TN1). It may seem plausible to suppose that a spread in TN1 due to sample inhomogeneity could induce these anomalous in spectra, where the quadrupole doublets and Zeeman lines correspond to paramagnetic and ordered portions of the sample respectively. We should pay attention to small and very different values of magnetic fields Bhf (T)T→20K for the Fe2+ ions in the Fe1 and Fe2 sites while hyperfine fields for Fe3 and Fe4 ions are reduced by only approximately 10% from its common values for ferric oxides.29 To discuss possible reasons for the observed reduction of the Bhf value, we took into account that the i-component of saturation value Bhf is the sum of several contributions:30 2 µB 1 µB ( g iie ff − 2) S i − ∑ Lij S j , 3 7 < r 3 > j = x,y,z Lij = 0 12 ( Lî Lˆ j + Lˆ j Lî ) − 13 L ( L + 1) ⋅ δij 0

Bi = BF S i −


(4)


where is the average value of the inverse cubic of the distance between 3d electron and the nucleus, Lî ( j ) is the i-component of the orbital angular momentum operator, geff is the effective spin g-factor, µB is the electron Bohr magneton, and 0 is the orbital wave function of the ion in its ground state. The first term in (4) is the Fermi contact contribution, BF = 8/3πgNµB|ψ(0)|2, produced by 3d-polarization effects on the ns-shells. The sign “+” indicates that the direction of the contact field BF coincides with the direction of iron spin SFe and is opposite to that of magnetic moment

µFe. Covalency effects are known capable to reduce considerably the BF value for high-spin Fe2+ ions.29 It is acceptable to use the BF/S ratio as a method of evaluation of the BF contribution in convenient systems and then extrapolate it to cases where this contribution cannot be directly measured. The only contribution to Bhf comes from Fermi contact term BF ≈ Bhf, therefore, it can be used to estimate the ratio of BF/S in the case of the high-spin Fe3+ ions. We used the saturated value of T→4.2K = 54.81 T (BF/S ≈ 22 T) for Fe3+ ions in the octahedral Fe(3)/Fe(4) sites in the Fe7(PO4)6 structure (see below), and the saturation field value of Bhf = 47 T (BF/S ~ 18.8 T) for Fe3+ ions in the distorted trigonal bipyramid (FeO5) clusters of the Fe3PO7 structure.31 Taking these values of BF/S, we evaluated the Fermi contact fields BF(O) = 22×2 = 44 T and BF(P) = 18.8×2 = 37.6 T for the high-spin Fe2+(S = 2) ions in the octahedral and trigonal bipyramidal surroundings, respectively (supertransferred fields are included in the BF terms). The second term in (4) is orbital field Borb produced due to orbital currents. Usually, the low-symmetry crystal field quenches the orbital angular moment , however, for orbitally nondegenerate states, the spin-orbital coupling restores the orbital contribution into magnetic moment µ = µB ~ gS with effective g~ -tensor instead of gs = 2. Thus, the anisotropic orbital term in Borb arises from the anisotropy of the g~ -tensor. The orbital angular momentum is directed parallel to the spin at low temperatures by the spin-orbital coupling (∼λLS). The third term in (4) is produced by the dipolar interaction (Bdip) of the d-electron spins with the nucleus, and does not vanish only when the d orbitals are such that the spin density is aspherical. This term is related to the electronic part of the EFG Vijval = 72 e(1 - R)Lij, which arises from an asymmetrical charge distribution of the electron shell, and is represented as Βidip =µB Viival /2e(1-R) 32 in the coordinate system of the principal axes of the electronic EFG tensor. For isolated high spin Fe3+ ions having spherical 3d electron distribution or for ideal FeO6 octahedra with orbital singlet ground 3d-state 6

A1g ( = 0), the V% val ≈ 0, and the Borb and Bdip terms turn into zero. For the ferrous ions within the Fe7(PO4)6 lattice, the electronic contributions Vijval are related

with features of local symmetry of the Fe1 and Fe2 sites. To simplify the following calculations, ACS Paragon Plus Environment

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we considered a more symmetrical oxygen environment of ferrous ions in Fe1 and Fe2 positions which can be obtained by a small displacement of the O2- anions from their equilibrium sites as is shown in Fig. 7a. The energy level schemes for the high-spin Fe2+ ions in the CS (Fe1) and D2h (Fe2) local crystal fields are shown in Fig. 7b. Five d-electrons with the same spin directions form a half-filled 3d-shell, and consequently do not contribute to the EFG tensor. The Vijval ≠ 0 can therefore be contributed only by the sixth minority-spin electron situated on the lowestenergy level. The ground orbital state for Fe2+ in the non-distorted trigonal bipyramidal crystal field (D3h) (the five identical ligands are equidistant from the origin) is the doublet (xz/yz) which produces a quadrupole slitting ( VZZval ∝ -2/7) roughly half that ( VZZval ∝ ±4/7) produced by any singlet ground state according to the diagram in Fig. 7b. Our crystal field calculations, taking into account the real distorted trigonal bipyramidal surrounding of the Fe1 site, shows that the low-symmetry component of the crystal field (CS) can mix the xz and yz orbitals to yield the singlet ground state ψg = α xz +β yz (α2 + β2 = 1) that is mainly xz with some yz admixture (α2 >> β2). The relative contributions α2/β2 of mixing orbitals depend upon the relative magnitudes ξ (= α2/α4) of the radial integrals α2 and α4 (αn ∝ 1/[]n+1) (see Supporting Information).33 For the Fe2 sites with nearly tetragonal compressed octahedral oxygen surrounding (Fig. 7a), the ground orbital state corresponds to the singlet yz orbital whatever of the ξ value, thus giving positive VZZval = 4/7|e|(1 - R). Taking Fe(II) = 4.59 ao-3 32

val , we obtain the positive and very large eQVZZ( value of 5.41 mm/s. 2)

