**7. Effect of molar concentration of magnetic NPs on the observed dielectric and MD properties**

As discussed in the above section, we have systematically investigated the colossal responses of dielectric behavior along with MD effect in rare earth oxide (RE2O3, RE *~* rare earth, a series of elements from La to Lu with stable RE3+) NPs embedded SiO2 glass composite systems with different RE2O3 NPs size. Properly annealed NPs-glass compo‐ sites, where RE *~* Sm, Gd and Er, show an intriguing colossal response of dielectric behavior and MD effect near room temperature. These reproducible experimental facts suggest simultaneously a question why only these three magnetic rare earth elements have larger effects than others. Herein, we have systematically synthesized together via sol–gel route the magnetic Gd2O3 and non-magnetic La2O3 NPs with different doping concentrations and size embedded in SiO2 matrix. The doping concentration and the corresponding sample index are highlighted in Table II [40]. Here, we report that the high-*k* and MD of these NPglass composite systems are very much conditional by magnetic property of Gd2O3 NPs size, concentration, and the degree of deformation of the host matrix. To improve the dielectric tunability in presence of external magnetic field, the crucial magnetic properties of dielectrics are necessary for the application of the devices.

22 systems.


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

17

previously

[16,20,39]

**Table 2.** Different doping concentrations of non-magnetic La2O3 and magnetic Gd2O3 (mol%) in SiO2 NP-glass composite systems. LGS2 0.120 0*.*030

LGS3 0.090 0*.*060

Figure 14 illustrated the *ε´*-*T* curves of La2O3/Gd2O3 NPs embedded SiO2 glass composite systems (henceforth referred to as LGS) with different doping concentrations in the absence of the magnetic field. All the curves have well-defined diffuse phase transition-like maxima at *Tm ~*320 K characteristic with oxygen vacancy-induced dielectric relaxation, thoroughly discussed in our previously reported sections [16,20,39] of other rare earth systems. Interest‐ ingly, at higher magnetic Gd2O3 doping concentrations, the LGS NP-glass composite systems show colossal enhancement of dielectric behavior near room temperature. Even, a very high magnetic dilution of Gd2O3 NPs (LGS2 sample *~* doping level 0.03 mol%) system, the dielectric value is higher than that of pure bulk crystalline counterpart [28]. LGS4 0.075 0*.*075 LGS5 0.060 0*.*090 LGS6 0.000 0*.*150 LGS7 0.000 0*.*500 13 Figure 14 illustrated the *´*-*T* curves of La2O3/Gd2O3 NPs embedded SiO2 14 glass composite systems 15 (henceforth referred to as LGS) with different doping concentrations in the absence of the magnetic 16 field. All the curves have well-defined diffuse phase transition-like maxima at *Tm ~*320 K 17 characteristic with oxygen vacancy-induced dielectric relaxation, thoroughly discussed in our

19 reported sections

**Figure 14.** (Color online) The *ε´*-*T* curves of LGS NP-glass composite systems with different doping concentrations cal‐ cined at 700o C.

Figure 15(a) illustrates the *ε´max* vs. Gd2O3 doping concentrations of NP-glass composite systems calcined at 700o C in the absence of the magnetic field. Here, *ε´max* increases with higher doping concentration of magnetic Gd2O3 NPs. The present systems also show strong MDR around the transition temperature (*Tm*). The MDR at several selective frequencies near *Tm* are plotted as a function of doping concentration of Gd2O3, shown in the Figure 15(b). MDR enhances with faster rate at relatively lower doping concentration (≤0.1 mol%) of magnetic Gd2O3, whereas at moderate concentration range (≥0.2 mol%), the colossal response are more pronounced. A profound analogy may be expected between the colossal MDR in magnetic NP-glass composite systems and the inhomogeneous magnetoelectric interaction, inducing through magnetic spin modulation (flexomagnetoelectric polarization) [41]. Depending on the characteristic size (particle radius) and magnetization in amorphous-like nanosized systems, the flexomagnetoelectric effect induces linear magnetoelectric tunability [42].

**Sample name Non-magnetic La2O3 (mol%) Magnetic Gd2O3 (mol%)**

17

previously

[16,20,39]

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

LGS1 0.150 0.000 LGS2 0.120 0*.*030 LGS3 0.090 0*.*060 LGS4 0.075 0*.*075 LGS5 0.060 0*.*090 LGS6 0.000 0*.*150 LGS7 0.000 0*.*500

 reproducible experimental facts suggest simultaneously a question why only these three magnetic rare earth elements have larger effects than others. Herein, we have systematically synthesized together via sol–gel route the magnetic Gd2O3 and non-magnetic La2O3 3 NPs with different doping concentrations and size embedded in SiO2 4 matrix. The doping concentration and the corresponding sample index are highlighted in Table II [40]. Here, we report that the high-*k* and MD of these NPglass composite systems are very much conditional by magnetic property of Gd2O3 6 NPs size, concentration, and the degree of deformation of the host matrix. To improve the dielectric tunability in presence of external magnetic field, the crucial magnetic properties of dielectrics are necessary for

**Table 2.** Different doping concentrations of non-magnetic La2O3 and magnetic Gd2O3 (mol%) in SiO2 NP-glass

*´*-*T* curves of La2O3/Gd2O3 NPs embedded SiO2 14 glass composite systems (henceforth referred to as LGS) with different doping concentrations in the absence of the magnetic field. All the curves have well-defined diffuse phase transition-like maxima at *Tm ~*320 K characteristic with oxygen vacancy-induced dielectric relaxation, thoroughly discussed in our

19 reported sections

21 of other rare earth

H=0T *f*: 1 kHz

160 200 240 280 320 360

Temperature (K)

**Figure 14.** (Color online) The *ε´*-*T* curves of LGS NP-glass composite systems with different doping concentrations cal‐

**Sample name Non-magnetic La2O3**

Table II. Different doping concentrations of non-magnetic La2O3 and magnetic Gd2O3 11 (mol%) in SiO2

**(mol%)** 

LGS1 0.150 0.000 LGS2 0.120 0*.*030 LGS3 0.090 0*.*060 LGS4 0.075 0*.*075 LGS5 0.060 0*.*090 LGS6 0.000 0*.*150 LGS7 0.000 0*.*500

**Magnetic Gd2O3 (mol%)** 

value is higher than that of pure bulk crystalline counterpart [28].

60 LGS6

 LGS5 LGS4 LGS3 LGS2 LGS1

15

'

30

45

Figure 14 illustrated the *ε´*-*T* curves of La2O3/Gd2O3 NPs embedded SiO2 glass composite systems (henceforth referred to as LGS) with different doping concentrations in the absence of the magnetic field. All the curves have well-defined diffuse phase transition-like maxima at *Tm ~*320 K characteristic with oxygen vacancy-induced dielectric relaxation, thoroughly discussed in our previously reported sections [16,20,39] of other rare earth systems. Interest‐ ingly, at higher magnetic Gd2O3 doping concentrations, the LGS NP-glass composite systems show colossal enhancement of dielectric behavior near room temperature. Even, a very high magnetic dilution of Gd2O3 NPs (LGS2 sample *~* doping level 0.03 mol%) system, the dielectric

composite systems.

10

13

22 systems.

cined at 700o

C.

9 the application of the devices.

192 Ferroelectric Materials – Synthesis and Characterization

12 NP-glass composite systems.

Figure 14 illustrated the

**Figure 15.** (Color online) (a) Maximum value of dielectric constant, and (b). MDR under 5 T applied field of LGS NPglass composite systems with different Gd2O3 doping concentrations calcined at 700o C.
