Effects of Lanthanum on Structural and Magnetic Properties of Sr_1−xLa$_{\frac {2}{3}x}$Fe₁₂O₁₉ Compounds: Theoretical and Experimental Results

Abstract

Pre-reacted powders of M-type strontium hexaferrites with chemical composition Sr_1−xLa$_{\frac {2}{3}x}$Fe₁₂O₁₉ (x = 0.1, 0.2, 0.3 0.5, 0.6) were obtained from the conventional solid state reaction method. The final consolidation of these powders were performed by using the spark plasma sintering (SPS) technique. The influence of the La³⁺ content on the crystal structure and the magnetic properties of the samples were investigated firstly under the framework of a phenomenological model that predicted the cation substitution/distribution in the Sr and/or Fe sites. The theoretical results indicated that La³⁺ ion mostly occupies the Sr²⁺ site. It was also found that as La content increased, a certain amount of Fe²⁺ ions appear as a consequence of the Fe³⁺ to Fe²⁺ reduction. However, the Fe²⁺ occupied preferably the 12k and 4f1 iron sites. The magnetic properties of the obtained samples were assessed by measurements performed in a vibrating sample magnetometer. Also, X-ray diffraction (XRD) measurements were presented as a complementary characterization. We have found that the magnetic properties of the samples degraded as the La³⁺ content increased and the increase of the Fe₂O₃ impurity phase.

1 Introduction

M-type hexaferrites are used in applications such as loudspeakers, windscreen wiper motors, and other small electric motors, as permanent magnets in refrigerator seal gaskets, small motors for cordless appliances, and in automobile applications, etc [1]. One of the most commonly used materials for hard magnets is the M-type strontium hexaferrite (SrM), whose chemical formula is SrFe₁₂O₁₉, having excellent magnetic properties, high chemical stability, and relatively low cost [1].

Several investigations have been carried out to study the influence of various dopants on its physical properties of M-type hexaferrites. In particular, the influence on the structural and magnetic properties of the rare earth as dopant element in SrM has been extensively studied. Buzinaro et al. [2] reported that the strontium hexaferrite doped with samarium (Sm³⁺) in the Sr²⁺ site causes the decrease in the saturation magnetization from about 68.8 emu/g at x = 0 to about 60.1 emu/g at x = 0.10 may be related to the changes in the valence state of iron from Fe³⁺ to Fe²⁺ in the 12k and 2a sites. Others works also discussed that the partial substitution of Sr²⁺ cations by rare earth elements has been carried out Pr³⁺ [3], Nd³⁺ [3, 4], Eu³⁺ [5], Gd³⁺ and Dy³⁺ [6], and La³⁺ [5,6,7,8,9,10,11]. According to the presented studies, the replacement of divalent Sr by trivalent rare earth elements in SrM hexaferrites is associated with a valence change of the Fe³⁺ by Fe²⁺ ions in the different iron sites. Therefore, the physical properties’ behavior can be influenced. The valence changes in the preferential sites were supported by the results of the Mössbauer experimental technique. However, to our knowledge, only few theoretical studies about M-type strontium hexaferrites have been reported regarding in relation with the cation distribution in the different crystallographic sites of this crystal structure [12,13,14].

Therefore, the aim of this work is to investigate the influence of the partial substitution of the Sr²⁺ by La³⁺ ions on the structural and magnetic properties of the Sr_1−xLa$_{\frac {2}{3}x}$Fe₁₂O₁₉ compounds. The framework of the phenomenological model was reported in our previous work [15], which allow the theoretical prediction of the cation substitution distribution in M-type hexaferrites.

2 Experimental Procedure

Polycrystalline samples of Sr_1−xLa$_{\frac {2}{3}x}$Fe₁₂O₁₉ (x = 0.1, 0.2, 0.3, 0.5, and 0.6) were prepared by the conventional solid–state reaction method. Powders of SrCO₃, La₂O₃, and Fe₂O₃ were mixed at the desired stoichiometric ratios. The mixed powders of each composition were milled for 8 h and calcined in air at 1000 °C for 8 h. The calcined powders were then ground for 4 h and pressed into pellets at 2.6 ton/cm². The obtained pellets were sintered at 1200 °C in air for 45 min. After that, the pellet samples were again reground and these powders will be hereafter referred to as pre-reacted powders.