Finally, the total EFG tensor V% tot was constructed (see Eq. 1) with respect to the ô(x,y,z) coordinate system chosen for the eigenvalues problem (Fig. 7a). The electronic part of this tensor takes both overlapping and valence 3d-electrons into account: V% el ≡ ( V% ov + V% val ). The total EFG tensors for the Fe2+ in the Fe1 and Fe2 sites were diagonalized and the resulting principal values {Viitot}i = X,Y,Z were designated according to the usual convention |VZZ| ≥ |VYY| ≥ |VXX| (Fig. 7a). The orientation of the Ô(Xi,Yi,Zi) principal axes of the total EFG tensor relative to the local coordinate systems ô(xi,yi,zi) for the ferrous Fei sites are shown in Fig. 7a. Using the spherical angles (θi, ϕi) (Table 3) that determine the orientation of the hyperfine Bhf field in the Ô(Xi,Yi,Zi) system, and also assuming that the electronic spin SFe is along the direction of Bhf, we can suggest the ferrous spin arrangement in Fe7(PO4)6. For both ferrous sites, the direction of Fe2+ spins is very close to a direction parallel to trigonal Fe1{O2O8O10} and tetragonal Fe2{2O12O6} planes. However, we must be cautions in these findings because the so-called ambiguity problem,34 which means that several sets of the full Hamiltonian parameters (eQVZZ, θ, ϕ,η) may describe the shape of the ACS Paragon Plus Environment


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spectra equally well. In this case, for quantitative evaluation of correctness of the model chosen to interpret the spectra we could use an estimation of the various contributions BF, Borb and Bdip to the total hyperfine field Bhf (see Eq. 4) in comparison with the experimental Mössbauer and ESR 15 data. The calculated values { Vijval }i,j=x,y,z were used to evaluate the components of the dipole field

Bdip relative to the local coordinate systems ô(xi,yi,zi) of the ferrous Fei sites: Bxdip = −

µB S Vxxval sin θ% cos ϕ% + Vxyval sin θ% sin ϕ%  2e 

Bydip = −

µB S Vyxval sin θ% cos ϕ% + V yyval sin θ% sin ϕ%  , 2e  Bzdip = −

(5)

µB S Vzzval cos θ%  2e

where SFe = S( sin θ% cos ϕ% , sin θ% sin ϕ% , cos θ% ), θ% and ϕ% are the spherical angles that determine the orientation of the hyperfine field Bhf (||SFe) in the coordinate system ô(xi,yi,zi) of the Fei sites.

The greatest uncertainty is associated with the orbital fields Borb( Bxorb , Byorb , Bzorb ) including unknown components of the orbital angular momentum L(Lx, Ly, Lz) of ferrous ions. The lowsymmetry crystal field quenches the orbital angular momentum, but spin-orbit coupling restores an amount = ( g% e ff - 2)S, so that Biorb ∝ ∑j ( g ijeff − 2) S j (Eq. 4). The coordinate system where e ff the g% Fei tensor is diagonal is not coaxial with the ô(xi,yi,zi) and Ô(Xi,Yi,Zi) coordinate systems.

The principal components { giie ff }i=X,Y,Z of the g% e ff tensor are not known for Fe7(PO4)6 but the use of the isotropic values of the effective g-factors, gFe1 = 2.20(1) and gFe2 = 2.35(1), determined from ESR measurements,15 is quite sufficient to ensure a good agreement between theoretical fields |Bhf| = (Bx2 + By2 + Bz2)1/2 with the components {Bi}i = x,y,z (Table 5) and experimental values of Bhf,Fe1 and Bhf,Fe2 (Table 3). To be more precisely we use the saturation hyperfine fields Bhf,Fe1(0) and Bhf,Fe2(0) extrapolated in accordance with Brillouin function for iron ion spin S = 2

to 0 K of the experimental values above 16 K. The calculated values of Bhf,Fe1(0) and Bhf,Fe2(0) obtained by such procedure are of 5.6(3) and 11.5(4) T, respectively. Such a good agreement indicates the self-consistency of our semi-quantitative calculation suggesting that the observed difference between the Bhf,Fe1 and Bhf,Fe2 values is mainly related to their different nearly orb dip isotropic orbital fields, BFe1 < BFeorb2 , whereas the dipolar hyperfine interactions, BFe1 ≈ BFedip2 , play a

minor role. From Mössbauer spectra, we can obtain only the absolute value of Bhf but no information about the sign. However, the sign of Bhf is important for discussion about the electronic state of


