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Magnetic nanostructures on non-magnetic or magnetic substrates have attractedstrong attention due to the development of new experimental methods with atomicresolution. Motivated by this progress we have extended the full-potentialKorringa-Kohn-Rostoker (KKR) Green function method to treat non-collinearmagnetic nanostructures on surfaces. We focus on magnetic 3d impuritynanoclusters, sitting as adatoms on or in the first surface layer on Ni(001),and investigate the size and orientation of the local moments and moreover thestabilization of non-collinear magnetic solutions. While clusters of Fe, Co, Niatoms are magnetically collinear, non-collinear magnetic coupling is expectedfor Cr and Mn clusters on surfaces of elemental ferromagnets. The origin offrustration is the competition of the antiferromagnetic exchange coupling amongthe Cr or Mn atoms with the antiferromagnetic (for Cr) or ferromagnetic (forMn) exchange coupling between the impurities and the substrate. We find that Crand Mn first-neighbouring dimers and a Mn trimer on Ni(001) show non-collinearbehavior nearly degenerate with the most stable collinear configuration.Increasing the distance between the dimer atoms leads to a collinear behavior,similar to the one of the single impurities. Finally, we compare some of thenon-collinear {\it ab-initio} results to those obtained within a classicalHeisenberg model, where the exchange constants are fitted to total energies ofthe collinear states; the agreement is surprisingly good.Comment: 11 page

physical review. b, condensed matter and materials physics

Noncollinear Korringa-Kohn-Rostoker Green function method: Application to<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>3</mml:mn><mml:mi>d</mml:mi></mml:mrow></mml:math>nanostructures on<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>Ni</mml:mi><mml:mo>(</mml:mo><mml:mn>001</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math>

Noncollinear Korringa-Kohn-Rostoker Green function method: Application to3dnanostructures onNi(001)