author's personal copy · 1406 s. k. misra et al. 1 3 3.4 scn/fsannealed a1285°c...

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Applied Magnetic Resonance ISSN 0937-9347Volume 49Number 12 Appl Magn Reson (2018) 49:1397-1415DOI 10.1007/s00723-018-1079-x

EPR and Magnetization Studies ofPolymer-Derived Fe-Doped SiCNNanoceramics Annealed at VariousTemperatures: Blocking Temperature,Superparamagnetism and SizeDistributionsSushil K. Misra, Sergey Andronenko,Ildar Gilmutdinov & Roman Yusupov

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Applied Magnetic Resonance (2018) 49:1397–1415https://doi.org/10.1007/s00723-018-1079-x

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ORIGINAL PAPER

EPR and Magnetization Studies of Polymer‑Derived Fe‑Doped SiCN Nanoceramics Annealed at Various Temperatures: Blocking Temperature, Superparamagnetism and Size Distributions

Sushil K. Misra1 · Sergey Andronenko2 · Ildar Gilmutdinov2 · Roman Yusupov2

Received: 30 May 2018 / Revised: 14 September 2018 / Published online: 11 October 2018 © Springer-Verlag GmbH Austria, part of Springer Nature 2018

AbstractX-band EPR spectra on SiCN ceramics, doped with Fe(III) ions, annealed at 800 °C, 1000 °C, 1100 °C, 1285 °C, and 1400 °C have been simulated to understand better their magnetic properties, accompanied by new magnetization measurements in the temperature range of 5–400 K for zero-field cooling (ZFC) and field cooling (FC) at 100C. The EPR spectra reveal the presence of several kinds of Fe-containing nano-particles with different magnetic properties. The maxima of the temperature varia-tion of ZFC magnetization were exploited to estimate (i) the blocking temperature, which decreased with annealing temperature of the samples and (ii) the distribu-tion of the size of Fe-containing nanoparticles in the various samples, which was found to become more uniform with increasing annealing temperature, implying that more homogenous magnetic SiCN/Fe composites can be fabricated by annealing at even higher temperatures than 1400 °C to be used as sensors. The hysteresis curves showed different behaviors above (superparamagnetic), below (ferromagnetic), and about (butterfly shape) the respective average blocking temperatures, ⟨TB⟩. An analysis of the coercive field dependence upon temperature reveals that it follows Stoner–Wohlfarth model for the SiCN/Fe samples annealed above 1100 °C, from which the blocking temperatures was also deduced.

AppliedMagnetic Resonance

* Sushil K. Misra [email protected]

1 Department of Physics, Concordia University, 1455 de Maisonneuve Boulevard West, Montreal, QC H3G 1M8, Canada

2 Institute of Physics, Kazan Federal University, ul. Kremlevskaya, 18, Kazan 420008, Russian Federation

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1398 S. K. Misra et al.

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1 Introduction

Silicon nitro carbide, SiCN, exhibits excellent high-temperature properties. It can withstand temperatures of up to 1800 °C, which is superior to those of Si, SiC and Si3N4. Magnetic composites, as well as electrically conductive ceramics, based on SiCN, can be developed. Therefore, SiCN constitutes a new class of materials for high-temperature electronics. SiCN doped with transition metal ions exhibiting superparamagnetic behavior are potentially useful in developing high-temperature magnetic-sensor devices. The unique advantage in the fabrication of SiCN ceramics is that a commercially available liquid polymer, CERASET™ (KiON group AG), is the starting material for their easy synthesis. They can be readily shaped using micro-moulds, or by microphotolithography [1–3]. Addition of polymers containing different magnetic transition metal ions to the initial polysilazane precursor leads to the formation of superparamagnetic SiCN ceramics, which can be used as magnetic sensors. Therefore, investigation of SiCN ceramic and its conductive and magnetic derivatives, e.g., by doping them with Fe ions (SiCN/Fe hereafter), is currently of great interest in their development for high-temperature thermistor and sensor appli-cations [4, 5]. As well, SiCN/Fe ceramics exhibit excellent microwave absorption performance [6, 7]. The magnetic properties of polymer-derived SiCN ceramics doped with transition metal ions, in particular, Fe ions, have attracted a great atten-tion in recent years [6–27].

