**Er2O3 NPs-glass composite system: colossal enhancement of dielectric constant and large MD effect**

Among various rare earth oxides, Er2O3 has been chosen first in the present work as it possesses most appealing properties viz. high resistivity (1012-1015 cm-3), large band gap (*E*g= 5–7 eV), static dielectric constant (*k* ~ 14) [23,24], good thermodynamic stability with silicon and, moreover, not yet been explored from the viewpoint of observing the high MD effect. Al‐ though, present TEM and XRD studies also stimulate us for further exhaustive investigation on typical Er2O3:SiO2 nano-glass composite system with different Er2O3 NPs size to throw more light exploring the origin and application feasibility on these rich dielectric materials. Typical data are shown for a Er2O3:SiO2 nano-glass composite system having 0.5 mol% dopant (Er2O3) concentration calcined at different temperatures, namely, 700, 800, 900, and 1200°C (henceforth referred as Er05-7, Er05-8, Er05-9 and Er05-12 respectively).

### **4.1. Temperature dependence dielectric response**

Figure 3(a) illustrates the relative dielectric constant (*ε*′) vs. temperature curves of typical Er05-8 sample without applied magnetic field measured at several selective frequencies (1– 100 kHz). The shape of the curves with a notable broadening around the well-defined maxima *ε*' *<sup>m</sup>* (maximum value of *ε*′) is indicative of a diffuse phase transition (DPT) presence [25-27] with high *ε*′ (~ 600 at 1 kHz), quite different from and much higher than pure bulk Er2O3 (*ε*′ ~ 11.5) [28] and SiO2 (*ε*′ ~ 3.9). Following the concept of DPT, the dielectric constant accords with a modified Curie–Weiss type equation viz. *ε*' <sup>−</sup><sup>1</sup> −*ε*' *m* <sup>−</sup><sup>1</sup> <sup>=</sup>*Ci* (*<sup>T</sup>* <sup>−</sup>*Tm*)*<sup>γ</sup>*, where γ is the diffuseness exponent indicative of degree of disorder, *C*<sup>i</sup> is a temperature independent coefficient (in general, dependent of frequency) and *ε*' *<sup>m</sup>* is the maximum value of *ε*′ at *T*m. For γ = 1, normal Curie–Weiss behavior and γ ~ 2, it implies typical DPT for the ideal ferroelectric relaxor [29]. 16 Er05-9 and Er05-12 respectively).

4 **B. Dielectric and magnetodielectric (MD) effect**

3

21

6 **effect** 

6 **Ferroelectrics**

sample obtained at 1200<sup>o</sup> 1 C are not emphasized because of the observed dielectric behavior (discussed

**1. Er2O3** 5 **NPs-glass composite system: colossal enhancement of dielectric constant and large MD** 

Among various rare earth oxides, Er2O3 7 has been chosen first in the present work as it possesses most appealing properties viz. high resistivity (1012-1015 cm-3 8 ), large band gap (*E*g= 5–7 9 eV), static dielectric constant (*k* ~ 14) [23,24], good thermodynamic stability with silicon and, 10 moreover, not yet been explored from the viewpoint of observing the high MD effect. Although, 11 present TEM and XRD studies also stimulate us for further exhaustive investigation on typical Er2O3:SiO2 nano-glass composite system with different Er2O3 12 NPs size to throw more light exploring 13 the origin and application feasibility on these rich dielectric materials. Typical data are shown for a

in the next section) is almost comparable with pure bulk Er2O3 (unsupported with SiO2 2 ).

17 Figure 3. (Color online) (a) The (-*T*) curves of Er05-8 at different selective frequencies, inset: representative plots of ln( ' ' ) <sup>1</sup> <sup>1</sup> *<sup>m</sup>* vs. ln( ) *T Tm* 18 of Er05-8 at temperatures > *Tm*, (b) (-*T*) curves of Er2O3 nanoparticles dopes SiO2 19 glass calcined at different temperatures, inset shows (-*T*) curves of Er05-12 with respect to Bulk Er2O3 and SiO2 20 showing non-DPT feature. **Figure 3.** (Color online) (a) The (*ε*′-*T*) curves of Er05-8 at different selective frequencies, inset: representative plots of ln(*ε*' <sup>−</sup><sup>1</sup> −*ε*' *m* <sup>−</sup><sup>1</sup> ) vs. ln(*<sup>T</sup>* <sup>−</sup>*Tm*) of Er05-8 at temperatures > *Tm*, (b) (*ε*′-*T*) curves of Er2O3 nanoparticles dopes SiO2 glass cal‐ cined at different temperatures, inset shows (*ε*′-*T*) curves of Er05-12 with respect to Bulk Er2O3 and SiO2 showing non-DPT feature.

