The supplementary materials for the article "Direct and Inverse Spin Splitting Effects in Alternmagnetic RuO₂" provide detailed experimental data and theoretical analysis supporting the findings. The materials include: 1. **Sample Characterization**: X-ray diffraction (XRD) and atomic force microscopy (AFM) images of the 20 nm-thick RuO₂ film deposited on a TiO₂(101) substrate, confirming the film's structure and surface morphology. 2. **Magnetic Properties**: In-plane magnetic hysteresis loops and longitudinal resistivity measurements of the (101)-RuO₂ film, showing saturation magnetization and resistivity values. 3. **Spin-Field-Dependent Resonance (ST-FMR)**: Results from ST-FMR measurements, including angular dependence of the mixing voltage and the presence of symmetric and antisymmetric components. 4. **Spin Pumping**: Detailed analysis of spin pumping signals, including temperature dependence, microwave power dependence, and the impact of crystal orientation on spin splitting. 5. **FMR Spectra**: Measured FMR spectra at various temperatures, showing the reduction in FMR intensity with decreasing temperature. 6. **Device Configuration**: Schematic diagrams of the experimental setup for ST-FMR and spin pumping measurements, detailing the device geometry and orientation of magnetic fields. 7. **Raman Spectroscopy**: Raman spectra of TiO₂/RuO₂ at different temperatures, indicating structural changes and energy band modifications. 8. **First-Principles Calculations**: Theoretical calculations of spin splitting energy in the band structure of RuO₂ under different lattice strains, confirming the relationship between strain and spin splitting effects. These supplementary materials provide comprehensive support for the experimental results and theoretical analysis, enhancing the understanding of the direct and inverse spin splitting effects in alternmagnetic RuO₂.The supplementary materials for the article "Direct and Inverse Spin Splitting Effects in Alternmagnetic RuO₂" provide detailed experimental data and theoretical analysis supporting the findings. The materials include: 1. **Sample Characterization**: X-ray diffraction (XRD) and atomic force microscopy (AFM) images of the 20 nm-thick RuO₂ film deposited on a TiO₂(101) substrate, confirming the film's structure and surface morphology. 2. **Magnetic Properties**: In-plane magnetic hysteresis loops and longitudinal resistivity measurements of the (101)-RuO₂ film, showing saturation magnetization and resistivity values. 3. **Spin-Field-Dependent Resonance (ST-FMR)**: Results from ST-FMR measurements, including angular dependence of the mixing voltage and the presence of symmetric and antisymmetric components. 4. **Spin Pumping**: Detailed analysis of spin pumping signals, including temperature dependence, microwave power dependence, and the impact of crystal orientation on spin splitting. 5. **FMR Spectra**: Measured FMR spectra at various temperatures, showing the reduction in FMR intensity with decreasing temperature. 6. **Device Configuration**: Schematic diagrams of the experimental setup for ST-FMR and spin pumping measurements, detailing the device geometry and orientation of magnetic fields. 7. **Raman Spectroscopy**: Raman spectra of TiO₂/RuO₂ at different temperatures, indicating structural changes and energy band modifications. 8. **First-Principles Calculations**: Theoretical calculations of spin splitting energy in the band structure of RuO₂ under different lattice strains, confirming the relationship between strain and spin splitting effects. These supplementary materials provide comprehensive support for the experimental results and theoretical analysis, enhancing the understanding of the direct and inverse spin splitting effects in alternmagnetic RuO₂.