© EDP Sciences, 2018

1 Introduction

Properties of magnetic nanoparticles (NPs) differ in many ways from their corresponding larger particles and bulk materials. There is a particular interest in Fe₃O₄ (magnetite) NPs which display superparamagnetic (SPM) properties. Magnetic properties depend mainly on the sizes and shapes of NPs [1]. Their morphologies and sizes are strongly correlated with the preparation techniques. A whole series of iron (II, III) oxide preparation methods are known, e.g. the co-precipitation [2], the solvothermal [3], the hydrothermal [4], the micro-emulsion [5], the thermo-decomposition [4] and the sol-gel method [6].

Nowadays, SPM Fe₃O₄ NPs are being studied on possibility of applications in various life domains such as carriers of drugs, hyperthermia, magnetic resonance imaging, electronics, environmental protection (wastewater treatment) and many others. Possible applications of nanomagnetic particles (like Fe₃O₄) depend in a large part on their surface functionalization. Functionalization of Fe₃O₄ NPs surface is beneficial in many ways: it stabilises NPs, prevents agglomeration and oxidation, helps to bind other ligands by forming hybrid systems, etc. Natural polymers (e.g. dextran, starch, arabic gum, gelatine) and synthetic polymers (e.g. polyethylene glycol, polyvinyl alcohol, polyacrylic acid, and polymethylmetaacryl) are used to coat and modify the surface of iron oxide NPs. Fe₃O₄ plays a major role in the field of polymer modification [7–9]. It is used as a filler for many polymer matrices and their hybrid composites display radical improvements in conductivity, magnetism, optical, fatigue resistance, thermal stability, sensing ability and mechanical properties. They found broad applications in medicine e.g. in cancer therapy (especially in the hyperthermia method), magnetic resonance imaging diagnosis and drug targeting. Furthermore, polymer foam containing magnetite NPs can serve as a kind of receiver for biological agents (drugs) associated with magnetic particles (implant assisted magnetic drug targeting), or as tissue scaffold for biological modifications. Fe₃O₄ NPs with bound silver NPs present an example of a hybrid nanomaterial. Iron (II, III) oxide NPs impregnated with silver may be an alternative in wastewater cleaning of pathogenic bacteria with the aid of the magnetic separation.

Antibacterial properties of silver against such species as Escherichia coli, Staphylococcus epidermidis and Bacillus subtilis have been known for a long time. Silver has ability to bind itself with thiol groups what curbs cell respiration and damages cell replication by binding with bacterial DNA. It is known that silver NPs are toxic not only for bacteria but also for other organisms including human beings [10]. Toxicity of silver NPs depends on their sizes [11]. Therefore after water disinfection silver must be precisely separated. Hybrid material combining properties of magnetic iron oxides and antibacterial silver may be easily separated from cleaned water with the help of external magnetic field. That recovered material may be applied repeatedly. In a previous work the morphology and antibacterial properties of Fe₃O₄/Ag nanomaterials were presented [12].

The aim of that work is to obtain magnetic characteristics of nanostructures based on Fe₃O₄/Ag NPs that could be helpful in preparation of effective antibacterial nanomaterials. Two complementary methods of studying magnetic properties will be applied in this research: SQUID magnetometry used to measure the dc magnetisation as a function of temperature and an external magnetic field, and magnetic resonance technique in the microwave frequency range to register the ferromagnetic resonance (FMR) spectra of magnetite NPs.

2 Experimental

NPs of Fe₃O₄ were obtained by the precipitation method. Sodium acetate as a precipitation agent was added to water-polyethylene glycol solution containing iron salts with Fe²⁺/Fe³⁺ mass ratio of 1:2. The precipitation process was carried out under inert atmosphere to protect Fe₃O₄ NPs from oxidation. Silver was added to Fe₃O₄ NPs by wet impregnation. Silver nitrate concentration was fixed to get an appropriate mass ratio of Ag:Fe₃O₄. This ratio in the samples designated as Fe₃O₄/Ag1 and Fe₃O₄/Ag2 was 1:100 and 2:100, respectively. Details of a preparation of Fe₃O₄, Fe₃O₄/Ag1, and Fe₃O₄/Ag2 NPs were described in the paper by Pachla et al. [12].

MPMS-7 SQUID magnetometer was used for dc magnetisation measurements in the 2–300 K temperature range in magnetic fields up to 70 kOe in the zero-field-cooled (ZFC) and field-cooled (FC) modes. Magnetic resonance study was carried out on a conventional X–band (ν = 9.4 GHz) Bruker E 500 spectrometer with the 100 kHz magnetic field modulation. FMR spectra were registered at RT and were in the form of first derivative of the absorption with respect to the sweeping external magnetic field.