The plots of ln(*ε*' <sup>−</sup><sup>1</sup> −*ε*' *m* <sup>−</sup><sup>1</sup> ) vs. ln(*<sup>T</sup>* <sup>−</sup>*Tm*) at several frequencies are illustrated in inset of Figure 3(a). We obtained average γ = 1.84 from different slopes of linear fitting, which is close to the relaxor value like other oxide relaxor systems [30]. The enhancement of dielectric value is observed even at temperatures below *T*m (~ 250–260 K), which ruled out the possibility of any space charge or interfacial polarization. The high dielectric value associated with DPT behavior (Figure 3(b)) diminishes with increasing calcined temperature (i.e., the Er2O3 NPs size). It is relevant to mention here that the temperature and frequency dependent dielectric phenomena of Er05-12 crystalline sample (calcined at 1200o C) without DPT behavior behaves like pure bulk Er2O3 [28] or SiO2 glass (inset of Figure 3(b)). The critical calcination temperature above which DPT behavior completely diminishes for this typical concentration of Er2O3 (~ 0.5 mol %) is found to be around 1000o C. The DPT behavior is thus confined to the low temperature calcined (< 1000o C) system only where the NPs are in the 2–10 nm range. 22 *1.1. Temperature dependence dielectric response* 23 Figure 3(a) illustrates the relative dielectric constant () vs. temperature curves of typical 24 Er05-8 sample without applied magnetic field measured at several selective frequencies (1–100 kHz). The shape of the curves with a notable broadening around the well-defined maxima *<sup>m</sup>* 25 ' (maximum 26 value of ) is indicative of a diffuse phase transition (DPT) presence [25-27] with high (~ 600 at 1 kHz), quite different from and much higher than pure bulk Er2O3 ( ~ 11.5) [28] and SiO2 27 ( ~ 3.9). 28 Following the concept of DPT, the dielectric constant accords with a modified Curie–Weiss type equation viz. ' ' ( ) <sup>1</sup> <sup>1</sup> *<sup>m</sup> Ci T Tm* 29 , where is the diffuseness exponent indicative of degree of

### **4.2. Dielectric relaxation analysis**

To shedmore light onthe relaxationdynamics ofrare earth oxide NPs-glass composite systems, temperature dependent dielectric loss tangent(tanδ) are carried out at various frequencies. The appearance of three maxima with strong frequency dispersion located at peak *A* ~180 K, peak *B* ~ 260 K, and peak *C* > 320 K are observed in tanδ vs. temperature curve. The formertwo peaks (peaks *A* and *B*) are shifted to high temperature with increasing frequency, whereas, the peak *C* with high-dielectric leakage (~ 7) is shifted to the lower temperature. In Figure 4(b), the temperature dependence logarithmic plot of the relaxation time (τ), determined as the inverse of the maximum peak frequency exhibit straight line, is shown in an Arrhenius representa‐ tion τ=τoexp(*E*relax/*kT*), with an energy barrier *E*relax. Near the DPT temperature (*Tm*), thermally

pure bulk Er2O3 [28] or SiO2 11 glass (inset of Figure 3(b)). The critical calcination temperature above which DPT behavior completely diminishes for this typical concentration of Er2O3 12 (~ 0.5 mol%) is found to be around 1000<sup>o</sup> 13 C. The DPT behavior is thus confined to the low temperature calcined (< RE2O3 Nanoparticles Embedded in SiO2 Glass Matrix — A Colossal Dielectric and Magnetodielectric Response http://dx.doi.org/10.5772/60677 183

at *T*m. For = 1, normal Curie–Weiss behavior and ~ 2, it implies typical

 7

' is

Colossal dielectric and MD response of RE2O3 nanoparticles in SiO2 glass matrix

disorder, *C*i is a temperature independent coefficient (in general, dependent of frequency) and *<sup>m</sup>* 1

 vs. ln( ) *T Tm* 3 at several frequencies are illustrated in inset of Figure 3(a). We obtained average = 1.84 from different slopes of linear fitting, which is close to the relaxor value like other oxide relaxor systems [30]. The enhancement of dielectric value is observed even at temperatures below *T*<sup>m</sup> (~ 250–260 K), which ruled out the possibility of any space charge or interfacial polarization. The high dielectric value associated with DPT behavior (Figure 3(b)) diminishes with increasing calcined temperature (i.e., the Er 9 2O3 NPs size). It is relevant to mention here that the temperature and frequency dependent dielectric phenomena of Er05-12 crystalline sample (calcined at 1200o 10 C) without DPT behavior behaves like

DPT for the ideal ferroelectric relaxor [29]. The plots of ln( ' ' ) <sup>1</sup> <sup>1</sup> *<sup>m</sup>*

32 Figure 4. (Color online) (a) Dielectric loss tan of Er05-8 at different frequency, (b) representative 33 Arrhenius plot of the relaxation time of Er05-8. The calculated activation energy values (in electron 34 volt (eV)) are illustrated in each case. **Figure 4.** (Color online) (a) Dielectric loss tanδ of Er05-8 at different frequency, (b) representative Arrhenius plot of the relaxation time of Er05-8. The calculated activation energy values (in electron volt (eV)) are illustrated in each case.

