The impact of Bi³⁺ ions on magnetization, dielectric parameters, and conductivity of soft Mg-Cu ferrite nanoparticles

3.1 FTIR analysis

Fig. 1 displays transmittance data for MCBF nanoferrites within the frequency range 200–2000 cm⁻¹, obtained by FTIR spectroscopy for studying the interaction of IR with the MCBF nanoparticles. The FTIR spectra manifest the existence of the O–H group and residual water in the MCBF samples, which are the main reasons for the bands around (υ₃) 1630, (υ₄) 2854, (υ₅) 2922, and (υ₆) 3425 cm⁻¹ (Harqani and Basfer, 2022). All the spectra acquire the vibrational bands of metal–oxygen (M−O) bonds at tetrahedral (A) and octahedral (B) positions of MCBF spinels (Ahmed et al., 2011). Band υ₁ is between 566.19 and 571.88 cm⁻¹, corresponding to the A site stretching mode (Abdo et al., 2021). The second one, υ₂, has values between 398.01 and 405.59 cm⁻¹, related to the B site stretching mode (Abdo and Sadeq, 2022). Variations in the lengths of the Fe³⁺–O^2- bonds due to differences in A and B coordination are the source of the discrepancy between υ₁ and υ₂ values (Abdo and Sadeq, 2021). Redistributions of cations between A and B sites are inferred from the non-constant values of υ₁ and υ₂ with increasing Bi³⁺ concentration (Al-Bassami et al., 2020). It is observed that the band ν₁ moves to a lower wavenumber value for Bi³⁺; meanwhile, υ₂ shifts to a higher wavenumber value. Spinel distortion occurs because of ion radius changes, involving Bi³⁺ ions and the rearrangement of Fe³⁺, Cu²⁺, and Mg²⁺. The Bi³⁺ radius is large (1.03 Å), so it is inclined to nestle the B-sites. At the same time the Mg²⁺ radius (0.72 Å) is greater than that of the Fe³⁺ ion (0.645 Å) and Cu²⁺ (0.57 Å). Therefore, Bi³⁺ ions filling B-sites will initiate some Mg²⁺ ions to move to A-sites, and specified Fe³⁺ and Cu²⁺ ions will migrate from A-sites to B-sites to improve the strain. Hence, a growing number of Mg²⁺ ions in A-sites increases the ionic radii of the A-sites and leads to the move to higher wavenumber value, with an increasing number of Cu²⁺ ions in B-sites decreasing the ionic radii of the B-sites and lead to the shift to lower wavenumber. Fig. 1 illustrates the values of all these bands for all MCBF nanoferrites. The lack other bands proves that all MCBF nanoferrites have a single spinel structure.

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Fig. 1

FTIR diffractograms of Mg_0.5Cu_0.5Bi_xFe_2-xO₄; x = 0.0, x = 0.02, x = 0.04, x = 0.06, x = 0.08 and x = 0.1 nanoferrites.

