Analysis on the energetics, magnetism and electronic properties in a 45° ZnO grain boundary doped with Gd

The structural stability and magnetic properties of a grain boundary (GB) formed by aligning two ZnO single crystals oriented at an angle of 45° is investigated by density functional theory, using generalized gradient approximation (GGA) and taking the U parameter into consideration for the 4f impurity states. We found that the GB is stable with no dangling bonds and inter-granular structures. The stability of defects such as Gd substituted to the Zn site (Gd_Zn), Zn vacancy (V_Zn) and O vacancy (V_O) as well as defect complexes Gd_Zn-Gd_Zn, Gd_Zn-V_Zn, and Gd_Zn-V_O are analyzed using formation energy calculations. It is found that Gd_Zn-Gd_Zn clusters prefers to form at the GB. The spin polarization at the Gd_Zn sites is too localized and the exchange coupling energy is insufficient to overcome the thermal fluctuations. However, we show that the presence of V_Zn increases the hybridization between p orbitals of O as well as d orbitals of Zn, which can assist in increasing the magnetic polarization of the system. This work advances the understanding of the ferromagnetism in Gd-doped ZnO, indicating that Gd clustering at the GB is not likely to contribute to the ferromagnetism.