Magnetic nanostructures are often considered as highly functional materials because they exhibit unusual magnetic properties under different external conditions. We study the effect of surface pinning on the core-shell magnetic nanostuctures of different shapes and sizes considering the spin-interaction to be Ising-like. We explore the hysteresis properties and find that the exchange bias, even under zero field cooled conditions, increases with increase of, the pinning density and the fraction of up-spins among the pinned ones. We explain these behavior analytically by introducing a simple model of the surface. The asymmetry in hysteresis is found to be more prominent in a inverse core-shell structure, where spin interaction in the core is antiferromagnetic and that in the shell is ferromagnetic. These studied of inverse core-shell structure are extended to different shapes, sizes, and different spin interactions, namely Ising, XY- and Heisenberg models in three dimension. We also briefly discuss the pinning effects on magnetic heterostructures.
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