Direct and Inverse Spin Splitting Effects in Altermagnetic RuO₂

Direct and Inverse Spin Splitting Effects in Altermagnetic RuO₂

2024 | Ya Qin Guo, Jing Zhang, Zengtai Zhu, Yuan-yuan Jiang, Longxing Jiang, Chuangwen Wu, Jing Dong, Xing Xu, Wenqing He, Bin He, Zhiheng Huang, Luojun Du, Guangyu Zhang, Kehui Wu, Xiufeng Han, Ding-fu Shao, Guoqiang Yu* and Hao Wu*
This supplementary material provides detailed information on the spin splitting effects in RuO₂ films. The study investigates both direct and inverse spin splitting effects in alternating RuO₂ structures. The RuO₂ films were deposited on TiO₂(101) substrates and characterized using X-ray diffraction (XRD), X-ray reflectivity (XRR), and atomic force microscopy (AFM). The films were then analyzed for in-plane magnetic properties using a vibrating sample magnetometer (VSM). The longitudinal resistivity of RuO₂(101) was measured, showing a resistivity of ~130 μΩ cm at room temperature for a 15 nm thick film. The study also explores spin pumping and spin Hall effect (SHE) in RuO₂/Py systems. The spin pumping signal was measured as a function of the applied magnetic field angle (φ_H) and crystal orientation (φ_C). The results show that the spin pumping signal is significantly influenced by the crystal orientation and the applied magnetic field. The spin Hall conductivity (SHC) was measured and found to be approximately 20 times smaller than the prediction for a single-domain RuO₂ sample. The study also investigates the temperature dependence of the spin pumping signal and the spin Hall effect. The results show that the spin pumping signal increases with decreasing temperature, indicating a stronger spin pumping efficiency at lower temperatures. The Gilbert damping coefficient (α) also increases with decreasing temperature, consistent with the enhanced spin pumping signal. The study further explores the effect of strain on the spin splitting energy in RuO₂. First-principles calculations were performed to investigate the spin splitting energy in the band structure of RuO₂ under different strain conditions. The results show that the spin splitting energy increases with compressive strain and decreases with tensile strain. These findings are consistent with the experimental observations of the spin splitting effects in RuO₂. The study also provides Raman spectroscopy data to support the structural changes in RuO₂ under different temperatures. The results indicate that the spin splitting energy and the spin Hall effect are significantly influenced by the structural changes in RuO₂. The study concludes that the spin splitting effects in RuO₂ are strongly dependent on the crystal orientation, applied magnetic field, and temperature, and that the spin Hall effect and spin pumping are important factors in understanding these effects.This supplementary material provides detailed information on the spin splitting effects in RuO₂ films. The study investigates both direct and inverse spin splitting effects in alternating RuO₂ structures. The RuO₂ films were deposited on TiO₂(101) substrates and characterized using X-ray diffraction (XRD), X-ray reflectivity (XRR), and atomic force microscopy (AFM). The films were then analyzed for in-plane magnetic properties using a vibrating sample magnetometer (VSM). The longitudinal resistivity of RuO₂(101) was measured, showing a resistivity of ~130 μΩ cm at room temperature for a 15 nm thick film. The study also explores spin pumping and spin Hall effect (SHE) in RuO₂/Py systems. The spin pumping signal was measured as a function of the applied magnetic field angle (φ_H) and crystal orientation (φ_C). The results show that the spin pumping signal is significantly influenced by the crystal orientation and the applied magnetic field. The spin Hall conductivity (SHC) was measured and found to be approximately 20 times smaller than the prediction for a single-domain RuO₂ sample. The study also investigates the temperature dependence of the spin pumping signal and the spin Hall effect. The results show that the spin pumping signal increases with decreasing temperature, indicating a stronger spin pumping efficiency at lower temperatures. The Gilbert damping coefficient (α) also increases with decreasing temperature, consistent with the enhanced spin pumping signal. The study further explores the effect of strain on the spin splitting energy in RuO₂. First-principles calculations were performed to investigate the spin splitting energy in the band structure of RuO₂ under different strain conditions. The results show that the spin splitting energy increases with compressive strain and decreases with tensile strain. These findings are consistent with the experimental observations of the spin splitting effects in RuO₂. The study also provides Raman spectroscopy data to support the structural changes in RuO₂ under different temperatures. The results indicate that the spin splitting energy and the spin Hall effect are significantly influenced by the structural changes in RuO₂. The study concludes that the spin splitting effects in RuO₂ are strongly dependent on the crystal orientation, applied magnetic field, and temperature, and that the spin Hall effect and spin pumping are important factors in understanding these effects.
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