1. Introduction

2. Materials and Methods

3. Results and discussions

3.1. Structural-Phase Composition of Nanocomposites Depending on the Alloy Content in the Dielectric Matrix

In Figure 1, we reproduce the diffraction patterns of nanocomposite samples from our previous work [21] with different alloy content x at.%, which is shown to the right of each diffraction pattern. For comparison, polycrystalline samples of cubic BCC iron α-Fe and hexagonal cobalt α-Co are presented on the two upper diffractograms, and powder of tetragonal MgF2 is presented on the lower diffractogram.

Obtained in [21] XRD data shows, that in the region of low concentrations (x≤25at.%) the metal alloy CoFeZr is in the X-ray amorphous state in the form of metal clusters distributed in MgF₂ nanocrystalline matrix, represented in diffraction patterns by two wide reflections (110) and (220.

The first phase transition in the composites is the formation of a nanocrystalline CoFeZr phase based on a hexagonal α-Co lattice thus correlating with the relative content of the metal component x ~ 35 at.% in the amorphous dielectric matrix MgF₂.

The second phase transition from the hexagonal structure of CoFeZr nanocrystals to the cubic bcc structure in the amorphous dielectric matrix MgF₂ occurs with an increase in the relative alloy content in the range x = 40-45 at.%, beyond the percolation threshold x_per=34 at.%

The average sizes of metallic nanocrystals, calculated by the Debye-Scherrer formula, increase from 10 nm at x = 34 at.% to 20 nm at x = 50 at.%.

Thus, as a result of self-organization under non-equilibrium conditions of ion-plasma sputtering at certain concentration ratios of the metal and dielectric components of nanocomposites, mutually inverse (antibate) phase transitions occur from the amorphous to the nanocrystalline state of the metal alloy with an increase in its content in the composite and the reverse transition of the MgF₂ dielectric phase from the nanocrystalline to the amorphous state.

At the same time, XRD showed, that MgF₂ nanocrystals of the dielectric matrix in the composites have slightly increased interplanar distances d₁₁₀ and d₂₂₀ as compared to the reference microcrystalline MgF₂ [21]. Wherein two other methods of diagnosing the phase composition of materials with a complex atomic composition, XPS and IR spectroscopy, which we used in [21], could not establish unambiguously the cause of these changes.

Figure 1. Diffractograms of nanocomposites with different compositions.(CoFeZr)_x (MgF₂)_100-x on the glass substrates.

Figure 1. Diffractograms of nanocomposites with different compositions.(CoFeZr)_x (MgF₂)_100-x on the glass substrates.

3.2. Determination of chemical bonds of iron atoms in a nanocomposite (CoFeZr)₅₁(MgF₂)₄₉ by the nuclear gamma resonance method of Mössbauer spectroscopy.

Since the increased values of the interplane distances d₁₁₀ and d₂₂₀ of the nanocrystals of the dielectric matrix of the MgF₂ were closer to the corresponding values in the iron and cobalt fluorides FeF₂ and CoF₂, that we had not previously detected by IR spectroscopy and XPS X-ray electron spectroscopy [21], we attempted to detect the interaction of iron atoms with fluorine by the Mössbauer nuclear spectroscopy.

Figure 2 shows two Mössbauer spectra, the calibration spectrum from α-Fe (left) and the spectrum from the sample (CoFeZr)₅₁(MgF₂)₄₉ with the maximum magnetic alloy content x=51 at. % (right).

The total amount of accumulation of statistics in the Mössbauer spectrum from this sample was more than 500 hours.

In the Mössbauer spectrum of the sample (CoFeZr)₅₁(MgF₂)₄₉ an intense magnetic sextet (hyperfine magnetic splitting) is isolated with parameters (Is = -0.08 mm/s, Q = 0 mm/s G = 0.70mm/s, H = 339 kE) close to α-Fe (see left calibration spectrum in Fig.2), which we refer to iron in the composition of nanocrystals of the CoFeZr alloy with the BCC structure α-Fe.