The previous investigations on polymer-derived SiCN/Fe ceramics [8–28], doped with Fe ions, reveal as to which kinds of magnetic nanoparticles are dispersed in diamagnetic SiCN nanoceramics. They indicate that these nanoparticles consist of α-Fe, Fe3Si, Fe5Si3, Fe3C, Fe4N, Fe3N, Fe2SiO4 depending on Fe-containing pre-cursors. These SiCN/Fe composites are superparamagnetic with the blocking tem-peratures (TB) being anywhere from 20 K [8] to 100 K [13]. Above TB, the coercive fields and remanent magnetization vanish. Yan et al. [9] reported low-temperature behavior of SiCN/Fe composite, annealed at 1100 °C. The EPR study reported in [27] showed that in the SiCN/Fe ceramics prepared with polysilazane as polymer precursor together with either Fe(III) acetylacetonate, or Fe(CO)5, annealed under nitrogen gas flow at temperatures above 1000 °C, the magnetization is predomi-nantly due to the nanograins of Fe5Si3, in accordance with that reported in [18, 22, 23].

The present paper presents new simulations of EPR data to further analyze the experimental results of previous investigations by EPR, and reports new magnetiza-tion measurements on the SiCN/Fe samples, annealed at 800°, 1000°, 1100°, 1285°, and 1400 °C. The main aim of this paper is to study the influence of annealing tem-perature on the magnetic properties of SiCN/Fe ceramic composites. To this end, the magnetization measurements will be exploited here, among others, to estimate the blocking temperature and size distributions of the nanoparticles in the various sam-ples to fabricate better magnetic sensors of interest.


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EPR and Magnetization Studies of Polymer-Derived Fe-Doped…

2 Synthesis and Structure of SiCN/Fe Samples

2.1 Synthesis and Composition

The 5–10 wt% of Fe(III)-doped samples were prepared using the well-known pro-cess of fabrication of SiCN ceramics as described in [27], using the liquid precur-sor CERASET™ polyureasilazane. The chemical analysis for the SiCN/Fe sample annealed at 1100 °C found it to be of composition SiC0.68N0.41, including the so-called free-carbon phase. At annealing temperatures above 1100 °C, the content of N decreased to 0.15, accompanied by 30 wt% of carbon in the free-carbon phase. Increasing the annealing temperature enhanced the removal of H atoms and forma-tion of sp2 carbon-related dangling bonds on the periphery of the free-carbon phase [29–32]. In addition, there were formed sp3 carbon-related dangling bonds were formed in the body of SiCN ceramic network as defects [4, 30–34]. Neutron-acti-vated analysis of SiCN/Fe composites determined the Fe content to be 0.2 Wt%.

2.2 X‑ray Powder Diffraction (XRD) Patterns

The XRD patterns for the samples prepared at different annealing temperatures stud-ied here are shown in Fig. 1a [27]. The salient features are summarized as follows. They revealed the amorphous structure for the SiCN/Fe samples annealed at 800° and 1000 °C. On the other hand, in the samples annealed at temperatures 1285 °C and 1400 °C, peaks due to crystallization of β-Si3N4 structure were found similar to that in pure SiCN [35]. The size of Si3N4 particles as determined from broaden-ing of X-ray diffraction peaks was estimated to be from 30 ± 5 nm for the sample annealed at 1285 °C to 50 ± 5 nm for the sample annealed at 1400 °C, showing an increase with the annealing temperature. In addition, the peaks due to (i) Fe5Si3 par-ticles [36], (ii) crystalline graphite, related to graphene layers, and (iii) α-Fe parti-cles were also observed (Fig. 1b).

Fig. 1 a Dependence of the X-ray patterns of the SiCN/Fe samples on the annealing temperature. The arrows show the peaks related to Si3N4 structure and their Miller indexes. b Shows the XRD patterns of SiCN/Fe sample annealed at 1100 °C with increased sensitivity. (adapted from [27])



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3 Simulation of EPR Spectra

X-band EPR spectra of SiCN/Fe samples, annealed at different temperatures, were reported previously at room temperature [27]. A simulation is carried here only for the central EPR line, near g ~ 2.0, to fit the EPR spectra observed for the various samples for a spin S = 1/2 characterized by an isotropic g matrix, to understand better the magnetic properties of these samples as a function of annealing temperature. Table 1 lists the fitted g values, linewidths, and lineshapes for the various SiCN/Fe samples. Some representative EPR spectra reported in [27] are shown in Figs. 2a, along with the simulated spectra for the central line for the various samples, annealed at 800 °C, 1000 °C, 1100 °C, 1285 °C and 1400 °C in Fig. 2b–f, respectively.

The EPR data help to understand the behavior of the magnetic properties. To this end, they were simulated in more detail here. Unfortunately, it is not possible to make exact identifications as to the sources of all EPR lines. Only the low-field line could be definitely identified as belonging to Fe5Si3 nanoparticles, as in [27] from its temperature behavior and its Curie temperature. The changes in EPR spectra for SiCN/Fe samples, annealed at different temperatures, involve chemical transformations from one kind of Fe-containing compound to another. However, for some lines, one can only speculate what their origins are.

The main features of room temperature (295 K) X-band EPR spectra [27] for the various samples relevant to the present study, along with simulated spectra as carried out presently, are as follows.

