We report on the effect of alginic acid capping on the behavior of magnetite nanoparticles. The capped nanoparticles exhibit improved crystalline structure of the surface which leads to an enhanced magnetization. The improved structure facilitates quantization of spin-wave spectrum in the finite size nanoparticles and this in turn is responsible for unconventional behavior at low temperatures. In electron magnetic resonance these anomalies are manifested as an unusual increase in the resonant field H_r(T) and as a maximum of the spectroscopic splitting g_eff parameter at low temperatures. This unconventional behavior leads also to pronounced upturn of magnetization at low temperatures and a deviation from the Bloch law M(T) ∼ T^3/2.