The final consolidation of the samples was performed in a SPS 1050 Dr Sinter^Ⓡ apparatus manufactured by Sumitomo Coal Mining Co. Ltd., Japan. Pre-reacted powders of Sr_1−xLa$_{\frac {2}{3}x}$Fe₁₂O₁₉ (∼ 3 g) were placed inside a cylindrical graphite die with dimensions of 50 mm (outer diameter) and 20 mm (inner diameter). Two graphite plungers of ∼ 40 mm in height and 20 mm in diameter were placed between the sample, in which the pressure was applied. In order to protect the die and facilitate the sample release after consolidation, graphite foils were inserted between the internal surfaces of the die and between the top and the bottom surfaces of the sample and the graphite plungers. The graphite die was then placed inside the chamber of the SPS apparatus and sintering was conducted under vacuum (from 10 to ∼30 Pa). The consolidation temperature, T_D, the holding time, t_D, and the heating rate, T_D/t_r, for all samples were 900 °C, 5 min, and ∼ 175 °C/min, respectively. The temperature was measured during the consolidation process by using a (K-type) thermocouple, which was inserted into a small hole in one side of the graphite die. The maximum uniaxial compacting pressure used to synthesize all samples experiments was 50 MPa reached by a gradual increase during the first 3 min. After the sintering process, each sample was first naturally cool for about 50 min and then removed from the die. The density of all consolidated pellets was determined by using the Archimedes method.

The phase identification of the samples was evaluated from X-ray diffraction patterns obtained in a Bruker-AXS D8 Advance diffractometer. These measurements were performed at room temperature using CuKα radiation in the 3°≤ 2𝜃 ≤ 80° range with a 0.05° (2𝜃) step size, and 5-s counting time.

The magnetization measurements as a function of applied magnetic field M(H) were carried out in a vibrating sample magnetometer (Lakeshore 7404, USA). M(H) data were taken at 300 K and under an applied magnetic field range -14 ≤ H ≤ 14 kOe.

3 Phenomenological Model

The SrM crystal structure has a great number of similar crystallographic sites that can be occupied by the cationic dopants. In this structure, the O²⁻ ions form a hexagonal closed packed lattice and every five oxigen layers, one O²⁻ ion is replaced with Ba²⁺, Sr²⁺ or Pb²⁺ in BaM, SrM or PbM respectively [16]. Fe³⁺ occupies the interstitial positions of the oxygen lattice [16]. In the unit cell of the SrM, Fe³⁺ ions occupy three octahedral sites (2a, 4f2, and 12k), one tetrahedral (4f1) site, and one bipyramidal (2b) site [16], according to Wyckoff’s notation. Also, there are six different sites: one polyhedral site for Sr²⁺ ions (2d) and other five for oxygen ions [17].

The process can be modeled as an interaction process between the cation and the site to be occupied. The model is only valid for low dopant concentrations per unit formula because possible effects due to the distortion of the lattice were not considered [15, 18]. Considering that the doping process obeys statistical laws , the central parameter of the model is the substitution index per site, SI [18]. This parameter can be interpreted as a measure of the site occupation probability of the dopant cation on the i th site and can be defined as [15]:

$$ SI^{\text{dop}}_{i}=\prod\limits_{j=1}^{8}F^{\text{dop}}_{i,j} $$

(1)

where i is the i th-site number

In (2a), σ_j = $k_{e} m^{\text {hcat}}_{j}$ is the standard deviation, and k_e ∼ 0.15 is a value obtained according to Pauling’s rules and the specific experimental conditions [19]. Also, ${\Delta }m_{j} = m^{\text {dop}}_{j}-m^{\text {hcat}}_{j}$ and m_j can be any of the following factors (see Table 1):

• 1) the cationic radius, $R_{\text {cat}_{\text {i}}}= \alpha _{e_{i}}R_{\text {ion}}$, where $\alpha _{\text {e}_{\text {i}}}$ is a coefficient that depends on the coordination number at the i th site, nc_i, and R_ion is the ionic radius;

• 2) the electron’s valence, q;

• 3) the ionic potential, $P_{\text {ion}_{\text {i}}}=q/R_{\text {cat}_{\text {i}}}$;

• 4) the electric charge per site, Q_i = q/nc_i, where nc_i is the coordination number at the i th site (see Table 1) and

• 5) the effective atomic number Z_eff = (Z_cat − q) + 2nc_i, where Z_cat is the atomic number of the cation;

• 6 the electronegativity, χ.