However, along with the magnetic sextet, the spectrum of the nanocomposite contains a paramagnetic quadrupole doublet related to iron fluoride FeF₂ with parameters (Is = -0.85 mm/s, Q = 1.92 mm/s). The ratio of the areas of these two spectra from the phases in the nanocomposite sample (magnetic alloy CoFeZr and paramagnetic phase FeF₂) is 82:18 with a total area of 100 for NC (CoFeZr)₅₁(MgF₂)₄₉ (Table 1).

Figure 2. Mössbauer spectra: Calibration α-Fe (left) and nanocomposite (CoFeZr)₅₁(MgF₂)₄₉ (right).

Figure 2. Mössbauer spectra: Calibration α-Fe (left) and nanocomposite (CoFeZr)₅₁(MgF₂)₄₉ (right).

Thus, the appearance of an additional doublet from the paramagnetic phase FeF₂ in the Mössbauer spectrum of the nanocomposite (CoFeZr)₅₁(MgF₂)₄₉ indicates that at the interfacial boundaries of nanocrystals of a magnetic alloy CoFeZr with a dielectric MgF₂, the boundary iron atoms interact with the fluorine atoms of the dielectric matrix to form the paramagnetic phase of iron fluoride FeF₂. This circumstance can significantly affect the magnetic properties of the studied nanocomposites.

3.3. Concentration dependences of electrical resistance and magnetoresistance

Concentration dependence of the electrical resistance of nanocomposites (CoFeZr)_x (MgF₂)_100-x with different alloy content x (at.%) is shown in Figure 3a and in Table 3. This dependence of the resistivity of the studied nanocomposites is characterized by nonlinear pattern of metal-dielectric composites behavior, when the electric transfer mechanism changes with variations in the relative content of metal and dielectric components [11,23,24,25,26,27,28,29]].

The Figure 3a and Table 3 shows, that in the range of x = 9 - 25 at.% the resistance of nanocomposites (CoFeZr)_x (MgF₂)_100-x falls by five orders of magnitude from 4*10⁹ to 3*10⁴, but remains characteristic of dielectrics. With a further increase in the alloy content from 35 to 50 at.% the resistance of nanocomposites drops sharply to values characteristic of that on for alloys and even some metals.

In the graph of the concentration dependence (Figure 3a), we draw two extrapolation lines with different angles of inclination. The range of intersection of these lines in the region (30-35 at.%) corresponds to the percolation threshold. Two straight lines on the concentration dependence indicate different current flow mechanisms before and after the percolation threshold along the high-resistance and low-resistance pathways. The obtained experimental data correlate well with the data for similar systems of composites with dielectrics of barium fluoride, calcium fluoride and aluminum oxide [23,24,25,26,27,28,29].

The absolute values ​​of the tunneling giant magnetic resistance (GMR) were determined in accordance with the expression:

$$\frac{\Delta R}{R\left(0\right)}=\frac{R\left(H\right)-R\left(0\right)}{R\left(0\right)}\ast 100\%,$$

where R(H) is the resistance of the sample in the presence of an external magnetic field H, R(0) is the resistance of the composite in the absence of an external magnetic field.

Figure 3b shows the concentration dependence of magnetoresistance for the samples of the system (CoFeZr)_x(MgF₂)_100-x. The resulting concentration dependence of magnetoresistance is extremely nonmonotonic. In the dielectric region of composites, small values of magnetoresistance are recorded far from the percolation threshold. With an increase relative to the content of the metal component in the range of 9<x<27, the GMR increases abruptly to the maximum value of ΔR/R(0) = 2.4%. With a further increase in the proportion of the metal component (x > 27 at. %) GMR is also sharply reduced.

The obtained concentration dependence of the magnetoresistive effect is fully consistent with the general model of tunneling magnetoresistance [25,26,27,28,29,30], according to which the number of electrons tunneling through the dielectric barrier increases with decreasing distance between neighboring alloy nanocrystals. Near the percolation threshold, the morphology of composites is such that the dielectric layer between the nanocrystals has a minimum thickness. The appearance of an exchange interaction between alloy nanocrystals/granules with decreasing distance follows from the analysis of Slonchevsky model [30].

