Structural, Magnetic, and Dielectric properties of Sr4Fe6O13 ferrite prepared of small crystallites.

A stable Sr4Fe6O13 was prepared as small crystallites by auto-combustion of a sol-gel in air followed by annealing the later at pertinent temperatures. A green sample, as annealed at elevated temperatures, yields a single Sr4Fe6O13 phase of tailored magnetic properties. The structural, morphological, magnetic and electrical properties were investigated by X-ray diffraction, transmission electron microscopy, vibrating sample magnetometer, and broadband dielectric spectrometer. Hard magnetic Sr4Fe6O13 properties arise with saturation magnetization Ms = 12.4 emu/g, coercivity Hc = 3956.7 Oe and squareness 0.512. Studies made at low temperatures reveals Ms decreasing on increasing temperature from 17.5 emu/g at 85 K down to 12.4 emu/g at 305 K, while Hc rises from 1483 Oe at 85 K to 1944 Oe at 305 K. The ac-conductivity follows the Jonscher relation. The dc-conductivity at high temperatures/low frequencies exhibits a plateau and it depends linearly on a characteristic frequency according to the Barton-Nakajima-Namikawa) relation.

Introduction

Perovskites are compounds of a structural formula ABC3, where A represents a rare earth, alkaline earth, alkali or large ions such as Pb2+, Bi3+, B represents a transition metal ion and C represents O, Fl, Cl, I etc[1]. A cation may be monovalent like Li, Na, K, divalent like Ca, Ba, Sr or trivalent like La, Nd, Pr, which is cubo-octahedrally coordinated to 12 O2− ions, while B cation, such as Ti, Ni, Fe, Co, or Mn is octahedrally coordinated to 6 O2− ions[2]. Recently, several investigations performed on a Sr-Fe-O structure reveal its amazing structural and physical features such as cheap price, high magnetic anisotropy, high Curie temperature, a significant magnetization of saturation and remarkable chemical and corrosion resistance[3]. The reason certainly presented by oxygen-lacking perovskites and by Ruddlesden-Popper (RP) type structure that possess a desirably negative magnetoresistance (-ve MR)[4-7]. A Sr-Fe-O system includes many types of perovskites and perovskite derivatives of widely varied crystalline and magnetic features[8-12]. These types of substances are constructed based on a K2NiF4 shape and involve slab segments of SrFeO3 and SrO, where SrFeO3 is resulting from a KNiF3 cubic perovskite of K2NiF4, and SrO is matching to a NaCl-class KF[8]. They characteristically contain paramagnetic Fe4+ ions.

In particular, a stoichiometric compound Sr4Fe6O13 has a construction of a perovskite or its derivatives[8]. It is observed that a Sr4Fe6O13±δ construction is a highly stable single-phase compound and it exhibits significant conductivity of combined-ions and electrons types[13]. That is composed of altered sections through a Sr-Fe-O layer (b-axis) and dual slabs of FeO in FeO5 polygons[14-16]. As a result, it owes an anisotropic shape in it conducts through O2− ions and vacancies across the a-c planes[17]. Actually, creation of O2− empty sites and interstitials develop non-perovskite slabs in a Sr4Fe6O13±δ phase keeps them in a broad array of O2− non-stoichiometry[18]. Mixed oxygen-ions and electron conducting oxides have attracted great interest owing to their promising use in ceramic separation filters of hydrocarbons incomplete oxidation and oxygen, fuel cell cathodes, or gas detectors[19-22].

According to the authors’ best knowledge and after searching international scientific databases, there are a few studies done on a Sr4Fe6O13 system. Little attention has been paid on its magnetic and electrical properties, whereas most studies are focused on its applications in oxygen membranes[23,24]. An auto-combustion method we used in the present work to prepare a stable Sr4Fe6O13 of small crystallites. The as-prepared powder was annealed at different temperatures in order to get a single Sr4Fe6O13 phase. A major objective of this work is to explore magnetic properties in small Sr4Fe6O13 crystallites at and below room temperatures. Further, ac conductivity and dielectric properties are studied on a broad range of frequencies and at different temperatures.

