1 Introduction

The hexaferrites have been widely studied for several decades because of the practical and potential applications in permanent magnets, magnetic recording media, high frequency electromagnetic wave absorbers and stealth technologies [1,2,3,4,5,6,7,8,9,10]. Particularly, Y-type hexaferrites, which correspond to nominal compositions of Ba2Me2Fe12O22 (Me = Mg, Co, Zn, etc.), were found to be multiferroic materials with magnetoelectric coupling [11,12,13,14,15,16,17,18]. The molecular unit of Y-type hexaferrites is constructed by one S and one T block. The S block (with a unit formula Me2Fe4O8) is formed by two spinel units and the T block (Ba2Fe8O14) is made of four oxygen layers, in which Fe ions occupy both tetrahedral and octahedral sites while Ba2+ always replace O2− ions somewhere in the oxygen lattice [2, 19, 20]. The special spiral magnetic structure of Y-type hexaferrites make the presence of ferroelectric polarization induced by applied magnetic field.

Ba2Co2Fe12O22 is the first discovered ferroxplana ferrite with an easy plane of magnetization perpendicular to the c-axis and exhibits attractive magnetic and dielectric properties [2, 16, 21]. Recently, in Sr-doped Y-type hexaferrites, the ferroelectric polarization induced by magnetic field could be observed at higher temperatures compared with undoped samples [11, 12, 22,23,24,25]. In addition, the dielectric properties are highly important for the application of multiferroic materials, especially for the microminiaturization of the electric devices [26, 27]. However, there are only a few studies on the dielectric properties of Sr-doped hexaferrites so far. [28, 29]. Therefore, the understanding of Sr doping effect on the dielectric properties of hexaferrites is still lacking.

In this work, systematic studies on the structural and dielectric properties of Sr-doped Ba2Co2Fe12O22 ceramics are performed. The result shows that dielectric constant presents different variation tendencies at 300 K and 600 K with increasing Sr doping content. The dielectric relaxation mechanisms and Sr doping effect are analyzed from the measurements of dielectric constant and dielectric loss. Afterwards the high temperature features are discussed based on the measurements and fits of impedance spectra and conductivity.

2 Experimental procedure

Polycrystalline ceramic samples of Ba2−xSrxCo2Fe12O22 (0 ≤ x≤0.5) were prepared by the conventional solid-state-reaction method. Stoichiometric amount of high purity (99.99 %) BaCO3, SrCO3, Co3O4, and Fe2O3 were weighed and mixed thoroughly in an agate mortar. The mixture was first calcined at 1373 K in air for 4 h. Then the resultant powders were adequately reground and pressed into pellets. Finally, the pellets were sintered in air at 1473 K for 18 h followed by slowly cooling down to room temperature at a rate of 1 K/min.

The crystal structures and microstructure of the ceramic samples were investigated by X-ray powder diffraction (XRD, Cu K, PANalytical) and scanning electron microscope (SEM, FEI Nova Nano SEM 450). Dielectric properties were measured using a precision impedance analyzer (Wayne Kerr 6500B).

3 Results and discussions

Room temperature XRD patterns of Ba2−xSrxCo2Fe12O22 (0 ≤ x≤0.5) ceramics are refined using GSAS software based on a rhombohedral structure with R-3 m space group, as presented in Fig. 1a–e. The reliability factors (Rp, Rwp and χ2) of the refinement are presented in corresponding figures. The small reliability factors are suggesting the high quality of refinements. The refined lattice parameters a, c and cell volume V are displayed in Fig. 1f. It is obvious that the lattice parameters and the cell volume decrease with the rise in Sr doping content, which is in accord with the smaller ionic radius of Sr2+ (1.32 Å) compared with that of Ba2+ (1.49 Å) [28].

Fig. 1
figure 1

a–e Room temperature XRD and refinement results of Ba2−xSrxCo2Fe12O22 (0 ≤ x≤0.5). f The refined lattice parameter a, c and cell volume V as a function of Sr concentration

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SEM images and grain size distributions of Ba2−xSrxCo2Fe12O22 ceramics are given in Fig. 2a–j, respectively. It can be seen that the well-separated hexagonal plate like grains are presented for all samples. The grain size distribution was obtained from the corresponding SEM image by Nano Measurer software, from which the average grain size of each sample was calculated. Surprisingly, the average grain size shows a complicated trend with a maximum value of 3.57 μm for the x = 0.125 sample and a minimum value of 2.56 μm for the x = 0.375 sample (see Fig. 2k). With a little Sr doping content (0 < x≤0.125), Sr2+ might increase the growth rate of the ceramic sample. When 0.125 < x≤0.375, the Sr2+ ions would reduce the stability of the bonds between the boundaries, leading to the reduction of the grain size [29]. With further rise in the doping content, the grain size increases again, which might be due to reduction of the activation energy of nucleation in the grains [30, 31].