Figure 3. Concentration dependences of electrical resistance (a) and magnetoresistance (b) of (CoFeZr)_x(MgF₂)_100-x nanocomposites.

Figure 3. Concentration dependences of electrical resistance (a) and magnetoresistance (b) of (CoFeZr)_x(MgF₂)_100-x nanocomposites.

Thus, with an increase in the content of CoFeZr alloy in the nanocomposite, the average size of nanocrystals increases from 10 to 20 nm [21], and the distance between them decreases. This leads to the mechanical contact of neighboring nanocrystals and the formation of extended fractal-like metal clusters. As a result, the number of energy barriers decreases and the mechanism of electric transfer through the nanocomposite starts to change from tunneling to Ohmic one (Table 1).

3.4. Capacitive/inductive nature of the resistance of (CoFeZr)_x(MgF₂)_100–x nanocomposites according to impedancemetry data

One of the most accessible methods for studying electrophysical processes is impedance spectroscopy [34,35].

Impedance is $Z=R-i\frac{1}{\omega C}$ ,

where i = √–1, ω is the cyclic frequency, С is the total capacitance of the composite. Z' = R is the real resistance component, $Z\text{'}\text{'}=\frac{1}{\omega C}$ is the imaginary resistance component.

The hodograph of the impedance Z (impedance diagrams) is a graphical dependence of the imaginary component of the impedance Z" on the real Z'.

For (CoFeZr)x(MgF2)100–x nanocomposites, impedancemetry data in Fig.4 show two different types of hodographs before percolation threshold and after the percolation threshold. On the hodograph for a nanocomposite with an alloy content up to the percolation threshold x≥34 at.%, a semicircle is observed, which corresponds to the typical behavior of the RC chain of metal clusters in a dielectric matrix[35]. At the percolation threshold x≥35 at.%, the hodograph takes the form of an inclined line, and then, as x increases beyond the percolation threshold, the hodographs become vertical lines, indicating the metallic nature with the ohmic character of conduction [35].

Figure 4. Impedance diagrams (hodographs) for nanocomposites(CoFeZr)_x(MgF₂)_100-x of different compositions.

Figure 4. Impedance diagrams (hodographs) for nanocomposites(CoFeZr)_x(MgF₂)_100-x of different compositions.

The resistance and capacitance values ​​of the nanocomposites according to the impedancemetry data given in Table 2 show that the capacitance of the nanocomposites in the prepercolation region does not exceed several picofarads. And only in the region of the percolation threshold (xper=35 at. %) the capacitance increases by three orders of magnitude up to two nanofarads. This increase in capacitance value is due to the beginning of formation of metallic nanocrystals and the remaining dielectric interlayers between them.

The presented data correlate well with the capacitive properties of a similar system (CoFeZr)x(PZT)100-x from [36].

Table 4. Concentration dependence of the total electric resistance R and capacitance C of the nanocomposites (CoFeZr)_x(MgF₂)_100-x.

Table 4. Concentration dependence of the total electric resistance R and capacitance C of the nanocomposites (CoFeZr)_x(MgF₂)_100-x.

x, at.%	R, Ohm	C, f
20	13*106	6*10-12
25	25*104	4*10-12
30	830	4*10-9
34	136	1.2*10-9
38	75	-
43	16	-
47	8	-
50	8	-

3.5. Magneto-optical and magnetic properties of (CoFeZr)_x(MgF₂)_100–x nanocomposite

The magneto-optical Kerr effect in transversal geometry [6,7,8,9], transversal Kerr effect (TKE), consists in changing the intensity of linearly polarized light reflected by a sample magnetized perpendicular to the plane of the incident light. The value and sign of TKE are defined as the ratio of the difference between the intensities of the light reflected by the sample in the magnetized (I) and demagnetized (I₀) states to the light intensity I₀:

δ=(I- I0)/I0 =ΔI/I0

The absolute value of TKE depends on the amount of the metal phase in the composite. Its increase leads to an increase in the TKE modulus, which attains maximum at a concentration corresponding to the percolation threshold.