Results and discussion

Structural properties

X-ray diffraction (XRD) patterns of the various samples are shown in Fig. 1. The as-prepared sample S0 in Fig. 1a reveals an amorphous pattern with no defined peaks. Figure 1b shows formation of two different phases in the as-prepared sample annealed at 500 °C for 3 h (S1). The main phase of an orthorhombic SrCO3 accompanies a secondary phase of a rhombohedral α-Fe2O3 according to JCPDS files 00-005-0418 and 00-073-0603, respectively. The SrCO3 forms in a chemical reaction of Sr(NO3) with CO2 during the synthesis[25]. The diffraction pattern in Fig. 1c of sample S2 annealed at 1100 °C for 3 h demonstrates three phases. The main phase orthorhombic Sr4Fe6O13 contains two secondary phases of hexagonal SrFe12O19 and cubic Sr3Fe2(OH)12. Figure 1d shows XRD of a single phase orthorhombic Sr4Fe6O13 (according to JCPDS file 78-2403) of sample S3 annealed at 1100 °C for 10 h. No any secondary phase is observed here. An average crystallite size of the fabricated powder was determined using the Scherrer relation[26,27].Here, k is the shape factor (commonly taken approximately as 0.89), λ is wavelength of the X-ray beam used, β is the full-width at half maximum of (251) peak and θ is the diffraction angle. An average D-value of Sr4Fe6O13 was found to be ~72 nm. A microstrain (α) present in the Sr4Fe6O13 crystallites was computed as per a model relation[26,27],

Figure 1

XRD patterns of (a) as-prepared (S0) and annealed samples at (b) 500 °C for 3 h (S1), (c) 1100 °C for 3 h (S2), and (d) 1100 °C for 10 h (S3).

A typical α = 0.04 value is found for sample S3. A dislocation density δ = 1.92 × 1017 lines/cm2 (looked as a dislocation line length) contained therein is estimated as[28],

A scanning electron microscope (SEM) was used to examine morphology of the Sr4Fe6O13 samples as illustrated in Fig. 2. Small grains are observed of irregular rectangular or cubic shapes, with an average size of 85 nm (S3) in a good agreement with the D-value estimated from Scherrer relation. The Sr4Fe6O13 images were studied more closely in a transmission electron microscope (TEM) as given in Fig. 3. Small particles are observed with an average 68 nm size, which exhibit electron diffraction rings with spots, characterizing a nanocrystalline phase in agreement with the XRD analysis.

Figure 2

SEM images of sample S3.

Figure 3

TEM images of sample S3, with SAED pattern in the inset.

Magnetic properties

Figure 4 depicts magnetic hysteresis loops of samples S1, S2, and S3 of a ferromagnetic behavior. Values of saturation magnetization (Ms), remanence magnetization (Mr), coercivity (Hc) and squareness ratio (R = Mr/Ms) determined from the loops are given in Table 1. Sample S1 shows soft ferromagnetic behavior with Ms = 5.8 emu/g and Hc = 102.0 Oe. The main phase in this sample is SrCO3, which has no magnetic moment. A secondary phase Fe2O3 contributes the magnetic features. Sample S2 displays improved Ms = 22.2 emu/g, Hc = 4223.6 Oe, and R = 0.487 values as it contains a main phase Sr4Fe6O13 with secondary phases Sr3Fe2(OH)12 and SrFe12O19. The hexagonal ferrite SrFe12O19 is considered to be made up of alternating spinel (S = Fe6O82) and hexagonal (R = SrFe6O112−) layers. The O2− ions are closely packed with Sr2+ ions in a hexagonal layer and the Fe3+ ions distribute in five distinct sites: three octahedral sites (12k, 2a and 4f2), one tetrahedral (4f1) site and one bipyramidal site (2b)[29]. The magnetic structure given by the Gorter model is ferromagnetic with five different sublattices, three parallel (12k, 2a, and 2b) and two anti-parallel (4f1 and 4f2), which are coupled with superexchange interactions through O2− ions[30]. The Sr2+ ions are responsible for a large uniaxial magnetic anisotropy controls perturbation of the crystal lattice[31]. Zhang et al. demonstrated the Sr3Fe2(OH)12 exhibits a weak ferromagnetic behavior with Ms = 0.86 emu/g and Hc = 258.43 Oe[32]. So, the magnetic behavior in sample S2 is mainly due to the SrFe12O19 and Sr4Fe6O13 ferrites. Further, sample S3 has Ms = 15.7 emu/ g, Hc = 3956.7 G and R = 0.512 as measured at room temperature.

Figure 4

M-H Hysteresis loops for S1, S2, and S3 samples.

Table 1

Magnetic properties of Sr4Fe6O13 samples prepared in different conditions.

Sample	Ms(emu/g)	Mr(emu/g)	Hc(Oe)	R
S1	5.8	0.2	102	0.034
S2	22.2	10.8	4223	0.48
S3	15.7	8.051	3956	0.51

