Nadezhda A. Zhuk, Boris A. Makeev, Sergey V. Nekipelov, Maria V. Yermolina, Anna V. Fedorova and Galina I. Chernykh

Magnetic behavior of Fe-doped of multicomponent bismuth niobate pyrochlore

Open Access
De Gruyter | Published online: January 27, 2021

Abstract

Two series of iron-containing solid solutions Bi2Mg1−xFexNb2O9+δ and Bi2MgNb2−2xFe2xO9−δ of pyrochlore structure were obtained by the traditional solid phase synthesis method. The electronic state and character of exchange interactions of iron atoms in solid solutions were investigated by methods of magnetic dilution and NEXAFS-spectroscopy. According to X-ray spectroscopy and magnetic susceptibility data, iron(III) atoms are distributed mainly in octahedral positions of niobium(V) and in a dominant amount are in the charge state of Fe(III) in the form of monomers and exchange-bonded clusters mainly with antiferromagnetic type of exchange. Differences in magnetic behavior of iron-containing solid solutions of both series have been revealed. Antiferromagnetic and ferromagnetic exchange can be realized between iron atoms, which, with increasing concentration of paramagnetic atoms and averaging structure distortions, becomes less significant. The parameters of exchange interactions in clusters and distribution of iron paramagnetic atoms depending on the concentration of solid solutions have been calculated.

1 Introduction

Synthetic pyrochlores have been a source of continued interest for scientists around the world for several decades. Compounds with pyrochlore structure show a wide range of practically useful properties and are promising for microelectronics and some industries. Among pyrochlores are found multiferroics, superconductors, semiconductors, catalysts [1,2,3,4]. They exhibit dielectric, magnetic, electrooptical and piezoelectric properties [5,6,7,8,9,10]. Materials based on pyrochlores have already found application in solid-state devices as thermistors, thick-film resistors and communication elements and are used as components of ceramic forms for radioactive waste. The comparatively low synthesis temperature of some pyrochlores, their dielectric properties and their chemical inertness with respect to Ag-electrodes make them promising materials for the manufacture of multilayer ceramic capacitors, electronic components and devices for the microwave range [11].

Due to the flexibility of the crystal structure pyrochlores meet wide areas of homogeneity of solid solutions [12,13,14,15,16,17]. By changing the stoichiometric composition of pyrochlore one can significantly vary its physical and chemical characteristics, which allows to study the influence of the chemical composition on its properties.

In the cubic structure of pyrochlore A2B2O7 (Fd-3m) two mutually interacting sublattices A2O’ and B2O6 are distinguished [1, 18]. The B2O6 sublattice consists of octahedrons [BO6] connected at the apex of an angle; the A2O’ sublattice is formed by tetrahedrons [O’A4]. The triple pyrochlores containing transition metals attract special attention [12,13,14,15,16,17, 19, 20]. Their characteristic feature is the location of transition metal cations on two non-equivalent positions A and B. Such peculiarity of the distribution of transition element cations in bismuth niobate with pyrochlore structure is noted in [14,15,16,17]. Complex bismuth-bearing pyrochlores have excellent dielectric properties [22,23,24,25,26,27,28]. Among them are Bi2Mg2/3Nb4/3O7 [8, 22, 23], Bi2(Zn1−xNix)2/3Nb4/3O7 [24], Bi2−xLaxMg2/3Nb4/3O7 [27], Cu–doped Bi2Mg2/3Nb4/3O7 [28].

Previously, we studied the possibility of obtaining cobalt-containing solid solutions of bismuth-magnesium niobate with pyrochlore structure when replacing magnesium or niobium atoms. As a result, it has been established that cobalt(II) atoms in both series of preparations mainly replace octahedral positions of niobium(V). This paper shows the results of the study by NEXAFS-spectroscopy and magnetic dilution of the distribution, electronic state and nature of interatomic interactions of iron atoms in Fe-doped of multicomponent bismuth niobate pyrochlore.

