Influence of the charge ordering and quantum effects in heterovalent substituted hexaferrites on their microwave characteristics

Journal of Alloys and Compounds 788 (2019) 1193e1202

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Influence of the charge ordering and quantum effects in heterovalent substituted hexaferrites on their microwave characteristics A.V. Trukhanov a, b, c, *, M.A. Almessiere d, e, A. Baykal e, S.V. Trukhanov a, b, c, Y. Slimani f, D.A. Vinnik a, V.E. Zhivulin a, A. Yu. Starikov a, D.S. Klygach a, i, M.G. Vakhitov a, i, T.I. Zubar a, b, D.I. Tishkevich a, b, E.L. Trukhanova b, c, M. Zdorovets g, h, i a

South Ural State University, 454080, Chelyabinsk, Russia SSPA “Scientific and Practical Materials Research Centre of the NAS of Belarus”, 220072, Minsk, Belarus National University of Science and Technology MISiS, 119049, Moscow, Russia d Department of Physics, College of Science, Imam Abdulrahman Bin Faisal University, P.O. Box 1982, Dammam, 31441, Saudi Arabia e Department of Nano-Medicine Research Imam Abdulrahman Bin Faisal University, P.O. Box 1982, Dammam, 31441, Saudi Arabia f Department of Biophysics, Institute for Research & Medical Consultations (IRMC) Imam Abdulrahman Bin Faisal University, P.O. Box 1982, Dammam, 31441, Saudi Arabia g L.N. Gumilyov Eurasian National University, 010008, Astana, Kazakhstan h The Institute of Nuclear Physics of Republic of Kazakhstan, Astana, Kazakhstan i Ural Federal University Named After the First President of Russia B.N. Yeltsin, Yekaterinburg, Russia b c

a r t i c l e i n f o

a b s t r a c t

Article history: Received 2 December 2018 Received in revised form 25 February 2019 Accepted 26 February 2019 Available online 28 February 2019

M-type hexagonal ferrites with heterovalent substitutions (Nd3þ-Zn2þ and Ti4þ) were synthesized. X-Ray diffraction (XRD) powder patterns of Sr(Nd,Zn)xFe12-xO19 and BaFe12-xTixO19 (0.1  x  1.0) confirmed the single phase constitution of all investigated samples. High frequency magnetic (permeability), electrical (permittivity), and resonant properties were analyzed. Unexpected behavior in the permittivity and permeability as a function of frequency was observed. Appearance of two peaks for samples with x ¼ 0.1 and 0.9 indicated mixed oxidation state for the Fe ions. Behavior for Sr(Nd,Zn)xFe12-xO19 (0.3  x  0.7) confirms the occurrence of the anomalous quantum effect, namely charge disproportionation. The permeability behavior of Ti-substituted samples with a double Fe oxidation state was theoretically discussed in terms of spin states crossover. The behavior of reflection losses for Sr(Nd,Zn)xFe12-xO19 and BaFe12-xTixO19 (0.1  x  1.0) samples was discussed in terms of the modalities of charge ordering in heterovalent substituted M-type hexaferrites. © 2019 Elsevier B.V. All rights reserved.

Keywords: Hexagonal ferrites Heterovalent substitution Quantum effects Microwave characteristics

1. Introduction Transition metal oxides with strong correlations between functional properties attract enormous attention due to a wide spectrum of unusual electronic and magnetic phenomena, caused by cooperative effects of charge and spin-orbit ordering [1e5]. This class of materials demonstrates quantum phenomena such as hightemperature superconductivity, Bose-Einstein condensation of magnons, and multiferroicity (the coexistence of magnetic and ferroelectric ordering). Many researchers have focused on complex metal oxides based on Fe ions. One of the most attractive systems

* Corresponding author. South Ural State University, 454080, Chelyabinsk, Russia. E-mail address: [email protected] (A.V. Trukhanov). https://doi.org/10.1016/j.jallcom.2019.02.303 0925-8388/© 2019 Elsevier B.V. All rights reserved.

for research are M-type hexaferrites and their solid solutions with different substitutions [6e9]. Until recently, hexaferrites were widely used only as magnets with a large magnetic force or as permanent magnets [10] and applied in magnetic storage media with perpendicular type of magnetization [11]. From a practical standpoint, hexagonal ferrites and compounds based on them also have great potential as materials for high frequency electromagnetic applications, such as in the effective absorption of microwaves which can provide electromagnetic compatibility (EMC) for special sensitive equipment [12,13]. The primary advantages of hexaferrites include large magneto-crystalline anisotropy, as well as a high ferrimagnet-paramagnet phase transition temperature, which result in efficient absorption in the high frequency band (20e80 GHz, 5G) [14e16]. Several studies also discuss the electromagnetic properties of magnetic oxides and their composites