3 Results and discussion

3.1 SQUID magnetometry

For a sample cooled from RT down to 2 K without external magnetic field (ZFC mode) the overall magnetic moment would be zero for a collection of randomly oriented crystallites because the magnetic moments of each NP would align along the easy axis in the lattice, an increase of temperature would release some magnetic moments from the easy axis and they will be align along the external field. The magnetocrystalline energy K·V (where K is the magnetocrystalline anisotropy energy density constant and V the volume of a NP) plays the leading role in that low-temperature range. At a specific temperature (T_B − the blocking temperature) the largest number of moments are align along the external field and yields the peak in magnetisation curve. The blocking temperature is usually determined from a simple relation between the magnetocrystalline and thermal energies: (1) where k is Boltzmann’s constant. For T > T_B the Zeeman energy μ·H (where μ is the magnetic moment and H an external magnetic field) is smaller than the thermal energy what causes randomization of the moments and the net magnetisation decreases with increasing temperature (the SPM phase). On the other hand, when a sample is cooled from RT in the presence of small external field (FC mode) the decrease in thermal energy causes orientation of the moments along the direction of the field and a subsequent magnetisation increase. The ZFC and FC magnetisation curves would coincide as temperature is decreased. The situation changes on further cooling below T_B: the Zeeman energy overcomes the thermal energy and causes the NPs moments to partially orient along the applied field, resulting in separation of ZFC and FC magnetisation curves. At very low temperature the Zeeman energy causes the maximum orientation of moments in the field direction and the biggest magnetisation.

In Figures 1–3 the temperature dependence of dc magnetic susceptibility χ (defined as χ = M/H) in ZFC and FC modes is shown for three investigated samples. Two panels in each figure present χ_ZFC and χ_FC curves registered in five different magnetic fields: H = 50, 100, 500 (upper panel), 6000 and 70 000 Oe (lower panel). These figures display the characteristic thermal irreversibility expected for an assembly of single domain magnetic NPs due to the blocking-unblocking of magnetic moments during temperature changes. In general, all samples display a similar thermal behavior. For small magnetic fields (H < 500 Oe) the χ_ZFC and χ_FC curves separate at RT or higher temperatures. It follows that the blocking temperature is 300 K or slightly higher for all our samples. If the value of magnetocrystalline anisotropy constant K = 1.4 × 10⁵ erg/cm³ for bulk magnetite and the estimated blocking temperature T_B = 300 K are used in equation (1), then the size D = 24.2 nm of an average NP is obtained. The average size of the particles estimated by microscopic method is about 20 nm [12]. As for NPs K is usually much higher than for a bulk material, that average size is probably smaller than that calculated from equation (1).

In Figure 4 comparison of the temperature dependences of magnetic susceptibilities in ZFC and FC modes in magnetic field H = 50 Oe of the three investigated samples are presented. Although the susceptibility curves look similar, there are subtle differences worth to be noticed. First of all the values of susceptibility at RT are different and the samples can be ordered in increasing value of χ as follows: Fe₃O₄/Ag1, Fe₃O₄/Ag2, and Fe₃O₄. It could be concluded that addition of Ag to magnetite decreases sample susceptibility, but the decrease depends not only on Ag concentration but also on other factor. To investigate what that factor could be, in Figure 5 the temperature derivatives of the (χ_FC − χ_ZFC) difference of three investigated samples are shown. It has been already proved that the temperature derivative of the ZFC-FC difference is in full coincidence with the T_B distribution in a sample, calculated as the inflection points of each size ZFC curve [13–15]. Thus this derivative also reflects the distribution of NPs sizes in a given sample. In Figure 5 the curves of Fe₃O₄ and Fe₃O₄/Ag2 are rather similar, showing a single minimum close to 120 K evidencing a single-mode size distribution. In contrast, Fe₃O₄/Ag1 displays a double-mode distribution, one minimum at T ∼ 75 K (smaller sizes) and the other close to RT (bigger NPs). Consequently, multi-mode sizes distribution could have detrimental effect on magnetic susceptibility of a sample decreasing its value along with Ag admixture.