Page 11 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Fe2+ cations, but is very difficult to be determined experimentally when magnetic moments are coupled antiferromagnetically as it is in our system. The sign of the internal field Bhf induced at 57

Fe nuclei is defined such that is positive when it is the same direction as the atomic magnetic

orb dip moment (µFe). An analysis of the data in the Table 5 shows that the large positive BFei and BFei

contributions significantly reduce the Fermi contact field BF,Fei, but do not change its negative sign. As in the case of high-spin ferric ions Fe3+, for both ferrous sites Fe1 and Fe2 the Bhf fields have negative signs, and are directed opposite to the magnetic moments µFe1 and µFe2. This result does not agree with Mössbauer studies of many other ferrous compounds, for example, FeCO3 32 and FeCl2.35 In these compounds, the positive contributions from Borb and Bdip exceeded the negative contribution from BF giving the positive resulting Bhf value. The reason for this is an orbital doublet ground state for Fe2+ with a trigonal local symmetry in FeCO3 and FeCl2.32,35 Such ground state produces a large orbital momentum ∼ 0.75 - 1.32 The local symmetry around Fe2+ ions at the sites Fe1 and Fe2 in Fe7(PO4)6 is fairly low and the degeneracy of the spin-orbit levels is lifted completely as discussed above. Therefore, of the ground states ψg ∼ xz

Fe1

and yz

Fe2

at both ferrous sites in Fe7(PO4)6 are considered to be quenched. The

exchange field and the ∼λLS coupling mixed the spin-orbit levels to yield the non-zero value of . However, the resulting value of ∼ 0.4 - 0.7 is estimated to be smaller than that in the cases of FeCO3 and FeCl2 where is not quenched by crystalline field. Low-temperature range, 4.2 K < T < TN2

We performed measurements of the spectra at temperatures T < TN2 (Fig. 5), and did not find any visible anomalies in the {eQVZZ(T)}Fei dependences (Fig. 7a). Coincidently, the isomer shift δ(T) gradually increase in accordance with the Debye approximation for the second-order Doppler shift (see Tables 1, 3, and 4).20 These findings show that there are no any electronic and structural transitions at low temperatures. However, the linewidths of the peaks (∼0.65 mm/s) for all subspectra Fe(i) are essentially wider than those expected for a single magnetic site as was observed for the spectra at TN2 < T < TN1 (W ≈ 0.35 mm/s). The observed line broadening (∆W ≈ 0.3 mm/s) can be attributed to either the distribution of the hyperfine field Bhf due to nonuniformity of the magnetic Fei sites or to the spin relaxation in the range of 10-11-10-7 s. In the latter case, the linewidths should become narrower as the temperature decreases because the relaxation time generally becomes longer at lower temperatures. The non-uniform magnetic environment also seems unlikely, since in this case the spectra measured at high temperatures TN2 < T < TN1 would have to have the similar wide lines.



Page 12 of 29

To analyze these spectra we reconstructed the distributions, pi(Bhf), of magnetic hyperfine fields in the frame of full Hamiltonian (3).21 The distribution reconstruction procedure was performed within the limits of the regularization method in its iteration variant where a linear correlation between the hyperfine parameters in the Hamiltonian (3) was assumed.18,19 Particularly a linear correlation between hyperfine fields Bhf and polar angles (θi, ϕi) which vary in the ranges of 0 < θi < π and 0 < ϕi < 2π was taken into account. Moreover, we linked mutually the areas of the p1(Bhf):p2(Bhf) and p3(Bhf):p4(Bhf) distributions to be 2:1 and 1:1, respectively, to minimize an ambiguity of the fitted parameters. The mean fields were determined (Table 4) from the resulting pi(Bhf) distributions. The hyperfine magnetic fields Fei gradually increase with temperature decreasing (Fig. 6b), following the temperature dependence of the magnetizations in iron sublattices. It would be interesting to analyze the experimental values of hyperfine magnetic fields for different iron valence states. It is known 21,29 that for the high-spin ferric ions Fe3+(S = 5/2) with a quenched orbital moment ( ≈ 0) the Fermi contact interaction (BF) with ns-electron is a dominant hyperfine coupling, implying that the hyperfine field Bhf = αµFe is proportional to the magnetic moment µFe, where α is a hyperfine constant.21,27 Using the α ≈ 11 T/µB value, that is a good approximation for the magnetically ordered phases of insulators,27 we estimated the values of µFe3,4 ≈ 4.90 µB which appear to be very close to the spin-only value (5µB) expected for the high-spin Fe3+ ions with ≈ 0. The minor discrepancy may be related to the partially unquenched orbital moment or the effects of covalency of the Fe-O bonds, making the effective g-factor for the half-filled d5 systems slightly lower than gs = 2.

