Phase diagram of a thin Heisenberg antiferromagnetic film

We investigate the thickness dependence of the Néel temperature of a thin quantum spin‐1/2 Heisenberg antiferromagnetic film as a function of the magnetic field on a simple cubic lattice. The Néel temperature T N ( H , ℓ) is obtained by using the framework of the effective‐field theory for films consisting of ℓ = 2, 3, 5, 10 and ∞ (bulk) interacting layers. We present the phase diagram of T versus H in the whole range of the magnetic field for several values of ℓ. A continuous phase‐transition line separating the antiferromagnetic and ferromagnetic phases is observed. The critical temperature T N ( H , ℓ) of the film is smaller than the corresponding bulk critical temperature $ T^{\rm b}_{\rm N} $ ( H ) ≡ T N ( H , ∞) of the infinite system, which has been analyzed recently by Bublitz Filho and de Sousa [Phys. Lett. A 323 , 9 (2004)]; as ℓ is increased, T N ( H , ℓ) also increases and approaches $ T^{\rm b}_{\rm N} $ ( H ) for large values of ℓ. We have, also, studied the quantum phase transition where three critical fields were found: H c (ℓ) = 6.224 for ℓ ≥ 3 (three‐dimensional regime), H c (ℓ = 2) = 5.210 (intermediate regime) for ℓ = 2 and, finally, the two‐dimensional regime at ℓ = 1 with H c (ℓ = 1) = 4.194. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)