For stronger external magnetic fields the blocking temperature shifts to lower temperatures because magnetic field lowers the barier between two easy axis orientations. This is clearly visible for our samples as in H = 500 Oe the χ_ZFC curve reaches maximum at 155, 200, and 130 K in Fe₃O₄, Fe₃O₄/Ag1, Fe₃O₄/Ag2, respectively. It confirms the former supposition that in Fe₃O₄/Ag1 the size distribution (bimodal) peaks at the largest size values. A rather broad size distribution of magnetic NPs in our samples is evidenced by the broadness of χ_ZFC curves and no saturation of FC magnetisation at low temperature. In strong external magnetic fields (H>5000 Oe) χ_ZFC and χ_FC curves coincide and shown only very weak increase with decreasing temperature. It is also apparent that there is no evidence of Verwey transition in magnetisation curves in the neighbourhood of 120 K.

In Figures 6–8 the isothermal (at T = 2 K) magnetisations of three investigated samples in magnetic fields up to 70 kOe are presented. Magnetisation of our samples were also measured at T = 100 and 300 K (not shown). As expected, magnetisation in form of the hysteresis loop was observed as samples were in the blocked, ferromagnetic (FM) state. On the other hand, at RT not very well developed hysteresis loop was registered because this temperature is rather close to the blocking temperature and the samples were in a mixed SPM/blocked state. The parameters of the observed loops: saturation magnetisation M_s, remanent magnetisation M_r, coercive field H_c were determined for each studied temperature and are displayed in graphical form in Figures 9 and 10.

In Figure 9, the obtained values of the saturation magnetisation and the coercive field for three samples at three temperatures are presented. The saturation magnetisation of bulk magnetite at RT is 92 emu/g (476.6 emu/cm³) and slightly higher at lower temperatures. For our samples saturation magnetisation is significantly smaller, but this is understandable considering that they are in nanopowder form (Fig. 9). The decrease of M_s for NPs is usually explained by disorder in the surface layer caused by defects and crystal imperfections. Therefore the smaller the NP, the bigger the role of the surface layer and the smaller M_s is expected to be measured. In case of our samples two factors should influence M_s: Ag concentration (decreasing of M_s with Ag concentration increase) and NPs sizes distribution. As expected the highest value of M_s is obtained for Fe₃O₄ sample. From the two samples with Ag doping the sample with higher concentration of Ag (i.e. Fe₃O₄/Ag2) has bigger M_s. This can be explained by the presence of greater fraction of smaller particles in Fe₃O₄/Ag1 sample (see Fig. 5) that decreases M_s more efficiently that does the Ag doping.

In Figure 10 two other important loop parameters − the coercive field H_c and the squareness ratio coefficient Q (defined as Q = M_R/M_s, where M_R is the remanent magnetisation) − are presented. For the non-interacting, randomly oriented particles with uniaxial magnetocrystalline anisotropy Q = 0.5, while for particles with cubic magnetocrystalline anisotropy Q = 0.831 [16]. Because the squareness ratio represents the fraction of blocked NPs at a specific temperature, its value increases with the decrease of temperature. In Figure 10 a strong correlation between H_c and Q is visible. In comparison with Fe₃O₄ sample, Fe₃O₄/Ag1 displays a higher coercive field (and the squareness ratio), while Fe₃O₄/Ag2 shows smaller value of H_c (and Q). Small values of Q indicate that individual particles are single domain and display a strong random anisotropy [17]. Reduction of Q could be due to different reasons, like interparticle interaction, distribution of particle sizes, the presence of various defects, etc. Petrychuk et al. investigated samples containing interacting magnetic NPs forming clusters of different sizes [18]. For small clusters the magnetic energy may be small enough to enable thermal energy the enhancement of the SPM contribution into magnetisation what results in small values of Q. On the other hand, for larger cluster the magnetic energy is large what leads to the corresponding enhancement of its superferromagnetic properties and the hysteresis loop becomes more rectangular causing an increase of Q. Thus the Q value might be considered as a measure of cluster sizes in a strongly interacting system of FM NPs. Applying these considerations to our samples it might be supposed that in Fe₃O₄/Ag2 the clusters of magnetite NPs are bigger in sizes than in Fe₃O₄/Ag1 sample.

Fig. 1 Temperature dependence of magnetic susceptibility in ZFC and FC modes in five external magnetic fields, H = 50, 100, 500 (upper panel), 6000 and 70 000 Oe (lower panel) of Fe3O4 sample.

Fig. 2 Temperature dependence of magnetic susceptibility in ZFC and FC modes in five external magnetic fields, H = 50, 100, 500 (upper panel), 6000 and 70 000 Oe (lower panel) of Fe3O4/Ag1 sample.

Fig. 3 Temperature dependence of magnetic susceptibility in ZFC and FC modes in five external magnetic fields, H = 10, 100, 500 (upper panel), 6000 and 70 000 Oe (lower panel) of Fe3O4/Ag2 sample.