All experimental distributions pi(Bhf) have a characteristic bimodal profile (lower panel of Fig. 8), very similar to those observed for the BiFeO3

36

and AgFeO2

non-collinear magnetic structure of the cycloid type. It was shown

36,37

37

ferrites, possessing a

that two maxima in the

p(Bhf) distribution indicate spatial anisotropy of hyperfine field Bhf, and the difference in the their

intensities is due to the anharmonicity (bunching) of the magnetic helicoid. In our case, the significant anisotropy of the hyperfine magnetic fields Bhf,Fe1 and Bhf,Fe2, apparently, is related to the anisotropic dipolar field Bdip( θ% , ϕ% ) (Eq. 5). In order to test this assumption, we reconstructed the polar diagrams |Bdip( θ% , ϕ% )|Fe1 and |Bdip( θ% , ϕ% )|Fe2 shown in Fig. 8. The maximum value of the anisotropy (∆Banis)max was evaluated as a difference between the two extreme values (maximum and minimum) of the Bdip( θ% , ϕ% ) function: (∆Banis)max = {Bdip( θ% 0 , ϕ% 0 )}max - {Bdip( θ% '0 , ϕ% '0 )}min


(6)

Page 13 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Our evaluations of the extreme (∆Banis)max values for Fe1 and Fe2 sites returned 20.2 T and 15.3 T, respectively, which cover the full range of the experimental values ∆Banis (Fig. 8a). Therefore, the highly broadened and asymmetric profile of the experimental spectra below TN2 may reflect a non-collinear spatially modulated spin ordering, proposed in 2+

model, the Fe

15

. According to our crystal field

cations in the Fe1 and Fe2 sites have a well-isolated ground orbital singlet and,

consequently, a small single ion magnetic anisotropy (SIMA). We speculate that the weak SIMA is much smaller than exchange interactions, which govern spatially modulated spin ordering below TN2. Therefore, the actual spin ordering can overcome the local magnetic anisotropy, and the magnetic moments scan all possible orientations relative to the crystal axes without sizeable bunching (the maxima in both bimodal distributions p(Bhf,Fe1) and p(Bhf,Fe2) are almost the same intensities, see Fig. 8a). A significantly lower anisotropy of the Bhf,Fe3 and Bhf,Fe4 fields for highspin Fe3+ ions (the p(Bhf,Fe3) and p(Bhf,Fe4) distributions have a weak resolved profile, with hyperfine field anisotropy of ~0.005 and ~0.028 T, respectively, see Fig. 8b) is also associated with the anisotropic dipole contributions, Bdip ∼ 1/R5, but due to the nearest magnetic neighbors at the distances R from the central ion.31 At all rates the degree of Fe3+ ions anisotropy of Bhf is not substantial and can not be quantitatively estimated without magnetic structure data. For further study the origin of the anisotropic interaction and magnetic ordering in Fe7(PO4)6 the neutron diffraction study is required.

CONCLUSIONS In conclusion, we performed a detailed

57

Fe Mössbauer spectroscopy study of Fe7(PO4)6

and found different unconventional features of the electronic and magnetic states of Fe2+/Fe3+ ions. Mössbauer data confirmed the valence-localized nature of the distinct Fe2+ and Fe3+ sites (at least at the time scale of the order of 10-8 s) over the entire temperature range of 4.2 K ≤ T ≤ 300 K. We argued that the induced electric dipole moments of oxygen O2- ions and electronic contributions related to overlapping of orbitals of the O2- anions and Fe3+ cations provide a significant contribution to the EFG tensor for

57

Fe nuclei. For Fe2+ cations in two different

environments, it was necessary to consider an additional electronic contribution to the EFG tensor related to different electronic populations of iron 3d-orbitals. From these observations, we developed a crystal field model that could account for the observed quadrupolar and magnetic hyperfine parameters. This model showed that Fe2+ cations have a well-isolated ground orbital singlet and a small single-ion magnetic anisotropy. The crystal field calculations suggested the pronounced difference between the magnetic hyperfine tensors for two Fe2+ sites, which is orb orb related to different orbital fields, BFe1 < BFe2 , whereas the dipolar hyperfine interactions play a

minor role. The Mössbauer data clearly indicated the existence of two temperature ranges below ACS Paragon Plus Environment


Page 14 of 29

TN1 ≈ 47 K separated by a second phase transition point at TN2 ≈ 16 K. The dipolar interactions

could cause a considerable spatial anisotropy of Bhf,Fe1 and Bhf,Fe2, which might be a possible reason for the line broadening of the spectra below TN2. This line broadening was approximated by the bimodal distribution of hyperfine fields p(Bhf) that is a characteristic feature of spinmodulated magnetic systems.

SUPPORTING INFORMATION This section consists of a figure with results of magnetic measurements (curves M vs H) and also includes detailed information about the procedure of the calculation of a lattice contribution to the electric field gradient (EFG) tensor as well as crystal field calculations.

ACKNOWLEDGMENTS This work was supported by the Russian Science Foundation (grant No. 17-73-30006).

REFERENCES (1) Moffat, J. B. Phosphates as Catalysts. Catal. Rev.: Sci. Eng. 1978, 18, 199-258. (2) Gadgil, M. M.; Kulshreshtha, S. K. Study of FePO4 Catalyst. J. Solid State Chem. 1994, 111, 357-364.

