Magnetic structures of small Fe, Mn, and Cr clusters supported on Cu(111):: Noncollinear first-principles calculations

The magnetic structures of small clusters of Fe, Mn, and Cr supported on a Cu(111) surface have been studied with noncollinear first-principles theory. Different geometries such as triangles, pyramids, and wires are considered and the cluster sizes have been varied between two and 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 neighbors are found to cause collinear antiferromagnetic ordering when the geometry allows it. If the antiferromagnetism is frustrated by the cluster geometry, noncollinear 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.