Figure 5 shows hysteresis loops of sample S3 measured at different temperatures 85 to 305 K. As shown in Fig. 6a, the Ms decreases with increasing temperature, assuming Ms = 17.5 emu/g at 85 K relative to Ms = 12.4 emu/g at 305 K. This is a typical behavior of ferromagnetic materials in the moment decreases on increasing thermal energy[33,34]. This can be realized by fitting the data using the Bloch’s law[35-37].where B is the Bloch constant and Ms(0) is the Ms at 0 K. A value α = 3/2 is assigned according to the mean-field theory for long-range ferromagnetism, with B = 10−4–10−5 for nanoferrites and 10−6 for bulk ferromagnets. The Bloch’s law is valid in our samples[36,38]. Cojocaru studied temperature Ms dependence for ferromagnetic nanoparticles in the experimental data follow the Bloch’s law[39]. Figure 6a also shows how Hc growing with temperature from 1483 Oe at 85 K to 1944 Oe at 305 K. It is a complicated function of reversal mechanism of spins, anisotropy energy, and magnetic microstructure, viz., shape and size of crystallites, grain boundaries, surfaces, etc. There are also examples in it increasing with temperature[40-42]. Figure 6b shows how R peaks-up with temperature, while the area enclosed in a hysteresis loop decreases up to 195 K and then increases. The area enclosed in a hysteresis cycle represents an irreversible work required to go through the cycle. It depends on dissipation of energy in spin reversals over the fields.

Figure 5

M-H hysteresis loops measured for sample S3 at selected temperatures in a range of 85–305 K.

Figure 6

Variations of (a) Ms and Hc and (b) squareness (R) and hysteresis area measured against temperature for sample S3.

Dielectric and electrical properties

Dielectric permittivity ε′ of sample S0 varies in two different trends as plotted against frequency in Fig. 7 at different temperatures of 253 to 293 K. In the first region at frequencies above 1 kHz, no remarkable effect of frequency or temperature is noticed. In the second region below 1 kHz up to 0.1 Hz (limited according to the frequency window studied), the ε′ value rises progressively at lower frequencies. As usual[43,44], the temperature progressively promotes the final ε′ values. Two factors govern enhanced ε′ values at low frequencies; (i) space charge polarization and (ii) interfacial polarization due to domain-wall motion, usually found in multicomponent materials[45-47]. They have induced oscillations compatible to low frequencies of applied external electric fields that facilitate the ε′ values. A field induced charge transport favors conductivity and in turn density and mobility of active charge carriers. It also promotes the interfacial polarization observed here. As oscillations of the charge carriers are reasonably damped, the ε′ value is reduced at higher frequencies. In order to gain a more insight of the effect of temperature on the charge transport even at high frequencies, one has to study separately the effect of temperature on imaginary counter part ε″ of permittivity. The inset in Fig. 7 describes temperature ε″ dependence studied at 100, 103 and 106 Hz frequencies. A resultant value ε*(ω,T) = ε′(ω,T) − iε″(ω,T) is related to the complex conductivity σ*(ω,T) = σ′(ω,T) + iσ″(ω,T), with σ*(ω,T) = iωεε*(ω,T), implying σ′ = εωε″ and σ″ = εωε′(ε = vacuum permittivity).

Figure 7

Frequency dependence of ε′-values measured for sample S0 at selected temperatures in a range 253–293 K, with temperature ε′′dependence given in the inset at 1 Hz, 1 kHz, and 1 MHz frequencies.

A gradually increased ε″ value with increasing temperature describes a thermally induced mobility of charge carriers at these frequencies. This confirms a glassy structure of sample S0. A linear dependence of conductivity on ε″ explains the results as observed here. A rate of σ′ increase with frequency is slowed down at high frequencies (1 MHz) in a lack of slow dynamic processes. Figure 8 illustrates how σ′ varies over frequencies for a representative sample S0 in two temperature regimes. In the 253 to 293 K regime, σ′ gradually decreases in Fig. 8a on lower frequencies, describing a highly insulating material in the ambient temperature in a freezing like behavior of cold charge carriers at low temperatures[47]. It is worth mentioning that, on warming the sample, the conductivity spreads out at low frequencies as the permittivity described in Fig. 7. The frequency σ′ dependence at higher temperatures (Fig. 8b) follows the well-known Jonscher power-law, as prevails in many conductive glasses and polymeric systems[43-45],

Figure 8

Frequency dependence of σ′-values measured for sample S0 at selective temperatures in (a) 253–293 K and (b) 363–473 K regions.

At lower frequencies, a less dependent, or even an independent trajectory (plateau) of frequency, builds up. The plateau yields the dc conductivity σdc and characteristic frequency νc in the dispersion of σ′ sets in and turns into a power law at higher frequencies. The σdc is varied by more than two orders in the 373 to 473 K regime.