(3) Attali, S.; Vigouroux, B.; Lenzi, M.; Persia, J. Determination of the Active Center in Calcium-Nickel Phosphate Dehydrogenation Catalyst. J. Catal. 1980, 63, 496-500. (4) Tan, H.; Fultz, B. Rapid Electron Dynamics at Fe Atoms in Nanocrystalline Li0.5FePO4 Studied by Mössbauer Spectrometry. J. Phys. Chem. C 2011, 115, 7787-7792. (5) Mixed Valency Systems: Applications in Chemistry, Physics and Biology; Prassides, K., Eds.; Springer Science and Business Media, Brighton, U.K., 2012. (6) Gorbunov, Yu. A.; Maksimov, B. A.; Kabalov, Yu. K.; Ivaschenko, A. N.; Mel’nikov, O. K.; Belov, N. V. Crystal Structure of Fe2+3Fe3+4[PO4]6. Dokl. Acad. Nauk. SSSR 1980, 254, 873-876.

(7) Redhammer, G. J.; Roth, G.; Tippelt, G.; Bernoide, M.; Lottermoser, W.; Amthauer, G. The Mixed-Valence Iron Compound Na0.1Fe7(PO4)6: Crystal Structure and

57

Fe

Mössbauer Spectroscopy Between 80 and 295 K. J. Solid State Chem. 2004, 177, 16071618. (8) Еl Kira, A.; Gerardin, R.; Malaman, B.; Gleitzer, C. Five-coordinated (Ni)(2+) in Ni3Fe4(PO4)6. Eur. J. Solid State Inorg. Chem. 1992, 29, 1119-1131.


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(9) Lightfoot, P.; Cheetham, A. K. Neutron Diffraction Study of the Cation Distributions in the Systems Fe7 –xMx(PO4)6 (M = Mn or Co). J. Chem. Soc. Dalton Trans. 1989, 9, 17651769. (10) Belik, A. A.; Pokholok, K. V.; Malakho, A. P.; Khasanov, S. S.; Lazoryak, B. I. Synthesis and Structure of Phosphates M3R4(PO4)6 (M = Cu, Co; R = Fe, Cr, Ga, In) and Their Interaction with Hydrogen. Rus. J. Inorg. Chem. 2000, 45, 1494-1509 (in Russian). (11) Belik, A. A.; Malakho, A. P.; Pokholok, K. V.; Lazoryak, B. I.; Khasanov, S. S. New Mixed-Valent Iron (II/III) Phosphates, Cu3-xFe4+x(PO4)6. J. Sol. State Chem. 2000, 150, 159-166. (12) Rojo, J. M.; Mesa, J. L.; Lezama, L.; Rodriguez Fernandez, J.; Pizarro, J. L.; Arriortua, M. I.; Rojo, T. Hydrothermal Synthesis, Spectroscopic and Magnetic Properties of Co7(HPO4)4(PO4)2: a Metamagnetic Behavior. Int. J. Inorg. Mater. 2001, 3, 67-74. (13) Rojo, J. M.; Larranaga, A.; Mesa, J. L.; Urtiaga, M. K.; Pizarro, J. L.; Arriortua, M. I.; Rojo, T. Hydrothermal Synthesis and Spectroscopic and Magnetic Behavior of the Mn7(HOXO3)4(XO4)2

(X

=

As,

P)

Compounds.

Crystal

Structure

of

Mn7(HOAsO3)4(AsO4)2. J. Solid State Chem. 2002, 165, 171-177. (14) Lafontaine, M. A.; Greneche, J. M.; Laligant, Y.; Ferey, G. β-Cu3Fe4(VO4)6: Structural Study and Relationships; Physical Properties. J. Solid State Chem. 1994, 108, 1-10. (15) Kozlyakova, E.; Danilovich, I.; Volkov, A.; Zakharov, K.; Dimitrova, O.; Belokoneva, E.; Shvanskaya, L.; Zvereva, E.; Chareev, D.; Volkova, O.; et al. Tuning of Physical Properties of Fe7(PO4)6 by Sodium Intercalation. J. Alloys Compd. 2018, 744, 600-605. (16) Belik, A. A.; Malakho, A. P.; Pokholok, K. V.; Lazoryak, B. I. X-ray Powder Diffraction, Mossbauer Spectroscopy, and Thermal Stability of Fe7(PO4)6. Rus. J. Inorg. Chem. 1999, 44, 1535-1543.

(17) Riou-Cavellec, M.; Riou, D.; Ferey, G. Magnetic Iron Phosphates with an Open Framework. Inorg. Chem. Acta 1999, 291, 317-325. (18) Matsnev, M. E.; Rusakov, V. S. SpectrRelax: An Application for Mössbauer Spectra Modeling and Fitting. AIP Conf. Proc. 2012, 1489, 178-185. (19) Matsnev, M. E.; Rusakov, V. S. Study of Spatial Spin-Modulated Structures by Mössbauer Spectroscopy Using SpectrRelax. AIP Conf. Proc. 2014, 1622, 40-49. (20) Menil, F. Systematic Trends of the

57

Fe Mossbauer Isomer Shifts in (FeOn) and (FeFn)

Polyhedra. Evidence of a New Correlation Between the Isomer Shift and the Inductive



Page 16 of 29

Effect of the Competing Bond T-X (→Fe) (where X is O or F and T Any Element with a Formal Positive Charge). J. Phys. Chem. Solids 1985, 46, 763-789. (21) Mössbauer Spectroscopy and Transition Metal Chemistry (Fundamentals and Applications); Gütlich, P.; Bill, E.; Trautwein, A. X., Eds.; Springer, Berlin, Heidelberg,

2012. (22) Stadnik, Z. M. Electronic field gradient calculations in rare-earth iron garnets. J. Phys. Chem. Solids 1984, 45, 311-318.

