Magnetic nanostructures of CoFe₂O₄ were synthesized via a microwave-assisted hydrothermal route. The prepared nanostructures were investigated using X-ray diffraction (XRD), field emission electron microscopy (FE-SEM), energy dispersive X-ray (EDX) spectroscopy, high-resolution transmission electron microscopy (HR-TEM), selective area electron diffraction (SAED) pattern, DC magnetization, and dielectric spectroscopy measurements. The crystal structure studied using HR-TEM, SAED, and XRD patterns revealed that the synthesized nanostructures had a single-phase nature and ruled out the possibility of any secondary phase. The lattice parameters and unit cell volume determined from the XRD data were found to be 8.4821 Å and 583.88 ų. The average crystallite size (~7.0 nm) was determined using Scherrer’s equation. The FE-SEM and TEM micrographs revealed that the prepared nanostructures had a spherical shape morphology. The EDX results showed that the major elements present in the samples were Co, Fe, and O. The magnetization (M) versus temperature (T) measurements specified that the CoFe₂O₄ nanostructures showed ferromagnetic ordering at room temperature. The blocking temperature (T_B) determined using the M-T curve was found to be 315 K. The magnetic hysteresis (M-H) loop of the CoFe₂O₄ nanostructures recorded at different temperatures showed the ferromagnetic behavior of the CoFe₂O₄ nanostructures at temperatures of 200 K and 300 K, and a superparamagnetic behavior at 350 K. The dielectric spectroscopy studies revealed a dielectric constant (ε′) and loss tangent (tanδ) decrease with the increase in the frequency, as well as demonstrating a normal dispersion behavior, which is due to the Maxwell–Wagner type of interfacial polarization. The values of ε′ and tanδ were observed to increase with the increase in the temperature.

BiFe_1−xCr_xO_3, (0 ≤ x ≤ 10) nanoparticles were prepared through the sol–gel technique. The synthesized nanoparticles were characterized using various techniques, viz., X-ray diffraction, high-resolution field emission scanning electron microscopy (HRFESEM), energy dispersive spectroscopy (EDS), UV–Vis absorption spectroscopy, photoluminescence (PL), dc magnetization, near-edge X-ray absorption spectroscopy (NEXAFS) and cyclic voltammetry (CV) measurements, to investigate the structural, morphological, optical, magnetic and electrochemical properties. The structural analysis showed the formation of BiFeO₃ with rhombohedral (R3c) as the primary phase and Bi₂₅FeO₃₉ as the secondary phase. The secondary phase percentage was found to reduce with increasing Cr content, along with reductions in crystallite sizes, lattice parameters and enhancement in strain. Nearly spherical shape morphology was observed via HRFESEM with Bi, Fe, Cr and O as the major contributing elements. The bandgap reduced from 1.91 to 1.74 eV with the increase in Cr concentration, and PL spectra revealed emissions in violet, blue and green regions. The investigation of magnetic field (H)-dependent magnetization (M) indicated a significant effect of Cr substitution on the magnetic properties of the nanoparticles. The ferromagnetic character of the samples was found to increase with the increase in the Cr concentration and the increase in the saturation magnetization. The Fe (+3/+4) was dissolved in mixed-valence states, as found through NEXAFS analysis. Electrochemical studies showed that 5%-Cr-doped BFO electrode demonstrated outstanding performance for supercapacitors through a specific capacitance of 421 F g⁻¹ measured with a scan rate of 10 mV s⁻¹. It also demonstrated remarkable cyclic stability through capacitance retention of >78% for 2000 cycles.

The nanoparticles of CeO₂, Ce_0.98Fe_0.02O₂, and Ce_0.78Fe_0.02Cu_0.20O₂ were synthesized using the co-precipitation-synthesis technique. The effect of co-doping of Fe and Cu on structural, optical, and magnetic properties as well as specific capacitance have been studied using X-ray diffraction (XRD), scanning-electron microscopy (SEM), UV-visible spectroscopy, Raman spectroscopy, dc magnetization, and electrochemical measurements at room temperature. The results of the XRD analysis infer that all the samples have a single-phase nature and exclude the formation of any extra phase. Particle size has been found to reduce as a result of doping and co-doping. The smallest particle size was obtained to be 5.59 nm for Ce_0.78Fe_0.02Cu_0.20O₂. The particles show a spherical-shape morphology. Raman active modes, corresponding to CeO₂, were observed in the Raman spectra, with noticeable shifting with doping and co-doping indicating the presence of defect states. The bandgap, calculated using UV-Vis spectroscopy, showed relatively low bandgap energy (1.7 eV). The dc magnetization results indicate the enhancement of the magnetic moment in the samples, with doping and co-doping. The highest value of saturation magnetization (1.3 × 10⁻² emu/g) has been found for Ce_0.78Fe_0.02Cu_0.20O₂ nanoparticles. The electrochemical behavior studied using cyclic-voltammetry (CV) measurements showed that the Ce_0.98Fe_0.02O₂ electrode exhibits superior-specific capacitance (~532 F g⁻¹) along with capacitance retention of ~94% for 1000 cycles.