2 Experimental

Iron-containing solid solutions Bi2Mg1−xFexNb2O9+δ and Bi2MgNb2−2xFe2xO9−δ were synthesized by the standard ceramic method from oxides of bismuth (III), niobium (V), magnesium (II) and iron (III) of special purity grade as a result of gradual calcination at 650, 850, 950 and 1100°C. The phase composition of the samples was monitored by means of scanning electron microscopy (electron scanning microscope Tescan VEGA 3LMN, energy dispersion spectrometer INCA Energy 450) and X-ray phase analysis (a DRON-4-13 diffractometer, CuKα emission). The unit cell parameters of solid solutions were calculated using the CSD software package [29]. The Faraday method was used to measure the magnetic susceptibility of solid solutions in a wide temperature range of 77–400 K and magnetic field strengths of 7240, 6330, 5230 and 3640 Oe. The measurement technique is described in detail in [30]. Samples of solid solutions were studied by X-ray absorption (NEXAFS – Near Edge X-ray Ab-sorption Fine Structure) spectroscopy at the Russian-German channel of the BESSY-II synchrotron source in Berlin. The NEXAFS spectra of solid solutions were obtained using the total electron yield (TEY) method [31].

2.1 X-ray phase analysis and microstructure

The formation of solid solutions of Bi2MgNb2−2xFe2xO9−δ and Bi2Mg1−xFexNb2O9+δ (x ≤ 0.06) composition was determined by the X-ray phase analysis (Figure 1a, 1b).

Figure 1 X-ray diffraction patterns of the series of the solid solutions Bi2MgNb2−2xFe2xO9−δ (a) and Bi2Mg1−xFexNb2O9+δ (b) at x=0(1), 0.005(2), 0.01(3), 0.03(4), 0.04(5), 0.06(6)

Figure 1

X-ray diffraction patterns of the series of the solid solutions Bi2MgNb2−2xFe2xO9−δ (a) and Bi2Mg1−xFexNb2O9+δ (b) at x=0(1), 0.005(2), 0.01(3), 0.03(4), 0.04(5), 0.06(6)

In the Bi2Mg1−xFexNb2O9+δ samples can be present in trace amounts the phases Bi5Nb3O15 and MgNb2O6 [32, 33].

Calculation of the unit cell parameters showed that the lattice constant of diluted solid solutions of both series slightly changes with the growth of iron content: for Bi2MgNb2−2xFe2xO9−δ a=1.05445 (x = 0.03) and a = 1.05441 nm (x = 0.06); for Bi2Mg1−xFexNb2O9a = 1.05369 (x = 0.03) and a = 1.05493 nm (x = 0.06) and close to the parameter of bismuth-magnesium niobate with pyrochlore structure [22,23,24]: a = 1.056 nm. Such a change of the cell parameter in the case of solid solutions Bi2MgNb2−2xFe2xO9−δ may be due to isomorphic substitution of niobium (V) atoms by close in size iron atoms Fe(III) (R(Nb(V))c.n.−6. =0.64, R(Fe(II))c.n.−6=0.61(L.S.) and 0.78(H.S.), R(Fe(III))c.n.−6=0.55(L.S.) and 0.645(H.S.)). The smaller parameter of the Bi2Mg1−xFexNb2O9 cell in comparison with undervalued bismuth-magnesium niobate (a=1.056 nm) also indicates the presence of iron mainly in the Fe(III) (R(Bi(III))c.n.−8=1.17, R(Fe(II))c.n.−8=0.92, R(Fe(III))c.n.−8=0.78 and R(Mg(II))c.n.−8=0.89 [34]. Meanwhile, the possibility of placing a part of iron (III) ions in Bi(III) position and the presence of some Fe(II) ions is not excluded.

2.2 NEXAFS-spectroscopy

To determine the charge state of doped iron atoms by NEXAFS (near-edge X-ray absorption fine structure) spectroscopy, Fe, Mg-codoped bismuth niobate pyrochlore and iron oxides FeO [35], Fe2O3 and Fe3O4 were investigated. Fe2p- absorption spectra are presented in Figure 2. The main components of the spectra of investigated samples practically coincide with each other in both number and energy position of the main absorption bands. Moreover, the Fe2p-spectra of Fe2O3oxide are almost identical. Based on this, we can assume that iron atoms in solid solutions of magnesium-bismuth niobate are mainly trivalent, i.e., they have the charge state of Fe3+. It is interesting to note that in the Fe2p spectrum of the Bi2Mg1−xFexNb2O9+δ solid solution the band at ~708 eV is blurred and its intensity is less than for Fe2O3 and Bi2MgNb2−2xFe2xO9−δ. This is possible for two reasons, one of which is the presence of Fe(II) ions and the other is the presence of Fe(III) ions in an oxygen environment other than the octahedral environment. This is possible provided that magnesium cations partially occupy bismuth positions, and if the latter are scarce, there are vacancies for iron ions.