The magnetization data for the various samples as displayed in Figs. 3, 4, 5, 6, 7, 8 are analyzed as follows.

Table 1 The g value (isotropic), linewidth, and lineshape as determined from X-band EPR spectra at 295 K in the SiCN/Fe ceramic sample annealed at 800 °C, 1100 °C and 1400 °C of the central line

SiCN/Fe sample annealing temperature

EPR lines g value ΔBpp (mT) Relative intensity Lineshape

800 °C S1 (blue) 2.055 16 0.4 LorentzianS2 (green) 2.15 84 0.1 Lorentzian

1000 °C S3 (blue) 2.15 80 0.4 LorentzianS4 (green) 2.03 100 0.04 Lorentzian

1100 °C S5 (blue) 2.14 72 0.38 GaussianS6 (green) 2.03 100 0.08 Lorentzian

1285 °C S7 (green) 2.10 70 0.16 GaussianS8 (blue) 2.045 10 0.06 Lorentzian

1400 °C S9 (green) 2.03 76 0.2 LorentzianS10 (blue) 2.045 10 0.06 Lorentzian


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Fig. 2 a Room temperature experimental X-band EPR spectra for the SiCN/Fe samples, annealed at vari-ous temperatures. The arrow indicates the narrow EPR line at g ~ 2.0, which is due to the sp2 carbon-related dangling bonds. The simulations of the wider central EPR line at g ~ 2.0 for the SiCN/Fe samples are shown as overlaps of two lines with the parameters listed in Table 1: b for the sample annealed at 800 °C; c for the sample annealed at 1000 °C; d for the sample annealed at 1100 °C; e for the sample annealed at 1285 °C; f for the sample annealed at 1400 °C (Adapted from [27])



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3.1 SiCN/Fe Sample Annealed at 800 °C

The EPR spectra of the SiCN/Fe sample, shown in Fig. 2b, annealed at 800 °C, are quite different from those annealed at higher temperatures. The simulated spectrum consists of one narrow EPR line (S1) with a linewidth 16 mT due to a paramagnetic center (probably, a remaining Fe-containing precursor), and a very broad weak line (S2), corresponding to a magnetically ordered compound, most likely due to α-Fe

Fig. 3 Temperature dependences of the ZFC and FC magnetizations from 5 to 400 K for the SiCN/Fe nanoceramics, annealed at 800 °C, 1000 °C, 1100 °C, 1285 °C, and 1400 °C


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nanoparticles, as discussed below. The very narrow EPR line is due to sp2 carbon-related dangling bonds, not simulated here.

3.2 SiCN/Fe Samples Annealed at 1000 °C

The EPR spectrum for this sample is significantly different from the sample annealed at 800 °C. There appears a new, rather wide, EPR signal near g = 12 in these samples (not simulated here) which is ascribed to Fe5Si3 nanoparticles [27].

Fig. 4 Magnetic field dependences of the magnetizations from 5 to 400 K, for the various SiCN/Fe nanoceramics annealed at a 800 °C, b 1000 °C, c 1100 °C, d 1285 °C, e 1400 °C



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The presence of these ferromagnetic nanoparticles is confirmed by XRD patterns of the SiCN/Fe sample annealed at 1100 °C as described in Sect. 2. The simula-tion is shown in Fig. 2c. The intensity of the broad EPR line S3, similar to that of the EPR signal S2 for the SiCN/Fe sample annealed at 800 °C, increases. The second broad EPR line S4 possesses much less intensity than that of S3 EPR line.

Fig. 5 Hysteresis loops for the magnetization of the SiCN/Fe sample annealed at 1100 °C, at T = 5 (< TB), 200(~ TB), 400(> TB) K

Fig. 6 Dependence of ΔM(H) = M↑ − M↓, on magnetic field for the SiCN/Fe sample, annealed at 1100 °C at different temperatures


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The simulated EPR spectra for this sample are shown in Fig. 2d. The central EPR line is found to be an overlap of two components S5 and S6. The line S5 corre-sponds to the S2 line simulated for the sample annealed at 800 °C, and to the line S3 simulated for the sample annealed at 1000 °C, but with slightly different g val-ues and linewidths. In particular, the shape of the central line S5 can be correctly simulated with a Gaussian shape, unlike most of the other lines simulated with Lor-entzian lineshapes. The lines S5 and S6 are due to α-Fe nanoparticles, dispersed in two different environments: (i) in the SiCN structure and (ii) in the “free-carbon” graphene layers, which are formed predominantly in these samples in the annealing temperature range of 900–1150 °C in accordance with the XRD results.