Table 1 Values of the parameters in calculations: the atomic number, Z_cat, atomic mass, m_A, the electron’s valence, q, the ionic ratio, R_ion, and the electronegativity, χ

Notice that (2a) quantifies the differences between the dopant cation (dop) and the host cation (hcat) that may be Sr²⁺ or Fe³⁺. Additionally, in (2b) and (2c), a binomial statistical distribution function was introduced to consider the relation between the occupation number of the ion in each site, N_i, and the fraction of dopant concentration, η^dop, and the relation between the coordination number of the ion in each site, nc_i, and the fraction of dopant electronic density, ρ^dop.

In the same manner as in (1) and (2a–c), it is possible to define a substitution index per site for the host cation (hcat), $SI^{\text {hcat}}_{i}$. In this case, the “dopant” cation and the host one are the same ion, i.e., Δ m_j = 0 [18].

Taking into account all the above considerations makes it possible to define the occupation probability of the dopant and the host cation, respectively, as:

Also, the site occupation number of the dopant cation can be calculated as:

$$ Q^{\text{dop}}_{i}=N_{i}-Q^{\text{hcat}}_{i}. $$

(5)

where Q$^{\text {hcat}}_{i}$ is the occupation number of the host cation, which is defined as:

In all above-mentioned equations, the host cation is referring to Sr²⁺ or Fe³⁺ according to the crystallographic site that occupies the dopant cation.

4 Results and Discussion

Let us first inspect the influence of La³⁺ content on the structural and the phase formation of the M-type strontium ferrite within the framework of the phenomenological model presented above. Figure 1a and b show the occupation probability of La³⁺ in the Sr and Fe sites, respectively. The obtained results indicate that $S_{i}^{\text {La}^{3+}}$ is eleven orders of magnitude higher in Sr site than in Fe; therefore, the La³⁺ should occupy the Sr²⁺ site in the crystal structure. This is not an unexpected result by considering the similitude between Sr²⁺ (host cation) and La³⁺ (dopant cation). However, values of the $S_{i}^{\text {La}^{3+}}$ in Sr site are also low mostly due to the difference between the valences of the La³⁺ and Sr²⁺. Such a difference also affect the charge neutrality of the samples as a whole, triggering the reduction of Fe³⁺ ions to Fe²⁺, as reported elsewhere [7, 9]. Under the above result, it is also necessary to investigate the occupation probability of the Fe²⁺ on both the Fe and the Sr sites.

Fig. 1

Probability of occupation of La³⁺ ($S^{\text {La}^{3+}}_{i}$) as function of the concentration (x) per unit formula, for Sr_1−xLa$_{\frac {2}{3}x}$Fe₁₂O₁₉, with x = 0,0.1,0.2,0.3,0.5,0.6. a Probability of occupation in Sr sites . b Probability of occupation in Fe sites

Figure 2a and b show the occupation probability of the Fe²⁺ in the Fe³⁺ and Sr²⁺ sites, respectively. The results indicate that the order of $S_{i}^{\text {Fe}^{2+}}$ is ∼ 10^− 4 for the iron sites, which is higher than the values of the $S_{i}^{\text {Fe}^{2+}}$ in the Sr²⁺ site (see Fig. 2a), even higher than the occupation probability of the La³⁺ in the Sr site (see Fig. 1a). Also, according to the results showed in Fig. 2b, $S_{i}^{\text {F}e^{2+}}$ increases with increasing of the La³⁺ content being more marked in the 12k site, followed by the 4f1 and 4f2 sites. The above findings suggest that the Fe²⁺ cation occupy the iron sites and not the strontium site inside the crystal structure of the SrM, and that when the SrM is doped with La³⁺ may occur the valence reduction of Fe³⁺ by Fe²⁺ in the 2a and 4f2 iron sites [7, 9].

Fig. 2

Probability of occupation of Fe²⁺ ($S^{\text {Fe}}_{i}$) as function of the concentration (x) per unit formula, for Sr_1−xLa$_{\frac {2}{3}x}$Fe₁₂ O₁₉, with x = 0,0.1,0.2, 0.3,0.5,0.6. a Probability of occupation in Sr sites. b Probability of occupation in Fe sites

We have also studied the influence of the La³⁺ content on the reticular energy, U_POT, of the SrM ferrite. In a previous work, the U_POT was calculated by using the Eqs. (4)–(7) of Ref. [15]. Additionally, our estimations of the reticular energy were conducted by assuming two physical scenarios: (A) considering only the La³⁺ dopant and (B) taken into account both La³⁺ and Fe²⁺ ions. As observed in the Fig. 3, if we consider the case A, then the reticular energy of the compound tends to increase with the La content. However, in the case B, the values of U_POT are lower than in the case B and slightly decreases with increasing the La content. The above result can be related to the difference of the ionic radius of Fe³⁺ and Fe²⁺, 0.67Å and 0.80Å, respectively (see Table 1). The Fe²⁺ ions in the SrM ferrite mostly appears in the form of Fe₂O₃ [7, 9], and the reticular energy of Fe₂O₃ is ∼ 1.48× 10⁴ kJmol^− 1, a value six time lower than the reticular energy estimated for the pure SrFe₁₂O₁₉ of ∼ 9.02× 10⁴ kJmol^− 1.

