## 1. Introduction

In the last decade, the rare-earth manganites have been studied extensively due to the underlying fundamental physics and their potential applications in advanced technology.^{1,2)} These materials can structurally be divided into two types of groups depending on the rare-earth ions.^{3)} The larger rare-earth ions adopt an orthorhombic structure, such as LaMnO_{3}, EuMnO_{3}, GdMnO_{3} manganites, while the smaller ones take a hexagonal structure, such as YMnO_{3}, YbMnO_{3}, and HoMnO_{3} manganites. Generally, dysprosium manganites DYMnO_{3} (DMO) can be formed in either orthorhombic or hexagonal structures because of the intermediate-sized Dy3+ ion.^{4,5)} As is known, different structure may have promising effects on the (anti)ferromagnetic or ferroelectronic orders in these materials. Therefore, the synthesis of DMO ceramics and studies on its physical properties are more attractive.

In this paper, we reported the fabrication of singlephased orthorhombic DMO ceramics by using solid-state reaction technique. The complex dielectric properties were investigated as functions of temperature (80 K ≤ *T* ≤ 360 K) and frequency (100 Hz ≤ *f* ≤ 100 KHz). Two sets of thermally activated relaxations were observed, and the dielectric behavior was explained by the universal dielectric response model. The impedance spectroscopic analysis in a broad frequency range (100 Hz-10 MHz) was used to discern the intrinsic DMO grain and grain boundary contributions to the dielectric responses.

## 2. Experimental

The ceramic polycrystalline DMO samples were fabricated through conventional solid-state reaction process using appropriate amounts of Dy_{2}O_{3} and MnO_{2}. (> 99.99 % purity). The stoichiometric raw materials were mixed and milled, then calcined in the temperature range of 1,000 ~ 1,200 °C for 10 h. The reaction-generated powders were grinded and pressed into high-density pellets for dielectric measurements, which were sintered at a temperature of 1,400 °C for 12 h. Under normal solid state synthesis conditions, DMO ceramics tend to form an orthorhombic perovskite phase. The crystalline structure of the prepared DMO samples were analyzed by x-ray diffraction (XRD) using a Rigaku diffractometer with Cu *Kα* radiation at 1.54 Ǻ. The measurements of complex dielectric properties were carried out on a QuadTech 1730 LCR Digibridge over a frequency range of 100 Hz ~ 100 kHz. The temperature dependence was controlled by a temperature controller (Lakeshore 332). The impedance spectroscopy was examined by using a HP4194A analyzer with signal amplitude of 50 mV. Data were taken in a frequency range of 100 Hz ~ 10 MHz.

## 3. Results and Discussion

Fig. 1 shows the powder diffraction pattern of DMO ceramics. The vertical lines indicate the allowed Bragg reflections. The location and intensity of all the reflection peaks could be indexed to an orthorhombic structure without any detectable impurity implying the single phase of the prepared sample within the detection limits of the diffractometer. The XRD data were analyzed using Rietveld refinement method, and the calculated lattice parameters of orthorhombic DMO were obtained to be a = 0.581 nm, b = 0.527 nm and c = 0.739 nm. The lattice parameters are comparable to that of JCPDS card No. 25-0330. The crystallographic structure and the values of lattice parameters of the present DMO are in good agreement with previously reported results.^{6,7)}

The temperature dependence of the real part of the complex permittivity and loss tangent tanδ (tanδ is defined as *ε*′′/*ε*', where *ε*' and *ε*′′ is the real and imaginary parts of the complex permittivity, respectively) for the prepared orthorhombic DMO ceramics at various frequencies are plotted in Figs. 2 and 3. The value of *ε* ' is weakly temperature and frequency dependent in the low temperature range from 80 to 150 K. With the increasing of T, *ε*' increases intensively and the characteristic of *ε*' (T) displays two distinct diffused transitions, which can be seen more clearly at lower frequency. Two corresponding peaks in loss tangent can be seen clearly in Fig. 3. The peaks of *ε*' and tanδ shift to higher temperatures as frequency increases indicates that there exist two sets of thermally activated relaxations in DMO ceramic samples, which possibly comes from the grain and grain boundary effects in polycrystalline ceramics. Such behavior is similar to that observed in several other works.^{8,9)}

In Fig. 3, the solid curves through the tanδ data points (open symbols) are the fitting results which were obtained by superimposition of two Gaussian functions and an exponential function. By this processing, the peak positions, *T _{p}*, can be extracted accurately. The dashed lines at the lower part are the typical fitting of the experimental data at frequency

*f*= 100 kHz.

