We study how crystal size influences magnetic ordering in arrays of molecular nanomagnets coupled by dipolar interactions. Compressed fluid techniques have been applied to synthesize crystals of ${\mathrm{Mn}}_6$ molecules (spin $S=12$) with sizes ranging from $28\mu \mathrm{m}$ down to 220 nm. The onset of ferromagnetic order and the spin thermalization rates have been studied by means of ac susceptibility measurements. We find that the ordered phase remains ferromagnetic, as in the bulk, but the critical temperature $T_{\mathrm{c}}$ decreases with crystal size. Simple magnetostatic energy calculations, supported by Monte Carlo simulations, account for the observed drop in $T_{\mathrm{c}}$ in terms of the minimum attainable energy for finite-sized magnetic domains limited by the crystal boundaries. Frequency-dependent susceptibility measurements give access to the spin dynamics. Although magnetic relaxation remains dominated by individual spin flips, the onset of magnetic order leads to very long spin thermalization time scales. The results show that size influences the magnetism of dipolar systems with as many as ${10}^{11}$ spins and are relevant for the interpretation of quantum simulations performed on finite lattices.

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• Magnetic interactions
• Magnetic order
• Magnetic phase transitions
• Magnetic susceptibility
• Magnetization dynamics
• Molecular magnetism
• Spin dynamics
• Transition temperature
• Ferromagnets
• Molecular magnets
• Nanoclusters
• AC susceptibility measurements
• Crystal growth
• Specific heat measurements
• X-ray diffraction