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3.2 Magnetic study

To determine the dominant magnetic phase and parameters, a VSM was employed to record the direct current (DC) magnetic field-dependent hysteresis loops of MCBF nanoferrites at RT. Fig. 2 shows the M(H) loops with zoomed-in depiction recorded via a field of ± 20 kOe. All the MCBF nanoferrites have ferrimagnetic characteristics with notable diverse magnitudes of saturation magnetization (M_S), coercivity (H_C), and remnant (M_r); see Table 1. M_S has a peculiar trend; it decreased gradually from 30.84 at MCBF0 to 27.60 emu/g for MCBF3 and increased, reached 30.15 and 31.31 emu/g for MCBF4 and MCBF5, respectively. This behavior can be justified as follows. Firstly, this decreasing behavior is a logical result of the substitution process of the Bi³⁺ ion with a magnetic moment of 3µ_B at the expense of the higher magnetic ion Fe³⁺ of 5µ_B (Kumar and Kumar, 2016). Indeed, the largest Bi³⁺ions (1.03 Å) (Shannon, 1976) can nestle in the largest B positions. Néel's two-sublattice ferrimagnetism model states that ions on the A and B sublattices have collinear spins and anti-parallel magnetic moments. Then, the lattice's net magnetic moment is the difference between the magnetic moments of the B and A sub-lattices µ_B = |µ_B(B) - µ_B(A)| (Ahmed et al., 2013). So, by doping Bi³⁺ ions instead of Fe³⁺ ones in the B sites, the net magnetic moment decreases, and then M_S also decreases. Secondly, for significant content of Bi³⁺, i.e., MCBF4 and MCBF5 nanoferrites, M_S introduces an increment behavior which can be assigned for cations redistribution of nonmagnetic Mg (0µ_B) (Mansour et al., 2017a), and magnetic Cu (1µ_B) (Mansour et al., 2018a) between A and B sites, as seen above in FTIR results. Increasing Bi³⁺ ions in B sites at the expense of Fe³⁺ ions forces some of the large Mg (0.72 Å, 0µB) to migrate into the site, which in turn forces some small Cu (0.57 Å, 1µB) to migrate into B sites. This process decreases the A sites' magnetic moment and increases the B sites' magnetic moment, increasing the overall M_S. Hence, Bi³⁺ ions substitution can tune the magnetization of pristine Mg-Cu ferrite nanoparticles. Nanoparticles have a distinguished surface-to-volume ratio; hence, the number of dangling bonds or spin tilting effects at the nanoparticles' surface rises, decreasing the allied magnetic moments number across the particles. Fig. 3 manifests the nearly direct relation between magnetization and the size of MCBF ferrite nanoparticles (Abdo and El-Daly, 2022). Also, the magnetization of the sample MCBF5 is enhanced with an improved ratio of 1.51 % compared to the pristine sample. Thus, the first aim of this paper, enhancing the magnetization with Bi³⁺ doping, is achieved. Also, the remnant magnetization is enhanced by decreasing its value compared with the pristine sample. The characteristic sample MCBF5 has a M_r value of 5.61 emu/g, whereas the pristine sample has M_r value of 6.36 emu/g. Hence, the remnant magnetization is decreased with a decreasing ratio of 11.83 % to the pristine sample. This was the second aim of this paper, which was also achieved.

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Fig. 2

VSM of all the MCBF nanoferrites with zoomed-in picture.

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Fig. 3

Dependence of crystallite size (D_nm), magnetization (M_S), and coercivity (H_C) on Bi³⁺ content for all MCBF nanoferrites.

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The squareness ratio (SQR) is a dimensionless quantity equals M_r/M_S (Mansour et al., 2021a), which notifies principally about the magnetic domain nature of the investigated magnetic samples behaving as ferri- or ferromagnetic material (Alqarni et al., 2022). According to Stoner-Wohlfarth’s theory, a value of 0.5 is necessary for nanoparticles' SQR to acquire a single-domain nature with uniaxial symmetry. The calculated SQR values of the investigated MCBF nanoferrites are within the range of 0.18 and 0.28. Hence, it is concluded that our prepared MCBF samples are ferrimagnetic nanoparticles with multi-domain nature. Another important magnetic parameter is the magnetic moment per chemical formula (η_B), which depends mainly on the M_S, density (ρ), and molecular weight (MW) of each formula through the formula (Abdo et al., 2023):

As expected, η_B has the same behavior of M_S and its values within the range 0.24 μ_B and 0.22 μ_B for all the MCBF nanoferrites; see Table 1. Observing the M_S, M_r, and SQR results, it is simple to deduce that the presence of Bi³⁺ ions positively adjust the magnetization data and achieve the required mission.

On the other hand, the H_C of the MCBF nanoferrites manifests a remarkable behavior within the range 105.61 and 59.90 Oe; see Table 1. As mentioned above, we aimed to decrease the H_C values through the Bi/Fe substitution process. H_C of the nanoferrite MCBF5 has the lowest value, 59.90 Oe, with an improving ratio of 50 %, compared to the pristine MCBF0 sample with 78.99 Oe. In fact, there are many reasons that govern H_C behavior, like substitution element, size of the nanoparticle, etc. The reason for decreasing coercivity to its lowest value has two justifications. The first one is that sample has the lowest M_S value; hence the required field to conquer this magnetization is also tiny, producing low H_C value. The second one is the particle size effect, where the relation between H_C and the nanomaterial size is an inverse one; see Fig. 3. Many authors reported an analogous inverse relation between H_C and particle size (Mansour et al., 2021b; Mansour et al., 2021c; Ali et al., 2021). Additionally, there are other magnetic parameters based on M_S, H_C, and crystallite size (D), anisotropy constant (k), and initial permeability (μ_i) can be determined through the following relations (Abdo and El-Daly, 2021; Abdo et al., 2022), and listed in Table 1.