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[17e19] and the multiferroic properties of hexaferrites [20,21]. The crystal structure of M-type hexaferrites is rather complex. The unit cell contains 5 nonequivalent oxygen environments or sublattices (three octahedral, one tetrahedral and one bipyramidal) with Fe ions located at the respective centers [22]. In the unsubstituted hexaferrite, the charge state of iron is Fe3þ. Collinear ferrimagnetic ordering develops, with aCurie temperature ~740 K due to strong sublattice exchange interactions [23]. Two main methods (based on changing the chemical composition) to control magnetic and absorption properties are: replacement of Fe3þ ions with ions of the same oxidation state (D3þ) or isovalent substitution [24,25] and replacement with ions of a different oxidation state (D2þ, D4þ or D5þ) or aliovalent substitution [26]. Both types of substitutions lead to frustration of the magnetic structure and weakening of the exchange interactions (due to decrease in the number of FeeO bonds). As a result, we can observe deviations from strict collinearity of magnetic moments. Aliovalent substitution results in a number of additional effects owing to the change in the Fe oxidation state, resulting in different configurations of electron shells and energy of quantum states. This uniquely affects electric, magnetic and microwave properties. In case of isovalent substitution, the Fe charge state does not change. For aliovalent substitution, a number of extremely interesting fundamental effects can be observed due to change in the Fe oxidation state. When a substitution is performed with divalent ions (D2þ) a part of Fe3þ ions (quantitatively equal to the

concentration of D2þ ions) should change the charge state to Fe4þ. On the other hand, when a substitution performed with tetravalent ions (D4þ), a part of Fe3þ ions should change the charge state to the Fe2þ. All three iron charge states are characterized by different configuration of electron shells and the energy of quantum states. For each local anionic environment, energies of the electronic states of Fe are different (different nature of degeneracy removal in the local crystal field). As a result, solid solutions of hexaferrites with aliovalent substitutions must exhibit new and even unique magnetic and microwave properties. It should be noted that in hexaferrites with Fe in a mixed valence state, anomalous effects of charge and spin ordering are theoretically possible. Thus, for Fe4þ ions, effects of charge disproportionation can be observed. Similarly, a crossover of spin states can be detected for Fe2þ ions. The development of the Internet, mobile technology and digital networks requires an increase in the speed and volume of the transferred information. This requires shifting from a centimeter to a millimeter wavelength range, corresponding to frequencies of 10e100 GHz. M-type hexaferrites, having large magneto crystalline anisotropy fields, are capable of operating in this frequency band as switches, circulators, phase shifters, elements of transceiver antennas, as well as effective absorbers of electromagnetic radiation (EMR) for improving the electromagnetic compatibility (EMC). Isovalent doping of barium hexaferrite with various diamagnetic ions (D3þ) facilitates tailoring of magnetic characteristics and, consequently, control of the operating frequency range. Depending on the type and level of substitution, the transmission and absorption spectra of BaFe12-xDxO19 (D ¼ Al3þ, In3þ and Ga3þ) display a change in the frequency and amplitude of the maximum

Fig. 1. XRD powder patterns for Sr(Nd,Zn)xFe12-xO19 (0.0  x  1.0) hexaferrites.

Fig. 2. XRD powder patterns for BaFe12-xTixO19 (0.0  x  1.0) hexaferrites.

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c, Å

V, Å3

c2

)xO19 5.881 5.885 5.883 5.888 5.884 5.885 5.886

23.048 23.049 23.047 23.036 23.055 23.037 23.049

687.97 648.99 640.96 690.97 691.26 691.20 691.20

1.93 1.74 1.47 1.11 1.44 1.29 1.58

superexchange interactions. It is well known that two main mechanisms are responsible for the selective absorption of EMR in complex magnetic oxides: resonances of domain boundaries and rotation of magnetization vector (NFMR). At elevated frequencies, the main contribution to absorption comes from NFMR. The operating frequencies for ferrites are determined by the frequency dispersion range where magnetic permeability undergoes strong variations, that is, near the NFMR. The frequency of NFMR for un-substituted BaFe12O19 is about 50 GHz and if the demagnetizing effects are neglected, it depends on the internal uniaxial anisotropy field Ha .

5.894 5.893 5.890 5.886

23.205 23.213 23.234 23.279

698.33 698.11 698.07 698.40

1.77 1.58 1.48 1.63

ur ¼ gHa

Table 1 Main structural parameters of Sr(Nd,Zn)xFe12-xO19 and BaFe12-xTixO19 (1.0  x  1.0) hexaferrites obtained from XRD data. Composition 3þ

SrFe12-x(Nd -Zn 0 0.1 0.3 0.5 0.7 0.9 1.0 BaFe12-xTixO19 0 0.1 0.5 1.0

a, Å 2þ

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absorption (associated with the natural ferromagnetic resonance (NFMR)) owing to the corresponding change in the crystalline magnetic anisotropy [14,15,17]. Additional contribution to the anisotropy field may arise from the occurrence of internal stresses and microdeformations. The change in crystalline anisotropy can be explained by the weakening of stiffness of the intrasublattice

(1)

here ur is the frequency of NFMR, and g is the gyromagnetic ratio. Typically, the NMFR region in polycrystalline ferrites is very broad due to the distribution of ur over several crystals (or grains). The demagnetizing effects cannot be neglected if the saturation magnetization Ms is not small. Moreover, due to difference in the shape of the crystals, the demagnetizing factors are not the same. If the crystals are magnetized along the hexagonal easy axis by an external magnetic field H0 , the resonance frequency is of the form:

Fig. 3. SEM images of Sr(Nd,Zn)xFe12-xO19 x ¼ 0.1 (a), 0.5 (b), 0.9 (c) and BaFe12-xTixO19 x ¼ 0.1 (d), 0.5 (e), 1.0 (f).