Fig. 2
figure 2

SEM images and corresponding grain size distributions of Ba2−xSrxCo2Fe12O22 samples with (a, f) x = 0, (b, g) x = 0.125, (c, h) x = 0.25, (d, i) x = 0.375 and (e, j) x = 0.5. (k) The average grain size as a function of Sr doping content x

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In order to investigate the Sr doping effect on the dielectric properties of Ba2Co2Fe12O22 ceramics, the measurement of dielectric constant (ε’) was performed in a frequency range from 100 Hz to 2 MHz at temperatures of 300 K and 600 K. Figure 3 shows the dielectric constant as a function of Sr doping content. At 300 K, ε’ slightly increases with doping content x, reaches the maximum near x = 0.25 and then monotonically decreases on further increase in x (see Fig. 3a). However, at 600 K, after a drop at x = 0.125, ε’ recovers until x = 0.375 and then falls again at x = 0.5 (see Fig. 3b). It should be noticed that the dielectric constants of all samples are higher than 103 at both 300 K and 600 K for each selected frequency, which can be called colossal dielectric constant [32, 33]. In addition, at both of the temperatures, ε’ distinctly decreases with increasing frequency, which is due to the fact that the electron exchange cannot follow the variation of the applied electric field.

Fig. 3
figure 3

Dielectric constant as a function of Sr doping content at a 300 K and b 600 K for selected frequencies of 100, 1 k, 10 k and 100 k Hz

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The dielectric response in Ba2Co2Fe12O22 is usually interpreted by the Maxwell–Wagner model [34, 35], where well conducting grains are separated by poorly conductive grain boundaries. The polarization effects can be categorized as intragranular and intergranular effects. The intragranular effect is in connection with the electron hopping between Fe2+ and Fe3+ as well as the hole transfer between Co2+ and Co3+ over the oxygen octahedrons within the grains, while the intergranular effect is related to the hopping of carriers between adjacent grains [15, 36]. For Sr doped samples, no extra carrier is introduced, hence the dielectric properties of doped samples have same origin as the undoped sample.

To further understand the Sr-doping effect on Ba2Co2Fe12O22, both dielectric constant and dielectric loss (tanδ) were measured with rising temperature under various frequencies. The experimental curves measured in the x = 0 and 0.5 samples are illustrated in Fig. 4a, b as well as in the corresponding insets. As seen in the figures, the dielectric response at 1 kHz shows different temperature dependent behaviors in low and high temperature ranges. In the low-temperature range, ε’ quickly increases with temperature, while it displays an almost temperature independent behavior in the high temperature range. The temperature region, in which ε’ quickly increases, gradually shifts toward a higher temperature range with increasing frequency. Besides, the samples present colossal dielectric constant over a wide range of both temperature and frequency (300–650 K and 1 kHz–1 MHz).As seen in the insets of Fig. 4a, b, with the rise in the measuring temperature, the dielectric loss first rapidly increases, then displays a peak at temperature near which ε’ shows a quick increase, and finally quickly increases again. To eliminate the influence of electrodes, the complex electric modulus (M*) was defined as.

$$M* = M^{\prime} - iM^{\prime\prime} = \frac{1}{{\varepsilon^{*} (\omega )}},$$
(1)

where M′ and M″ are the real and imaginary parts of the complex electric modulus, respectively, and \(\omega = 2\pi f\) is the angular frequency [37, 38]. The information of dielectric relaxation could be obtained from the peaks in M″(T). M″ for the x = 0 and 0.5 samples are presented as a function of temperature, as seen in Fig. 4c, d. It is obvious that the peaks gradually shift toward higher temperature and the peak intensity increases with a growth in frequency, indicating a thermally activate relaxation. The dielectric relaxation could be investigated based on the Arrhenius law:

$$f = f_{0} \exp ( - {{E_{\text{a}} } \mathord{\left/ {\vphantom {{E_{\text{a}} } {k_{\text{B}} T}}} \right. \kern-0pt} {k_{\text{B}} T}}),$$
(2)

where f0 is the pre-exponential factor, Ea is activation energy of the relaxation, and kB is the Boltzmann constant [38, 39]. The Arrhenius plots for the samples are illustrated in Fig. 4e. The activation energy is estimated from the slope of the linear fitting as presented in Fig. 4f. It can be seen that the activation energy first increases from 0.669 eV at x = 0 to 0.688 eV at x = 0.25, and then monotonically decreases to 0.651 eV at x = 0.5. With the rise in the doping content, the variation tendency of the activation energy is in accordance with that of the dielectric constant at 300 K (see Fig. 3a), suggesting that, at a relatively lower temperature, Sr doping at Ba site could affect the activation energy and sequentially change the dielectric constant.