Figure 9 depicts σ′ and electric loss modulus as a function of frequency at near 0 K for the four samples. Sample S2, which contains SrFe2O19 with a secondary phase Sr3Fe2(OH)12, reveals the highest σ′ value in Fig. 9a at a characteristic frequency (usually called hoping frequency), which is characterized by a maximum peak position in the M″(ν) plot in Fig. 9b. Samples S0 and S1 peak up σ′ at higher frequencies and it reflects in a small peak in the M″ plots as a result of charges accumulate at potential wells in a kind of interfacial polarization. The charge carriers move short distances accompanied by the relaxation polarization dynamics consistently with what is it is reported earlier[48-50]. Here, a σdc value is related to the characteristic frequency in the maximum peak position in the M″(ν) plot and not to the peak intensity as marked by the rows. An increasing σdc with increasing characteristic frequency agrees well with the Barton-Nakajima-Namikawa (BNN) relation correlated between dc and ac conductivities, according to σdc ≈ νc[51-54]. Further, the M″(ν,T) spectra suggest a remarkably enhanced conductivity on generating mono and multiphase structures over an amorphous sample S0. Thus, sample S2 of three phases has the highest conductivity in the shortest hopping time. Two main parameters of charge transport σdc and νc can be deduced by fitting the data in the Jonscher’s universal power law in Eq. 5, with 1 > s > 0.5. Figure 10 plots so obtained values over T−1 for the four samples. Almost all data found to follow an Arrhenius relation:where S could be the dc-conductivity or any other characteristic parameter, E is the activation energy and K is Boltzmann constant. A value E = 78.1 kJ/mol found for sample S0 (amorphous) is reduced to be 73.2 kJ/mol for sample S1 (of two phases), or 53.0 kJ/mol for sample S3 of a single phase. In sample S2, which contains three phases, the said plots deviate from the Arrhenius relation, extending a wide peak like behavior. This reflects higher ability of ions to transport in promoted conductivity over other samples. Identical behavior of both parameters in these samples confirms validity of the BNN-relation.

Figure 9

Frequency variations of (a) σ′ and (b) M′′ values plotted at 273 K for four samples S0, S1, S2 and S3 prepared in this investigation.

Figure 10

Temperature dependence of (a) νc and (b) σdc values determined by fitting the data in Eq. 5.

Experimental work

Synthesis of samples

Sr4Fe6O13 was synthesized using a citrate auto-combustion method. Ferric nitrate and strontium nitrate were mixed in citric acid in the stoichiometric ratio to get a clear solution. Ratio of metal nitrates to citric acid was 1:1. Ammonia solution was added dropwise until the pH became 7. The mixture was stirred at 600 rpm and slowly evaporated at 130 °C to form a gel. Viscosity and color were changed as sol turned into a brown puffy porous dry gel, which then was ignited to burn in a strong auto-combustion process with evolving gases (CO2, NO2, NO, NH3, CH4, etc.). The as-synthesized powder S0 was calcined at 500 °C for 3 h (S1) and at 1100 °C for 3 h (S2), or 10 h (S3), with a heating rate 4 °C/min[55].

Measurements and analyses

The structure was examined by an X-ray diffractometer (XRD) of Burker-D8 with Cu-kα radiation of wavelength λ = 1.5418 Å. Morphology and surface shape of the fine particles was analyzed using a field emission scanning electron microscope (model QUANTA-FEG250, Netherlands) and a transmission electron microscope (TEM) of JEOL-1010. The magnetic measurements were performed using a vibrating sample magnetometer (VSM, LakeShore 7410, USA) with applied fields up to 20 kOe at room temperature. The electrical and dielectric properties were studied of the samples on a long-range of frequency (0.1 Hz to 10 MHz) using a powerful broadband dielectric spectrometer, BDS. It is utilizing a high-resolution Alpha analyzer with an active sample head (Novocontrol GmbH concept 40). All measurements were done isothermally at selected temperatures over 223 to 473 K, which were controlled by a Quatro Novocontrol cryo-system with stability better than ±0.1 K. The samples were sandwiched between two gold-plated brass electrodes of 10 or 20 mm in diameter in parallel plate geometry. The control and data acquisition processes were performed by a WINDETA software[56,57].

Conclusions

A fine Sr4Fe6O13 powder was synthesized through a sol-gel auto-combustion method and then annealed at 500 °C for 3 h and at 1100 °C for 3 h, or 10 h in finely tuning its yield of small crystallites. A major phase Sr4Fe6O13 forms in 1100 °C annealing, with a secondary phase of SrFe12O19 and Sr3Fe2(OH)12. A single phase Sr4Fe6O13 appears on prolong anneal to 10 h. It shows hard magnetic behavior with Ms = 12.4 emu/g, Hc = 3956.7 Oe, and R = 0.512. It slowly loses Ms but gains Hc on warming over 85 to 305 K in a typical hard magnet. The ac-conductivity follows the well-known Jonscher relation at higher temperatures and it linearly decreases on decreasing frequency at lower temperatures indicating an insulating feature due to freezing of mobility of the charge carriers. The dc-conductivity is related to a characteristic frequency in the Barton-Nakajima-Namikawa relation.