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ur ¼ gðH0 þ Ha þ ðNt  Nl ÞMs Þ

(2)

In Eq. (2), it is considered that the crystallites have the shape of an ellipsoid of rotation. Nt  Nl is the difference between the transverse and longitudinal demagnetizing factors, which depends on the ratio of the crystal dimensions. Therefore, by controlling the internal parameters Ha and Ms by the concentration of substituent ions, we can change the parameters of NFMR (resonance frequency and line width). Due to their large magneto crystalline anisotropy, M-type hexaferrites are capable of operating within the 30e100 GHz frequency range for applications in high frequency functional devices (antenna, circulators, switches etc.) as well as absorption materials for EMC [27e29]. In this study, the influence of aliovalent substitution (with Nd3þ2þ Zn and Ti4þ ions) on electromagnetic properties of M-type hexaferrites SrFe12-x(Nd,Zn)xO19 and BaFe12-xTixO19 (0.1  x  1.0) has been investigated. The observations have been explained on the basis of quantum phenomena (crossover of spin states and charge disproportionation) caused by fine charge ordering in these materials. 2. Experimental Samples were synthesized using standard methods [30,31]. The Sr(Nd,Zn)xFe12-xO19 samples were grown using citrate sol-gel method. Nitrates of corresponding ions (Fe3þ, Sr2þ, Nd3þ, and Zn2þ) were mixed in stoichiometric ratio and citric acid and deionized water were added at a temperature of 355 K. The BaFe12xTixO19 samples were synthesized using solid state reaction method. The crystal structure and phase composition of samples were investigated using X-ray diffraction (XRD) with Cu Ka radiation (Rigaku D/MAX-2400, Japan) [30]. The microstructure was analyzed by scanning electron microscopy (SEM) (Hitachi S-4800, Japan). Frequency dependences of permeability and permittivity were investigated by co-axial method using Agilent network analyzer in the wide frequency range. Impedance of the co-axial line was normalized (Z ¼ 50 Ohm). Based on the obtained values of permittivity and permeability, we calculated the reflection coefficient [32]. For this, we used the formula from the theory of propagation of an electromagnetic wave in a transmission line:

Zin ¼ Z0

rffiffiffiffiffi mr 2pft pffiffiffiffiffiffiffiffiffi tanh j mr εr c εr

  Z  Z 0   RL ¼ 20lg in Zin þ Z0 

samples. An impurity hematite phase Fe2O3 is also present with space group R-3c, having six molecules in the unit cell (Z ¼ 6). This is the result of slight a dissolution of SrO*Fe2O3 (tetragonal lattice) in M-type hexaferrites. This impurity phase formation can be eliminated by introducing a small amount of SrO (0.4 mol%.) during the synthesis. The features of the crystal structure (a and c unit cell parameters and V e volume of unit cell) for each sample were obtained from the XRD data (Table 1). XRD patterns were processed using Rietveld Refinement (FullProf. Software). The analysis of the following parameters: Rwp (weighted profile R-value), Rexp (expected R-value), RB (Bragg R-factor) and c2 (goodness-of-fit quality factor), obtained after refinement, suggests that the investigated samples are of good quality and the refinements are adequate. The main structural parameters of Sr(Nd,Zn)xFe12-xO19 and BaFe12-xTixO19 (0.0  x  1.0) hexaferrites are summarized in Table 1. It should be noted that lattice parameters a and c fluctuate with increasing x in Sr(Nd,Zn)xFe12-xO19 hexaferrites as a result of the differences in the ionic radii between Fe3þ (0.64 Å), Nd3þ (0.98 Å), and Zn2þ (0.74 Å). Since Nd3þ and Zn2þ ions have greater ionic radii than Fe3þ, even equivalent amounts of Nd3þ and Zn2þ ions substituted for Fe3þ may cause fluctuations in the lattice parameters. For BaFe12-xTixO19 hexaferrites, aliovalent substitution of Fe3þ with Ti4þ may cause changes in the iron oxidation state from Fe3þ to Fe2þ. It can also induce the formation of vacancies (anion deficit site) to maintain electroneutrality. The effect of Ti substitution on cell parameters can be seen from Table 1. This behavior is limited by

(3)

(4)

where Zin is the input impedance of the sample, Z0 is the impedance of air, εr and mr are the relative complex permittivity and permeability, f is the frequency, t is the thickness of the sample and c is the velocity of light. 3. Results and discussion 3.1. Structural data Figs. 1 and 2 show the XRD powder patterns of Sr(Nd,Zn)xFe12and BaFe12-xTixO19 (0.0  x  1.0) hexaferrites, respectively. All samples reveal the formation of M-type hexaferrite with a hexagonal crystal structure and space group P63/mmc (No. 194) having two molecules in the unit cell (Z ¼ 2). Presence of minor impurities is observed for Sr(Nd,Zn)xFe12-xO19 (x ¼ 0.1 and 0.3)

xO19

Fig. 4. Histograms of the crystallite size distribution for the Sr(Nd,Zn)xFe12-xO19 (x ¼ 0.1, 0.5 and 0.9) (a) and BaFe12-xTixO19 (x ¼ 0.1, 0.5 and 1.0) (b) hexaferrites.

