  The object of this work is to study the magnetic properties of the Lieb
structure based on magnetic particles with core-shell nano-structure. This
system is consisting of a ferromagnetic 2D Ising model formed with spins:
sigma=1/2, S=1 and q=3/2. Firstly, we examine the magnetic properties of this
nanostructure. On the other hand, we study the effect of the coupling exchange
interactions and the crystal field. We use the Monte Carlo simulations to
investigate also the behavior of the Lieb nano-structure. Finally, we study the
influence of the temperature on the critical and compensation behaviors of the
studied system. The obtained results are summarized in the phase diagrams.
