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Electronic structures of ordered double perovskites Ba2MReO6 (M=Fe, Co, and Ni) are investigated by using the linearized muffin-tin orbitals band method in the local spin-density approximation (LSDA) and the LSDA+U method. The half-metallic ferrimagnetic ground states are obtained for M=and Ni in the LSDA+U, whereas the insulating ground state is obtained for M=in the LSDA+U incorporating the spin-orbit interaction. For M=the antiferromagnetic ground state is stabilized in the LSDA+U by invoking the structural distortion.