Magnetic structure of Fe, Mn, and Cr clusters supported on Cu(111)

The magnetic structures of small clusters of Fe, Mn, and Cr supported on a Cu(111) surface have been studied with non-collinear first principles theory. Different geometries such as triangles, pyramids and wires are considered and the cluster sizes have been varied between two to ten atoms. The calculations have been performed using a real space linear muffin-tin orbital method. The Fe clusters are found to order ferromagnetically regardless of the cluster geometry. For Mn and Cr clusters, antiferromagnetic exchange interactions between nearest-neighbours are found to cause collinear antiferromagnetic ordering when the geometry allows it. If the antiferromagnetism is frustrated by the cluster geometry non-collinear ordering is found. A comparison between the calculated structures and ground states obtained from simplified Heisenberg Hamiltonians show that the exchange interaction varies for different atoms in the clusters as a result of the different local structure.