Figure 2 NEXAFS Fe2p -spectra of Bi2MgNb2−2xFe2xO9−δ and Bi2Mg1−xFexNb2O9+δ

Figure 2

NEXAFS Fe2p -spectra of Bi2MgNb2−2xFe2xO9−δ and Bi2Mg1−xFexNb2O9+δ

Due to the fact that iron cations in iron oxides (II,III) occupy octahedral positions it can be concluded that iron ions in Fe, Mg-codoped bismuth niobate pyrochlore also have predominant coordination six. Since in solid solutions of Bi2Mg1−xFexNb2O9+δ there is a large proportion of six-coordinated Fe(III) ions, according to NEXAFS spectroscopy, we can speak, in general, about the desire of iron ions (III) to take octahedral positions [36,37,38,39,40,41,42].

2.3 Magnetic properties

Calculation of paramagnetic components of magnetic susceptibility [χpara(Fe)] and values of effective magnetic moments [μeff (Fe)] of iron atoms at different temperatures and for different concentrations of solid solutions was carried out (Figures 3a–3d). The main contribution to the magnetic susceptibility is made by paramagnetic iron ions. The correction from the diamagnetic ions Bi (III), Nb (V), Mg (II) is very small [43]. The methods of measuring magnetic susceptibility and calculation are described in [30]. The dependence of the inverse value of paramagnetic susceptibility ( 1 / χ Fe para ) on temperature is linear over the entire temperature range and is subject to Curie-Weiss law. The Curie-Weiss constant for both series of solid solutions is negative, which indicates the dominant antiferromagnetic interactions between paramagnetic atoms. For Bi2Mg1−xFexNb2O9 solid solutions, it varies slightly from −15.8 (x = 0.005) to −10.8 K (0.06); for Bi2MgNb2−2xFe2xO9−δ, in contrast, it decreases from −11.2 to −26.7 K, respectively.

Figure 3 Isotherms of the paramagnetic component of the magnetic susceptibility of the solid solutions Bi2MgNb2−2xFe2xO9−δ (a) and Bi2Mg1−xFexNb2O9+δ (b); Temperature dependences of the magnetic moment of iron atoms in Bi2MgNb2−2xFe2xO9−δ (c) and Bi2Mg1−xFexNb2O9+δ (d)

Figure 3

Isotherms of the paramagnetic component of the magnetic susceptibility of the solid solutions Bi2MgNb2−2xFe2xO9−δ (a) and Bi2Mg1−xFexNb2O9+δ (b); Temperature dependences of the magnetic moment of iron atoms in Bi2MgNb2−2xFe2xO9−δ (c) and Bi2Mg1−xFexNb2O9+δ (d)

The change in the Weiss constant indicates that the proportion of antiferromagnetically bonded units increases with the increase in iron atom content in Bi2MgNb2−2xFe2xO9−δ. The difference in Weiss constant values for both series of solid solutions may be due to the presence of some fraction of noninteracting Fe(III) monomers in bismuth positions in Bi2Mg1−xFexNb2O9. Paramagnetic isotherms of the magnetic susceptibility of iron atoms are typical for diluted antiferromagnetics (Figures 3a, 3c). The value of the effective magnetic moment of single iron atoms in an infinitely diluted solid solution of Bi2MgNb2−2xFe2xO9−δ increases with temperature rise from 7.99 μB (90 K) to 8.27 μB (320 K). The overshoot of the magnetic moment with respect to the pure spin value of Fe(III) atoms (μeff = 5.92 μB, therm 6A1g) and Fe(II) (μeff = 4.9 μB, 5T2g) may be associated with the formation of exchange-bound units from iron atoms with predominantly ferromagnetic exchange. Apparently, the formation of clusters from iron atoms (III) in an infinitely diluted solid solution helps to stabilize the structure of solid solutions of heterovalent substitution by including oxygen vacancies in the cluster or by localizing the cluster near it. The possibility of ferromagnetic exchange, atypical for iron atoms (III), is due to geometric distortions in the polyhedral environment of iron atoms caused by anionic vacancies. The probability of realization of ferromagnetic exchange is high through cross-exchange channels, for example, dx2y2px⊥dxy,dx2y2pxpydxy, dxypy⊥pz‖ dxz[36,37,38,39,40,41].