Fig. 7 Dependences of coercive fields on temperature for the various SiCN/Fe nanoceramics, annealed at 800 °C, 1000 °C, 1100 °C, 1285 °C, and 1400 °C

Fig. 8 Dependences of remanent magnetizations as measured at zero magnetic field on temperature for the various SiCN/Fe nanoceramics annealed at 800 °C, 1000 °C, 1100 °C, 1285 °C, and 1400 °C



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The EPR spectra for this sample change significantly from that for the sample annealed at 1100 °C, as shown in Fig. 2e. The central line consists of two compo-nents, S7 and S8. The first component (S7) is again Gaussian and similar to the S5 EPR line, observed in the SiCN/Fe sample, annealed at 1100 °C. A new nar-row EPR line S8 appears in this sample.

3.5 SiCN/Fe Sample Annealed at 1400 °C

The EPR spectrum in this SiCN/Fe samples is similar to that for the sample annealed at 1285 °C, but different from those annealed at 1000 °C and 1100 °C. The intensity of the wide EPR line near g = 12, not simulated here, decreases sig-nificantly. This is due to the continuous decomposition of Fe5Si3 nanoparticles with increasing annealing temperature, along with decrease of the free-carbon phase. The simulated central EPR line near g = 2.03 (S9) is probably due to the SiCN structure and does not change much, as compared to the EPR line S5 in the sample annealed at 1100 °C. The shape of this broad EPR signal is simu-lated to be Lorentzian to fit the experimental spectrum. The simulated narrow EPR line (S10) is similar to that for the samples annealed at 1285 °C (line S8). It is most likely due to some new Fe-containing phase formed at these temperatures, probably Fe70SixC30-x, as discussed below. The samples of SiCN/Fe annealed at 1285 °C and 1400 °C exhibit both ferromagnetic (g = 12) and superparamagnetic (g = 2.03) EPR lines, but the ferromagnetic line becomes relatively weak in the sample annealed at 1400 °C, whereas the central broad line (S9) becomes more intense. The latter implies that this sample tends to acquire a more homogeneous state due to the increased annealing temperature. The simulated broad EPR line at g = 2.03 (line S9) is due to a superparamagnetic center, because the shape/width of this line is very similar to that calculated by Kliava et al. [37] for an assembly of superparamagnetic particles, randomly dispersed in a diamagnetic material.

It is further noted here that SiCN/Fe samples annealed at 1285 °C and 1400 °C exhibit EPR spectra which are different from those of the samples annealed at lower temperatures. It is due to the changes in the structure of SiCN/Fe ceramics. As deduced from the XRD patterns, the SiCN structure changes from amorphous to poly-crystalline state above 1200 °C, implying that SiCN structure becomes more ordered, so that distribution of particle sizes becomes more uniform. New Fe-containing nanocrystallites also appear above 1200 °C. Probably, these are Fe70SixC30-x, with the magnetic phase transition at 620 K [38], detected in SiCN/Fe ceramics by magnetization measurements and EPR spectra [27]. As a conse-quence, the narrow S8 and S10 lines simulated here for the samples annealed at 1285 °C and 1400 °C, respectively, are deduced to be due to this new Fe-con-taining phase, being narrow because of a more uniform distribution of magnetic moments of Fe-containing nanocrystallites.


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3.6 Fe‑Containing Crystallites

The magnetization and EPR measurements enable the determination of what kind of Fe-containing crystallites exist in SiCN/Fe ceramics samples. In accordance with the EPR measurements reported in [27], these ferromagnetic crystallites are most likely those of Fe5Si3, as confirmed by its particular Curie temperature (TC = 393 K) [28], determined both from the temperature dependences of the magnetization here (Sect. 4) and the temperature dependences of the EPR linewidth in [27]. There are at least two contributions to the magnetization of SiCN/Fe ceramics from: (i) the fer-romagnetic part of SiCN/Fe ceramic with the Curie temperature of TC = 390 K [28], corresponding to that of Fe5Si3 and (ii) from the superparamagnetic part of SiCN/Fe ceramics, most likely due to α-Fe particles as indicated by XRD patterns. The low-field wide EPR line (g = 12) appeared only in the SiCN/Fe samples annealed at or above 1000 °C, which corresponds well to the phase diagram of Si–Fe [39] for the formation of Fe5Si3. The simulated narrow EPR lines, S8 and S10, are due to a new ferromagnetic phase, most probably that of Fe70SixC30-x with the Curie temperature TC = 620 K, as reported by Yelsukov et al. [38].

