We have carried out systematic studies on well-characterized monodisperse Fe3O4/gamma-Fe2O3 core/shell nanoparticles of 2-30 nm having a very narrow size distribution and possessing a uniquely mono-layer of surface gamma-Fe2O3. This unique core-shell structure, probably having a disordered magnetic surface state, leads us to three key observations of unusual magnetic properties: i) a very large magnetic exchange anisotropy reaching over 7 x 10(6) erg/cm(3) for the smaller particles, ii) exchange bias behavior in the magnetization data of the core/shell Fe3O4/gamma-Fe2O3 nanoparticles, and iii) the temperature dependence of the coercive field following an unusual exponential behavior. (C) 2011 Elsevier B.V. All rights reserved.