Magnetic and electronic structures of superconducting RuSr${}_2$GdCu${}_2$O${}_8$

The coexistence of ferromagnetism and superconductivity in RuSr${}_2$GdCu${}_2$O${}_8$ was reported both from experiments (by Tallon et. al.) and first-principles calculations (by Pickett et. al.). Here we report that our first-principles full-potential linearized augmented plane wave (FLAPW) calculations, employing the precise crystal structure with structural distortions (i.e., RuO${}_6$ rotations) determined by neutron diffraction, demonstrate that antiferromagnetic ordering of the Ru moments is energetically favored over the previously proposed ferromagnetic ordering. Our results are consistent with recently performed magnetic neutron diffraction experiments (Lynn et. al). Ru $t_{2g}$ states, which are responsible for the magnetism, have only a very small interaction with Cu $e_g$ states, which results in a small exchange splitting of these states. The Fermi surface, characterized by strongly hybridized $dp\sigma$ orbitals, has nesting features similar to those in the two-dimensional high $T_c$ cuprate superconductors.