1 Introduction

Magnetic nanomaterials are highly desirable due to the enormous possibilities they offer in a broad range of applications in biomedical applications [1], photothermal therapy [2], as radiosensitizers in cancer therapy [3], in hydrophobic drug delivery [4], as supercapacitors [5], in copper removal from water [6], as adsorbents of toxic heavy metals [7], and many others. Among the magnetic nanomaterials, magnetite (Fe3O4) nanoparticles are the most extensively studied because they can be manipulated and controlled with an external magnetic field.

Many approaches for the synthesis of magnetite nanoparticles have been developed for attaining high-quality materials with particular phase purities and particle sizes. One of the main challenges for the synthetic methods is to produce materials with a good particle size distribution and desired composition uniformity, structure and crystallinity [8]. It was recently shown that the coprecipitation approach is the simplest, most useful [9], widely used [10], most efficient, and the least expensive [11] method for the preparation of ferrous oxide nanoparticles. Additionally, it allows control over the particle size and morphology [12]. Therefore, for the abovementioned reasons, we used this method for the preparation of the nanoparticle samples.

Saturation magnetization is an important parameter for magnetite nanomaterial applications. One way to obtain a higher saturation magnetization is by introducing Mn ions to form a Mn x Fe3−x O4 system. Theoretically, the substitution of a Fe2+ ion with a Mn2+ ion in the system will increase its magnetization because a Mn2+ ion has a 25 % higher magnetic moment than a Fe2+ ion [13]. Several authors also reported that the particle size had a significant effect on the saturation magnetization of the Mn x Fe3−x O4 system [14–16]. However, they did not investigate whether there was a magnetic saturation effect originating from the clustering of the particles. To study the magnetic properties of the Mn x Fe3−x O4 nanoparticles in more detail, we examined their saturation magnetization dependence not only on the Mn content but also on the presence of the primary particles (or individual particles as defined by [2, 17]) and the secondary structures. The secondary structures are defined as the clusters of the primary particles. To explore these dependencies, a powerful small-angle scattering technique is required. This technique has the capability to examine the hierarchical nanostructures, the primary particles, the clusters within the samples [18], and fractal structures of the particles [19].

In this work, we report a method for Mn x Fe3−x O4 nanoparticle synthesis using a local magnetite powder from iron sand as the main source. We probe the particles’ microstructures, particularly the primary particles, the clusters, and their associated magnetic properties. The microstructures were investigated using small-angle neutron scattering (SANS) and high-resolution transmission electron microscopy (HRTEM). The SANS data analysis was carried out using the two lognormal spherical model and the mass fractal model to reveal the size of the primary, the secondary, and the fractal structures. Finally, the saturation magnetization and the magnetic blocking temperature were investigated using a superconducting quantum interference device (SQUID) magnetometer. We also discuss the relationship between the microstructure and the corresponding magnetic properties.

2 Experimental Procedure

The synthesis of the Mn x Fe3−x O4 particles was conducted using a simple coprecipitation method. The starting material, magnetite powder, was extracted and purified from local iron sand using a magnetic separator. The powder was then dissolved in hydrochloric acid (HCl) and mixed with MnCl2∙ 4H2O using a magnetic stirrer followed by the drop-wise addition of ammonium hydroxide (NH4OH) to obtain the precipitates. The HCl, MnCl2∙ 4H2O, and NH4OH were analytical grade from Sigma-Aldrich without further purification. The precipitates were washed using distilled water until a normal pH was reached. The pH, reaction time, and mixing speed were thoroughly controlled. All processes were kept at room temperature. The formation of the Mn x Fe3−x O4 particles was believed to occur as follows [20] with modification after the Mn doping:

$$\begin{array}{@{}rcl@{}} &&2\text{FeCl}_{\text{3}} +(1-x)\text{FeCl}_{2} +x\text{MnCl}_{2} \cdot 4\mathrm{H}_{2} \text{O}+8\text{NH}_{4} \text{OH}\\ &&\quad\to \text{Mn}_{x} \text{Fe}_{3-x} \mathrm{O}_{4} +\text{8NH}_{4} \text{Cl+4(1+}x\text{)H}_{2} \mathrm{O} \end{array} $$
(1)