activated response is described with an energy barrier *E*relax of about 1.13 eV. However, the temperature dependent relaxation response above 300 K becomes reversed with the activa‐ tionenergy1.21eV.Theseexperimentalfacts suggestthepresenceofthermallyactivatedoxygen vacancies associated with the dielectric relaxation process as presented earlier with activation energy ~ 0.7-1.2 eV [30,31]. Our present results support the recent experimental finding of perovskite type ABO3 [31] material, closely related to the thermally activated reorientation of dipolemomentviatheoxygenionjumpingthroughtheoxygenvacancy,whichcanbecontrolled by sintering process. The dielectric response and DPT behavior diminishe by long-time annealing of the sample at higher temperature, which might be associated with reduced concentration of oxygen vacancies. Here, electrode effect in dielectric measurement is exclud‐ ed by using different thickness of the samples with different electrode materials, indicating the intrinsic nature of this system. 36 *1.2. Dielectric relaxation analysis* 37 To shed more light on the relaxation dynamics of rare earth oxide Nps-glass composite 38 systems, temperature dependent dielectric loss tangent (tan) are carried out at various frequencies. 39 The appearance of three maxima with strong frequency dispersion located at peak *A* ~180 K, peak *B* ~ 40 260 K, and peak *C* > 320 K are observed in tan vs. temperature curve. The former two peaks (peaks 41 *A* and *B*) are shifted to high temperature with increasing frequency, whereas, the peak *C* with high-42 dielectric leakage (~ 7) is shifted to the lower temperature. In Figure 4(b), the temperature 43 dependence logarithmic plot of the relaxation time (), determined as the inverse of the maximum peak frequency exhibit straight line, is shown in an Arrhenius representation =oexp(*E*relax 44 /*kT*), with an energy barrier *E*relax 45 . Near the DPT temperature (*Tm*), thermally activated response is described with an energy barrier *E*relax 46 of about 1.13 eV. However, the temperature dependent relaxation 47 response above 300 K becomes reversed with the activation energy 1.21 eV. These experimental facts 48 suggest the presence of thermally activated oxygen vacancies associated with the dielectric relaxation

### **4.3. Polarization studies**

2 the maximum value of

35

1000<sup>o</sup> 14 C) system only where the NPs are in the 2–10 nm range.

The plots of ln(*ε*'

DPT feature.

101

102

*'*

103

equation viz.

26 value of

21

ln(*ε*' <sup>−</sup><sup>1</sup> −*ε*' *m*

3

6 **effect** 

calcined (< 1000o

<sup>−</sup><sup>1</sup> −*ε*' *m*

22 *1.1. Temperature dependence dielectric response*

representative plots of ln( ' ' ) <sup>1</sup> <sup>1</sup> *<sup>m</sup>*

Temperature (*K*)

23 Figure 3(a) illustrates the relative dielectric constant (

200 250 300 350

Er05-12 with respect to Bulk Er2O3 and SiO2 20 showing non-DPT feature.

kHz), quite different from and much higher than pure bulk Er2O3 (

17 Figure 3. (Color online) (a) The (

%) is found to be around 1000o

 ' 

**4.2. Dielectric relaxation analysis**

of Er05-12 crystalline sample (calcined at 1200o

' ( ) <sup>1</sup> <sup>1</sup> *<sup>m</sup> Ci T Tm*

<sup>−</sup><sup>1</sup> ) vs. ln(*<sup>T</sup>* <sup>−</sup>*Tm*) at several frequencies are illustrated in inset of Figure 3(a).

10<sup>1</sup>

10<sup>2</sup>

10<sup>3</sup>

*'*

10<sup>4</sup>

 Er05-7 Er05-8 Er05-9 *f*: 1.5 kHz


200 250 300 350

Temperature (*K*)

19.2

19.6 *'*

200 240 280 320

*<sup>f</sup>* : 1.54 kHz Bulk Er2O3 Pure SiO2

Er05-12

Temperature (*K*)

) vs. temperature curves of typical


3.5 3.6 11

12

13


' (maximum

~ 3.9).

(~ 600 at 1

C) without DPT behavior behaves like pure

C. The DPT behavior is thus confined to the low temperature

We obtained average γ = 1.84 from different slopes of linear fitting, which is close to the relaxor value like other oxide relaxor systems [30]. The enhancement of dielectric value is observed even at temperatures below *T*m (~ 250–260 K), which ruled out the possibility of any space charge or interfacial polarization. The high dielectric value associated with DPT behavior (Figure 3(b)) diminishes with increasing calcined temperature (i.e., the Er2O3 NPs size). It is relevant to mention here that the temperature and frequency dependent dielectric phenomena

**Figure 3.** (Color online) (a) The (*ε*′-*T*) curves of Er05-8 at different selective frequencies, inset: representative plots of

<sup>−</sup><sup>1</sup> ) vs. ln(*<sup>T</sup>* <sup>−</sup>*Tm*) of Er05-8 at temperatures > *Tm*, (b) (*ε*′-*T*) curves of Er2O3 nanoparticles dopes SiO2 glass cal‐ cined at different temperatures, inset shows (*ε*′-*T*) curves of Er05-12 with respect to Bulk Er2O3 and SiO2 showing non-

