Influence of the lattice structure on the Curie temperature of a thin quantum spin 12 Heisenberg film

The dependence of the critical temperature Tc(ℓ,Δ) on film thickness ℓ and ratio of surface (Js) to bulk (Jb) exchange interaction strengths Δ≡(Js/Jb)−1 in quantum spin 12 Heisenberg model is studied by using the variational principle within the framework of the mean field approximation. It is found that for Δ<Δc (where Δc=0.29), the critical temperature Tc(ℓ,Δ) of the film is smaller than the corresponding bulk critical temperature Tcb of the infinite system and as ℓ is increased, Tc also increases approaches Tcb for large value of ℓ. However, in the case of Δ>Δc, Tc is larger than both, the bulk Tcb and the surface Tcs critical temperatures of the corresponding semi-infinite systems and, as the film thickness ℓ further increases, Tc decreases and approaches, for large value of ℓ, the surface magnetic transition Tcs. We also investigate the influence of the lattice structure on the critical temperature, and we show that Tc[FCC(001)]<Tc[FCC(111)] is in accordance with experimental results in films of Ni(001) and Ni(111) (i.e., Tc[Ni(001)<Tc[Ni(111)]]).