For Bi2Mg1−xFexNb2O9+δ solid solutions, the effective magnetic moment varies from 5.79 to 6.06 μB and is close to the pure spin value of single iron atoms (III) in Fe(III) solid solutions Fe(III) (μeff = 5.92 μB, 6A1g), which indicates a practically monomeric state of iron atoms in solid solutions at infinite dilution. The isolated state of iron atoms can be realized by assuming that iron atoms occupy cationic bismuth positions. A slight increase in the magnetic moment indicates weak antiferromagnetic interactions between the paramagnetic atoms and is due to the fact that some portion of iron ions is distributed in the cationic positions of niobium(V).

The decrease in the paramagnetic component of the magnetic susceptibility of iron atoms with an increase in the concentration of solid solutions of both series is associated with the manifestation of antiferromagnetic interactions between iron atoms. The temperature dependence of the effective magnetic moment of iron atoms in solid solutions with different concentrations of paramagnetic atoms is also indicative of this assumption.

Comparison of isotherms of magnetic susceptibility of both series of solid solutions is shown in the Figure 4. We can see from the Figure 4, that in all concentration interval the receptivity of solid solutions of Bi2MgNb2−2xFe2xO9−δ is much more, than for Bi2Mg1−xFexNb2O9+δ. This may indicate that the exchange interaction between paramagnetic atoms, e.g., ferromagnetic type, and clusters in Bi2MgNb2−2xFe2xO9−δ solid solutions can be realized compared to Bi2Mg1−xFexNb2O9+δ.

Figure 4 A compassion between paramagnetic components of magnetic susceptibility for Bi2Mg1−xFexNb2O9+δ (open symbols) and Bi2MgNb2−2xFe2xO9−δ (close symbols) solid solutions

Figure 4

A compassion between paramagnetic components of magnetic susceptibility for Bi2Mg1−xFexNb2O9+δ (open symbols) and Bi2MgNb2−2xFe2xO9−δ (close symbols) solid solutions

In order to clarify the nature of the distribution of iron atoms in both series of solid solutions and describe the exchange interactions in the clusters, the theoretical calculation of susceptibility and comparison of the values obtained with the experimental ones was performed.

Calculation of experimental dependencies of χpara(Fe) on solid solutions concentration was carried out within the framework of the diluted solid solution model, according to which magnetic susceptibility is defined as the sum of contributions from single paramagnetic atoms and their exchange-bound aggregates. When calculating the magnetic susceptibility for Bi2Mg1−xFexNb2O9+δ, the existence of Fe(II) atoms was neglected. In order to estimate differences in the distribution of iron atoms in both series of solid solutions, we recorded the value of the exchange parameter in the clusters. The general formula for calculating the paramagnetic component of the magnetic susceptibility of iron atoms is a sum of contributions of the magnetic susceptibility of monomers, dimers, trimmers and tetramers with antiferro and ferromagnetic type of exchange:

(1) χ calc para ( Fe ) = a Fe ( III ) mon χ Fe ( III ) mon + a Fe ( III ) dim ( f ) χ Fe ( III ) dim ( f ) + a Fe ( III ) dim ( aa ) χ Fe ( III ) dim ( a ) + a Fe ( III ) trim ( f ) χ Fe ( III ) trim ( f ) + a Fe ( III ) trim ( ar ) χ Fe ( III ) trim ( a ) + + a Fe ( III ) tetr ( ae ) χ Fe ( III ) tetr ( a ) + a Fe ( III ) tetr ( f ) χ Fe ( III ) tetr ( f )
(2) a Fe ( III ) mon + a Fe ( III ) dim ( f ) + a Fe ( III ) dim ( a ) + a Fe ( III ) trim ( f ) + a Fe ( III ) trim ( a ) + a Fe ( III ) tetr ( a ) + a Fe ( III ) tetr ( f ) = 1 .

This is a Fe ( III ) mon , a Fe ( III ) dim ( f ) , a Fe ( III ) dim ( a ) , a Fe ( III ) tetr ( a ) , a Fe ( III ) trim ( f ) , a Fe ( III ) trim ( a ) , a Fe ( III ) tetr ( a ) and a Fe ( III ) tetr ( a ) – fraction of monomers, dimers, trimers and tetramers from iron atoms (III) with ferromagnetic -and antiferromagnetic type of interaction, χ Fe ( III ) mon , χ Fe ( III ) dim ( f ) , χ Fe ( III ) dim ( a ) , χ Fe ( III ) trim ( f ) , χ Fe ( III ) trim ( a ) , χ Fe ( III ) tetr ( f ) , χ Fe ( III ) tetr ( a ) – magnetic susceptibility of monomers, dimers, trimers and tetramers with ferromagnetic – and antiferromagnetic exchange.