4 Magnetization Data: Measurements in the Range of 5–400 K

New magnetization data were acquired to understand better the magnetic proper-ties as revealed by the EPR data discussed in Sect. 3. The magnetizations of SiCN ceramics, doped with Fe ions, annealed at 800°, 1000°, 1100°, 1285° and 1400 °C, were recorded using a PPMS9 magnetometer. For temperature-dependency meas-urements, the rate of temperature increase was 2 K/min for about 200 min, in the temperature range from 5 to 400 K, with ~ 10-s interval between successive meas-urements. The samples were in the form of small 4–7 mg ceramic pieces, firmly attached to a sample holder. Two sets of measurements were made: (i) field-cooling (FC) and zero-field-cooling (ZFC) measurements and (ii) temperature variation of magnetizations. They are described below.

4.1 Superparamagnetism

In general, SiCN/Fe ceramic samples exhibit superparamagnetic behavior. A super-paramagnetic system consists of a large number of paramagnets aligned in the same direction. A superparamagnet is, thus, a system with a rather large paramagnetic susceptibility. The reduced magnetization, (M/MS), of a superparamagnetic system, where M and MS are the magnetization and saturation magnetization, respectively, exhibits a Brillouin-function B(x) behavior with respect to x = H/T, where H is the external magnetic field and T is the temperature, characterized by anhysteretic mag-netization isotherms [40], the same as that for a paramagnetic system. An impor-tant indication of superparamagnetic behavior is the existence of a significant dif-ference between ZFC and FC magnetizations below the so-called “irreversibility



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temperature”, and the existence of “blocking temperature”, characterized by the maximum in the ZFC magnetization, above which the coercive field and remanent magnetization vanish [41]. As well, the ZFC and FC magnetizations are expected to be the same in an ideal superparamagnet above the blocking temperature.

4.2 Field‑Cooling (FC) and Zero‑Field‑Cooling (ZFC) Measurements: Estimation of Blocking Temperature and Size Distribution of Nanoparticles

The temperature dependences of the magnetization for both FC (at 100 Oe) and ZFC of these ceramics were measured from 5 to 400 K as shown in Fig. 3.

The blocking temperature, TB, is identified to be the temperature at which the maximum of the ZFC magnetization occurs. TB can, thus, be determined from Fig. 3. The value so determined for = 10.6 K for the SiCN/Fe sample annealed at 800 °C is not at all reliable, because of lack of sufficient data points about the maxi-mum to qualify this temperature to be the one at which true maximum of magneti-zation occurs. As for the sample annealed at 1000 °C, there occurs no maximum, indicating that there is a large variation in the size of nanoparticles for a true block-ing temperature to become defined for this system. The maxima in the ZFC magneti-zations for the samples annealed at 1100 °C, 1285 °C, and 1400 °C are well defined; the corresponding TB are 203.8, 103.5, and 38.6, respectively.

4.3 Coincidence of FC and ZFC Magnetizations Above TB

The coincidence between the ZFC and FC magnetizations above TB becomes more enhanced for the samples annealed at 1100 °C, 1285 °C and 1400 °C as the anneal-ing temperature of the sample increases. This is presumably due to particle sizes becoming more uniform as the annealing temperature of these samples increases, this coincidence becoming almost identical for the sample annealed at 1400 °C. This indicates that the superparamagnetic property of the samples becomes more pro-nounced with increasing annealing temperature.

4.4 Distribution of Nanoparticle Sizes as Estimated from the Maximum of ZFC Magnetization: Lognormal Distribution

The distribution of particle diameters in a nanoparticle assembly is often charac-terized by a lognormal shape [42, 43]. This particle diameter distribution can be described as:

In Eq. (1), the diameter D0 is close to the distribution maximum and λ charac-terizes the width of the distribution. For the lognormal distribution, the average

(1)f (D) =1√2��D

exp

⎛⎜⎜⎜⎝−ln2

�D

D0

�

2�2

⎞⎟⎟⎟⎠


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particle diameter is given by ⟨D⟩ = D0·exp(− λ2/2), implying that the value of λ decreases with greater uniformity in the size of the various nanoparticles. For an assembly of nanoparticles with a distribution of the size of nanoparticles, the maximum of ZFC magnetization occurs at a temperature Teff, which is an effec-tive blocking temperature. It differs considerably from the true blocking tempera-ture, TB (D), for a system consisting of all the particles with the same diameter (D) due to a rather wide distribution of diameters of the nanoparticles in the sam-ples investigated here [44].

The temperature at which the maximum of ZFC magnetization occurs can be exploited to estimate � , the width of distribution, as given by Eq. (1). To this end, one can use the calculations of Usov [44], the ZFC magnetization dependency on temperature is characterized by a maximum, which shifts to lower temperatures as λ decreases. In particular, comparing with the plot in [44], λ = 0.1, 0,2, 0.3 correspond to the ZFC magnetization in SiCN/Fe sample annealed at 1400 °C, 1285 °C, and 1100 °C, respectively. On the other hand, the ZFC magnetization in the SiCN/Fe sample, annealed at 1000 °C, exhibits no well-defined maximum, and can be characterized by λ = 0.3, comparing with the plot in [44] correspond-ing to a much wider distribution D of nanoparticles. As deduced from the calcu-lations shown in Fig. 7 of [44], the correspondences for λ as listed in Table 2 are found for the present ZFC magnetization measurements. Table 2 shows that the particle size becomes more uniform as the annealing temperature of the sample increases, because the corresponding value of λ decreases with increasing anneal-ing temperature.