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the differences in ionic radii (r(Ti4þ) ¼ 0.42 Å and r(Fe3þ) ¼ 0.64 Å) and concentration of titanium ions. Concentration of Ti4þ is equal to concentration of Fe2þ. Correlation of these two competing factors, namely the ionic radii of Ti4þ, Fe3þ, and Fe2þ and their concentrations, leads to concentration behavior of the main structural parameters. Fig. 3 shows SEM images of Sr(Nd,Zn)xFe12-xO19 (Fig. 3aec) and BaFe12-xTixO19 (Fig. 3def) (0.0  x  1.0) hexaferrites. The samples have a hexagonal-plate structure with a high rate of agglomeration. The samples represent densely packed polycrystals (>96%) with an average crystallite size between 500 nm and 15 mm. It is interesting that the average density of the (Nd,Zn)-substituted samples is higher in comparison with the Ti-substituted ones. It is obvious that the average grain size for Sr(Nd,Zn)xFe12-xO19 hexaferrites is lower than that for BaFe12-xTixO19 hexaferrites. Increase in the concentration of Nd, Zn ions leads to an insufficient increase in the average grain size of Sr(Nd,Zn)xFe12-xO19 samples. At the same time, increase in the concentration of Ti ions leads to an increase in the average grain size of BaFe12-xTixO19 samples. This behavior can be observed from the SEM images (Fig. 3) and from the grain size analysis (Fig. 4). We can assume that this is due to difference in the ionic radii of the diamagnetic ions Al3þ (0.535 Å) and In3þ (0.812 Å). Larger Nd3þ (0.98 Å) and Zn2þ (0.74 Å) ions induce the formation of bigger hexaferrite crystallites due to an increase in the microstress on their surface [23]. This leads to an increase in defect surface area and, as a result, contributes to the growth of the crystallites. 3.2. Electrodynamics characteristics The electromagnetic parameters measured in centimeter waves are shown in Fig. 5. This demonstrates real ε0 and imaginary ε} parts

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of permittivity as a function of the frequency for Sr(Nd,Zn)xFe12(0.1  x  0.9) and BaFe12-xTixO19 hexaferrites. Real (Fig. 5a and c) and imaginary (Fig. 5b and d) parts of ε have complex behavior for all samples and depend on frequency. In the range of 5e18 GHz nonlinear behavior was observed. As is evident from Fig. 5, the total value of the real and imaginary parts of permittivity is low for all samples. Average values of permittivity for Sr(Nd,Zn)xFe12-xO19 hexaferrites are higher than for BaFe12-xTixO19 hexaferrites. From analysis of Fig. 5a and c, we can conclude that the main peak for each sample is in the range of 10e12 GHz. However, for the compound with x ¼ 0.9 we observed a second peak in higher frequency region (14e15 GHz). It is widely known that the imaginary part of ε corresponds to electrical losses in materials. As a rule, in complex oxides, there occurs only one peak in ε}. A second peak can correspond to a second (impurity) phase or some changes in the electronic structure of the material. Based on previous results for phase composition and crystal structure, we can assume that the second peak arises due to electronic structure frustration. It can be due to the presence of Fe ions with oxidation states other than 3 þ in Sr(Nd,Zn)xFe12-xO19 (0.1  x  0.9) hexaferrites. As was mentioned in the introduction, aliovalent substitution (Zn2þ - aliovalent ions) can lead to changes in oxidation state of Fe ions and some electronic effects can be observed. Concentration of Fe ions with altered oxidation state is proportional to the concentration of Zn ions. However, a large fraction of Fe ions remains in the Fe3þ oxidation state. Concentration for Fe ions with altered oxidation state is x/2 for Sr(Nd,Zn)xFe12-xO19 (0.1  x  0.9) hexaferrites. The most probable Fe oxidation state for aliovalent substitution is Fe4þ (to preserve electroneutrality in samples). The low-intensity values were observed for BaFe12-xTixO19 xO19

Fig. 5. Frequency dependences of the real (a,b) and imaginary and (c,d) parts of permittivity for Sr(Nd,Zn)xFe12-xO19 (a, c) and BaFe12-xTixO19 (b, d) (0.0  x  1.0) hexaferrites.