According to the Heisenberg-Dirk-Wan-Fleck model [44], the magnetic susceptibility of tetramers consisting of paramagnetic atoms was calculated by formula (3):

(3) χ tetr S 1 S 2 = 1 4 S S 12 S 34 g 2 ( S ) S ( S + 1 ) ( 2 S + 1 ) e E ( J , S ) / kT 8 T S S 12 S 34 ( 2 S + 1 ) e E ( J , S ) / kT
Where E( J, S) = − J[ S( S + 1) − 4 S 1( S 1 + 1)], S 12 = S 1 + S 2, S 1 + S 2 −1, . . . , | S 1S 2|, S 34 = S 3 + S 4, S 3 + S 4 −1, . . . , | S 3S 4|, S = S 12 + S 34, S 12 + S 34 − 1, . . . , | S 12S 34|.

Here S1 and S2, S3 and S4 – the spin values of the atoms that form tetramers, in our case S1 = S2 = S3 = S4 = 5/2 for the tetrameter Fe(III)-O-Fe(III)-O-Fe(III)-O-Fe(III), S and S12 and S34 – values of total spin and intermediate moments, g – Lande factor for iron atoms (III), J – exchange parameter, T – absolute temperature.

To calculate the magnetic susceptibility of dimers, the following formula is proposed (4):

(4) χ uM S 1 S 2 = 1 2 S g 2 ( S ) S ( S + 1 ) ( 2 S + 1 ) e E ( J , S ) / kT 8 T S ( 2 S + 1 ) e E ( J , S ) / kT ,

Here E(J, S) = −J[S(S + 1) − Sa(Sa + 1) − Sb(Sb + 1)], S = Sa + Sb, Sa + Sb − 1, . . . , |SaSb|; Sa, Sb – the spin values of the atoms that form dimers.

After substitution of the values, the formula 4 is converted to the formula 5:

(5) χ a ¨ é i ´ = 1 4 T 330 e 12.5 x + 180 e 2.5 x + 84 e 5.5 x + 30 e 11.5 x + 6 e 15.5 x 11 e 12.5 x + 9 e 2.5 x + 7 e 5.5 x + 5 e 11.5 x + 3 e 15.5 x + e 17.5 x ,
Here x = J/ kT, k – Boltzmann's constant.

The alignment of the calculated and experimental values is achieved by minimizing the function i j ( χ ij calc χ ij exp ) 2 , where i – summation by all concentrations; j – temperature totalling; χ ij calc , χ ij exp – experimental and calculated values of paramagnetic component of magnetic susceptibility of solid solutions.

Best agreement of experimental and design data for solid solutions Bi2MgNb2−2xFe2xO9−δ and Bi2Mg1−xFexNb2O9+δ obtained at the values of the parameter of antiferromagnetic exchange in dimers Jdim = −25 cm−1, in trimers Jtrim = −14 cm−1 and tetrameters Jtetr = −9 cm−1; ferromagnetic – Jdim = 20 cm−1, in trimers Jtrim = 16 cm−1 and tetrameters Jtetr = 11 cm−1. Comparison of experimental and theoretical values of magnetic susceptibility of solid solutions is shown in the Figures 5a, 5b and Table 1.

Figure 5 A compassion between calculated (open symbols) and experimental (close symbols) paramagnetic components of magnetic susceptibility for Bi2MgNb2−2xFe2xO9−δ (a) and Bi2Mg1−xFexNb2O9+δ (b) solid solutions

Figure 5

A compassion between calculated (open symbols) and experimental (close symbols) paramagnetic components of magnetic susceptibility for Bi2MgNb2−2xFe2xO9−δ (a) and Bi2Mg1−xFexNb2O9+δ (b) solid solutions

