Tailoring zero-point energies in nanocrystalline 3D Hofmann-type spin-crossover networks {Fe_1−<i>x</i>M_<i>x</i>(pz)[Pd(CN)₄]}: impact of size, composition, and surrounding matrices

We report the variation in zero-point energies, and their distribution, investigated through changes in thermal spin relaxation behavior and cooperativity, in the 3D Hofmann-type guest-free, different-sized nanocrystalline spin-crossover coordination networks, {Fe_1-<i>x</i>M_<i>x</i>(pz)[Pd(CN)₄]}, 0 ≤ <i>x</i> ≤ 1, where M(II) = Zn(II), Co(II), and Ni(II). Additionally, we synthesize the [Fe(pz)Pd(CN)₄] nanocrystals embedded in different polymeric matrices, including Poly(methyl methacrylate) (PMMA), Polyethylene glycol 6000 (PEG-6000), and Polyvinylpyrrolidone K-30 (PVP K-30). The resulting nanostructures are phase-pure, well-crystallized and exhibit a tetragonal phase. High-resolution transmission electron microscopy (HRTEM) confirms that the nanostructures are nearly square-shaped, with well-defined sizes. The abrupt, incomplete, and gradual nature of the thermal spin relaxation behavior observed from the magnetic data for pure, doped, and polymer-embedded nanocrystals is collectively explained by the local and long-range fluctuations in the crystal fields experienced by the Fe(II) spin-crossover centers, variation in nucleation barrier energy influencing elastic properties, kinetic effects linked to modification in nucleation preferential sites during spin-state switching, as well as chemical pressure, lattice-strains and imperfections, thus altering the in-plane and out-of-plane interactions that influence the cooperativity variation and are responsible for the relative stabilization of the high-spin or low-spin states by modifying the . A 3D mechanoelastic model is employed to interpret the observed magnetic behavior of pure, doped, and polymer-embedded nanocrystals, offering deeper insights into the underlying mechanisms governing spin-state transitions at the nanoscale.