Fig. 4 shows the variation of ln *f* versus 1000/T_{p}. This linear relationship can be described by the Arrhenius law^{10)}

$\tau ={\tau}_{0}\mathrm{exp}\left(E/kT\right),$
where τ is the relaxation time, *E* is the activation energy and k is the Boltzmann constant. At peak position of tanδ (*T*) (*T* = *T _{p}*), the values of most probable relaxation time were defined by $\omega \tau =1$
($\omega =2\pi f$
is the angular frequency), then the linear relationship of ln

*f*versus 1/

*T*was quite clear. The Arrhenius plots in Fig. 4 are typical of Debye-type relaxations, and the changes of slope and intercept suggest the difference of activation energy (

_{p}*E*) and the preexponential factor (${\tau}_{0}$ ) for the two relaxations. The values of E were determined to be 0.32 eV and 0.24 eV, while factor ${\tau}_{0}$ were 2.04 × 10

^{−11}s and 3.18 × 10

^{-11}s, respectively. The reported E and ${\tau}_{0}$ values are comparable with those of manganite HoMnO

_{3}.11) The results further show the existing two thermally activated relaxations in DMO ceramics which may be from the grain and grain boundary effects.

It is well known that, over a wide range of frequencies, the dielectric behavior of oxide materials can be described as the universal dielectric response (UDR) model. The complex dielectric constant can be expressed as^{10,12)}$\omega {\epsilon}^{\u2033}=\left(A/\epsilon \right){\omega}^{s},$ and $\omega {\epsilon}^{\prime}-\omega {\epsilon}_{\infty}+\left(A/{\epsilon}_{0}\right)\mathrm{tan}\left(s\pi /2\right){\omega}^{s},$, where *A* and *s* are temperature dependent constants, *ε*_{0} is the electric permittivity of free space, *ε*_{∞} is the high-frequency value of *ε*'(ω).

According to the UDR power laws, a straight line with the slope of s should be obtained in the log-log plot of *fε*’′ versus *f* at a given temperature, and the same character can be observed in the log-log plot of f*ε*′ versus *f* pattern. The assumption was well confirmed by the plots in Figs. 5 and 6. The value of *ε*′′ was determined from the loss tangent (tanδ) data. Quite good straight lines can be observed for log*f* dependence of log*f**ε*′′ [Fig. 5], and log*f* dependence of log*f**ε*′ [Fig. 6]. The obtained values of s were in the range of 0.52-0.61 for the log*f**ε*′′ versus log*f* plots, 0.58-0.79 for the log f*ε*′ versus log*f* plots, which is consistent with the UDR model.^{12)} As is known, the exponential increasing background in loss tangent [Fig. 3] implies that the relaxation is associated with the hopping of charged carriers with appropriate relaxation of surrounding ions. Moreover, localized charged carriers hopping between lattice potentials in DMO ceramics give rise to dipolar effects, which is the main contribution to the polarization. These actions agree with the UDR law. With decreasing temperature, the localized carriers are becoming frozen, which reduces the dipolar effects, resulting in some data (T = 100 K) deviating from the straight line in Fig 5.

As is known, the polycrystalline ceramic materials are electrically inhomogeneous, and usually have at least three electrical components contribute to the electrical and dielectric effects.^{13)} These are the intrinsic grains, grain boundaries, and electrodes effects. In order to separate the different dielectric responses, impedance spectroscopy is often used to reliably illustrate different dielectric relaxations with demarking frequencies. Fig. 7 shows the complex impedance |*Z*''| versus |*Z*'| spectroscopy of DMO ceramics in a broad frequency range (100 Hz- 10 MHz) at room temperature, where *Z** = *Z*' − *jZ*'' is the complex impedance. The complex plots form semicircular arcs, and the fitting results are shown as solid curves. Each experimental point (open symbol) corresponds to a frequency value.

The most commonly assumed equivalent circuit for these types of materials consisting of a series association of RC components is shown in the inset of Fig. 7. The subscript *g* denotes grain, and that *gb* means grain boundary. The impedance *Z** of this ideal equivalent circuit can be defined as^{14)}

By using the impedance spectroscopy analysis method,^{13,14)} the observed two arcs from high to low frequencies can be assigned, respectively, to the dielectric response from grains and grain boundaries in DMO ceramics with demarking frequency *f* = 221 kHz. The dielectric response from electrodes cannot be discerned from Fig. 7, because electrodes effects may be covered by the increasing exponential background resulting from the electric conductivity at room temperature, and the electrode relaxation frequency is much lower than the bulk grain and grain boundary relaxation frequencies.

## 4. Conclusion

In summary, we fabricated single-phased orthorhombic DMO polycrystalline ceramics and presented the complex dielectric properties as functions of temperature and frequency. Two thermally activated relaxations in DMO ceramics were observed, and the activation energies were determined to be 0.32 eV and 0.24 eV, respectively. The dielectric properties of DMO ceramics were consistent with the universal dielectric response model. The intrinsic grain and grain boundary effects on the dielectric behaviors of DMO ceramics were discerned with demarking frequency *f* = 221 kHz by using the impedance spectroscopy analysis.