The phase characterization was carried out using X-ray diffractometry (XRD) (Philips X’pert MPD diffractometer) in the 2 θ range from 20° to 70° using CuK α radiation to investigate the phase purity and the formation of the Mn x Fe3−x O4 particles. The size and morphology of the crystallites were investigated using HRTEM (Tecnai G2 F20 X-Twin). A 36-m SANS spectrometer at the National Nuclear Agency of Indonesia was also employed to investigate the primary and secondary particles and fractal structures. In the SANS experiment, the scattering vector, q=(4π/λ) sin θ ranged from 0.003 Å −1 < q < 0.1Å −1, where θand λ are the scattering angle and the neutron wavelength, respectively. Details of the instrument for the SANS experiment were provided elsewhere [21]. A data reduction program, GRASP [22], was applied to correct all the scattering data for an empty cell as the background, noise of the dark electronic current, the detector efficiency, and transmission of the samples. The scattering data were fitted using two lognormal spherical and single mass fractal models by a data analysis program, SASfit [23]. The magnetic properties of the Mn x Fe3−x O4 nanoparticles were investigated using a Quantum Design’s MPMS SQUID magnetometer by applying magnetic sweeping from 5 to −5 T. The zero-fieldcooled (ZFC) and fieldcooled (FC) protocols were carried out to examine the magnetic blocking temperature of the Mn x Fe3−x O4 particles according to the literature [24]. The ZFC patterns were attained by cooling the samples (without applying an external magnetic field) from 400 to 5 K, and then the magnetization data (at an external magnetic field of 5 Oe) was collected during the heating process from 5 to 400 K. Furthermore, the FC patterns were obtained during the cooling process over the same temperature range and in the same field. Finally, the magnetic properties of the Mn x Fe3−x O4 particles were correlated with their nanostructures obtained from the SANS data analysis.

3 Results and Discussion

XRD patterns of all the samples are displayed in Fig. 1. The data confirm the presence of only magnetite (PDF No. 19-0629) without any impurities for all samples. The broad peaks had an average full-width at half-maximum (FWHM) of >2°2 θ, suggesting that the magnetite exhibits a nanometric dimension [25]. Moreover, the diffraction peaks shift to a lower angle as x increases, implying that the lattice parameter increases with Mn2+ incorporation. The increasing lattice parameter and the crystal volume of the magnetite system are shown in Fig. 2. The increase can be attributed to the fact that the ionic radius of Mn2+ (0.89 Å) is larger than that of Fe2+ (0.77 Å) and Fe3+ (0.64 Å) [26]. This provides evidence that Mn2+ ions were successfully inserted into Fe3O4 [27] by partially replacing Fe2+ or Fe3+ ions to form Mn x Fe3−x O4. Additionally, the lattice parameters of the Mn x Fe3−x O4 nanoparticles increased from 8.377 to 8.439 Å. This indication of successful incorporation has also been reported by others for powder [28], film [29], and single crystal microspheres [26].

Fig. 1
figure 1

XRD patterns (using CuK α radiation) of the Mn x Fe3−x O4 (0 ≤ x ≤ 1) powders prepared by the coprecipitation method

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Fig. 2
figure 2

Lattice parameter and crystal volume of the Mn x Fe3−x O4 (0 ≤ x ≤ 1) powders after the Rietveld analysis of the XRD data, as shown in Fig. 1

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In our previous work, the XRD data analysis of the Fe3O4 prepared by the coprecipitation method followed by the calcination at a higher temperature showed that the nanoparticles had a crystal size of approximately 16 nm [25]. However, due to the limitation of XRD for studying the hierarchical size of nanostructures, we have not yet been able to explain in detail the particle size and clustering. In this work, the details of the particle size, particularly the primary and secondary structures, i.e., their nanosized clustering, is investigated using SANS and HRTEM.