Fig. 3

Reticular energy U_POT as function of the La concentration per unit formula, x, for Sr_1−xLa$_{\frac {2}{3}x}$Fe₁₂O₁₉, with x = 0,0.1,0.2,0.3,0.5,0.6

We want to remark that the reticular energy for the La-doped SrM ferrite is lower considering the reduction of the Fe³⁺ to Fe²⁺ ions. The above statement can be verified experimentally by the presence of the Fe₂O₃ in XRD analysis as reported elsewhere [7, 9, 20, 21]. Also, taken into account the slight decreases of U_POT with increasing the La content (see Fig. 3), the preparation conditions for all samples were the same (see Section 2).

Now, let us check the theoretical findings with the experimental data. Figure 4 shows the X-ray diffraction spectra of Sr_1−xLa$_{\frac {2}{3}x}$Fe₁₂O₁₉ samples with x = 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6. The obtained results shown that most of the indexed reflections belonging to the pure SrM hexaferrite. However, as La³⁺ content increases (x ≥ 0.1) some impurities of Fe₂O₃ and/or Sr₂Fe₂O₅ were detected. The type and the phase content for each value of x are reported in the Table 2. It was found that the amount of Fe₂O₃ increases from ∼ 7% (x = 0.1) to ∼ 22% (x = 0.6) with increasing the La content. Notice that the presence of this impurity is not an unexpected result as discussed above. In addition, it was not detected La-based impurity or extra phases for any value of x, suggesting the partial substitution of Sr in the crystal structure. The unit-cell parameters were also calculated from X-ray diffraction reflections and by using the Cohen method. The obtained values are listed in the Table 3. In this case, all values of a and c are in line with those reported elsewhere for the same compound [7]. Also, it was not observed appreciable variations of the above mentioned parameters with increasing the La content.

Fig. 4

X-ray diffraction patterns taken in powder of Sr_1−xLa$_{\frac {2}{3}x}$ Fe₁₂O₁₉ samples. The reflections belonging the SrFe₁₂O₁₉ phase are marked by Miller indexes (COD file number: 96-100-6001). Extra phase Sr₂Fe₂O₅ and Fe₂O₃ are identified as (+) and (*), respectively

Table 2 Phase composition of Sr_1−xLa$_{\frac {2}{3}x}$Fe₁₂O₁₉ samples for different values of La content, x

Table 3 Concentration (x) per unit formula, lattice parameters (a and c), X-ray density (ρ_XRD), and theoretical density (ρ_mod) of Sr_1−xLa$_{\frac {2}{3}x}$Fe₁₂O₁₉ samples

Values of the theoretical density ρ_mod estimated by using the reticular energy U_POT (see Eq. (8) in Ref. [15]), which in turn is calculated from the cation distribution obtained from the phenomenological model as above mentioned, and those obtained from XRD diffraction patterns, ρ_XRD, for different La content are listed in the Table 3. It is possible to observe from these values that the changes in the density of the compound do not exceed 2.9%. The experimental volume density of the samples after the SPS consolidation, determined by the Archimedes method was ρ_exp ∼ 4.75 g/cm³. Thus, the relative density ρ_exp/ρ_XRD is ∼ 92 % in all samples. Note that the difference between the experimental density ρ_exp and the theoretical density ρ_mod estimated by using the phenomenological model results does not exceeded 5.1%.