Fig. 4 Comparison of the temperature dependence of magnetic susceptibilities in ZFC and FC modes in magnetic field H = 50 Oe of three investigated samples.

Fig. 5 Temperature derivative of the (χFC – χZFC) difference of the three investigated samples. Arrows indicate minima of those functions.

Fig. 6 Isothermal magnetisation at T = 2 K of Fe3O4 sample. The inset shows expanded views of the low magnetic field behaviour (the solid lines are guides for the eyes).

Fig. 7 Isothermal magnetisation at T = 2 K of Fe3O4/Ag1 sample. The inset shows expanded views of the low magnetic field behaviour (the solid lines are guides for the eyes).

Fig. 8 Isothermal magnetisation at T = 2 K of Fe3O4/Ag2 sample. The inset shows expanded views of the low magnetic field behaviour (the solid lines are guides for the eyes).

Fig. 9 The saturation magnetisation (left axis) and the coercive field (right axis) at three temperatures of the three investigated samples. The solid lines are guides for the eyes.

Fig. 10 The dependence of the squareness ratio on the coercive field in three studied temperatures in the investigated samples.

3.2 FMR study

Figure 11 presents FMR spectra of three investigated samples at RT. FMR response of each samples is rather similar, constituting a strong, broad and slightly asymmetric single line. The analysis of FMR spectra will be done by a method proposed by Griscom [19] and followed by many researchers studying magnetite NPs [20–23]. Effective g-factors g_i will be calculated from the well know resonance condition (2) where h is the Planck’s constant, ν is the spectrometer resonance frequency, μ_B is the Bohr magneton, H_i magnetic fields corresponding to different FMR line features. Three H_i fields will be considered referring to characteristic points in FMR spectrum: H_max, H_min, and H_ms. They refer to a maximum (H_max), a minimum (H_min), and a maximum of negative slope (H_ms) of the derivative of FMR absorption. The g_i factors calculated from equation (2) corresponding to fields H_max, H_min, and H_ms will be designated as g₁, g₃, and g₂, respectively. Figure 12 shows the calculated values of the g-factor components for the three investigated samples at RT. These g_i factors have generally bigger values than previously observed for the coated magnetite NPs [20,22,23]. A bigger shift of FMR line from the reference field H₀ corresponding to g₀ ∼ 2.0 could be explained by agglomeration of magnetite NPs in form of elongated assemblies along an external magnetic field. The shape anisotropy field H_sa is adding as a vector to the external magnetic field. If elongated aggregate of NPs is situated parallel to the external field direction, the following equations could be use: (3)where γ the gyromagnetic ratio for electron. According to this equation the observed resonance field H_r decreases (g-factor increases) by the shape anisotropy field. From Figure 12 it could be seen that the largest shift from the reference field (the biggest g_i factors) are registered for Fe₃O₄/Ag1 and thus the shape anisotropy field seems to be biggest in this sample. This can be correlated with a multi-size distribution of NPs in that sample and the presence of significant portion of small NPs for which H_sa will be bigger.

Lineshape analysis also enables to determine the effective magnetocrystalline anisotropy constant K, using the following equation (4) where H_a is the anisotropy field. Anisotropy field can be calculated from a simple equation [16] (5)

The anisotropy field H_a, calculated from equation (5) is equal to 466, 451, and 430 G for Fe₃O₄, Fe₃O₄/Ag1, and Fe₃O₄/Ag2 samples, respectively. Using values of the saturation magnetisation M_s determined in dc susceptibility measurements, from equation (4) the following values of K can be calculated: 6.7 × 10⁴, 5.9 × 10⁴, and 6.0 × 10⁴ erg/cm³ for Fe₃O₄, Fe₃O₄/Ag1, and Fe₃O₄/Ag2 samples, respectively. These values are roughly half of that for bulk magnetite (14 × 10⁴ erg/cm³), but it can be argued that smaller values are for an ensemble of randomly oriented, strongly agglomerated NPs. Addition of silver NPs to magnetite NPs seems to decrease the value of the effective anisotropy constant.