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Fig. 6. Frequency dependences of the real (a,b) and imaginary and (c,d) parts of permeability for Sr(Nd,Zn)xFe12-xO19 (a, c) and BaFe12-xTixO19 (b, d) (0.0  x  1.0) hexaferrites.

conductivity. Non-monotonic variation of dielectric properties can be explained using statistical distribution of Ti ions in oxygen environments. The imaginary part of dielectric permittivity decreases with increase in concentration of Ti ions (Fig. 5d). Negative values for the imaginary part of BaFe11Ti1O19 (x ¼ 1.0) and BaFe11.5Ti0.5O19 (x ¼ 0.5) samples can be also explained by increase of hopping-type conductivity contribution to ε}. For analysis of the magnetic structure of samples and the magnetic state of Fe ions, we performed measurements of magnetic spectra (real m0 and imaginary m} part of permeability). Fig. 6 shows the frequency dependence of permeability for Sr(Nd,Zn)xFe12-xO19 and BaFe12-xTixO19 (0.1  x  1.0) hexaferrites in the range of the NFMR. It is interesting that permeability data shows good correlation with permittivity data for Sr(Nd,Zn)xFe12-xO19 hexaferrites (Fig. 6a and c and Fig. 5a and c). Presence of second peaks for Sr(Nd,Zn)xFe12-xO19 hexaferrites with x ¼ 0.1 and 0.9 confirm double oxidation state for iron ions Imaginary part of permeability corresponds to magnetic losses in materials in the high frequency region. The frequency of the peaks in the permeability confirms that the source of electrical and magnetic losses is the crystal field of the Fe ions. Electrical losses can be explained by the overlapping

hexaferrites due to specific characteristics of the measurement system. However, the absolute value of ε is strongly dependent on Ti ionic content. In un-substituted BaFe12O19 the value of permittivity ε0 ~3.5 shows good correlation with literature. Permittivity 0 values in the range of ε ~7.5e11 were observed in BaFe12O19 ceramics produced via wet chemistry method (co-precipitation). A value of ε0 ~2.1 was observed for the pure Ba-hexaferrite produced by combustion method. In this case, the real part of permittivity did not depend on frequency in the range of 8e12 GHz. Our result of ε0 ~3.5 observed in this paper for un-substituted BaFe12O19 correlates perfectly with previous results obtained in this frequency range. Aliovalent substitution with Ti ions leads to sufficient increase of ε0 and as high as ε0 ~6.2 was reached for BaFe11Ti1O19 (x ¼ 1.0) sample. But, the increase of real part of permittivity wasn't proportional to the titanium ions concentration. From Fig. 5b we can conclude that for BaFe11Ti1O19 (x ¼ 1.0) and BaFe11.5Ti0.5O19 (x ¼ 0.5) samples the values of ε0 are very similar. Lower values of permittivity obtained for the Ti-substituted samples (in comparison with (Nd,Zn)substituted samples) may be a result of the mixed valence of the Fe ions (coexistence of Fe3þ and Fe2þ ions). This leads to decrease in the dielectric constant due to the enhancement of hopping-type

Table 2 Effective concentrations of the B-sites ions as part of formula unit for Sr(Nd,Zn)xFe12-xO19 (0.1  x  0.9) hexaferrites. x

C(Fe3þ) in f.u.

C(Nd3þ) in f.u.

C(Zn2þ) in f.u.

C(Fe4þ) in f.u.

C(Fe5þ) in f.u. for Ch. Disp.