Fig. 4 displays the dependance of ${\eta }_B,{\mu }_i,\mathrm{a}\mathrm{n}\mathrm{d}k$ on Bi³⁺ content. $k$ performance is ruled by both M_S and H_C values but takes the general behavior of H_C. Basically, magnetic anisotropy refers to the phenomenon whereby the magnetic properties of a ferrite material exhibit a dependency on the direction. Therefore, the nature of magnetic anisotropy plays a significant role in deciding whether a certain magnetic material is appropriate for a particular application. The significance of magnetic anisotropy is particularly apparent in both soft and hard magnetic materials. Due to the direct relationship between magnetic anisotropy and coercivity, soft magnetic materials typically exhibit minimal magnetic anisotropy. As seen $k$ augmented for the nanoferrite MCBF1 (3224.74 erg/cm³) and then generally decreased for further Bi doping. Hence Bi substitution decreases the crystalline anisotropy and generates samples that are easy to demagnetize. As for ${\mu }_i$ , it has a general increasing behavior, which increased from 11.50 for the nanoferrite MCBF0 to 17.84 for the nanoferrite CMCF5 with enhancing the ratio of 55.12 %. This increment confirms that the magnetic flux strengthens within the MCBF nanoferrite via the weaker magnetic ion Bi doping.

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Fig. 4

Dependence of magnetic moment per formula unit (η_M), anisotropy constant (k), and initial permeability (μ_i) on Bi³⁺ content for all MCBF nanoferrites.

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3.3 Dielectric studies

3.3.1

3.3.1 Frequency dependence of dielectric parameters

The dielectric constant (ε′) quantifies a material's ability to retain energy in response to an alternating field. Using the following Eq. (Mansour et al., 2018a), the ε′ values of all the MCBF nanoferrites were determined.

(4)

$$\epsilon \prime =\frac{\mathit{Ct}}{{\epsilon }_{o}A}$$ For each ferrite pellet, we have C, t, and A, which stand for its capacitance, thickness, and area, respectively; ε_o is the permittivity of free space. Fig. 5(a) shows the frequency dispersion of ε′ of all the MCBF nanoferrites at RT, which exhibit the typical dispersion of all ferrite materials. The dielectric constant is mainly determined by the polarization types present in a substance. Ferrite materials were declared to include four polarization types at different frequencies: interfacial and orientational at lower frequencies (mHz to 1 MHz), ionic and electronic at higher frequencies (1 MHz to above GHz). The obtained dispersion in Fig. 5(a), interfacial and orientational types are the principal cause for the ε′ behavior for all the MCBF samples. The ε $\prime$ values of all the MCBF nanoferrites decrease with further increasing frequency. In fact, ε′ has large values at a low frequency domain (≤10 kHz), which reduces rapidly with increasing frequency. Then, in the range of 10 kHz ≤ f ≤ 5 MHz, ε′ decreases slowly and becomes frequency-independent. It was reported that the ferrites’ structure is composed of grains (G_S) and grain boundaries (GB_S) (Ahmed et al., 2013). Based on the Maxwell-Wagner model, in the range ≤ 10kH, polarization is generated by the buildup of charge carriers at the GB_S and produces high ε′ values. The significant decrease in this area is due to the cessation of polarization since the charges cannot follow the frequency of the applied field. Regarding the range 10 kHz ≤ f ≤ 5 MHz, the ε′ behavior is due to orientational polarization, where the dipoles' inability to follow the field frequency is the reason behind the ε′ nearly constant values.

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Fig. 5

(a-c): Frequency dependence of (a) dielectric constant ε′, (b) dielectric loss tangent tanδ, and (c) conductivity σ_ac of all the MCBF nanoferrites at RT.

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The dielectric loss tangent (tanδ) is the consequence of the delayed action to the frequency, originating from diverse reasons. When a nanoferrite material is subjected to a field, the dipoles inside the material move closer and closer to the electrode. The dipoles' movement is then resisted by friction inside the ferrite material, leading to heat production and dielectric loss (shown by tanδ). The tanδ readings of all MCBF samples are directly taken from the RLC apparatus. Fig. 5(b) shows the frequency dispersion of tanδ of all the MCBF nanoferrites at RT, which displays the characteristic dispersion of all ferrite materials. Obviously, tanδ has a rapid decay in the low frequency domain (≤10 kHz) followed by a slower decay within the span 10 kHz ≤ f ≤ 5 MHz. The operation of charge carrier hopping is slowed down by GB_S, leading to more absorption and more significant loss, especially at lower frequencies (Mansour et al., 2019a). Specifically, at low frequencies, the Fe²⁺↔ Fe³⁺ exchange processes need more energy, which correlates with high resistive GB_S and leads to large tan values. On the other hand, the G_S function is more effective at high frequencies because charge carriers hop among ions in the octahedral sites. Consequently, tanδ decreases with frequency because absorption is less at higher frequencies, where electrons need less energy at higher frequencies (Mansour et al., 2018b).

