First-principles prediction on long-range ferromagnetism induced by vacancies in SnO₂ nanosheet

We perform first-principles calculations to study the geometric, electronic, and magnetic properties in SnO₂ nanosheet (NS) with intrinsic oxygen (V_O) or tin (V_Sn) defects. VO defect preserves the semiconducting behavior of pure SnO₂NS, while V_Sn-induced magnetic state is relatively complex. The induced states mainly come from the unpaired electrons on oxygen atoms surrounding the tin vacancy. Depending on different initial spin distributions, we find three spin configurations with half-metallic state (S = 1), low spin semi-conductive state (S = 0) and high spin metallic state (S = 2). More importantly, there exists the long-range FM order between two 100% spin-polarized states, attributed to the hole-mediated double exchange through the strong p-d interaction between neighboring oxygen atoms. Our predicted diverse and intriguing magnetic properties induced by V_Sn defects provided an insight into the origin of ferromagnetism for designing new spintronics devices based on SnO₂NS.