Table 1

The results of calculating the distribution of iron atoms in the solid solutions Bi2Mg1−xFexNb2O9+δ

x a Fe ( III ) trim ( a ) a Fe ( III ) mon a Fe ( III ) dim ( f ) a Fe ( III ) dim ( a ) χcalc//χexp· 103, emu/mol
90 K 140 K 200 K 260 K 320 K
0 0 0.960 0.010 0.03 47.3/46.2 30.5/31.0 21.4/22.3 16.5/17.4 13.4/14.2
0.005 0 0.952 0.008 0.04 46.8/47.0 30.2/31.9 21.2/23.0 16.3/18.0 13.3/14.8
0.010 0 0.936 0.004 0.06 45.8/43.4 29.6/29.6 20.8/21.4 16.1/16.8 13.1/13.8
0.015 0 0.927 0.003 0.07 45.4/45.1 29.3/29.8 20.7/21.2 16.0/16.4 13.1/13.4
0.020 0 0.918 0.002 0.08 44.9/44.7 29.1/30.1 20.5/21.6 15.9/16.9 13.0/13.8
0.030 0 0.880 0 0.12 43.1/40.6 28.0/27.1 19.9/19.4 15.4/15.1 12.7/12.4
0.040 0 0.840 0 0.16 41.4/41.4 27.0/27.9 19.3/20.1 15.0/15.7 12.4/12.9
0.060 0.01 0.790 0 0.20 39.5/39.6 25.9/27.2 18.5/19.8 14.5/15.5 12.0/12.8

    Note 1 – a Fe ( III ) mon , a Fe ( III ) dim ( f ) , a Fe ( III ) dim ( a ) – fractions of monomers, trimers and dimers from iron (III) atoms with antiferro- and ferromagnetic type of exchange

The distribution of iron atoms depending on the concentration of solid solutions Bi2MgNb2−2xFe2xO9−δ and Bi2Mg1−xFexNb2O9+δ is shown in the Figures 6a, 6b.

Figure 6 Dependence of portions of the monomers 
aFe(III)mon\begin{align}&\chi_{\ddot{a}\grave{e}\acute{i}} = \frac{1}{4T} \cdot \\ \nonumber &\frac{330e^{12.5x} + 180e^{2.5x}+84e^{-5.5x}+30e^{-11.5x}+6e^{-15.5x}}{11e^{12.5x}+9e^{2.5x}+7e^{-5.5x}+5e^{-11.5x}+3e^{-15.5x}+e^{-17.5x}},\end{align}
 (1), dimers with the antiferromagnetic 
aFe(III)dim(a)\sum\limits_i \sum\limits_j {(\chi _{ij}^{calc} - \chi _{ij}^{\exp })^2}
 (2) and ferromagnetic 
aFe(III)dim(f)\sum\limits_i 
 types of exchange (5); trimers with antiferromagnetic 
aFe(III)trim(a)\sum\limits_j 
 (3); tetramers with the antiferromagnetic exchange type 
aFe(III)tetr(a)\chi _{ij}^{calc}
 (4) and ferromagnetic 
aFe(III)tetr(f)\chi _{ij}^{\exp }
 types of exchange (6) on the content of iron atoms in Bi2Mg1−xFexNb2O9+δ (a) and Bi2MgNb2−2xFe2xO9−δ (b)

Figure 6

Dependence of portions of the monomers a Fe ( III ) mon (1), dimers with the antiferromagnetic a Fe ( III ) dim ( a ) (2) and ferromagnetic a Fe ( III ) dim ( f ) types of exchange (5); trimers with antiferromagnetic a Fe ( III ) trim ( a ) (3); tetramers with the antiferromagnetic exchange type a Fe ( III ) tetr ( a ) (4) and ferromagnetic a Fe ( III ) tetr ( f ) types of exchange (6) on the content of iron atoms in Bi2Mg1−xFexNb2O9+δ (a) and Bi2MgNb2−2xFe2xO9−δ (b)

As a result of investigations of iron-containing solid solutions of Bi2MgNb2−2xFe2xO9−δ it was found that in an infinitely diluted solid solution iron (III) atoms are mainly in the aggregate state and form dimers, trimers and tetramers with antiferro – and ferromagnetic type of exchange. Despite the large proportion of aggregates in an infinitely diluted solution with ferromagnetic type of exchange, the exchange is generally antiferromagnetic. Apparently, this is due to a more effective overlap of the orbits involved in the exchange of atoms through the channels of antiferromagnetic exchange, and relatively small geometric distortions of the structure of solid solutions causing ferromagnetic exchange. The share of clusters with ferromagnetic type of exchange with increasing concentration of solid solutions decreases, which is due to the averaging of local structure distortions and the formation of aggregates mainly with antiferromagnetic type of exchange.