Fig. 5(c) shows the frequency-dependence of alternating current (AC) conductivity (σ_ac) for the investigated MCBF samples at RT, where the σ_ac values were assessed using the formula.

(5)

$${\sigma }_{\mathit{ac}}=2\pi f{\epsilon }_o{\epsilon }^{\prime }tan\delta$$

These results show that up to 10 kHz, σ_ac has small values but that beyond 10 kHz, significant increments occur. Multiple reports (Mansour et al., 2019b; Mansour et al., 2023) have established that ferrite's polarization process is like its conduction approach. Usually, the conduction route in ferrites arises mainly due to the exchange process of Fe³⁺ ⟷ Fe². As was previously noted, GB_S becomes further effective at lower frequencies, impeding these electron exchange processes and leading to lower values for the σ_ac. Whereas, at higher frequencies, the enhanced carrier exchange activities inside the G_S are responsible for the larger σ_ac values.

3.3.2

3.3.2 Bi content dependence of dielectric parameters

Fig. 6 shows the ε′ values of all MCBF nanoferrites at RT and 50 Hz. It was noticed that the ε′ value increased as the Bi³⁺ content increased. The nanoferrite MCBF5 has the optimum ε′ value of 365.68 with an improving ratio of 125.97 % to the pristine MCBF0 nanoferrite, which has just an ε′ value of 159.61. This remarkable behavior is justified as follows. Bi³⁺ replaced Fe³⁺ ions and occupied the B-sites, as mentioned above, forcing the B sites' iron ions to emigrate to the A sites. As a result, more Fe²⁺ and Fe³⁺ ions are in the A sites, and more electrons are hopping between Fe²⁺↔Fe³⁺ ions in the A sites. Therefore, the possibility of electron accumulation on the GB_S increased in polarization and ε′ value.

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Fig. 6

Dependence of dielectric constant ε′, conductivity σ_ac, and dielectric loss tangent tanδ on Bi³⁺ content for all MCBF nanoferrites at RT.

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As for σ_ac dependence on Bi³⁺ content, it has an increment behavior with further Bi doping, as seen in Fig. 6. The nanoferrite MCMF5 has an σ_ac value of 691.8 μ(Ω.m)^-1, which is an outstanding outcome compared to the pure MCBF0 sample, which acquires an σ_ac value of 42.1 μ(Ω.m)^-1. It is noteworthy that the conductivity was enhanced with an enhancing ratio of 1543.23 % via Bi doping. As stated before, the causes of dielectric constant are comparable to those of conductivity in ferrite materials. So, the proposed mechanism for interpreting the ε′ results is also valid for explaining the σ_ac results. Moreover, Jacob et al. declared that the conductivity of Mg-Cd-Bi nanoferrites was enhanced via hoping between Bi²⁺ and Bi³⁺ at octahedral sites (Jacob et al., 2023). Hence, these two reasons are the motives for enhancing conductivity of the MCBF with further increasing Bi content.

Fig. 6 also shows the tanδ values for MCBF nanoferrites at RT and 50 Hz. Amazingly, it was noticed that the loss diminished gradually with the rise of the bismuth element, which is a wonderful result. Liu et al. summed up the dielectric losses caused in dielectric materials, which can be classified into intrinsic and extrinsic roles (Liu et al., 2023). Intrinsic losses are caused by the anharmonic interaction of the applied electric field with the phonon system. Extrinsic losses, on the other hand, relate to crystal structure properties such as density, grain boundaries, porosity, etc. Then, it was declared that the relation between the system density and dielectric losses is an inverse relationship. For our MCBF samples, the substitution process is a large molecular weight element (Bi = 208.9804 g/mol) instead of a small one (Fe = 55.845 g/mol). Therefore, it is normal for the density to increase with further increasing Bi³⁺ content, leading to a decrease in dielectric loss. Table 1 shows all the calculated values of the MCBF densities. The nanoferrite MCBF5 has a loss of 6.49 with an enhancing ratio of 80.22 % compared with the nanoferrite MCBF0 loss of 32.81. Therefore, the dielectric parameters of the investigated CMBF nanoferrites can be remarkably tuned by Bi³⁺ ion doping.