Total B-sites concentration

0.1 0.3 0.5 0.7 0.9

11.85 11.625 11.375 11.125 10.65

0.05 0.15 0.25 0.35 0.45

0.05 0.15 0.25 0.35 0.45

0.05 e e e 0.45

e 0.075 0.125 0.175 e

12 12 12 12 12

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of delocalized electron wave functions (in FeeO chemical bonds). Magnetic losses are due to the characteristics of the electronic configuration of localized d-electrons. In this regard, the appearance of the second peak in permeability can only be due to a change in the electronic structure of the samples during aliovalent substitution (transition of part of Fe3þ ions to Fe4þ oxidation state). Moreover, an interesting fact is that a clear second peak is observed only for the minimum (x ¼ 0.1) and the maximum (x ¼ 0.9) concentrations. This may be due to the competition of two factors: i. the charge state of Fe ions for electroneutrality, and ii. the influence of the crystal field energy. Presence of second peaks for compounds with x ¼ 0.1 and 0.9 confirms double oxidation state for Fe ions. In addition, this can theoretically confirm our assumption regarding charge disproportionation for compounds with x ¼ 0.3, 0.5 and 0.7 under the influence of the crystal field energy. Moreover, if there is a clear second peak for compositions 0.1 and 0.9, it can correspond to the charge state Fe4þ. For other compounds (x ¼ 0.3, 0.5 and 0.7), the absence of a clear second peak may be due to the charge disproportionation of a part of Fe4þ under the influence of the crystal field energy. Charge disproportionation is one of the most unconventional ways of changing the energy of a system when the ground state is reached. This phenomenon is a kind of charge ordering in multicomponent transition metal oxides with a high oxidation degree such as Fe4þ (3d4). In such materials, a temperature change can induce charge redistribution among equivalent crystallographic positions (according to the following scheme: 2Fe4þ ¼ Fe3þ þ Fe5þ). This charge redistribution often leads to superstructure formation. Thus, based on our assumption (charge disproportionation for compounds with x ¼ 0.3, 0.5 and 0.7), we have double oxidation state for Fe ions: Fe3þ and Fe5þ. In addition, effective concentration of Fe4þ ions is equal to x/2. In case of charge disproportionation according to the following scheme: 2Fe4þ ¼ Fe3þþFe5þ concentration of Fe5þ ions in two times lower than concentration of Fe4þ ions and in four times lower than x. We did not observe this probably due to extremely low concentration of Fe5þ ions. For electroneutrality in Nd,Zn-substituted Sr hexaferrites, the concentration of Fe4þ ions must be proportional to that of Zn ions. This is because the concentrations of Nd3þ and Zn2þ are equal: C(Nd3þ) ¼ C(Zn2þ). Hence, Nd3þ þ Zn2þ ¼ x, and thus C(Zn2þ) ¼ x/2. In addition, effective concentration of Fe4þ ions is equal to x/2. In case of charge disproportionation according to the following scheme: 2Fe4þ ¼ Fe3þ þ Fe5þ, the concentration of Fe5þ ions is two times lower than concentration of Fe4þ ions and four times lower than x. Due to this reason, we have extremely low concentrations of Fe5þ ions for compounds with x ¼ 0.3, 0.5 and 0.7 and do not observe a clear second peak. Table 2 shows the results of numerical calculations of the effective concentrations of B-sites ions (Fe/Nd,Zn) as a part of a formula unit. In Fig. 6 b and d, the dependence of the real part of magnetic permeability for BaFe12-xTixO19 samples is shown. For unsubstituted Ba-hexaferrite, the average value is m0 ~0.95 which shows good agreement with previous data for BaFe12O19 produced by sol-gel method. In our case, the real part of magnetic permeability for BaFe11.5Ti0.5O19 (x ¼ 0.5) and BaFe11Ti1.0O19 (x ¼ 1.0) hexaferrites was observed to be in the range of m0 ~1.0e1.15. Imaginary part of magnetic permeability for BaFe12-xTixO19 samples was observed to be m}~ (0.22) with minor variation with frequency, for all samples. Non-linear behavior of real and imaginary parts of permeability can be explained by the processes inducing high-frequency losses, associated with the magnetization in its own magnetic anisotropy field. These frequencies (frequencies of maximum magnetic losses) correspond to the frequencies of spin precession. The non-linear behavior of magnetic permeability for samples with a mixed valence state of Fe can be theoretically

1199

Fig. 7. Frequency dependences of the reflection losses for Sr(Nd,Zn)xFe12-xO19 (a) and BaFe12-xTixO19 (b) (0.1  x  1.0) hexaferrites.

described by the effect of the spin states crossover. Spin states crossover is a quantum mechanical effect. Fe2þ ions contain six electrons in the d-shell (3d6). Depending on the splitting ratio under the local crystal field (Dcf) between t2g and eg levels and the Hund energy (Jh) for the most abundant Fe2þ ion, both low-spin (LS, 6t2g-0eg, S ¼ 0) and high-spin (HS, 4t2g-2eg, S ¼ 2) configurations are possible. Theoretical predictions have been made about a possible intermediate state - a configuration with an intermediate spin (IS, 5t2g-1eg, S ¼ 1). The splitting in the crystal field is entirely

Table 3 Main amplitude-frequency characteristics for Sr(Nd,Zn)xFe12-xO19 and BaFe12xTixO19 (b) (0.1  x  1.0) hexaferrites: Ares (amplitude of resonance); Fres (resonant frequency); Wres (resonance peak width at half height). x

Ares (dB)

Sr(Nd,Zn)xFe12-xO19 0.1 39.81 0.3 50.95 0.5 43.32 0.7 45.07 0.9 29.22 BaFe12-xTixO19 P0 0.1 14.3 0.5 8.97 1.0 45.3

P00 e 15.56 29.4

Fres (GHz)

Wres (GHz)

10.77 11.15 10.24 12.19 10.94

2.01 1.15 1.65 1.67 3.33

P0 10.75 9.5 9.29

P00 e 11.2 10.19

P0 1.61 0.83 0.07

P00 e 1.94 0.54

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determined by local oxygen environment of Fe ions. In the case of domination of Jh in an octahedral coordination, the HS state (S ¼ 2) of Fe2þ ion is realized, which causes distortion in the arrangement of the ligands. Local distortions in the crystal structure can not only lead to changes in the parameters of the exchange interaction (changes in the FeeO bond lengths and FeeOeFe bond angles), but also to the formation of a nonzero electric dipole moment (spontaneous electric polarization). As Dcf increases, a stable LS state (S ¼ 0) can be realized. The possibility of realizing an IS state (S ¼ 1) is being actively discussed, and the corresponding calculations consider the spin-orbit interaction and quantum instability in both t2g and eg levels of the 3d-shell. Due to a fine balance between Dcf

and Jh in BaFe3þ12-2x Fe2þ xD4þxO19, the crossover between LS and HS states can be observed experimentally: the LS state observed at low temperatures changes to the magnetic IS or HS state at high temperatures. 3.3. Microwave properties Amplitude-frequency characteristics of resonance are critically dependent on the features of magnetic fine structure (charge ordering and magnetic state of Fe ions). Modification of the chemical composition by diamagnetic substitution with nonmagnetic ions changes the electromagnetic parameters. Fig. 7a

