Ab initio density-functional calculations including spin–orbit coupling (SOC) havebeen performed for Ni and Pd clusters with three to six atoms and for 13-atomclusters of Ni, Pd, and Pt, extending earlier calculations for Pt clusters with upto six atoms (2011 J. Chem. Phys. 134 034107). The geometric and magneticstructures have been optimized for different orientations of the magnetization withrespect to the crystallographic axes of the cluster. The magnetic anisotropy energies(MAE) and the anisotropies of spin and orbital moments have been determined.Particular attention has been paid to the correlation between the geometric andmagnetic structures. The magnetic point group symmetry of the clusters varies withthe direction of the magnetization. Even for a 3d metal such as Ni, the changein the magnetic symmetry leads to small geometric distortions of the clusterstructure, which are even more pronounced for the 4d metal Pd. For a 5d metal theSOC is strong enough to change the energetic ordering of the structural isomers.SOC leads to a mixing of the spin states corresponding to the low-energy spinisomers identified in the scalar-relativistic calculations. Spin moments are isotropiconly for Ni clusters, but anisotropic for Pd and Pt clusters, orbital momentsare anisotropic for the clusters of all three elements. The magnetic anisotropyenergies have been calculated. The comparison between MAE and orbital anisotropyinvalidates a perturbation analysis of magnetic anisotropy for these small clusters.