La₃Ga₅HfO₁₄: Rare-Earth Polyhedron Coupled with Structural Protected Octahedron for Designing Nonlinear Optical Material with Wide Bandgap and Well-Balanced Properties

Laser damage threshold (LDT) is one of the key parameters of nonlinear optical (NLO) crystals, which can seriously affect the energy output of frequency conversion laser. The traditional design of NLO crystals introduces strongly distorted structural units, which hope to obtain an enhanced second harmonic generation (SHG) coefficient. However, this approach presents a fundamental conflict with the bandgap; it inevitably induces bandgap compression, which in turn significantly degrades the LDT. Herein, we propose a highly symmetric octahedron [HfO₆] to enhance the bandgap of La₃Ga₅SiO₁₄ (LGS) while keeping sufficient SHG response. Incorporating Hf into the LGS framework allows us to leverage the symmetry protection of the octahedra, effectively mitigating the bandgap reduction typically associated with cation energy level splitting in the distorted octahedra. We successfully synthesized a novel NLO crystal La₃Ga₅HfO₁₄ (LGHf), which possesses a wide bandgap of 5.06 eV, which leads to a significantly enhanced LDT of 1.59 GW/cm² (@ 1064 nm), while its SHG intensity reaches 3.5 × KH₂PO₄ (@1064 nm) and 0.35 × AgGaS₂ (@ 2090 nm). This design strategy successfully achieves the synergistic optimization between wide bandgap characteristics and balanced NLO response, offering a new material solution for high-power mid-infrared laser systems.