Applying the procedure of a rapid synthesis in the aqueous system, nanocrystalline form of ZIF-8 and Cu-ZIF was obtained. The composition of the latter was inferred from the comparison of vibration spectra and lattice specific heats of both compounds which become nearly identical. The nanocrystalline character of both compounds prevented direct comparison of powder XRD patterns and manifested by the appearance of a boson peak in the diamagnetic ZIF-8 specific heat. The low-temperature magnetic contribution in Cu-ZIF specific heat and a Curie-Weiss tail in low-temperature susceptibility may originate from the effect of surface spins while the round maximum observed in the susceptibility at 135 K indicates the presence of strong low-dimensional correlations with the exchange coupling ∼200 K. Corresponding magnetic contribution cannot be observed in the specific heat due to the huge overlap by the high-temperature lattice contribution. Negligible magnetization values at low temperatures correspond to the aforementioned strong antiferromagnetic coupling. Future experimental scenarios are discussed which should provide better understanding of the bulk and surface magnetism in this unique quantum system.