Superspin glass originating from dipolar interaction with controlled interparticle distance among γ-Fe₂O₃ nanoparticles with silica shells

γ-Fe₂O₃/SiO₂ core-shell nanoparticles with different shell thicknesses were prepared to elucidate the condition for superspin-glass (SSG) dynamics. As the shell thickness decreases, the contribution of interparticle dipolar interaction becomes apparent in the magnetic dynamics of nanoparticle assembly. The frequency dependence of peaks in ac-magnetic susceptibility in samples with strong interactions slows down, which is characterized as the emergence of a spin-glasslike phase. Aging in magnetization relaxation is found in a strongly interacting sample with an interparticle distance of L≤14 nm but is scarce in a sample with L = 18 nm. Scaling analysis reveals an increase in superparamagnetic properties with an increase in L. Therefore the critical interparticle distance necessary for SSG transition is 15-18 nm with 11-nm γ-Fe₂O₃ nanoparticles. This corresponds to the ratio of interparticle-interaction energy to the magnetic-anisotropy energy E_dip/E_a of 6-12%.