An important spectroscopic parameter is the integrated intensity I_int. It is calculated as the area under the absorption curve or, equivalently, as the product of line amplitude and squared linewidth, I_int = A (ΔH)². Integrated intensity is proportional to the imaginary part of ac magnetic susceptibility of the investigated samples at microwave frequency and also to the number to magnetic moments participating in resonance. Integrated intensities of the investigated samples calculated for the unit mass are shown in Figure 13. It is evident that Fe₃O₄ and Fe₃O₄/Ag1 samples have a similar value of I_int, while the FMR response from Fe₃O₄/Ag2 is significantly weaker. The greatest influence on I_int has the linewidth ΔH and for the latter sample it is the smallest. On the other hand the shift δH of this line from the reference field H₀ (in our case H₀ = 3380 G) is the smallest as compared to the other two samples. This is consistent with the observations made for many NP systems that δH ∼ (ΔH)ⁿ, where the exponent n ≈ 3 [22]. As the shift δH is mostly the result of magnetite NPs sizes and their agglomeration in form of elongated assemblies along the lines of an external magnetic field, it could be suggested that not so small silver doping (in our case 2%) prevents such rearrangements so the FMR line shift is expected to be small.

Fig. 11 FMR spectra of three investigated samples at RT.

Fig. 12 Values of g-factor components of the three investigated samples at RT calculated from equation (2).

Fig. 13 Relative integrated intensities of the investigated samples calculated for a unit mass (Iint = 1 for Fe3O4 was assumed).

4 Conclusions

Temperature dependence of magnetic susceptibility suggests a broad distribution of NPs sizes and similar values of the blocking temperature (close to RT) in all three studied samples. Addition of silver NPs decreases magnetic susceptibility of the magnetite samples. An additional detrimental effect is connected with the multi-modal distribution of NPs sizes which was observed for Fe₃O₄/Ag1 sample (bigger number of smaller NPs in comparison to the two other samples). Saturation magnetisation of samples containing Ag NPs is diminished in comparison to pure magnetite sample and the effect is positively correlated with Ag concentration and the content of smaller sizes NPs. The shape of FM loop registered at T = 2 K suggests the existence of smaller NPs clusters in Fe₃O₄/Ag1 than in Fe₃O₄/Ag2 sample. The FMR measurements corroborated the above results of magnetometric studies.

Author contribution statement

Janusz Typek – analysed the data and wrote the manuscript with input  from all authors; Nikos Guskos – designed the magnetic measurements; Grzegorz Zolnierkiewicz – performed the magnetic measurements; Zofia Lendzion-Bielun, Anna Pachla, Urszula Narkiewicz – synthesized the  samples, contributed to the interpretation of the results.

References

All Figures

	Fig. 1 Temperature dependence of magnetic susceptibility in ZFC and FC modes in five external magnetic fields, H = 50, 100, 500 (upper panel), 6000 and 70 000 Oe (lower panel) of Fe3O4 sample.
In the text

	Fig. 2 Temperature dependence of magnetic susceptibility in ZFC and FC modes in five external magnetic fields, H = 50, 100, 500 (upper panel), 6000 and 70 000 Oe (lower panel) of Fe3O4/Ag1 sample.
In the text

	Fig. 3 Temperature dependence of magnetic susceptibility in ZFC and FC modes in five external magnetic fields, H = 10, 100, 500 (upper panel), 6000 and 70 000 Oe (lower panel) of Fe3O4/Ag2 sample.
In the text

	Fig. 4 Comparison of the temperature dependence of magnetic susceptibilities in ZFC and FC modes in magnetic field H = 50 Oe of three investigated samples.
In the text

	Fig. 5 Temperature derivative of the (χFC – χZFC) difference of the three investigated samples. Arrows indicate minima of those functions.
In the text

	Fig. 6 Isothermal magnetisation at T = 2 K of Fe3O4 sample. The inset shows expanded views of the low magnetic field behaviour (the solid lines are guides for the eyes).
In the text

	Fig. 7 Isothermal magnetisation at T = 2 K of Fe3O4/Ag1 sample. The inset shows expanded views of the low magnetic field behaviour (the solid lines are guides for the eyes).
In the text

	Fig. 8 Isothermal magnetisation at T = 2 K of Fe3O4/Ag2 sample. The inset shows expanded views of the low magnetic field behaviour (the solid lines are guides for the eyes).
In the text

	Fig. 9 The saturation magnetisation (left axis) and the coercive field (right axis) at three temperatures of the three investigated samples. The solid lines are guides for the eyes.
In the text

	Fig. 10 The dependence of the squareness ratio on the coercive field in three studied temperatures in the investigated samples.
In the text

	Fig. 11 FMR spectra of three investigated samples at RT.
In the text

	Fig. 12 Values of g-factor components of the three investigated samples at RT calculated from equation (2).
In the text

	Fig. 13 Relative integrated intensities of the investigated samples calculated for a unit mass (Iint = 1 for Fe3O4 was assumed).
In the text