Strain- and Defect-Engineered Modulation of Structural, Morphological, Optical, and Magnetic Properties in Ho³⁺-Doped β-Ga₂O₃ Nanoparticles

This study presents an investigation into the structural, morphological, vibrational, optical, and magnetic properties of holmium-doped β-Ga₂O₃ nanoparticles synthesized via the solid-state combustion method. X-ray diffraction (XRD) and Williamson–Hall (W–H) analysis confirm the substitution of Ho³⁺ (0.90 Å) for Ga³⁺ (0.62 Å), introducing substantial lattice strain due to the ionic size mismatch. This strain leads to a reduction in crystallite size at 1 wt% doping, while partial strain relaxation at higher concentrations (2–3 wt%) results in moderate grain coarsening. However, the sizes remain below those of the undoped sample. FESEM analysis reveals that grain size follows a similar trend, with morphology characterized by quasi-spherical, polydispersed grains exhibiting agglomeration and non-uniform distribution, reflecting the competing effects of lattice distortion, dopant accommodation, and defect dynamics. Energy-dispersive X-ray spectroscopy (EDS) confirms uniform Ho³⁺ distribution without secondary phase segregation. FTIR spectra exhibit blue-shifted Ga–O vibrational modes, indicating enhanced bond stiffness and structural distortion. UV–Vis diffuse reflectance spectra reveal a doping‑dependent Burstein–Moss shift, corresponding to bandgap widening caused by increased carrier concentration and strain‑altered electronic states. Absorption bands at 361, 419, 454, 487, 643, and 801 nm arise from Ho³⁺ intra‑4f transitions, confirming substitutional incorporation. Photoluminescence (PL) spectra exhibit broad visible emission spanning 400–600 nm, with peaks at 427, 467, and 518 nm, corresponding to the violet, blue, and bluish-green regions. A systematic quenching in PL intensity is observed with increasing Ho³⁺ concentration, attributed to enhanced non-radiative recombination via defect centers. Magnetic measurements using vibrating sample magnetometry (VSM) reveal a transition from intrinsic diamagnetism in undoped β‑Ga₂O₃ to weak ferromagnetism in Ho³⁺‑doped samples, arising from the magnetic moment of Ho³⁺ ions and defect‑mediated exchange interactions. To the best of our knowledge, this is the first report of substitutional Ho³⁺ doping in β‑Ga₂O₃ via solid‑state combustion synthesis. The tunable multifunctionality observed in structural, optical, and magnetic domains highlights the potential of Ho³⁺‑doped β‑Ga₂O₃ for future optoelectronic and spintronic applications.