Spin glass like transition in a highly concentrated Fe-C nanoparticle system

A highly concentrated (17 vol.%) Fe-C nano-particle system, with a narrow size distribution $d = 5.4\pm 0.4$ nm, has been investigated using magnetic ac susceptibility measurements covering a wide range of frequencies (17 mHz - 170 Hz). A dynamic scaling analysis gives evidence for a phase transition to a low temperature spin-glass-like phase. The critical exponents associated with the transition are $z\nu = 10.5 \pm 2$ and $\beta = 1.1 \pm 0.2$. The reason why the scaling analysis works for this sample, while it may not work for other samples exhibiting collective behavior as evidenced by aging phenomena, is that the single particle contribution to $\chi''$ is vanishingly small for $T>T_g$ and hence all slow dynamics is due to collective behavior. This criterion can only be fulfilled for a highly concentrated nano-particle sample with a narrow size distribution.