A new computational scheme is presented based on a combination of the conjugate gradient
and the Newton-Raphson method to self-consistently minimize the energy within local
spin-density functional theory, thus to identify the ground state magnetic order of
a finite cluster of atoms. The applicability of the new ab initio optimization method
is demonstrated for Fe chains deposited on different metallic substrates. The optimized
magnetic ground states of the Fe chains on Rh(111) are analyzed in details and a good
comparison is found with those obtained from an extended Heisenberg model containing
first principles based interaction parameters. Moreover, the effect of the different
bilinear spin-spin interactions in the formation of the magnetic ground states is
monitored. In case of Fe chains on Nb(110) spin-spiral configurations with opposite
rotational sense are found as compared to previous spin-model results which hints
on the importance of higher order chiral interactions. The wavelength of the spin-spiral
states of Fe chains on Re(0001) was obtained in good agreement with scanning tunneling
microscopy experiments.