) is indicative of a diffuse phase transition (DPT) presence [25-27] with high

24 Er05-8 sample without applied magnetic field measured at several selective frequencies (1–100 kHz).

28 Following the concept of DPT, the dielectric constant accords with a modified Curie–Weiss type

29 , where is the diffuseness exponent indicative of degree of

increasing frequency

H = 0T 1.5 3.0 4.5 -10

vs. ln( ) *T Tm* 18 of Er05-8 at temperatures > *Tm*, (b) (

Er2O3 nanoparticles dopes SiO2 19 glass calcined at different temperatures, inset shows (

The shape of the curves with a notable broadening around the well-defined maxima *<sup>m</sup>* 25

~ 11.5) [28] and SiO2 27 (

6 **Ferroelectrics**

sample obtained at 1200<sup>o</sup> 1 C are not emphasized because of the observed dielectric behavior (discussed

**1. Er2O3** 5 **NPs-glass composite system: colossal enhancement of dielectric constant and large MD** 

Among various rare earth oxides, Er2O3 7 has been chosen first in the present work as it possesses most appealing properties viz. high resistivity (1012-1015 cm-3 8 ), large band gap (*E*g= 5–7 9 eV), static dielectric constant (*k* ~ 14) [23,24], good thermodynamic stability with silicon and, 10 moreover, not yet been explored from the viewpoint of observing the high MD effect. Although, 11 present TEM and XRD studies also stimulate us for further exhaustive investigation on typical Er2O3:SiO2 nano-glass composite system with different Er2O3 12 NPs size to throw more light exploring 13 the origin and application feasibility on these rich dielectric materials. Typical data are shown for a Er2O3:SiO2 nano-glass composite system having 0.5 mol% dopant (Er2O3 14 ) concentration calcined at 15 different temperatures, namely, 700, 800, 900, and 1200°C (henceforth referred as Er05-7, Er05-8,

> H = 0T Er05-8

in the next section) is almost comparable with pure bulk Er2O3 (unsupported with SiO2 2 ).

4 **B. Dielectric and magnetodielectric (MD) effect**

16 Er05-9 and Er05-12 respectively).

182 Ferroelectric Materials – Synthesis and Characterization

 1.0 kHz 2.5 kHz 5.0 kHz 10.0 kHz 100.0 kHz

ln(*T*-*T*m)

 1.0 kHz 2.5 kHz 5.0 kHz 10.0 kHz 100.0 kHz


ln('-1


m)

bulk Er2O3 [28] or SiO2 glass (inset of Figure 3(b)). The critical calcination temperature above which DPT behavior completely diminishes for this typical concentration of Er2O3 (~ 0.5 mol

C) system only where the NPs are in the 2–10 nm range.

To shedmore light onthe relaxationdynamics ofrare earth oxide NPs-glass composite systems, temperature dependent dielectric loss tangent(tanδ) are carried out at various frequencies. The appearance of three maxima with strong frequency dispersion located at peak *A* ~180 K, peak *B* ~ 260 K, and peak *C* > 320 K are observed in tanδ vs. temperature curve. The formertwo peaks (peaks *A* and *B*) are shifted to high temperature with increasing frequency, whereas, the peak *C* with high-dielectric leakage (~ 7) is shifted to the lower temperature. In Figure 4(b), the temperature dependence logarithmic plot of the relaxation time (τ), determined as the inverse of the maximum peak frequency exhibit straight line, is shown in an Arrhenius representa‐ tion τ=τoexp(*E*relax/*kT*), with an energy barrier *E*relax. Near the DPT temperature (*Tm*), thermally Figure 5 shows the frequency and temperature dependence hysteresis loop (*P-E* curves) of typical Er05-8. The values of remanent polarization (*P*<sup>r</sup> ~ 0.032 *μ*C/cm2 ) and coercive field (*E*<sup>c</sup> ~ 0.78 kV/cm) of relatively narrow *P*-*E* loop near *Tm* (~270 K) without saturation are attributed to noncanonical ferroelectric-like (FEL) correlation in the sample, similar to those commonly observed in ABO3 perovskites [32]. However, the present NP-glass composite system has very high magnetic dilution of the NPs Er2O3 concentration (0.5 mol% Er2O3 : 99.5 mol% SiO2) and hence small amount of dipole moment per unit volume are not high enough to induce significant changes in the polarization. The spurious hysteresis loop reveals some contribution of lossy dielectric (space charge such as oxygen vacancies) or nicknamed as "banana loops," the terminology recently coined by Scott [33]. At lower frequency, the hysteresis loop becomes slightly fatter. However, to check the possible FEL correlation in the sample, temperature 29 intrinsic nature of this system.

7 volt (eV)) are illustrated in each case.