Fig. 8. Concentration dependences of the main amplitude-frequency characteristics for Sr(Nd,Zn)xFe12-xO19 (aec) and BaFe12-xTixO19 (def) (0.0  x  1.0) hexaferrites: a, d) Ares (amplitude of resonance); b, e) Fres (resonant frequency); c, f) Wres (resonance peak width at half height).

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and b demonstrate reflection or return losses for Sr(Nd,Zn)xFe12(7a) and BaFe12-xTixO19 (7b) (0.1  x  1.0) hexaferrites in the range of the NFMR. Table 3 shows the main amplitude-frequency characteristics for Sr(Nd,Zn)xFe12-xO19 and BaFe12-xTixO19 (b) (0.1  x  1.0) hexaferrites obtained from the fitting of the frequency dependences of reflection losses (RL). As main parameters, we determined e resonant frequency (Fres ) or maximal value (in modulus) of reflected EMR attenuation; resonance amplitude (Ares ) or position of Fres ; and resonance peak width at half height (Wres ). For all Sr(Nd,Zn)xFe12-xO19 (0.1  x  0.9) hexaferrites attenuation was observed in reflected electromagnetic energy in the frequency range of 8e15 GHz. This can be explained by the NFMR in the material. The local minimum of frequency dependence or maximal value (in modulus) of attenuation corresponds to Fres . Data for RL as a function of frequency is shown in Figs. 5 and 6. As it is seen from the reflection data, the increase in concentration x in Sr(Nd,Zn)xFe12-xO19 leads to non-linear changes in Fres . It was observed that the values of Fres do not strongly correlate with the level of chemical substitution. However, for Sr(Nd,Zn)xFe12-xO19 hexaferrites with x ¼ 0.1 and x ¼ 0.9, very similar values of Fres were obtained (Table 3). This change in Fres can be explained by non-linear deviations in the magneto crystalline anisotropy field. This shows good agreement with magnetic measurements performed earlier. Minimal values (as modulus) of amplitude were obtained for x ¼ 0.1 and x ¼ 0.9, which decreases from 39.81 dB (for 0.1) to 29.22 dB (for 0.9). This can be explained by the decrease of Fe3þ content due to due to non-magnetic substitution. Maximal values of Ares (as modulus) were observed for compounds with x ¼ 0.3, 0.5 and 0.7 (Fig. 8b and Table 3), due to charge disproportionation in Fe ions. On comparing the values of Wres (Fig. 8c), we observe that most narrow peaks are typical for compounds with x ¼ 0.3, 0.5 and 0.7. For Sr(Nd,Zn)xFe12-xO19 hexaferrites with x ¼ 0.1 and 0.9, broad peaks are observed. This can be the result of overlapping peaks for reflection from Fe3þ ions and Fe4þ ions (first and second peaks of permeability and permittivity). For all BaFe12-xTixO19 (0.1  x  1.0) samples, attenuation was observed in the reflected electromagnetic energy in the frequency range of 8e12 GHz. This can be explained by the NFMR, like in case of Sr(Nd,Zn)xFe12-xO19 samples. Data for RL is in agreement with frequency dependences of the permittivity and permeability (Figs. 5 and 6). However, for samples BaFe12-xTixO19 with x ¼ 0.5 and 1.0 we observed presence of a second peak. At the same time, for the Ti-substituted sample with the lowest concentration (x ¼ 0.1), only one broad peak could be observed. It can be assumed that the occurrence of the second peak can be the result of the mixed valence state of Fe ions (Fe3þ-Fe2þ). For compounds with x ¼ 0.5 and 1.0, the second peak is clearly seen. For x ¼ 0.1, the broad peak may be the result of two overlapping peaks (with low intensities). It must be noted that the average width (Wres ) for Tisubstituted samples decrease with increase in the content of Ti4þ ions. Intensity of the RL peaks (Fres ) increase with increase in the content of Ti4þ ions. This can be explained by features of the indirect exchange interactions in BaFe12-xTixO19 (0.1  x  1.0) samples where the Fe ions are in a mixed valence state. An increase in the concentration of Ti ions leads to an increase in the concentration of bivalent iron (Fe2þ). This enhances the interlattice double exchange (Fe2þeOeFe3þ) and superexchange (Fe3þeOeFe3þ) interactions. And also it presumably weakens the interlattice superexchange interactions Fe3þeOeFe3þ. xO19

4. Conclusions Single-phase Sr(Nd,Zn)xFe12-xO19 and BaFe12-xTixO19 (0.1  x  1.0) samples were produced. All samples revealed the