(23) Sharma, R. R.; Teng, B. Quadrupole Coupling Constants of Fe3+ in Yttrium Iron Garnet. Phys. Rev. Lett. 1971, 27, 679-681.

(24) Sharma, R. R. Nuclear Quadrupole Interactions in Several Rare-Earth Iron Garnets. Phys. Rev. B 1972, 6, 4310-4323.

(25) Taft, C. T. Oxygen Dipolar Contributions to the EFG Tensor in Crystals of the AFeO2 Type (A = Na, Cu, Ag). J. Phys. C: Solid State Phys. 1977, 10, L369. (26) Robin, M. B.; Day, P. Mixed-Valence Chemistry: A Survey and Classification. Adv. Inorg. Radiochem. 1967, 10, 247-422.

(27) Chadwick, J.; Thomas, M. F.; Johnson, C. E.; Jones, D. H. A Mössbauer Investigation of Critical Fluctuations in Antiferromagnets. J. Phys. C: Solid State Phys. 1988, 21, 61596167. (28) Levinson, L. M.; Luban, M.; Shtrikman, S. Mössbauer Studies on

57

Fe near the Curie

Temperature. Phys. Rev. 1969, 177, 864-871. (29) Sawatzky, G. A.; van der Woude, F. Covalency Effects in Hyperfine Interactions. J. Phys. 1974, 35, C6-47-C6-60.

(30) Johnson, C. E. Hyperfine Interactions in Ferrous Fluosilicate. Proc. Phys. Soc. 1967, 92, 748-757. (31) Sobolev, A. V.; Akulenko, A. A.; Glazkova, I. S.; Pankratov, D. A.; Presniakov, I. A. Modulated Magnetic Structure of Fe3PO7 as Seen by

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Fe Mössbauer Spectroscopy.

Phys. Rev. B 2018, 97, 104415.

(32) Okiji, A.; Kanamori, J. Theoretical Analysis of the Mössbauer Data in Some Fe2+ Compounds. J. Phys. Soc. Japan 1964, 19, 908-915. (33) Companion, A. L.; Komarynsky, M. A. Crystal Field Splitting Diagrams. J. Chem. Education 1964, 41, 257-262.


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(34) Dabrowski, L.; Piekoszewski, J.; Suwalski, J. The Ambiguity Problem in the Evaluation of Mössbauer Spectra for 57Fe. Nucl. Instrum. Methods 1971, 91, 93-95. (35) Ôno, K.; Ito, A.; Fujita, T. The Mössbauer Study of the Ferrous Ion in FeCl2. J. Phys. Soc. Jpn. 1964, 19, 2119-2126.

(36) Sobolev, A.; Presniakov, I.; Rusakov, V.; Belik, A.; Matsnev, M.; Gorchakov, D.; Glazkova, Ya. Mössbauer investigations of hyperfine interactions features of 57Fe nuclei in BiFeO3 ferrite. AIP Conf. Proc. 2014, 1622, 104-108. (37) Sobolev, A.; Rusakov, V.; Moskvin, A.; Gapochka, A.; Belik, A.; Glazkova, I.; Akulenko, A.; Demazeau, G.; Presniakov, I.

57

Fe Mössbauer study of unusual magnetic

structure of multiferroic 3R-AgFeO2. J. Phys.: Condens. Matter 2017, 29, 275803.



Fe1

Fe2

c

Fe O

c

b

b

a

0

a

∆ Banis

p(Bhf) (a.u.)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 29

∆ Banis

4

8

12

16 20 Bhf (T)

