Features of the spin dynamics in ensembles of interacting (FH-chem) and weakly interacting (FH-coated) magnetic ultrasmall ($\langle d\rangle \sim 2$ nm) ferrihydrite nanoparticles have been explored. The dc and ac magnetic susceptibilities $[{\chi }^{\prime }\left(T\right)$ and ${\chi }^{\prime \prime }\left(T\right)]$ of the investigated samples have been thoroughly measured in a weak magnetic field (2 Oe) around the temperatures of superparamagnetic blocking of the nanoparticle magnetic moments (19 and 50.4 K for FH-coated and FH-chem, respectively, according to the dc magnetization data). It has been shown that the magnetic interactions between nanoparticles induce the formation of the cluster spin-glass state below the superparamagnetic blocking temperature ($T_g=18$ and 49.5 K for FH-coated and FH-chem, respectively). It has been found that coating of nanoparticles increases the critical scaling index from $z\nu =5.9$ (FH-chem) to $z\nu =8.0$ (FH-coated). This indicates a general slowdown of the dynamics of correlated spins, which is also expressed as an increase in relaxation time ${\tau }_0$ after switching on the interparticle interactions. We attribute this phenomenon to a consequence of a change in the volume of correlated spins with the increasing size of a cluster of interacting nanoparticles. It has been demonstrated using the simulated ${\chi }^{\prime \prime }\left(T\right)$ dependence that the dissipation of the magnetic energy occurs in two independent stages. The first stage is directly related to the blocking of the nanoparticle magnetic moments, while the second stage reflects the spin-glass behavior of surface spins and depends strongly on the intensity of the interparticle interactions.

• Received 10 January 2023
• Revised 7 February 2023
• Accepted 7 March 2023

DOI:https://doi.org/10.1103/PhysRevB.107.115413