The composition and cationic distributions of the Mn x Fe3−x O4 particles for x composition between 0 and 1 can be analyzed using the following formula [30]:

$$ \left( {\text{Mn}_{x}^{2+} \text{Fe}_{1-x}^{3+}} \right)\left[ {\text{Fe}_{1-x}^{2+} \text{Fe}_{1+x}^{3+} } \right] $$
(2)

The iron metal ions (Fe2+ and Fe3+) enclosed in the square bracket represent those in the octahedral positions, while the other metal ions (Mn2+ and Fe3+) in the round bracket represent those in the tetrahedral positions depending on the x value. Six oxygen atoms surround the metal ions in the octahedral sites, while four oxygen atoms surround the metal ions in the tetrahedral sites. In the Mn x Fe3−x O4 system, the spinel structure can be classified into three types: inverse, mixed, and normal spinel. The structure for x = 0 is inverse spinel, which has eight Fe3+ ions located in the tetrahedral sites and eight Fe2+ and eight Fe3+ ions randomly placed in the octahedral sites [31]. The systems for x = 0.25, 0.5, and 0.75 form mixed spinel structure because Mn2+ ions partially shift the Fe3+ ions in the tetrahedral positions. Furthermore, the structure for x = 1 constructs normal spinel in which the tetrahedral sites are fully occupied by Mn2+ ions and the other site is fully occupied by Fe3+ ions.

The SANS curves of the Mn x Fe3−x O4 nanoparticles for x composition, 0 ≤ x ≤ 1, are presented in Fig. 3. The SANS curve at a high q range represent the behavior of primary (small) particles in the samples. Meanwhile, the curves at medium and low qranges explain the secondary particles and fractal dimension, respectively. Visually, the curves at the high q range for x = 0 and 0.25 exhibit similar trends corresponding to similar primary particle sizes, while for x = 0.5, 0.75, and 1, different trends occur that correspond to smaller primary particle sizes. The curves at a medium q represent the different trends associated with the differences in the secondary particles, and the curves at the low q range show a relatively similar gradient that corresponds to the similar fractal dimension of the samples. However, this qualitative analysis cannot be used to justify the detail and exact microstructures of the systems. To further examine the primary and secondary particles and the fractal dimensions simultaneously, the SANS data analysis using mathematical models with a global fitting approach is required.

Fig. 3
figure 3

SANS curves and fitting model of the Mn x Fe3−x O4 (0 ≤ x ≤ 1) nanoparticles. The data were shifted for clarity. The circles represent the SANS data, and the solid lines represent the fitting model using the two lognormal spherical model and the single mass fractal model

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All the SANS curves were fitted by assuming a two lognormal spherical model for the size distributions of the primary and secondary structures as form factor and a single structure factor for the mass fractal model [32] according to

$$\begin{array}{@{}rcl@{}} I(q)&\approx& \int\limits_{0}^{\infty} N_{1} (R_{1} ){{F_{N}^{2}}} (q,R_{1} )dR_{1} S(q,\xi ,D,R_{1} )\\ &&+\int\limits_{0}^{\infty} {N_{2} (R_{2} ){{F_{N}^{2}}} (q,R_{2} )} dR_{2} S(q,\xi ,D,R_{2} ) \end{array} $$
(3)

where Nis the number density of the particles, F(q, R) is the scattering amplitude, and S(q, ξ, D, R) is the structure factor for a mass fractal. The curves were fitted and satisfied by two lognormal spherical models and a single structure factor model using mass fractal for the clusters. Equation (3) can then be rewritten as follows:

$$\begin{array}{@{}rcl@{}} I(q)&\approx& \int\limits_{0}^{\infty} N_{1} (R_{1} ){{F_{N}^{2}}} (q,R_{1} )dR_{1} \\&&+\int\limits_{0}^{\infty} {N_{2} (R_{2} ){{F_{N}^{2}}} (q,R_{2})} dR_{2} S(q,\xi ,D,R_{2} ) \end{array} $$
(4)

