Gadolinium and Oxygen co-doping of Gallium Nitride: an LSDA + U study
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Gadolinium and Oxygen co-doping of Gallium Nitride: an LSDA + U study Walter R. L. Lambrecht1 and Paul Larson1,2 1 Department of Physics, Case Western Reserve University, 10900 Euclid Avenue, LC 7079, Cleveland, OH, 44106-7079 2 Department of Physics & Astronomy, University of Missouri, Columbia, MO, 65211
ABSTRACT Results of first-principles supercell calculations for Gd impurities, with and without O-impurities in the same cell are presented. The possibility of colossal magnetic moments, as reported by Dhar et al., [Phys. Rev. Lett. 94, 037205 (2005)] is discussed in view of the results. Particular attention is paid to the size of the conduction band spin splitting, induced by Gd. It is argued that O plays a more active role than merely providing the electrons leading to the magnetic moment. Estimates are made of the splitting of the conduction band required to explain the occurrence of colossal magnetic moments. INTRODUCTION In the recent pursuit of dilute ferromagnetic semiconductors, the rare-earth elements have received far less attention than the 3d transition metal elements as candidate magnetic dopants. Although rare-earth elements have large spin as well as orbital magnetic moments, arising from the open 4f-shell, it is generally believed that their coupling is weak because of the localized character of the 4f orbitals. The bulk rare-earth nitrides for example have rather low Curie temperatures, e.g. about 65 K in GdN. However, by putting these relatively large atoms as dopants in a semiconductor like GaN with a small lattice constant, one might expect stronger interactions. Still, it came as a surprise that doping of Gd in GaN showed above room temperature ferromagnetism [1, 2]. Even more surprising was the result by Dhar et al. [3-6] that in the dilute limit of only 1015 cm-3, the magnetic moment per Gd was found to be of order 4000 µB per Gd and the room-temperature ferromagnetism persisted even in this low doping limit. By comparison to achieve ferromagnetism in Mn-doped GaAs, concentrations of Mn of order a few percent are required. In the paper by Dhar et al. [3] a phenomenological model was proposed to explain these so-called “colossal” magnetic moments. The key feature of this model is that the Gd produces a magnetic moment in the surrounding matrix in a region of about 30 nm diameter around each Gd. The theory explained successfully how the magnetic moment per Gd becomes smaller as the spheres of influence start having larger and larger overlap with increasing Gd concentration. The mechanism of the polarization of the medium, however, was left unspecified. Shortly afterwards, Dalpian and Wei [7] made the key observation that in a tetrahedral environment, the f-electrons can interact with the s-electrons, unlike in an octahedral environment where the interaction is symmetry forbidden.
Hence, they showed that in hypothetical zincblende GdN, the occupied f-electrons of majority spin will push the majority spin s-electrons at the conduction band minimum at Γ up in energy while the empt
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