In infinitely diluted Bi2Mg1−xFexNb2O9 solid solutions, the magnetic moment value almost corresponds to the pure spin value for Fe(III). Therefore, the fraction of Fe(III) monomers is much larger than in Bi2MgNb2−2xFe2xO9−δ. The small dependence of magnetic moment on temperature is caused by the fraction of antiferromagnetically bound dimers from Fe(III) atoms. This indicates that some of the Fe(III) atoms replace the position of niobium(V), between which antiferromagnetic exchange takes place. This conclusion does not contradict the known data on the distribution of iron atoms on cationic positions in bismuth niobate with pyrochlore structure [16]. With increasing iron atom content, the proportion of monomers decreases and the proportion of clusters increases, which also indicates the location of iron atoms in octahedral positions. It is interesting to note that solid solutions of both series differ significantly in their cluster composition. The share and nuclearity of clusters in Bi2MgNb2−2xFe2xO9−δ solid solutions is higher than in Bi2Mg1−xFexNb2O9. There may be two reasons for this. The first one is related to the distribution of part of iron(III) atoms in the bismuth(III) position, and the second may be related to the indirect influence of magnesium atoms on Fe(III) clustering.

Relatively low values of exchange parameters in clusters are obviously connected with competition of antiferro and ferromagnetic interactions. According to the theory of exchange channels [45], an indirect exchange of antiferro-magnetic type is realized if the angle of connection between paramagnetic atoms is 180°C, deviations from this value contribute to the realization of the exchange of ferromagnetic type. In the pyrochlore structure, the octahedrons are connected by the vertices, forming a three-dimensional framework of niobium-oxygen octahedron chains. Within the chains, the Fe-O-Fe connection angle is less than 180°C, namely 135°C, which greatly reduces pπ-dπ the overlap between the channels of antiferromagnetic exchange, for example, dxy ‖py‖ dxy. In addition, the introduction of iron atoms into the niobium position leads to local distortions of the octahedron, including in the plane perpendicular to the axis connecting the two atoms through oxygen, then the contribution of the second channel of antiferromagnetic exchange will greatly reduce dxz ‖pz‖ dxz.

3 Conclusions

Two series of iron-containing solid solutions Bi2Mg1−xFexNb2O9 and Bi2MgNb2−2xFe2xO9−δ of pyrochlore structure were obtained by solid phase synthesis method. The parameter of the unit cell of solid solutions is close to the constant cell for bismuth-magnesium niobate. As a result of NEXAFS-study of solid solutions and iron oxides it has been established that the main details of the spectra of solid solutions practically coincide with each other both in number and energy position of the main absorption bands and are identical to Fe2p-spectrum of Fe2O3 oxide. Iron(III) cations are distributed mainly in the octahedral positions of niobium(V) and in a dominant amount are in the charge state of Fe(III) in the form of monomers and exchange-bound clusters mainly with anti-ferromagnetic type of exchange. The main differences in the magnetic behavior of iron-containing solid solutions of both series may be related to the uneven distribution of cations in bismuth and niobium positions. As a result of calculating the parameters of metabolic interactions in dimers and the distribution of iron paramagnetic atoms as a function of the concentration of Bi2MgNb2−2xFe2xO9−δ and Bi2Mg1−xFexNb2O9 solid solutions, the presence of high nuclear clusters with antiferro and ferromagnetic type of interaction was established. The share and nuclearity of clusters in Bi2MgNb2−2xFe2xO9−δ solid solutions is considerably higher than in Bi2Mg1−xFexNb2O9.

    Author contributions:Nadezhda A. Zhuk: Investigation, Visualization, Writing – Original Draft preparation, Writing – Review & Editing; Galina I. Chernykh: Formal analysis, Synthesis of samples; Maria V. Yermolina: Formal analysis, Resources; Anna V. Fedorova: Formal analysis, Resources; Sergey V. Nekipelov: Investigation, Visualization, Software, Resources; Boris A. Makeev: Software, Resources

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Received: 2020-09-03
Accepted: 2020-11-19
Published Online: 2021-01-27

© 2021 Nadezhda A. Zhuk et al., published by De Gruyter

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