Magnetic behavior of Fe-doped of multicomponent bismuth niobate pyrochlore

2.1 X-ray phase analysis and microstructure

The formation of solid solutions of Bi₂MgNb_2−2xFe_2xO_9−δ and Bi₂Mg_1−xFe_xNb₂O_9+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 Bi₂MgNb_2−2xFe_2xO_9−δ (a) and Bi₂Mg_1−xFe_xNb₂O_9+δ (b) at x=0(1), 0.005(2), 0.01(3), 0.03(4), 0.04(5), 0.06(6)

In the Bi₂Mg_1−xFe_xNb₂O_9+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 Bi₂MgNb_2−2xFe_2xO_9−δ a=1.05445 (x = 0.03) and a = 1.05441 nm (x = 0.06); for Bi₂Mg_1−xFe_xNb₂O₉ a = 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 Bi₂MgNb_2−2xFe_2xO_9−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 Bi₂Mg_1−xFe_xNb₂O₉ 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 Bi₂Mg_1−xFe_xNb₂O_9+δ solid solution the band at ~708 eV is blurred and its intensity is less than for Fe₂O₃ and Bi₂MgNb_2−2xFe_2xO_9−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 Bi₂MgNb_2−2xFe_2xO_9−δ and Bi₂Mg_1−xFe_xNb₂O_9+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 Bi₂Mg_1−xFe_xNb₂O_9+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 [χ^para(Fe)] and values of effective magnetic moments [μ_eff (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/χFepara) 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 Bi₂Mg_1−xFe_xNb₂O₉ solid solutions, it varies slightly from −15.8 (x = 0.005) to −10.8 K (0.06); for Bi₂MgNb_2−2xFe_2xO_9−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 Bi₂MgNb_2−2xFe_2xO_9−δ (a) and Bi₂Mg_1−xFe_xNb₂O_9+δ (b); Temperature dependences of the magnetic moment of iron atoms in Bi₂MgNb_2−2xFe_2xO_9−δ (c) and Bi₂Mg_1−xFe_xNb₂O_9+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 Bi₂MgNb_2−2xFe_2xO_9−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 Bi₂Mg_1−xFe_xNb₂O₉. 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 Bi₂MgNb_2−2xFe_2xO_9−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 (μ_eff = 5.92 μB, therm ⁶A_1g) and Fe(II) (μ_eff = 4.9 μB, ⁵T_2g) 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, d_x²−_y²⊥p_x⊥d_xy,d_x²−_y²‖p_x⊥p_y‖ d_xy, d_xy‖p_y⊥p_z‖ d_xz[36,37,38,39,40,41].

For Bi₂Mg_1−xFe_xNb₂O_9+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) (μ_eff = 5.92 μB, ⁶A_1g), 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 Bi₂MgNb_2−2xFe_2xO_9−δ is much more, than for Bi₂Mg_1−xFe_xNb₂O_9+δ. This may indicate that the exchange interaction between paramagnetic atoms, e.g., ferromagnetic type, and clusters in Bi₂MgNb_2−2xFe_2xO_9−δ solid solutions can be realized compared to Bi₂Mg_1−xFe_xNb₂O_9+δ.

Figure 4

A compassion between paramagnetic components of magnetic susceptibility for Bi₂Mg_1−xFe_xNb₂O_9+δ (open symbols) and Bi₂MgNb_2−2xFe_2xO_9−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 χ^para(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 Bi₂Mg_1−xFe_xNb₂O_9+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:

This is aFe(III)mon , aFe(III)dim(f) , aFe(III)dim(a) , aFe(III)tetr(a) , aFe(III)trim(f) , aFe(III)trim(a) , aFe(III)tetr(a) and aFe(III)tetr(a) – fraction of monomers, dimers, trimers and tetramers from iron atoms (III) with ferromagnetic -and antiferromagnetic type of interaction, χFe(III)mon , χFe(III)dim(f) , χFe(III)dim(a) , χFe(III)trim(f) , χFe(III)trim(a) , χFe(III)tetr(f) , χFe(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):

Where E(J, S^′) = −J[S^′(S^′ + 1) − 4S₁(S₁ + 1)], S₁₂ = S₁ + S₂, S₁ + S₂ −1, . . . , |S₁ − S₂|, S₃₄ = S₃ + S₄, S₃ + S₄ −1, . . . , |S₃ − S₄|, S^′ = S₁₂ + S₃₄, S₁₂ + S₃₄ − 1, . . . , |S₁₂ − S₃₄|.

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):

Here E(J, S^′) = −J[S^′(S^′ + 1) − S_a(S_a + 1) − S_b(S_b + 1)], S^′ = S_a + S_b, S_a + S_b − 1, . . . , |S_a − S_b|; S_a, S_b – the spin values of the atoms that form dimers.

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

Here x = J/kT, k – Boltzmann's constant.

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

Best agreement of experimental and design data for solid solutions Bi₂MgNb_2−2xFe_2xO_9−δ and Bi₂Mg_1−xFe_xNb₂O_9+δ obtained at the values of the parameter of antiferromagnetic exchange in dimers J_dim = −25 cm⁻¹, in trimers J_trim = −14 cm⁻¹ and tetrameters J_tetr = −9 cm⁻¹; ferromagnetic – J_dim = 20 cm⁻¹, in trimers J_trim = 16 cm⁻¹ and tetrameters J_tetr = 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 Bi₂MgNb_2−2xFe_2xO_9−δ (a) and Bi₂Mg_1−xFe_xNb₂O_9+δ (b) solid solutions

The distribution of iron atoms depending on the concentration of solid solutions Bi₂MgNb_2−2xFe_2xO_9−δ and Bi₂Mg_1−xFe_xNb₂O_9+δ is shown in the Figures 6a, 6b.

Figure 6

Dependence of portions of the monomers aFe(III)mon (1), dimers with the antiferromagnetic aFe(III)dim(a) (2) and ferromagnetic aFe(III)dim(f) types of exchange (5); trimers with antiferromagnetic aFe(III)trim(a) (3); tetramers with the antiferromagnetic exchange type aFe(III)tetr(a) (4) and ferromagnetic aFe(III)tetr(f) types of exchange (6) on the content of iron atoms in Bi₂Mg_1−xFe_xNb₂O_9+δ (a) and Bi₂MgNb_2−2xFe_2xO_9−δ (b)

As a result of investigations of iron-containing solid solutions of Bi₂MgNb_2−2xFe_2xO_9−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 Bi₂Mg_1−xFe_xNb₂O₉ 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 Bi₂MgNb_2−2xFe_2xO_9−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 Bi₂MgNb_2−2xFe_2xO_9−δ solid solutions is higher than in Bi₂Mg_1−xFe_xNb₂O₉. 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 p_π-d_π the overlap between the channels of antiferromagnetic exchange, for example, d_xy ‖p_y‖ d_xy. 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 d_xz ‖p_z‖ d_xz.