24

Toc Graphic


28

32

Page 19 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


FIGURES Figure 1. Crystal structure of Fe7(PO4)6, where only the FeOn polyhedra are shown and the PO4 tetrahedra are omitted. Iron oxygen environments with Fe-O bond lengths are given in the bottom (from Ref. 16). Figure 2. (a) Temperature dependencies of specific heat (Cp/T vs T (the left-hand axis) and Cp vs T (the right-hand axis)) of Fe7(PO4)6 at zero magnetic field (the dashed lines indicate the successive magnetic phase transitions at TN1 ≈ 47(2) K and TN2 = 16(1) K. (b) Temperature dependencies of magnetic susceptibility (χ vs T (the left-hand axis) and d(χT)/dT vs T (the righthand axis)) of Fe7(PO4)6 measured at H = 1 T in the zero-field-cooled (ZFC) and field-cooled (FC) regimes. Figure 3. Experimental 57Fe Mössbauer spectra (hollow dots) of Fe7(PO4)6 recorded above the Neel temperature (TN1) at 300 K (T >> TN1) and 50 K (T > TN1). Solid lines are simulation of the experimental spectra as the superposition of quadrupole doublets as described in the text. Figure 4. Experimental 57Fe Mössbauer spectra (hollow dots) of Fe7(PO4)6 recorded in the temperature range TN2 < T < TN1. Color lines are simulation of the experimental spectrum as the superposition of magnetic subspectra (see the text). In the lower figure (at T = 35 K), besides the four Zeeman sextets, a paramagnetic components Fe(i) are shown (as in Fig. 3). Figure 5. Experimental 57Fe Mössbauer spectra (hollow dots) of Fe7(PO4)6 recorded in the temperature range T < TN2. Color lines are simulation of the experimental spectra as the superposition of four distributions p(Bhf) (see text). Figure 6. Temperature dependences of (a) the quadrupole coupling constants eQVZZ(T)Fe(i) and (b) the average values of the hyperfine field (T) (T < TN2) and values of hyperfine field Bhf(T)Fe(i) (TN2 < T < TN1). Figure 7. Schematic views of the local crystal structure for the ferrous Fe1 and Fe2 sites in Fe7(PO4)6, directions of the principal EFG axes in the local coordinate systems ô(xi,yi,zi), and the orientation of the hyperfine field Bhf at 57Fe nuclei (θ and ϕ are the spherical angles). Schematic representations of crystal field splitting of Fe2+:3d levels in the idealized non-distorted trigonal bipyramidal (FeO5) polyhedra (Fe1 site) and the tetragonal compressed oxygen (FeO6) polyhedra (Fe2 sites). The change in the position of the energy levels as a function of the ratio ξ (= α2/α4) of radial integrals (α2 and α4) is shown (see text); the removal of the degeneracy by the crystal field in the distorted real structure. Figure 8. (a) (Upper part of the figure) Surface plots of the |Bdip( θ% , ϕ% )|Fei fields in the local coordinate systems ô(xi,yi,zi) of the ferrous Fe1 and Fe2 sites in Fe7(PO4)6. The lower part of the figure shows the hyperfine field distributions p(Bhf) for ferrous iron resulting from simulation of the spectrum recorded at 4.2 K (below TN2); (b) the hyperfine field distributions p(Bhf) for ferric iron sites, Fe1 and Fe2, resulting from simulation of the spectrum recorded at 4.2 K (below TN2).



Page 20 of 29

TABLES Table 1. Mössbauer parameters for the Fe7(PO4)6 spectra recorded at 300 K. The symbol I denote relative contribution of the particular subspectrum Fe(i), while the symbol W stands for the resonant line width. Subspectrum

δ, mm/s

∆, mm/s

W, mm/s

I, %

Fe(1)

1.15(1)

2.46(1)

0.26(1)*

28.3(1)

Fe(2)

1.27(1)

2.52(1)

0.26*

14.6(1)

Fe(3)

0.44(1)

0.79(2)

0.26*

28.7(1)

Fe(4)

0.44(1)

0.50(2)

0.26*

28.4(2)

* These parameters were taken to be equal to each other.

Table 2. Calculated values of the principal components { Viilat + Viiov }i = X,Y,Z of the EFG tensor, the asymmetry parameters ηlat/ov, and the theoretical quadrupole splittings ∆theor for ferrous and ferric ions in Fei sites. Site/valence state Fe1“D3h”→ Fe2+

ov ( VXXlat + VXX )⋅1021, ( VYYlat + VYYov )⋅1021, V/m2 V/m2 0.041 0.551

( VZZlat + VZZov )⋅1021, V/m2 -0.591

ηlat/ov

∆theor, mm/s

0.86

-1.237

Fe2“Oh” → Fe2+

-0.301

-0.643

0.944

0.36

1.806

Fe3“Oh”→ Fe3+

-0.199

-0.296

0.495

0.20

0.789

Fe4“Oh” → Fe3+

0.009

0.192

-0.201

0.91

-0.359

Table 3. Mössbauer parameters for the Fe7(PO4)6 spectra recorded at 20 K (TN2 < T < TN1). θ and ϕ denote polar and azimuthal angles of the hyperfine field, Bhf, in the principal axes of the EFG tensor. Subspectrum

δ, mm/s

eQVZZ, mm/s

Bhf, T

θ, deg

ϕ, deg

η

I, %

Fe(1)

1.25(1)

4.99(1)

5.01(5)

79(1)

36(3)

0.39(4)

28.3(2)

Fe(2)

1.40(1)

4.96(3)

10.06(2)

41(2)

46(4)

0.95(1)

12.6(2)

Fe(3)

0.55(1)

-1.00(9)

50.84(2)

31(1)

0

0.67(4)

29.2(2)

Fe(4)

0.56(1)

1.70(7)

48.68(1)

41(2)

0

0.46(6)

29.9(2)


Page 21 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 4. Mössbauer parameters for the Fe7(PO4)6 spectra recorded at 4.2 K. Subspectrum

δ, mm/s

eQVZZ, mm/s

, T

W, mm/s

I, %

Fe(1)

1.26(1)

5.07(1)

6.55(4)

0.27(1)*

28.6(1)**

Fe(2)

1.46(1)

5.10(5)

23.72(1)

0.27*

14.2(1)**

Fe(3)

0.54(1)

-1.08(4)

54.95(3)

0.27*

28.6(1)*

Fe(4)

0.56(1)

1.85(5)

54.67(3)

0.27*

28.6(1)*

* These parameters were taken to be equal to each other; ** The Fe(1) subspectrum area for the p(Bhf)Fe1 distribution was set as doubled area for Fe(2) component in accordance with structure and Mössbauer data above 16K.

