An ensemble of nanoparticles in which the inter-particle magnetic interactions are sufficiently weak shows superparamagnetic behaviour as described by the Néel–Brown model. On the contrary, when inter-particle interactions are non-negligible, the system eventually shows collective behaviour, which overcomes the individual anisotropy properties of the particles. At sufficiently strong interactions a magnetic nanoparticle ensemble can show superspin glass (SSG) properties similar to those of atomic spin glass systems in bulk. With a further increase in concentration, but still below physical percolation, sufficiently strong interactions can be experienced to form a superferromagnetic (SFM) state. SFM domains in a non-percolated nanoparticle assembly are expected to be similar to conventional ferromagnetic domains in a continuous film, with the decisive difference that the atomic spins are replaced by the superspins of the single-domain nanoparticles. In this review we highlight the most important developments in the field of supermagnetism, which comprises three fascinating subjects: superparamagnetism, SSG and superferromagnetism.

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Dipolar superferromagnetism with reentrant low-temperature superspin glass behavior is observed on a randomly distributed ferromagnetic nanoparticle systems in discontinuous metal-insulator multilayers ͓Co 80 Fe 20 (t)/Al 2 O 3 ͑3 nm͔͒ 10 with nominal thickness 1.1рtр1.3 nm by use of ac susceptometry and dc magnetometry. At tϭ1.0 nm, superspin glass-like freezing is evidenced by the criticality of dynamic and nonlinear susceptibilities.

First-order Raman scattering of A1g and Eg modes originating from the antiferrodistortive F2u soft mode confirms the cubic-tetragonal (Oh-D4h) phase transition in Sr0.993Ca0.007TiO3, at T0=125 K. Within the cubic and the tetragonal phase first-order Raman scattering of the soft ferroelectric F1u mode (TO1) and of the hard TO2 and TO4 optic modes evidences the existence of Ca2+-centred polar microregions. Their size increases rapidly on cooling towards the ferroelectric ordering temperature, Tc=18 K. Splitting and incomplete softening of the F1u components is consistent with an order-disorder transition into an orthorhombic low-temperature phase with C2v symmetry.