4.5 Temperature Variation of Magnetization

The magnetic field dependence of the magnetization was measured at 5, 10, 20, 50, 100, 200, 300, and 400 K as shown in Fig. 4.

4.6 Hysteresis Loops

The samples exhibit different types of butterfly loops depending on their various magnetic states as described below.

Table 2 The λ parameter dependency on the annealing temperature of the sample

a λ characterizes the width of the distribution, following Eq. 1

Annealing temperature of SiCN/Fe sample

Temperature at which the maximum of ZFCmagnetization occurs

λa

1000 °C None 0.31100 °C 204 K ~ 0.251285 °C 103 K 0.21400 °C 38 K 0.1



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4.7 Butterfly‑Like Shape

Figure 5a–c show the variation of the hysteresis loop with increasing temperature for the SiCN/Fe sample annealed at 1100 °C. Figure 5a shows the hysteresis loop at 5 K, well below the blocking temperature TB = 204 K for this sample, where the non-zero values of the coercive field and remanent magnetization are clearly seen. Figure 5b shows the “butterfly-like” shape of the hysteresis loop at 200 K, just below TB, characterized by zero coercive field and remanent magnetization with a clear non-coincidence of the magnetizations for increasing and decreasing magnetic fields, M↑(H) and M↓(H), respectively, typical for temperatures slightly below and above the blocking temperature. Specifically, “butterfly-shaped” hys-teresis curve refers to a hysteresis curve that possesses almost zero coercive field for increasing and decreasing magnetic fields, implying that although the magnet-ization at H = 0 is negligible, the difference between the increasing- and decreas-ing-field magnetizations before reaching saturation magnetization is significant, making the hysteresis curve look like a butterfly wing. The butterfly shape of the magnetization curve is due to the diverse spatial orientations of the easy magnetic axes of the various anisotropic nanoparticles with respect to the external mag-netic field near and above the blocking temperature for increasing magnetic field. The magnetization M↑ observed here is quite similar to the magnetization calcu-lated for an assembly of superparamagnetic nanoparticles with the angle α0 = 60° between their easy anisotropy axis and the external field (see, Fig. 3 in [45]). This implies that in the samples studied here, there are some nanoparticles pre-sent with their easy anisotropy axes which lie at angles around 60° with the exter-nal magnetic field that exhibit hysteresis curves which look like butterfly wings. Such a shape of the magnetization curve was predicted to appear only near the blocking temperature, which is the temperature at which the coercive force van-ishes. The coercive field is still small but finite about the blocking temperature, and it vanishes completely well above it. This effect is most pronounced about the blocking temperature. It decreases progressively with increasing temperature. The butterfly shape is most pronounced for the samples annealed at 1000 °C and 1100 °C, as seen from Fig. 4b, c. It becomes less and less pronounced for the samples annealed at higher temperatures. Figure 5c shows the usual pattern of hysteresis loop for a superparamagnetic sample, at 400 K, well above TB, charac-terized by zero coercive field and almost coincident values of M↑(H) and M↓(H).

Figure 6 shows the dependence of the remanent magnetization ΔM (H) = M↓ − M↑ on the magnetic field for SiCN/Fe samples annealed at 1100 °C for T = 5, 20, 100, 200, 300, and 400 K. It is clearly seen from this figure that the sharp maxima of the remanent magnetization for this sample occur at 4.1 mT, 8.6 mT, 13.5 mT at 200, 300, and 400 K, respectively. It is noted that there is observed negligible remanent magnetization below the blocking temperature TB = 200 K for this sample. All these peculiarities, which are similar for the SiCN/Fe nanoparticle samples annealed at the lower temperatures 800 °C, 1000 °C and 1100 °C, suggest that they exhibit a sig-nificant deviation from the “ideal” superparamagnetic behavior, presumably because the size distributions of the particles are less uniform in them as compared to those annealed at the higher temperatures 1285 °C and 1400 °C.


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4.8 Discussion of Magnetization Data

To help the discussion, Figs. 7 and 8, respectively, show the dependency of the coercive fields and remanent magnetizations on temperature for the various sam-ples as deduced from Fig. 4.