9 *1.2. Dielectric relaxation analysis*

8

28 excluded by using different thickness of the samples with different electrode materials, indicating the

Colossal dielectric and MD response of RE2O3 nanoparticles in SiO2 glass matrix

5 Figure 4. (Color online) (a) Dielectric loss tan of Er05-8 at different frequency, (b) representative 6 Arrhenius plot of the relaxation time of Er05-8. The calculated activation energy values (in electron

 To shed more light on the relaxation dynamics of rare earth oxide Nps-glass composite systems, temperature dependent dielectric loss tangent (tan) are carried out at various frequencies. The appearance of three maxima with strong frequency dispersion located at peak *A* ~180 K, peak *B* ~ 260 K, and peak *C* > 320 K are observed in tan vs. temperature curve. The former two peaks (peaks *A* and *B*) are shifted to high temperature with increasing frequency, whereas, the peak *C* with high- dielectric leakage (~ 7) is shifted to the lower temperature. In Figure 4(b), the temperature dependence logarithmic plot of the relaxation time (), determined as the inverse of the maximum peak frequency exhibit straight line, is shown in an Arrhenius representation =oexp(*E*relax 17 /*kT*), with an energy barrier *E*relax 18 . Near the DPT temperature (*Tm*), thermally activated response is described with an energy barrier *E*relax 19 of about 1.13 eV. However, the temperature dependent relaxation response above 300 K becomes reversed with the activation energy 1.21 eV. These experimental facts suggest the presence of thermally activated oxygen vacancies associated with the dielectric relaxation process as presented earlier with activation energy ~ 0.7-1.2 eV [30,31]. Our present results support the recent experimental finding of perovskite type ABO3 23 [31] material, closely related to the thermally activated reorientation of dipole moment via the oxygen ion jumping through the oxygen vacancy, which can be controlled by sintering process. The dielectric response and DPT behavior

7

**Figure 5.** (Color online) Dielectric hysteresis loop of Er05-8, measured near DPT (275 K) and above room temperature (320 K) using 2.0 and 1.0 kHz polarization frequency.

dependent *P*-*E* characteristics are carried out at highest polarization frequency (2.0 kHz), obtained in our instrument (Precision LC meter, Radiant Technologies). It is noted that the measured hysteresis loop at high frequency is closely related with the intrinsic ferroelectric switching processes of the system [34]. Although, the values of remanent polarizaion and coercive field of *P-E* curves becoming more pronounced with decreasing temperature from 320 to 275 K suggesting ferroelectric-like ordering in NPs-glass composite system, further investigations are certainly needed to delineate it.

### **4.4. Equivalent circuit analysis**

Materials exhibiting colossal enhancement of dielectric value are usually adopted to explain by Maxwell–Wagner (MW) mechanism. The present NPs-glass composite system is basically NPs grain of rare earth oxide (uniformly distributed) embedded in more insulating SiO2 matrix. The enhancement of dielectric constant along with DPT behavior might be a signature of the effect of internal barrier layer capacitance depending on the ration of grain size and the grain-boundary thickness. The complex impedance curves in Figure 6 have also been analyzed using an equivalent circuit, consisting of the two inclined semicircular arc (deviation from the ideal Debye response). Thus, the two depressed semi-arc in the Nyquist plot (complex impedance Z″-Z′plane) of the impedance data could be modeled on two parallel resistor– capacitor (RC) networks connected in series, one corresponds to the conducting part in high frequency region assigned to the intrinsic effect of grain (typical Er2O3 NPs) and the other arc in low frequency side corresponds to the more resistive part (SiO2 matrix) of the sample. Interestingly, the entire measured frequency region (20 – 2 × 106 Hz) at the temperature below *Tm* (*<*270 K) is governed by the grain response (intrinsic effect). The temperature dependence of grain (Er2O3) resistance (*Rg*) values are obtained from equivalent circuit model with the help of commercial software (Z-VIEW, version 2.9c). The contribution of grain resistance (intrinsic

response of NPs-glass systems) in the presence of magnetic field effect are discussed in the next section. temperature dependence of grain (Er2O3) resistance (R<sup>g</sup> 15 ) values are obtained from equivalent circuit 16 model with the help of commercial software (Z-VIEW, version 2.9c). The contribution of grain 17 resistance (intrinsic response of NPs-glass systems) in the presence of magnetic field effect are

Colossal dielectric and MD response of RE2O3 nanoparticles in SiO2 glass matrix

Materials exhibiting colossal enhancement of dielectric value are usually adopted to explain by Maxwell–Wagner (MW) mechanism. The present NPs-glass composite system is basically NPs grain of rare earth oxide (uniformly distributed) embedded in more insulating SiO<sup>2</sup> 4 matrix. The enhancement of dielectric constant along with DPT behavior might be a signature of the effect of internal barrier layer capacitance depending on the ration of grain size and the grain-boundary thickness. The complex impedance curves in Figure 6 have also been analyzed using an equivalent circuit, consisting of the two inclined semicircular arc (deviation from the ideal Debye response). Thus, the two depressed semi-arc in the Nyquist plot (complex impedance Z″-Z′plane) of the impedance data could be modeled on two parallel resistor–capacitor (RC) networks connected in series, one corresponds to the conducting part in high frequency region assigned to the intrinsic effect