For the particle size distribution of the magnetic nanoparticles, the lognormal function is the best model to describe the size distribution of the particle radii [33]. For spherical particles with a diameter, D = 2R, it is modified from [34]

$$ N(R)=P(R)=\frac{1}{\sigma R\sqrt {2\pi} } \exp^{\left( {-\frac{(\ln \text{R}-\ln R_{0} )^{2}}{2\sigma^{2}}} \right)} $$
(5)

where R 0 and σ are the characteristic radius of the distribution and standard deviation or polydispersity index, respectively. The structure factor S for a mass fractal [35] is given as

$$\begin{array}{@{}rcl@{}} S(q)&=&1+\frac{D{\Gamma} (D-1)}{(qR)^{D}\left[ {1+1/(q^{2}\xi )^{2}} \right]^{(D-1)/2}}\\&&\times\sin\left[ {(D-1)\tan^{-1}(q\xi )} \right] \end{array} $$
(6)

where qis the scattering vector, Γ is a gamma function, D is the fractal dimension, and ξ is the cutoff distance. The results of the pattern analysis of the SANS curves of the Mn x Fe3−x O4 nanoparticles are displayed in Table 1.

Table 1 Result of the fits for the SANS data using Fig. 3. and Eqs. 3–6 for the Mn x Fe3−x O4 nanoparticles
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According to Table 1, when the Mn content becomes larger, the size of the Mn x Fe3−x O4 (0 ≤ x ≤ 1) nanoparticles becomes smaller. In general, small particles (with radius R 1) as primary particles construct larger particles or secondary structures (with radius R 2) as clusters with agglomeration and/or aggregation [17]. The cluster formation is affected by the magnetic interparticle interactions between the nanoparticles [18] and the fractal dimension, indicating that a reaction-limited mechanism occurs in the magnetic nanoparticles system [36]. The fractal dimension of Mn x Fe3−x O4 tends to be similar to 3, corresponding to the growth of the structures in three dimensions. Such a Dvalue can be associated with a construction of a three-dimensional building block. To achieve a stable state, the magnetic nanoparticles with a high surface free energy tend to cluster. Therefore, the formation of clusters leads to the reduction of the surface area of the magnetic nanoparticles [37]. Additionally, the magnetic nanoparticles with smaller particle sizes have a larger affinity to aggregate into clusters, which is related to the lower energy barriers [38].

Further insight into the morphology and structure of the samples, which is represented by x = 0.5, is provided by the HRTEM images shown in Fig. 4. The primary particles have a radius of approximately 2.5 nm, and the secondary structures form clusters that have a radius of approximately 8 nm when compared with the results from the SANS data. These results are in a good agreement with the work by Giri and coworkers in which the TEM photographs of their Mn0.4Fe2.6O4 nanoparticles showed nearly a spherical shape with a radius of approximately 12 nm and nanoclusters [39]. In addition, Fig. 4 also shows that the Mn0.5Fe2.5O4 sample has a high crystalline nature with the lattice parameter scale approximately 0.8 nm, which corresponds to the XRD data presented in the above discussion.

Fig. 4
figure 4

HRTEM image of Mn0.5Fe2.5O4 sample. The green circles represent the primary particles, and the yellow circles represent the secondary particles

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Figure 5 shows the magnetic hysteresis loop of the Mn x Fe3−x O4 nanoparticles via the SQUID magnetometer with the applied magnetic field sweeping from −5 to 5 T at room temperature. The figure shows that the samples exhibit the patterns with nearly negligible coercive forces and remanent magnetizations. Therefore, the prepared Mn x Fe3−x O4 nanoparticles exhibit superparamagnetic properties. In good agreement with this work, another experiment showed that the magnetic nanoparticles exhibit remanent magnetization and a coercive force that is approximately negligible, indicating superparamagnetic behavior [40]. The phenomenon of superparamagnetism can be explained by the size effects and thermal fluctuations. The superparamagnetic behavior occurs when the particle sizes are smaller than the critical size, and the thermal fluctuations lead to spontaneous demagnetization of the preceding saturated assembly of the magnetic nanoparticles [41]. The samples have a random orientation in the absence of an external magnetic field; however, under the presence of one, the moment orientates parallel to the field direction and achieves its saturation [42].