4.8.1 SiCN/Fe Sample Annealed at 800 °C

The magnetization data for the various samples as displayed in Figs. 3, 4, 5, 6, 7, 8 are analyzed as follows. As seen from Figs. 3, 4, 5, 6, 7, 8, the behavior of the magnetic properties of the SiCN/Fe sample annealed at 800 °C is quite dif-ferent from those of all other samples. This is because of the presence of many phases in it which have not blended well due to its low annealing temperature. It is seen from Fig. 4a that the saturation magnetization of this sample is much smaller compared to those of other SiCN/Fe samples, annealed at higher tem-peratures. It implies that sufficient ferromagnetic Fe-containing crystallites had not been formed when annealing at 800 °C, so that its ferromagnetic property is rather weak. However, the coercive fields and remanent magnetization shown in Figs. 7 and 8, respectively, are still appreciable for this sample at all tem-peratures up to 400 K, implying that some Fe-containing nanocrystallites have, indeed, been formed. The susceptibility of this sample, as measured from the linear part of the magnetization at low magnetic field, fits well to �p =

C

T with

C = 8·10−5 ± 0.1·10−5 emu/g/Oe, in the 5–50 K temperature range, and the total magnetization is a sum of paramagnetic and ferromagnetic contributions. It is also noted from Fig. 2a that a rather large difference between the ZFC and FC magnetizations is observed for this sample up to 400 K, confirming its inhomoge-neous magnetic structure.

4.8.2 SiCN/Fe Sample Annealed at 1000 °C

This sample also exhibits complex magnetic behavior due to the localized Fe3+ moments at lower temperatures with almost the same Curie constant C = 7·10−5 emu/g/Oe when fitted to the susceptibility expression �p =

C

T as that for

the SiCN/Fe sample annealed at 800 °C. Furthermore, as deduced from the EPR observation of a wide EPR signal at low magnetic field (g = 12) due to nanocrys-tallites of Fe5Si3 [27], in the samples annealed at or above 1000 °C, nanocrystal-lites of Fe5Si3, contribute to the magnetic behavior of this sample. The satura-tion magnetization for this sample is larger as compared to that for the SiCN/Fe sample annealed at 800 °C. It impliess that at 1000 °C Fe-containing crystal-lites start to form readily and their contribution to the magnetization becomes rather significant. For this sample, the coercive fields and remanent magnetiza-tions are also appreciable at all temperatures up to 400 K, as seen from Figs. 7 and 8, respectively, confirming the superparamagnetic nature of the sample. This



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sample’s superparamagnetic behavior is further confirmed by the rather large dif-ference between the ZFC and FC magnetizations as seen from Fig. 3b.

4.8.3 SiCN/Fe Samples Annealed at 1100 °C, 1285 °C and 1400 °C

These samples are superaramagnetic, since a significant difference between the zero-field-cooling (ZFC) and field-cooling (FC) magnetizations is observed below the so-called blocking temperature, as seen in Fig. 3c–e, according to the criterion described in Sect. 4.1. As well, the nanoparticle sizes in them become more uniform and homogeneous with increasing annealing temperature, as seen from the analysis of the maxima of the ZFC plots in Sect. 4.2 above.

4.9 EPR Data Versus Magnetization Data: Simultaneous Superparamagnetic and Ferromagnetic Behavior

From the magnetization data, it appears that most of the SiCN/Fe samples investi-gated here are superparamagnetic. They are characterized by blocking temperatures. No hysteresis loop is exhibited (coercive field and remanent magnetization) above this temperature, but below that, a hysteresis loop is exhibited, indicating ferromag-netic behavior. There is only the sample SiCN/Fe annealed at 800 °C, which exhib-its a coercive field over a very large temperature range, indicative of ferromagnetic behavior. The magnetization measurements provide information only on the domi-nant contribution to the magnetization. On the other hand, the EPR data indicate that the SiCN/Fe ceramics studied here really consist of many clusters of Fe-containing nanoparticles, which can be superparamagnetic as well as ferromagnetic, e.g., the low-field EPR line is certainly due to ferromagnetic cluster of nanoparticles. There-fore, in fact, these SiCN/Fe ceramics are not uniquely superparamagnetic, or fer-romagnetic. They exhibit both of these magnetic behaviors. Only EPR can provide information about the sources of magnetization.