3.3.3

3.3.3 Temperature dependence of dielectric parameters

Now, we will discuss the impact of temperature on the dielectric behavior of our MCBF nanoferrites. Fig. 7(a) manifests the ε′ temperature-dependence of the nanoferrite MCBF4 (as a model for the reminder samples) at the frequency domain 50 Hz-5 MHz. The reminder MCBF nanoferrites have a similar general performance, which displays the typical response of all ferrite materials. The ε′ values exhibit a growing disposition as the applied temperature rises. This trend may be explained by thermal energy, which causes the electrons to move more quickly and induces local dipoles to line up in the field direction, resulting in larger polarizations and ε′ values (Mansour et al., 2018c).

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Fig. 7

(a-c): Frequency dependence of (a) dielectric constant ε′, (b) dielectric loss tangent tanδ, and (c) conductivity σ_ac of all the MCBF nanoferrites different temperature.

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Fig. 7(b) shows the σ_ac temperature-dispersion of the nanoferrite MCBF4 (as a model for the reminder samples) at the frequency range 50 Hz-5 MHz. The reminder MCBF nanoferrites have the same general behavior, which displays the typical response of all ferrite materials. When the applied temperature rises, σ_ac rises, which may be ascribed to the thermal energy that increases charge carrier mobility (Mansour et al., 2023). The charge carriers’ exchanges are mainly through electron hopping between Fe³⁺↔Fe²⁺ and Bi³⁺↔Bi²⁺, besides the hole exchange between Cu²⁺↔Cu¹⁺.

Fig. 7(c) shows the tanδ temperature-dependence of the nanoferrite MCBF4 (as a model for the reminder samples) at the frequency range 50 Hz-5 MHz. The reminder MCBF nanoferrites have the same general behavior, which can be understood as follows. Indeed, tanδ temperature-dependent behavior is primarily due to the existence of temperature-dependent charge carriers scattered throughout the ferrite material (Mansour et al., 2017b). Hence, the scattering of charge carriers through the mainly hopping of Fe²⁺↔Fe³⁺ and Bi³⁺↔Bi²⁺ besides exchange through the other divalent cation.

3.3.4

3.3.4 Conduction mechanism

As all other ferrite materials, σ_ac for all the MCBF samples at diverse temperatures and frequencies follows Jonscher law:

(6)

$${\sigma }_{\mathit{ac}}={\sigma }_{\mathit{dc}}+A{\omega }^S$$ where dc stands for dc conductivity, $\omega$ for angular frequency ( $\omega$  = 2πf), A for a particular parameter, and S for an exponent term with a value between 0.0 and 1.0, indicating that the migration of charge carriers. Jonscher power law fitting is shown in Fig. 8 for a typical plot of ac for the nanoferrite MCBF4. Our MCMF samples' conduction mechanism may be inferred from the S factor and its temperature dependency. Fig. 9 displays the S factor for all MCBF samples within the temperature range of 303 to 737 K. Elliott's results demonstrated when the S factor decreases with increasing temperature, the conduction can be attributed to the correlated barrier hopping (CBH) model of electrons. However, the conduction can be attributed to small polaron tunneling (SPT) when the S factor increases with increasing temperature. In fact, the term “small polaron” refers to an electron or hole that has been confined by its self-induced atomic (ionic) displacement field in an area of linear dimension (“radius”) of the order of the lattice constant (Appel, 1968). This SP in a solid, can tunnel through a potential barrier to an unoccupied state in a neighboring state with energy conserved by a tunneling process. wo distinct temperature ranges can be identified: (I) spanning from 303 to 473 K, and (II) spanning from 473 to 737 K. The CBH model accurately predicts a decrease in S as the temperature increases in area I. On the other hand, in area II, the value of S increases as the temperature increases, which aligns with the expected result according to the SPT model. Accordingly, CBH and SPT models will govern the MCBF samples' conduction mechanism over temperatures in regions I and II.

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Fig. 8

A representative graph of σ_ac for the nanoferrite CMCF4, along with Jonscher power law fitting.

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Fig. 9

S factor for all the MCBF nanoferrite.

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