Fig. 5
figure 5

Magnetic hysteresis loops of the Mn x Fe3−x O4 nanoparticles at 300 K

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More detailed studies on the superparamagnetic properties of the Mn x Fe3−x O4 nanoparticles can be conducted using a ZFC-FC measurement, as displayed in Fig. 6. As shown, the maximum peak of the ZFC curve tends to shift to lower temperature as x increases. The maximum peak observed in the ZFC curve is defined as the magnetic blocking temperature (T B) [43–45] and occurs where the anisotropy energy barrier is comparable to the thermal energy of the particles. Due to the effect of magnetic randomization, the magnetic nanoparticles do not magnetically interact above T B; however, they do interact and exhibit ferromagnetic-like properties below T B [46]. In general, starting from the low temperature region, the magnetization in the ZFC curve increases until a maximum is achieved at T B and then decreases. The FC curve is nearly stable below T B, and it overlaps with the ZFC curve above T B. The temperature at which the magnetization data in the ZFC and FC curves starts to bifurcate is defined as the transition [47] or magnetic irreversibility [48, 49] temperature. Here, the transition and blocking temperatures in the ZFC and FC curves are similar, except for x = 1. The separating magnetizations of the ZFC and FC curves of the magnetic nanoparticles correspond to the de-blocking of their magnetic moments [50]. In ideal monodisperse magnetic nanoparticles, the blocking and transition temperatures should overlap at the same point [39]. However, due to the van der Waals or molecular forces in magnetic nanoparticles, it is difficult to obtain monodispersed nanoparticle samples.

Fig. 6
figure 6

Magnetization (ZFC-FC curves) of the Mn x Fe3−x O4 nanoparticles as a function of temperature. For clarity, the curves were shifted, and the ZFC curve for x = 1 was zoomed out (upper right picture) around its T B

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In this experiment, the T B values of the Mn x Fe3−x O4 nanoparticles decrease with x, which is in good agreement with other experimental results [39]. According to Table 1, higher x values correspond to smaller sized primary particles and clusters, which significantly relates to the reduced T B. T B, which indicates the transition between the blocked state and superparamagnetic behavior is strongly dependent on the particles size of the nanoparticles as displayed in the following equation [51]:

$$ T_{\mathrm{B}} =\frac{KV}{25k_{\mathrm{B}}} $$
(7)

where k Band K are Boltzmann’s constant and the anisotropy constant, respectively, and V represents the particle size (volume).

Dutta and coworkers reported that the T B decreased upon reducing the particle size of the magnetic nanoparticles [52]. Meanwhile, Rumpf et al. reported that the T B was also dependent on the particle-particle distance [46], and their samples exhibited superparamagnetism and followed the Curie-Weiss law above the T B in which the thermal energy was larger than the magnetic energy barrier [47]. Therefore, we presume that the Mn x Fe3−x O4 nanoparticles exhibited superparamagnetic behavior at room temperature, except for x = 0 in which the T B is higher than room temperature. To better understand the magnetic properties of these superparamagnetic materials, the saturation magnetization of the Mn x Fe3−x O4 nanoparticles is discussed as follows.

