## 2 Experimental Details  
High-purity precursor powders of Al\({}_{2}\)O\({}_{3}\), Y\({}_{2}\)O\({}_{3}\), Lu\({}_{2}\)O\({}_{3}\), Ga\({}_{2}\)O\({}_{3}\), and Tb\({}_{4}\)O\({}_{7}\) (purity range: 99.99-99.999%) were employed in the preparation of single-crystal scintillators. These powders were precisely measured to achieve the desired LuYAGG composition, with Tb\({}^{3+}\) incorporated at doping levels of 0.5, 1, 5, and 10 mol\(\%\). To prepare each sample, the precursor powders were thoroughly ground using an agate mortar to achieve uniform mixing. The resulting mixture was placed into an elastomeric mold and compacted into cylindrical rods via isostatic pressing. These green bodies were then sintered at 1200 \({}^{\circ}\)C for 10 h to improve their mechanical integrity and density. Following sintering, single crystals were grown using a dual halogen lamp floating-zone furnace (Canon Machinery FZD0192, Shiga, Japan), operating at a pulling speed of 4 mm/h and a rotation rate of 20 rpm. The grown crystals were subsequently sectioned and polished to obtain samples suitable for characterization.  
The crystal structures of the samples were analyzed using X-ray diffraction (XRD) within the 20 range of 10-60\({}^{\circ}\), utilizing a Shimadzu XRD-6100 diffractometer with Cu-K\(\alpha\) radiation (40 kV, 15 mA). The resulting diffraction patterns were compared to standard reference data (PDF#63-0291) to verify phase purity and crystallinity. Optical transmission properties were assessed through diffuse transmission spectra, measured with a Shimadzu SolidSpec-3700 spectrophotometer. Photoluminescence (PL) emission behavior was examined using a spectrofluorophotometer(RF-5301 PC, Shimadzu Corporation, Kyoto, Japan), while the photoluminescence (PL) contour map was measured with a Quantaurus-QY C11347 system (Hamamatsu Photonics, Shizuoka, Japan). PL decay time measurements were conducted using Quantaurus-\(\tau\) C11367 (Hamamatsu Photonics, Shizuoka, Japan).  
The scintillation behavior of the polished LuYAGG:Tb single crystals was assessed using a range of characterization techniques. Radioluminescence spectra were obtained using a custom-built system comprising a High Voltage Electronics Monoblock XRB80N100/CB X-ray generator (Spellman High Voltage Electronics Corporation, Hauppauge, NY, USA) and a DU-420-BU2 CCD (Andor-Oxford Instruments, Abingdon, Oxfordshire, England), which allowed for detailed spectral analysis under X-ray stimulation. The generator was operated at 40 kV and 1.2 mA [18]. During measurements, each sample was placed in direct contact with a fiber optic cable linked to the spectrometer to ensure optimal light collection. An X-ray dose of 1 Gy was applied, and emission spectra were collected over the 200-700 nm wavelength range.  
The scintillation light yield (\(L\gamma\)) was determined using a pulse height analysis system under excitation with 662 keV \(\gamma\)-rays from a \({}^{137}\)Cs source. The experimental setup followed our original design for scintillators with slow decay times. A near-infrared sensitive photomultiplier tube (PMT; R7600-200; Hamamatsu Photonics) operated at \(-\)550 V was used as the photodetector [19]. The \(L\gamma\) of the LuYAGG:Tb single crystals was estimated from the photoelectric absorption peak by comparison with that of a Bi\({}_{4}\)Ge\({}_{3}\)O\({}_{12}\) (BGO) single crystal. Scintillation decay characteristics were measured with a custom-built system featuring a pulsed X-ray source and a PMT (R7400P-06, Hamamatsu Photonics), operated in a time-correlated single-photon counting configuration [20]. Figure 1 shows images of Tb-doped Lu\({}_{2.5}\)Y\({}_{0.5}\)(Al\({}_{2.5}\)Ga\({}_{2.5}\))O\({}_{12}\) single crystals under normal lighting and UV light source at wavelength 254 nm conditions.