Figure 4 from our previous work [22] shows the concentration dependences of TKE for (CoFeZr)_x(MgF₂)_100-x nanocomposites at three values ​​of the incident light photon energy of Е=1.14 eV; 1.97 eV and 3.17 eV. The concentration dependences of TKE in the NC (CoFeZr)_x(MgF₂)_{100 – x} system showed two maxima, one of which at х =30-34 at.% corresponded to the formation of hexagonal nanocrystals of the CoFeZr alloy and the second maximum at x=45 at. % corresponded to the phase transition of the hexagonal structure to the cubic BCC structure α-Fe.

Thus, magneto-optical spectra respond to changes in the composition, atomic structure, and magnetic order of a complex heterophase systems.

Figure 5. Concentration dependencies of transversal Kerr effect (TKE) for nanocomposites (CoFeZr)_x(MgF₂)_100-x at different values of the incident light energy.

Figure 5. Concentration dependencies of transversal Kerr effect (TKE) for nanocomposites (CoFeZr)_x(MgF₂)_100-x at different values of the incident light energy.

Since the magnetic percolation threshold x_fm is defined as the concentration of the metal phase when the magnetization sharply increases and a coercive force arises in nanocomposites, further, in Figure 6 we present the dependences of magnetizations on the magnetic field arising parallel and perpendicular to the sample plane, which show the first appearance of a hysteresis loop with coercive force Нс≈18 Oe in a (CoFeZr)₃₄(MgF₂)₆₆ sample for the alloy content x=34 at.%.

Figure 6. Appearance of hysteresis in (CoFeZr)₃₄(MgF₂)₆₆ and its absence in (CoFeZr)₃₀(MgF₂)_70.

Figure 6. Appearance of hysteresis in (CoFeZr)₃₄(MgF₂)₆₆ and its absence in (CoFeZr)₃₀(MgF₂)_70.

It means that the magnetic percolation threshold in the (CoFeZr)_x(MgF₂)_100-x system at x_fm=34 at.% coincides with the resistive percolation threshold x_per=34 at.% due to the exchange interaction between electrons and spins of the formed hexagonal CoFeZr nanocrystals.

Figure 7 shows the dependence of coercive force H_c on the concentration of the metal component for nanocomposites (CoFeZr)_x(MgF₂)_100-x on the glass. The measurements of the NCs magnetic properties with a vibration magnetometer showed that the value of the coercive force H_c in all of the nanocomposites at x≤30 at.% is equal to zero.

Thus, in concentration region of x≤30 at.%, nanocomposites (CoFeZr)_x(MgF₂)_100-x are superparamagnets, and the critical magnetic percolation threshold for this system is x_fm=34 at.%. However, as the x value increases, hysteresis loops with non-zero H_c values appear in the samples.

Figure 7. Concentration dependence of the coercive force H_c for (CoFeZr)_x(MgF₂)_100-х. nanocomposites.

Figure 7. Concentration dependence of the coercive force H_c for (CoFeZr)_x(MgF₂)_100-х. nanocomposites.

According to the magnitude of the coercive force N_с, magnetic materials are divided into magnetically hard and magnetically soft. Materials with values of N_с < 50 Oe are soft magnetic, and materials with N_с > 50 Oe are magnetic hard (GOST 19693 – 74). Based on this classification, the studied nanocomposites (CoFeZr)_x(MgF₂)_100-x should be attributed to soft magnetic materials with a maximum value of Н_с < 30 Oe (Figure 7).

It should be noted that the nanocomposites of less complex composition Co_x(MgF₂)_100-x studied by us recently [20] exhibit a more hard magnetic character at approximately the same concentrations of cobalt with a maximum value of the coercive force about 90Oe. Apparently, the decrease in magnetic order in NCs (CoFeZr)_x(MgF₂)_100-x is influenced by the diamagnetic phase FeF₂ that we discovered at the interface of magnetic nanocrystals CoFeZr with a dielectric matrix MgF₂ by the Mössbauer spectroscopy.

4. Conclusion

Declaration of Competing Interest

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