To understand the saturation magnetizations (M s) due to the effect of the Mn contents, we tabulated the data in Table 2. Based on Fig. 5 and Table 2, the saturation magnetization of the Mn x Fe3−x O4 nanoparticles increases from x = 0 to x = 0.25, but it decreases and remains stable for x = 0.5, 0.75, and 1. However, based on the theoretical prediction, substituting Fe2+ by Mn2+ ions in the system of the Mn x Fe3−x O4 nanoparticles increases their magnetization because Mn2+ (5 μ B) has a higher magnetic moment than Fe2+ (4 μ B) [13]. The different magnetic moments of Mn2+, Fe2+, and Fe3+ located between the tetrahedral and octahedral sites have contributed to the saturation magnetization of Mn x Fe3−x O4. The interaction of the antiparallel spin-coupling occurring between Fe and Mn ions in the tetrahedral and octahedral sites corresponds to antiferromagnetism. However, the incomplete cancellation of the spin moments contributes to the net ferromagnetic moments; thus, the saturation magnetization of the Mn x Fe3−x O4 system can be calculated using the net magnetic moment. The Mn x Fe3−x O4 system exhibits a linear increase in magnetic moment of 4 + x μ B in the Bohr magneton per formula unit [39]. For x = 0.25, the saturation magnetization increases by approximately 19.1 % from x = 0, which is higher than the theoretical calculation that was predicted to be approximately 6.25 %. In this case, the primary particles of x = 0 and x = 0.25 are similar, but their clusters are different. Therefore, this increases the saturation magnetization (12.85 %) due to the effect of the increasing Mn doping and particle sizes of the clusters. Recently, Shen et al. reported that the magnetite nanoparticles in bigger clusters have a higher saturation magnetization than smaller clusters and individual particles [2], which is in accordance with this experiment. Further, for x = 0.5, 0.75, and 1, the theoretical calculation of the saturation magnetization increased by approximately 12.5, 18.75, and 25 %, respectively. However, in this experiment, they have smaller values than those of x = 0 and 0.25. This reduced value is predicted to be an effect of the reduced size of the primary particles and clusters. In accordance with this result, another experimental report also showed that the saturation magnetization of the magnetic nanoparticles was affected by the size of their primary particles and clusters [53]. In addition, Goya et al. reported that the saturation magnetization decreases for smaller particles, which is associated with the increasing effects of the spin disorder at the surface of the particles, yielding a reduction in the net magnetic moment [54].

Table 2 Saturation magnetization of the Mn x Fe3−x O4 nanoparticles, calculated from Fig. 5
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Wang and coworkers reported that the saturation magnetizations of Mn x Fe3−x O4 films are different from the theoretical prediction, so they recommended a modified growth process [29]. In single crystalline microspheres, the saturation magnetization decreased significantly from x = 0 to x = 1 due to the weaker spin-spin interaction [26]. Meanwhile, in the Zn x Fe3−x O4 system, the saturation magnetizations exhibited an arbitrary trend for x < 0.3 and reduced for x ≥ 0.3, which was strongly affected by the Zn2+ contents and their particle sizes [55]. The magnetic properties of nanoparticles are also influenced by dead layer formation on the surface, random canting of particle surface spins, particle random distribution in the resulting non-saturation effect, cation site disorder, and the presence of adsorbed water [10]. Therefore, despite the Mn doping effect, other mechanisms could explain the saturation magnetizations of Mn x Fe3−x O4 nanoparticles. Furthermore, to study the magnetic saturation of Mn x Fe3−x O4 as the only effect on the Mn contents, certain parameters should be controlled by controlling the parameters during synthesis. However, this is still a challenge that needs to be solved for the synthesis of Mn x Fe3−x O4 in several forms, such as in micro- or nanosized particles with special shapes, single crystalline microspheres, thin or thick films, and fluid systems. Based on our SANS experiments, we conclude that the Mn contents and particle sizes, such as the primary particles and their clustering, are the most probable combined effects that play a role in saturated magnetizations.

4 Conclusions

Single-phase Mn x Fe3−x O4 (0 ≤ x ≤ 1) nanoclusters have been successfully prepared from natural magnetite using a simple coprecipitation method. The Mn ions successfully substituted the Fe ions into the Fe3O4 nanoparticles and increased their lattice parameters. The data analysis of the SANS profiles revealed that all samples had primary particles ranging from 1.5 to 3.8 nm, and they tended to construct clusters in three-dimensional structures. The M-H curves showed that all samples exhibited superparamagnetic behavior. The saturation magnetizations of the Mn x Fe3−x O4 nanoparticles increased from x = 0 to x = 0.25, but they decreased and remained stable for x = 0.5, 0.75, and 1. This phenomenon was caused by the Mn content, the size of the primary particles, and the clusters of the Mn x Fe3−x O4 nanoparticles. Furthermore, the magnetic blocking temperature of the samples, which was acquired from the ZFC-FC curves, is strongly correlated with the size of the particles, and the lowest value was 145 K.