Quantum Model for Ferromagnetic Thin Films with an Alternating Crystal Field

The ferromagnetic Blume–Capel–Ising (BCI) model has been studied within the mean field approximation [1], the effective field theory [2], the two-spin cluster approximation in the cluster expansion method [3, 4], Monte Carlo simulations [5], a thermodynamically self-consistent theory based on an Ornstein–Zernike approximation [6], the exact solution based on the Bethe lattice by means of the exact recursion relations [7]. Most of the studies mentioned above displays also the existence of a tricritical point at which the phase transition changes from second order to first order when the value of K2 becomes negative. Our work represents the first atempt to consider a quantum version of BCI model. Within quantum Blume–Capel (QBC) model we will study the influence of the enhancement of the surface exchange coupling and the alternative single-ion anisotropy K2(1) on the odd atomic layers and K2(2) on the even ones on the critical behaviour of thin ferromagnetic films. The Hamiltonian of the considered system consists a Heisenberg exchange interaction with strength Jij > 0 between nearest neighbour lattice sites, an exchange anisotropy with strength D > 0, and a second-order single-ion anisotropy with strength K2 > 0: