Coexistence of ferromagnetic ordering and cluster spin-glass behavior in a nickel-vanadium hexacyanoferrate Prussian blue analogue molecular magnet

We report the coexistence of long-range ferromagnetic ordering and cluster spin-glass behavior in a face-centered cubic nickel vanadium hexacyanoferrate molecular magnet (space group Fm3m, lattice parameter of ∼10.14 Å). The dc magnetization measurements exhibit Curie-Weiss behavior in the high-temperature paramagnetic region, followed by a transition to long-range ferromagnetic ordering below the Curie temperature (T_C) of ≈18 K. This ferromagnetic ground state is further confirmed by neutron depolarization measurements, providing evidence of the presence of ferromagnetic domains. The emergence of ferromagnetic ordering in the compound could be attributed to Ni²⁺ incorporation, which enhances the Ni-NC-Fe superexchange interaction through effective orbital overlap between Ni e_g, cyanide π*, and Fe t_2g states, thereby stabilizing long-range ferromagnetic ordering. At lower temperatures, the compound undergoes a crossover to a cluster spin-glass state, characterized by a clear bifurcation between zero-field-cooled and field-cooled magnetization curves. The frequency-dependent ac susceptibility measurements further confirm the cluster spin-glass nature of the compound. The dynamical behavior of the spin freezing phenomenon has been analyzed using Arrhenius, Vogel-Fulcher, and power-law models, yielding characteristic parameters associated with cooperative spin dynamics and inter-cluster interactions. The fitted values (using the Vogel-Fulcher law) of τ₀ and E_a/k_B are found to be ∼6.7 × 10^-6 s and ∼6 K for the compound. Furthermore, the fitting of values using the power law yields τ₀ = 7.58 × 10^-10 s and zν ≈ 5.2, falling within the typical range of spin-glass systems.