  Using first-principles calculations, we demonstrate that an Fe monolayer can
assume very different magnetic phases on hexagonal hcp (0001) and fcc (111)
surfaces of 4d- and 5d-transition metals. Due to the substrates' d-band
filling, the nearest-neighbor exchange coupling of Fe changes gradually from
antiferromagnetic (AFM) for Fe films on Tc, Re, Ru and Os to ferromagnetic on
Rh, Ir, Pd, and Pt. In combination with the topological frustration on the
triangular lattice of these surfaces the AFM coupling results in a 120-degree
Neel structure for Fe on Re and Ru and an unexpected double-row-wise AFM
structure on Rh, which is a superposition of a left- and right-rotating
90-degree spin spiral.