9

29 Figure 6. (Color online) (a) Complex plane plots, Z″-Z′, of Er05-8 at several temperatures and (b) 30 schematic model of equivalent electrical circuits indicating of two parallel resistor–capacitor (RC) combinations [(RgCg): Er2O3 nano-grain, (RgbCgb): SiO<sup>2</sup> 31 matrix] connected in series. **Figure 6.** (Color online) (a) Complex plane plots, Z″-Z′, of Er05-8 at several temperatures and (b) schematic model of equivalent electrical circuits indicating of two parallel resistor–capacitor (RC) combinations [(*RgCg*): Er2O3 nano-grain, (*RgbCgb*): SiO2 matrix] connected in series.

### 32 1.5. Magnetodielectric effect 33 The observation of colossal MD effect is the most interesting finding of Er05-8 system as **4.5. Magnetodielectric effect**

1 1.4. Equivalent circuit analysis

18 discussed in the next section.

dependent *P*-*E* characteristics are carried out at highest polarization frequency (2.0 kHz), obtained in our instrument (Precision LC meter, Radiant Technologies). It is noted that the measured hysteresis loop at high frequency is closely related with the intrinsic ferroelectric switching processes of the system [34]. Although, the values of remanent polarizaion and coercive field of *P-E* curves becoming more pronounced with decreasing temperature from 320 to 275 K suggesting ferroelectric-like ordering in NPs-glass composite system, further

**Figure 5.** (Color online) Dielectric hysteresis loop of Er05-8, measured near DPT (275 K) and above room temperature


Electric field (*kV/cm*)

275K

 275 K (2.0 kHz) 320 K (2.0 kHz) 320 K (1.0 kHz)

320K

Colossal dielectric and MD response of RE2O3 nanoparticles in SiO2 glass matrix

5 Figure 4. (Color online) (a) Dielectric loss tan of Er05-8 at different frequency, (b) representative 6 Arrhenius plot of the relaxation time of Er05-8. The calculated activation energy values (in electron

 To shed more light on the relaxation dynamics of rare earth oxide Nps-glass composite systems, temperature dependent dielectric loss tangent (tan) are carried out at various frequencies. The appearance of three maxima with strong frequency dispersion located at peak *A* ~180 K, peak *B* ~ 260 K, and peak *C* > 320 K are observed in tan vs. temperature curve. The former two peaks (peaks *A* and *B*) are shifted to high temperature with increasing frequency, whereas, the peak *C* with high- dielectric leakage (~ 7) is shifted to the lower temperature. In Figure 4(b), the temperature dependence logarithmic plot of the relaxation time (), determined as the inverse of the maximum peak frequency exhibit straight line, is shown in an Arrhenius representation =oexp(*E*relax 17 /*kT*), with an energy barrier *E*relax 18 . Near the DPT temperature (*Tm*), thermally activated response is described with an energy barrier *E*relax 19 of about 1.13 eV. However, the temperature dependent relaxation response above 300 K becomes reversed with the activation energy 1.21 eV. These experimental facts suggest the presence of thermally activated oxygen vacancies associated with the dielectric relaxation process as presented earlier with activation energy ~ 0.7-1.2 eV [30,31]. Our present results support the recent experimental finding of perovskite type ABO3 23 [31] material, closely related to the thermally activated reorientation of dipole moment via the oxygen ion jumping through the oxygen vacancy, which can be controlled by sintering process. The dielectric response and DPT behavior diminishe by long-time annealing of the sample at higher temperature, which might be associated with reduced concentration of oxygen vacancies. Here, electrode effect in dielectric measurement is excluded by using different thickness of the samples with different electrode materials, indicating the

7

Materials exhibiting colossal enhancement of dielectric value are usually adopted to explain by Maxwell–Wagner (MW) mechanism. The present NPs-glass composite system is basically NPs grain of rare earth oxide (uniformly distributed) embedded in more insulating SiO2 matrix. The enhancement of dielectric constant along with DPT behavior might be a signature of the effect of internal barrier layer capacitance depending on the ration of grain size and the grain-boundary thickness. The complex impedance curves in Figure 6 have also been analyzed using an equivalent circuit, consisting of the two inclined semicircular arc (deviation from the ideal Debye response). Thus, the two depressed semi-arc in the Nyquist plot (complex impedance Z″-Z′plane) of the impedance data could be modeled on two parallel resistor– capacitor (RC) networks connected in series, one corresponds to the conducting part in high frequency region assigned to the intrinsic effect of grain (typical Er2O3 NPs) and the other arc in low frequency side corresponds to the more resistive part (SiO2 matrix) of the sample. Interestingly, the entire measured frequency region (20 – 2 × 106 Hz) at the temperature below *Tm* (*<*270 K) is governed by the grain response (intrinsic effect). The temperature dependence of grain (Er2O3) resistance (*Rg*) values are obtained from equivalent circuit model with the help of commercial software (Z-VIEW, version 2.9c). The contribution of grain resistance (intrinsic

investigations are certainly needed to delineate it.

