We have studied the magnetic properties of free cobalt clusters in two semi-independent Stern-Gerlach deflection experiments at temperatures between 60 and 307 K. We find that clusters consisting of 13 to 200 cobalt atoms exhibit behavior that is entirely consistent with superparamagnetism, though complicated by finite-system fluctuations in cluster temperature. By fitting the data to the Langevin function, we report magnetic moments per atom for each cobalt cluster size and compare the results of our two measurements and all those performed previously. In addition to a gradual decrease in moment per atom with increasing size, there are oscillations that appear to be caused by geometrical shell structure. We discuss our observations in light of the two competing models for Langevin-like magnetization behavior in free clusters, superparamagnetism and adiabatic magnetization, and conclude that the evidence strongly supports the superparamagnetic model.

We have used the Stern-Gerlach deflection technique to study magnetism in chromium clusters of 20-133 atoms. Between 60 K and 100 K, we observe that these clusters have large magnetic moments and respond superparamagnetically to applied magnetic fields. Using superparamagnetic theory, we have determined the moment per atom for each cluster size and find that it often far exceeds the moment per atom present anywhere in the bulk antiferromagnetic lattice. Remarkably, our cluster beam contains two magnetically distinguishable forms of each cluster size with ≥ 34 atoms. We attribute this observation to structural isomers. Even before the rise of nanoscience, atomic clusters were of keen interest to people trying to understand how the physical properties of atoms and molecules evolve with size and shape into those of bulk materials. Clusters are true many-body quantum systems, too large for exact solutions in ordinary space and too small for exact solutions in momentum space, and the properties they exhibit are often rich and complex.One such property, magnetism, offers unparalleled insight into clusters because it is sensitive to electronic and spatial structure, quantum size effects, surface to volume ratio, symmetry, and even temperature. Magnetism has been studied in low-dimensional supported systems (e.g., powders, granular metals, surfaces, and films) since Neel's pioneering work in the late 1940s and in isolated clusters since 1990. Even more dramatic enhancements of magnetism were predicted in clusters of rhodium [12,13] and manganese, [14] 4d and 3d transition metals that are merely paramagnetic in the bulk.Experimental measurements of isolated rhodium and manganese clusters find large magnetic moments in small clusters of these two elements. [15,16,17] Chromium, another of the 3d transition metals, is an itinerant antiferromagnet in the bulk. Below its ∼311 K Néel temperature, bulk chromium exhibits a transverse spin-density wave (SDW) that becomes a longitudinal spin-density wave below ∼123 K.[18] At zero temperature, chromium's SDW has a moment per atom of 0.43 µ B rms and 0.62 µ B peak.If chromium clusters had this same itinerant antiferromagnetic order, as though they were simply portions of the bulk bcc lattice, their moments per atom could not exceed 0.62 µ B .Even 0.62 µ B per atom is small compared to what is observed in iron, cobalt, and nickel clusters. [6,8,9,19] It came as no surprise then when an early study in our laboratory was unable to detect magnetism in chromium clusters of 9-31 atoms and set an upper limit of 0.77 µ B per atom for their magnetic moments. [20] More recently, chromium clusters supported on Au surfaces were shown to be antiferromagnetic.[21] Nonetheless, several theoretical studies predicted that small chromium clusters should be magnetic. [22,23,24,25,26,27]

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