Table 5. Hyperfine field contributions Bidip and Biorb in the local coordinate systems ô(xi,yi,zi) of the ferrous Fei sites in Fe7(PO4)6 and theoretical field | Bhftheor | = (Bx2 + By2 + Bz2)1/2 {Bidip}i=x,y,z, T x y z

{Biorb}i=x,y,z, T x y z

| Bhftheor |, T

Site

BF*, T

Fe1

-37

4.79

2.74

6.06

12.97

8.44

17.02

5.77

Fe2

-44

6.63

0.46

-9.61

32.54

2.25

23.59

12.28

*BF/BF = ( sin θ% i cos ϕ% i , sin θ% i sin ϕ% i , cos θ% i ), Fe1:(0.564, 0.367, 0.740), Fe2:(0.808, 0.056, 0.586)



Page 22 of 29

O Fe P

Fe1

(Fe2+O5)

Fe2

Fe3

(Fe2+O6)

(Fe3+O6)

Fe4

(Fe3+O6)

Figure 1. Crystal structure of Fe7(PO4)6, where only the FeOn polyhedra are shown and the PO4 tetrahedra are omitted. Iron oxygen environments with Fe-O bond lengths are given in the bottom (from Ref. 16). ACS Paragon Plus Environment

Page 23 of 29

150

4

100

2

50

0 0.28

0 0.6

χ ZFC χ FC

(b)

0.24

0.4

0.20

0.2

d(χT)/dT ZFC TN1 d(χT)/dT FC

TN2

0.16 0

20

40

60

d(χΤ)/dΤ (cm3/mol/f.u.)

χ (cm3/mol/f.u.)

Cp/T (J/K/K/mol)

(a) 6

Cp (J/K/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.0

T (K)

Figure 2. (a) Temperature dependencies of specific heat (Cp/T vs T (the left-hand axis) and Cp vs T (the right-hand axis)) of Fe7(PO4)6 at zero magnetic field (the dashed lines indicate the successive magnetic phase transitions at TN1 ≈ 47(2) K and TN2 = 16(1) K. (b) Temperature dependencies of magnetic susceptibility (χ vs T (the left-hand axis) and d(χT)/dT vs T (the righthand axis)) of Fe7(PO4)6 measured at H = 1 T in the zero-field-cooled (ZFC) and field-cooled (FC) regimes.



Fe(4)

Transmission (%)

Fe(3) Fe(1)

Fe(2)

100

95

300 K 90 -4

-2

105

0 v (mm/s) v (mm/s)

Fe(4) Fe(2)

100 Transmission (%)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 29

2

Fe(3)

4

Fe(1)

95 90 85 50 K 80 75 -4

-2

0 (mm/s) vv (mm/s)

2

4

Figure 3. Experimental 57Fe Mössbauer spectra (hollow dots) of Fe7(PO4)6 recorded above the Neel temperature (TN1) at 300 K (T >> TN1) and 50 K (T > TN1). Solid lines are simulation of the experimental spectra as the superposition of quadrupole doublets as described in the text.


Page 25 of 29

102

Fe(3)

Fe(4)

Fe(1)

Fe(2)

100 98 96 94

20 K

92 100

Transmission (%)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


98 96 94

30 K 92

100

98

-12

Fe(4) Fe(1)

Fe(3) Fe(2)

35 K

-8

-4

0

v (mm/s)

4

8

12

Figure 4. Experimental 57Fe Mössbauer spectra (hollow dots) of Fe7(PO4)6 recorded in the temperature range TN2 < T < TN1. Color lines are simulation of the experimental spectrum as the superposition of magnetic subspectra (see the text). In the lower figure (at T = 35 K), besides the four Zeeman sextets, a paramagnetic components Fe(i) are shown (as in Fig. 3). ACS Paragon Plus Environment


100 98 Fe(2) Fe(4)

96

Fe(1)

94

Fe(3)

4K

92 100

Transmission (%)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 29

98 96 10 K

94 92 100

98 12.5 K 96 -12

-8

-4

0

4

8

12

v (mm/s)

Figure 5. Experimental 57Fe Mössbauer spectra (hollow dots) of Fe7(PO4)6 recorded in the temperature range T < TN2. Color lines are simulation of the experimental spectra as the superposition of four distributions p(Bhf) (see text).


Page 27 of 29

6

eQVZZ(mm/s)

4 (a)

2 0 -2 Fe(3)

50 Bhf> Bhf

Magnetic Hyperfine Interactions in the Mixed-Valence Compound Fe7

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