On the other hand, the magnetic properties are affected by the presence of the Fe₂O₃ impurities, as well as by the Fe³⁺-Fe²⁺ valence reduction in the iron sites. The room temperature M(H) curves and the magnetic properties of Sr_1−xLa$_{\frac {2}{3}x}$Fe₁₂O₁₉ samples, with (0≤x ≤ 0.6), are shown in Fig. 5. It can be seen that, in general, when the concentration of dopant per unit formula increased, the saturation magnetization and the remanent magnetization decreased from 57.5 emu/g at x = 0 to about 27.1 emu/g at x = 0.6 and from 27.7 emu/g at x = 0 to about 13.4 emu/g at x = 0.6, respectively. According to the results showed in Fig. 5, the lowest values of the magnetic properties (e.g., M_s and M_r) correspond to the samples with x = 0.2 (M_s= 27.5 emu/g and M_r= 10.9 emu/g) and x = 0.6, which may be explained by considering that the amount of Fe₂O₃ secondary phase was significantly greater in these samples than the rest, as indicated the intensity of peaks on X-ray pattern in Fig. 4.

Fig. 5

M − H curves of Sr_1−xLa$_{\frac {2}{3}x}$Fe₁₂O₁₉ samples at room temperature, for each value of concentration (x) per unit formula

Also, SrM hexaferrite have a ferrimagnetic structure with the magnetic moments of the Fe³⁺ cations aligned parallel to each other and to the crystallographic c-axis in 2a, 2b, and 12k, whereas in 4f2 and 4f1 sites, the magnetic moments of the Fe³⁺ cations point in the opposite direction [7]. Therefore, taking into account the collinear array of the magnetic moments in the unit cell of Sr_1−xLa$_{\frac {2}{3}x}$Fe₁₂O₁₉, the saturation magnetization can be calculated as: $M_{s}={\sum }_{i=1}^{5}\left ({\mu }^{\text {Fe}^{3+}}Q^{{\text {Fe}^{3+}}}_{i}+{\mu }^{\text {Fe}^{2+}}Q^{\text {Fe}^{2+}}_{i}\right )$.

Due to at T = 0 K the magnetic moment of the Fe³⁺ (${\mu }^{\text {Fe}^{3+}}=5.0\mu _{B}$) and the magnetic moment of the Fe²⁺ (${\mu }^{\text {Fe}^{2+}}=4.0\mu _{B}$), the decreasing of the saturation magnetization may be attributed mainly to the reduction of Fe³⁺ to Fe²⁺. As mentioned above (see Fig. 2), such process occurs in 12k spin up sites because the probability of occupation values of the Fe²⁺ cation in this site is higher than the rest of the iron sites. The theoretical magnetization of saturation calculated from the above-mentioned equation, for x = 0 and x = 0.6, was 20.00 μ_B and 19.87 μ_B, respectively. These results indicated that the diminution of the values of the magnetization of saturation do not exceed 0.65%. However, the experimental values of the magnetization of saturation for x = 0 and x = 0.6 were 57.5 emu/g and 27.1 emu/g, respectively, which indicated a diminution of 52.87%, that is much greater than 0.65% obtained from theoretical values above mentioned. It suggests that the decreasing in the magnetization of saturation values was fundamentally result of the presence of the Fe₂O₃ secondary phase in the samples, although for real samples at room temperature, the assumption of the collinear array of magnetic moments in the unit cell is no longer valid.

On the other hand, values of the coercivity H_c were found to increase from 1 to 3 kOe with the increasing of the La content. A result similar to that was reported elsewhere [6, 7, 10]. Since the coercivity, H_c depends on grain shape, size, distribution, etc [20], the lower value of the coercivity of the sample with x = 0.2 may be related to any substantial change on the microstructure for this sample. Additionally, the coercivity enhancement was reported in other ferrites and related to a microstructure with grains with core/shell morphology [22]. We want to point out that the spark-plasma consolidation promotes this kind of morphology because the process occurs under vacuum [23]. In this case, the core should be comprised of stoichiometric Sr_1−xLa$_{\frac {2}{3}x}$Fe₁₂O₁₉ and the shell could be similar, but oxygen deficiency. However, the existence and a possible relationship between the shell/core morphology and the magnetic properties of these materials must be investigated in details in a future work.

5 Conclusions

High-density samples of Sr_1−xLa$_{\frac {2}{3}x}$Fe$_{12}\textit {O}_{19}\thicksim$ 92% were obtained by spark plasma technique. The obtained X-ray diffraction data showed that the presence of the Fe₂O₃ secondary phase increased with La content of the samples. From the results obtained by using of the phenomenological model, it was found that (i) La³⁺ ion only occupies the Sr²⁺ site; (ii) as La content increased, the Fe²⁺ ions appear as a consequence of the Fe³⁺ to Fe²⁺ reduction; and (iii) the Fe²⁺ ion occupies preferably the 12k and 4f1 iron sites. Such a sequence of processes impacts negatively the magnetic properties of SrM compounds.