Magnetization measurements of well-characterized monodisperse Pt clusters consisting of 13 2 atoms in a zeolite confirm the predicted extraordinary magnetic polarization with up to 8 unpaired electrons on a cluster, corresponding to a magnetic moment of 0:65 5 B per atom. The effect is partly quenched by hydrogen chemisorption. The study provides insight into the electronic structure of the cluster and is fundamental for an understanding of how magnetism develops in small clusters. DOI: 10.1103/PhysRevLett.97.253401 PACS numbers: 36.40.Cg, 36.40.Mr, 61.10.Ht, 61.46.Bc While enhanced magnetism in clusters of elements that are ferromagnetic as bulk solids is well known and has been demonstrated in Stern-Gerlach deflection experiments [1], theoretical studies predicted high-spin ground states for clusters of up to 13 atoms also of Pd and Pt, i.e., of elements which do not show magnetic ordering in the bulk [2 -4]. Nanoparticles comprising several hundred atoms of Au, Pd, and Pt embedded in a polymer revealed magnetic moments corresponding to several unpaired electron spins per entire particle [5,6], but no experimental studies exist for smaller clusters. The electronic structure of small metal clusters is a strong function of size [7]. This is because the average energy spacing of electronic states at the Fermi level, the Kubo gap N, scales as =N, where N is the number of atoms in the cluster. is the width of the valence band which is only a weak function of size and assumes typically values on the order of a few eV. For a given value of N the cluster undergoes a thermal transition from an insulator to a semiconductor at the temperature where the valence electrons can overcome the Kubo gap, providing the band is incompletely filled with electrons. Alternatively, for a given temperature this transition can occur as a function of N. Furthermore, when N is sufficiently small, electrons will occupy the levels with parallel spins, following Hund's rule [3], which leads to a high spin state that is accompanied with a high magnetic moment. But when N exceeds the spin pairing energy the system switches to a low spin state. On this basis, a small cluster could be expected to be in a low spin state, because of its relatively large value of N. However, the picture is complicated further by symmetry. A high symmetry may lead to a highly degenerate HOMO (highest occupied molecular orbital), favoring high spin states. When the symmetry is broken, degeneracy is lifted and the ground state may be one of lower spin, depending on the extent to which the symmetry is broken. Additional complications can arise in applied magnetic fields when the Zeeman or spin-orbit energies compete with level splittings at the Fermi level, leading to magnetic field and also temperature dependent spin states. Furthermore, when the surface is capped, each chemisorbed species engages one of the potential conduction electrons of the cluster and pins them in a localized chemical bond.It is vis-à-vis this complex background that the present results with...