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formation of M-type hexaferrite with space group P63/mmc (No. 194). Anomalous behavior was observed in the frequency dependences of the permittivity and permeability for Sr(Nd,Zn)xFe12xO19 (0.1  x  1.0) samples. Presence of a second peak, for compounds with x ¼ 0.1 and 0.9, confirms double oxidation state for the Fe ions. In addition, this theoretically confirms our assumption for charge disproportionation in compounds x ¼ 0.3, 0.5 and 0.7, under the influence of the crystal field energy. Reflection losses were measured as a function of frequency for all Sr(Nd,Zn)xFe12-xO19 and BaFe12-xTixO19 (0.1  x  1.0) samples. It was demonstrated that the values of Fres have no strong correlation with the level of substitution for Sr(Nd,Zn)xFe12-xO19 samples while strong correlations were observed for BaFe12-xTixO19 samples. This can be explained by the features of indirect exchange interactions in BaFe12-xTixO19 (0.1  x  1.0) samples, where Fe ions are in mixed valence state. An increase in the concentration of titanium ions leads to an increase in the concentration of bivalent iron (Fe2þ). This enhances the interlattice double exchange (Fe2þeOeFe3þ) and the interlattice superexchange interactions (Fe3þeOeFe3þ). Acknowledgements The work was supported by Act 211 Government of the Russian Federation, contract N 02.A03.21.0011. And also it was performed with partial financial supports from the Ministry of Education and Science of the Russian Federation in the framework of Increase Competitiveness Program of NUST « MISiS» (grants No. П02-20172-4, No. К3-2018-026, No. К4-2017-041) and SUSU (grant No. 4.1346.2017/4.6). Financial supports from Institute for Research & Medical Consultations (IRMC) of Imam Abdulrahman Bin Faisal University (IAU e Saudi Arabia) are greatly acknowledged [Grant No. 2018-IRMC-S-1]. The Core Labs of King Abdullah University of Science and Technology (KAUST) are greatly acknowledged for their technical assistance. Electromagnetic measurements were performed at the expense of a grant from the Russian Science Foundation (project No. 18-79-00154). References [1] M. Basini, A. Guerrini, M. Cobianchi, F. Orsini, D. Bettega, M. Avolio, C. Innocenti, C. Sangregorio, A. Lascialfari, P. Arosio, Tailoring the magnetic core of organic-coated iron oxides nanoparticles to influence their contrast efficiency for magnetic resonance imaging, J. Alloys Compd. 770 (2019) 58e66. [2] S.V. Trukhanov, D.P. Kozlenko, A.V. Trukhanov, High hydrostatic pressure effect on magnetic state of anion-deficient La0.70Sr0.30MnOx perovskite manganites, J. Magn. Magn. Mater. 320 (2008) 88e91. [3] Liwei Qian, Jingguang Peng, Zhen Xiang, Yifan Pan, Wei Lu, Effect of annealing on magnetic properties of Fe/Fe3O4 soft magnetic composites prepared by insitu oxidation and hydrogen reduction methods, J. Alloys Compd. 778 (2019) 712e720. [4] V.A. Ketsko, E.N. Beresnev, M.A. Kop’eva, L.V. Elesina, A.I. Baranchikov, A.I. Stognii, A.V. Trukhanov, N.T. Kuznetsov, Specifics of pyrohydrolytic and solid phase syntheses of solid solutions in the (MgGa2O4)x(MgFe2O4)1ex system, Russ. J. Inorg. Chem. 55 (2010) 427e429. [5] A.V. Trukhanov, S.V. Trukhanov, V.G. Kostishin, L.V. Panina, M.M. Salem, I.S. Kazakevich, V.A. Turchenko, V.V. Kochervinskii, D.A. Krivchenya, Multiferroic properties and structural features of M-type Al-substituted barium hexaferrites, Phys. Solid State 59 (4) (2017) 737e745. [6] L. Wang, H. Yu, X. Ren, G. Xu, Magnetic and microwave absorption properties of BaMnxCo1xTiFe10O19, J. Alloys Compd. 588 (2014) 212e216. [7] P. Meng, K. Xiong, L. Wang, S. Li, Y. Cheng, G. Xu, Tunable complex permeability and enhanced microwave absorption properties of BaNixCo1xTiFe10O19, J. Alloys Compd. 628 (2015) 75e80. [8] Kyoung-Seok Moon, Eun-Soo Lim, Young-Min Kang, Effect of Ca and La substitution on the structure and magnetic properties of M-type Sr-hexaferrites, J. Alloys Compd. 771 (2019) 350e355. [9] Weihu Zhang, Qishan Zhu, Rujun Tang, Hao Zhou, Jianmin Zhang, Jiaxing Jiang, Hao Yang, Xiaodong Su, Temperature dependent magnetic properties of conical magnetic structure M-type hexaferrites BaFe10.2Sc1.8O19 and SrFe10.2Sc1.8O19, J. Alloys Compd. 750 (2018) 368e374. [10] E. Richter, T.J.E. Miller, T.W. Neumann, et al., IEEE Trans. Ind. Appl. 644 (1985) 21e32.

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