(320 K) using 2.0 and 1.0 kHz polarization frequency.



Polarization (

*C/cm2*

)

7 volt (eV)) are illustrated in each case.

9 *1.2. Dielectric relaxation analysis*

29 intrinsic nature of this system.

184 Ferroelectric Materials – Synthesis and Characterization

8

0.00

0.04

0.08

Er05-8

**4.4. Equivalent circuit analysis**

34 shown in Figure 7(a) at a specific frequency of 2.5 kHz. The large enhancement of dielectric constant 35 (~2.75 times) is observed around the transition regime 260–300 K under 9T magnetic field. The 36 inverse of dielectric constant with temperature under magnetic field (upper inset of Figure 7(a)) are 37 also fitted by Curie–Weiss law with Curie constant (C) (3968.82, 6211.29 and 6918.04 K for 0, 5 and 9 T, respectively) and Curie–Weiss temperature (T<sup>o</sup> 38 ) (260.06, 270.12 and 271.64 for 0, 5 and 9 T, respectively). It is obvious that both dielectric temperatures (Tm and T<sup>o</sup> 39 ) are shifted to higher 40 temperatures with increasing magnetic field, indicating the occurrence of magnetic spin-ordering at 41 higher temperature under magnetic field and hence exhibit a reduced spin-lattice coupling strength The observation of colossal MD effect is the most interesting finding of Er05-8 system as shown in Figure 7(a) at a specific frequency of 2.5 kHz. The large enhancement of dielectric constant (~2.75 times) is observed around the transition regime 260–300 K under 9 T magnetic field. The inverse of dielectric constant with temperature under magnetic field (upper inset of Figure 7(a)) are also fitted by Curie–Weiss law with Curie constant (C) (3968.82, 6211.29 and 6918.04 K for 0, 5 and 9 T, respectively) and Curie–Weiss temperature (*T*o) (260.06, 270.12 and 271.64 for 0, 5 and 9 T, respectively). It is obvious that both dielectric temperatures (*Tm* and *T*o) are shifted to higher temperatures with increasing magnetic field, indicating the occurrence of magnetic spin-ordering at higher temperature under magnetic field and hence exhibit a reduced spin-lattice coupling strength under magnetic field. Temperature and frequency dependent dielectric constant of Er05-7 and Er05-8 are measured at a typical higher magnetic field (~9 T), shown in Figures 7(b) and 7(c). One may speculate about particle size dependent field effect playing a role of the larger ε′ response in the lower temperature annealed samples [35]. Within this scenario, the system in which we observed MD effect as well as Curie–Weiss behavior is the single phase of amorphous Er2O3 NPs of 2–10 nm size embedded in SiO2 glass calcined at 700–900°C. The estimated field dependent MD response (MDR) near *Tm* (~275 K) is defined by {*Δε* ' (*H* )/ *ε* ' (0)*%* = *ε* ' (*H* )−*ε* ' (0) / *ε* ' (0) ×100} as a function of the square of the magnetization as shown in the lower inset of Figure 7(a). Strikingly, the fractional change of the magnetic field induced change in the dielectric constant can be well approximated by the scaling function, *Δε* ' / *ε* ' ≈ *αM* <sup>2</sup> , where magnetoelectric interaction constant, α is estimated at 0.782.

Similar behavior of the change in dielectric constant on the square of the magnetization is also observed in several materials including intrinsic multiferroics, such as BiMnO3 [36], suggesting MD response in the present system (magnetic NPs of the guest oxide and SiO2 host glass) are closely related to the magnetism, typical size and concentration of the Er2O3 NPs.

**Figure 7.** (Color online) (a) The magnetic field dependence of (*ε*′-*T*) curves of Er05-8 at a fixed frequency 2.5 kHz. Up‐ per inset of (a): inverse of ε′ with temperature under magnetic field exhibiting the Curie–Weiss behavior and the lower inset of (a): the fractional change of the magnetic field induced change in the dielectric constant (*∆ε*′/*ε*′) of Er05-8 showing linear variation with the square of magnetization *M* <sup>2</sup> , measured in the vicinity of *T*<sup>m</sup> (~ 275K). [(b), (c)] (*ε*′-*T*) curves of Er05-7 and Er05-8 samples measured with several selective frequencies under 9 T applied magnetic field.

