Canted ferromagnetism in RuSr$_2$GdCu$_2$O$_8$

First principles calculations using the full-potential linearized augmented plane wave (FLAPW) method including intra-atomic noncollinear magnetism have been performed to determine the magnetic structures of RuSr$_{2}$GdCu$_{2}$O$_{8}$. The magnetism clearly arises from the RuO$_{6}$ octahedra where the moments on neighboring Ru sites order antiferromagnetically but cant perpendicular to the AFM axis - and so induce a weak ferromagnetism. The projected Ru moments along the AFM and FM axes result in magnetic moments of 1.16 and 0.99 $\mu_{B}$ respectively. The results are consistent with the possible coexistence of canted ferromagnetism and superconductivity in the RuSr$_{2}$GdCu$_{2}$O$_{8}$ - inferred from experiments.