Structural and magnetic properties of Gd-doped ZnO

We use density functional theory to investigate structural and magnetic properties of Gd doped ZnO, accounting for the impurity 4f states using the GGA + U method. (i) We calculate the binding energy of forming [Gd-Gd] dimers, [V-O - Gd-Zn] and [V-Zn Gd-Zn] complexes and find that while the formation of [V-Zn - Gd-Zn] is favourable, [Gd-Zn - Gd-Zn] and [V-O - Gd-Zn] complexes are less likely to form. Next, (ii) we investigate the spacial arrangement of two (and three) Gd-Zn impurities in a 3 x 3 x 2 supercell and find that the magnetic impurities are energetically favourable when occupying distant lattice sites. Finally, we study the nature of interactions between the magnetic impurities (iii) for Gd in nearest-neighbour and non-nearest-neighbour Zn sites, (iv) in the presence of Zn or O vacancies, and (v) with and without additional charge carriers. Our results show mainly paramagnetic behaviour. In a few cases, e. g. magnetic impurities occupying in-plane nearest-neighbour zinc sites with n-type carrier doping, weak ferromagnetic coupling is observed. This magnetic ordering is of the order of a few meV and can be easily destroyed by thermal fluctuations. We thus expect Gd:ZnO to show paramagnetic behaviour at temperatures approaching room temperature.