5 Blocking Temperature

In the blocked state, the magnetic moments are blocked from movement. The blocked state exists at T < TB, whereas the superparamagnetic state exists at T > TB. In the superparamagnetic state the hysteresis loop has no width. The blocking tem-perature has here been estimated in two ways:

(a) the temperature (TB) at which the maximum of ZFC magnetization occurs [46, 47] (see also inflection-point criterion) [48] and [41, 49–52]), is already deter-mined in Sect. 4.2 above;

(b) the average blocking temperature ⟨TB⟩, above which the coercive field and rema-nent magnetization vanish, is estimated by the expression for the temperature dependence of the coercive fields, as follows [53, 54]. According to Stoner–Wohlfarth model [53, 54], for an assembly of non-interacting, due to the rather


1413

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low concentration of Fe ions so that they are sufficiently far apart, single-domain particles with uniaxial anisotropy, the coercive field in the temperature range from 0 to TB, i.e., the range over which all superparamagnetic particles remain blocked, follows the relation:

In Eq. (2), MS is the saturation magnetization; α = 1 if the easy axes of the various particles are aligned, but α = 0.48 if they are randomly oriented; K is the magnetic anisotropy constant, and T is the temperature. The temperature dependence of the coercive fields for the various SiCN/Fe samples is shown in Fig. 7. Fitting the values of HC (T) for each SiCN/Fe sample to Eq. (2), where 2K

MS

and ⟨TB⟩ are the two fitting

parameters, the following values are estimated: ⟨TB⟩ = 22.3 K, 58.1 K, 126 K, 448 K for SiCN/Fe samples annealed at 1400 °C, 1285 °C, 1100 °C and 1000 °C, respec-tively. These values are rather lower than those obtained from the maxima of the ZFC magnetization curve, as deduced in Sect. 4.2. This is expected, in general, because of different considerations for calculating the blocking temperatures.

6 Concluding Remarks

The salient features of the EPR simulation and magnetization measurements on SiCN/Fe ceramic samples annealed at 800 °C, 1000 °C, 1100 °C, 1285 °C and 1400 °C presented here are as follows:

1. These samples are superparamagnetic at temperatures 5–400 K, except for the sample annealed at 800 °C which is not quite superparamagnetic. An analysis of the EPR spectra reveals that this superparamagnetism is mainly due to the pres-ence of the nanoparticles of Fe5Si3 (TC = 390 K), α-Fe particles (TC = 1043 K), and Fe3Si (TC = 800 K) in the samples. There is also a contribution from Fe70SixC30-(TC = 620 K) nanoparticles, dispersed in SiCN/Fe samples synthesized at higher annealing temperatures.

2. The large difference between the ZFC and FC magnetizations for the SiCN/Fe samples annealed at 800 °C and 1000 °C is due to rather large distribution of the sizes of nanoparticles. This distribution becomes progressively narrower with increasing annealing temperatures of the samples, as reflected in the change of the shape of the ZFC magnetization, and its maximum that occurs at the block-ing temperature for the samples annealed at 1100 °C, 1285 °C and 1400 °C. This is accompanied by enhanced overlaps of ZFC and FC magnetization above the respective blocking temperatures as the annealing temperature of the sample increases.

(2)HC = �

�2K

MS

��1 −

�T

⟨TB⟩�1∕2

�



1 3

3. An analysis of the coercive field dependence on temperature confirms the Stoner–Wohlfarth behavior only for the SiCN/Fe samples annealed at 1100 °C, 1285 °C and 1400 °C. The average blocking temperatures, ⟨TB⟩, over the assembly of par-ticles with various sizes, estimated from this model, are found to be ⟨TB⟩ = 22.3 K, 58.1 K, 126 K, and 448 K for SiCN/Fe samples annealed at 1400 °C, 1285 °C, 1100 °C and 1000 °C, respectively. These are lower than the blocking tempera-tures, TB, determined from the maxima of the ZFC magnetization curve, which are 203.8 K, 103.5 K, and 38.6 K, respectively, for the samples annealed at 1100 °C, 1285 °C, and 1400 °C, presumably because these two blocking temperatures are defined differently.

4. The most homogenous SiCN/Fe composite is the SiCN/Fe ceramic annealed at 1400 °C. An analysis of its maximum of the ZFC curve reveals a very narrow distribution of the size of Fe-containing nanoparticles due to increased order of SiCN/Fe structure above 1200 °C. This is also consistent with the narrow simu-lated central EPR lines S8 and S10 due to Fe-containing Fe70SixC30-x nanocrys-tallites, which appear only in the samples annealed at 1285 °C and 1400 °C, respectively, that possess the most uniform distribution of particle sizes of all the samples. This result can be exploited to fabricate more homogenous magnetic materials for fabricating better magnetic sensors by synthesizing SiCN/Fe ceram-ics at annealing temperatures even higher than 1400 °C, which is the maximum here of the various investigated samples.

Acknowledgements This research was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC; SKM); SIA is grateful to the Ministry of Education and Science of Russian Federation, for partial support in the frame of research project, allocated to Kazan Federal University for the state assignment in the sphere of scientific activities (#3.2166.2017/4.6). The magnetic measurements were carried out at the Federal Center of Shared Facilities of Kazan Federal University. SIA acknowl-edges Prof. I. Stiharu’s interest in this research.

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