### **4.6. Micro-structural correlated resistivity analysis**

Figure 8 shows the contribution of amorphous NP Er2O3 grain resistance *R*g (calculated from equivalent circuit element analysis in Figure 6) of Er05-8 under external magnetic field as a function of measuring temperature. The temperature dependence of *ac* conductivity (σac) at various frequencies is demonstrated in Figure 9. In the inset of Figure 9, the *ac* conductivity as a function of temperature under external magnetic field is illustrated. Concomitantly, the grain resistance *R*g(*T*) in Figure 8 exhibits a metal to insulator like transition coinciding with the dielectric maxima temperature *Tm* of ε′(*T*) (Figure 3(a)) as well as σac(*T*) (Figure 9). Interestingly, the *R*g decreases under magnetic field, similarly observed in colossal magnetoresistive materials [25]. These experimental facts truely corroborate that the nature of charge carriers responsible for *dc* conduction in the grain interior and the dielectric relaxation maxima belongs to the same category.

Similar behavior of the change in dielectric constant on the square of the magnetization is also observed in several materials including intrinsic multiferroics, such as BiMnO3 [36], suggesting MD response in the present system (magnetic NPs of the guest oxide and SiO2 host glass) are

200 240 280 320

 2.5 kHz 5.0 kHz 10.0 kHz 100.0 kHz

Temperature (*K*)

(b): Er05-7 **Magnetic field: 9 T**

**Figure 7.** (Color online) (a) The magnetic field dependence of (*ε*′-*T*) curves of Er05-8 at a fixed frequency 2.5 kHz. Up‐ per inset of (a): inverse of ε′ with temperature under magnetic field exhibiting the Curie–Weiss behavior and the lower inset of (a): the fractional change of the magnetic field induced change in the dielectric constant (*∆ε*′/*ε*′) of Er05-8

curves of Er05-7 and Er05-8 samples measured with several selective frequencies under 9 T applied magnetic field.

Figure 8 shows the contribution of amorphous NP Er2O3 grain resistance *R*g (calculated from equivalent circuit element analysis in Figure 6) of Er05-8 under external magnetic field as a function of measuring temperature. The temperature dependence of *ac* conductivity (σac) at various frequencies is demonstrated in Figure 9. In the inset of Figure 9, the *ac* conductivity as a function of temperature under external magnetic field is illustrated. Concomitantly, the grain resistance *R*g(*T*) in Figure 8 exhibits a metal to insulator like transition coinciding with the dielectric maxima temperature *Tm* of ε′(*T*) (Figure 3(a)) as well as σac(*T*) (Figure 9). Interestingly, the *R*g decreases under magnetic field, similarly observed in colossal magnetoresistive

275K

Er05-8

 H = 0T H = 5T H = 9T

280 320 360

Temperature (*K*)

0.0 0.4 0.8 1.2 1.6 <sup>0</sup>

M2 (Am-2 kg-1 ) 2

250 300

Temperature (*K*)

 H= 0 T H= 5 T H= 9 T

(c): Er05-8 **Magnetic field: 9 T**

, measured in the vicinity of *T*<sup>m</sup> (~ 275K). [(b), (c)] (*ε*′-*T*)

(a): Er05-8 *f* **: 2.5 kHz**

<sup>240</sup> <sup>280</sup> <sup>320</sup> <sup>0</sup>

Temperature (*K*)

closely related to the magnetism, typical size and concentration of the Er2O3 NPs.

0

 2.5 kHz 5.0 kHz 10.0 kHz 100.0 kHz

40 80 120 = 0.782

10

1/e' (x 10-3

)

100

e'(H)/e'(0)%

e*'*

showing linear variation with the square of magnetization *M* <sup>2</sup>

**4.6. Micro-structural correlated resistivity analysis**

200

400

600

e*'*

186 Ferroelectric Materials – Synthesis and Characterization

800

1000

**Figure 8.** Color online) Temperature dependence of grain resistance (*R*g) calculated from impedance complex plane plots with external magnetic field. Inset: The region close to *Tm* is highlighted.

**Figure 9.** (Color online) Temperature dependence of *ac* conductivity (σac) of Er05-8 for various frequencies. Inset: tem‐ perature dependence of *ac* conductivity (σac) at 2.5 kHz with external magnetic fields.

The magnetoresistive property of magnetic NPs is attributed by spin-polarized tunneling [37]. Although, the observed strong positive magnetoelectric interaction constant (α~ 0.782) has a similar appearance to intrinsic multiferroics, the MD effect can also be achieved through a combination of magnetoresistance and the Maxwell–Wagner effect, as predicted by Catalan [38]. Since the current results suggest that MD behavior is probably a manifestation of magnetoresistance changes, depending on the NP size and separation. Enhancement of MD response (i.e., positive MD effect) through the decreases of NPs Er2O3 resistance under external magnetic field, (i.e., negative magnetoresistance) might imply the possible tunability of the resistive MD effect.

**Figure 10.** (Color online) (a) The (*ε*′-*T*) curves of Eu05-8 at different frequency, inset: representative plots of ln(*ε*' <sup>−</sup><sup>1</sup> −*ε*' *m* −1 ) vs ln(*T* −*Tm*) at temperatures higher than *Tm* for the Eu05-8 at different frequency values.

**Figure 11.** (Color online) (a), (b) The (*ε*′-*T*) curves of Eu05-7 and Eu05-9 measured under different applied magnetic fields at a fixed frequency 2.5 kHz.