Fig. 4
figure 4

Temperature dependence of dielectric response under different frequencies in the x = 0 and 0.5 samples: dielectric constant (a, b), dielectric loss (the insets of a, b), imaginary of the complex electric modulus (c, d). e Arrhenius plots of the samples. f The activation energy as a function of doping content

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As mentioned above, the polarization originates from the contribution of grains and grain boundaries. It has been widely deemed that the polarization would be dominated by the intergranular effect at high temperature [39, 40]. For the purpose of identifying the effect of Sr doping on the polarization contributed from grains and grain boundaries, the impedance spectra of all samples were measured. The experimental data obtained at 450 K are plotted in the form of Z′ vs. Z″, in which two semicircular arcs were clearly observed, as shown in Fig. 5a–e. As reported in previous studies, low frequency (right sides) and high frequency arcs (left sides) are related to intergranular and intragranular relaxation, respectively [38,39,40]. The impedance data are further analyzed by the equivalent circuit shown in the inset of Fig. 5f, where Rgb and Rg represent the resistances of grain boundaries and grains, respectively, CPE1 and CPE2 are constant phase elements. Based on such an equivalent circuit, Rgb and Rg are obtained and plotted as functions of Sr doping content in Fig. 5f. Clearly, with increasing Sr doping content, Rg monotonically increases, while Rgb shows a trend similar to the dielectric constant at 600 K (see Fig. 3b). Considering that the polarization of the samples at high temperature mainly comes from the space charges at the grain boundaries, the evolution of dielectric constant at high temperature with increasing Sr doping content might on account of the variation of Rgb.

Fig. 5
figure 5

a–e Nyquist plots of experimental data of impedance spectra measured at 450 K for samples of x = 0–0.5. f Resistances of grain boundaries and grains as a function of doping content. The inset is the equivalent circuit

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To support the impedance results, ac conductivity analysis is conducted. Figure 6a–e show the ac conductivity as a function of frequency recorded at 450 K for Ba2−xSrxCo2Fe12O22 (0 ≤ x≤0.5). It can be seen that all of the curves present a flat at low frequencies followed by a significant increase, and then a soft increase at high frequencies. According to previous studies [41, 42], the flat at low frequencies is connected with the jumping relaxation, since the frequency is exceedingly low and the electric field cannot upset the hopping conduction mechanism. Therefore, the flat value indicates the dc conductivity of the grain boundaries, which could be obtained directly from the conductivity plots. The significant increase and soft increase in the \(\sigma (f)\) curves are due to the grain boundary blocking effect and the bulk conductivity relaxation, respectively [43]. In high frequency range, the ac conductivity could be described by “universal dielectric response” [44]:

Fig. 6
figure 6

a–e The frequency dependence of ac conductivity at 450 K for samples of x = 0–0.5. The lines at high frequencies (right sides) are fitting results based on Eq. (3), and the lines at low frequencies (left sides) represent the dc conductivity of the grain boundaries. f Resistances of grain boundaries and grains as a function of doping content

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$$\sigma = \sigma_{\text{g}} + a_{0} f^{s}$$
(3)

where \(\sigma_{g}\) is the dc conductivity of grains, \(a_{0}\) and s (0 ≤ s≤1) are the temperature dependent constants. The lines at high frequencies are fitting curves based on Eq. (3). Moreover, the resistances of grain boundaries and grains can be calculated by \(R_{i} = d/(\sigma_{i} S)\) (i = gb or g), where d is the thickness of the sample and S is the area of the electrode, as presented in Fig. 6f. It is obvious that the variation tendency of Rgb and Rg is consistent with the results from impedance analysis in Fig. 5f.

As indicated earlier, with the rise in the Sr doping content, the lattice parameters decreases and the crystal structure becomes more compact, leading to a reduction in the mobility of charge carriers and resulting in the increase of Rg [45, 46]. It should be noticed that Rgb (see Figs. 5f and 6f) shows the opposite trend to the average grain size (see Fig. 2k) with increasing Sr concentration. As the grain size decreases, more pores could be observed at the grain boundary region, which in turn increase the resistivity of grain boundaries, and hence hinder the hopping of charge carriers between adjacent grains. Meanwhile, this also causes an accumulation of space charges therein, which is beneficial to the enhancement of dielectric constant [47]. Based on the above results, the variation of dielectric constant at 600 K (see Fig. 3b) mainly originates from the impact of Sr doping on average grain size.

4 Conclusions

In this work, the structural and dielectric properties of Sr-doped Ba2Co2Fe12O22 ceramic samples have been investigated. The lattice parameters monotonically decrease while the average grain size shows a complicated trend with increasing Sr concentration. The dielectric measurements show that, with the rise in Sr doping content, the variations of dielectric constant present different tendencies at 300 K and 600 K. The evolution of dielectric constant at 300 K is suggested to be dominated by activation energy of the relaxation. The resistances of grain boundaries and grains, which are respectively in connection with the average grain size and the lattice parameters, are obtained from both the impedance spectra and conductivity analysis. Since intergranular effect would dominate at high temperature, the variation of dielectric constant at 600 K is mainly related to the average grain size.