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physica status solidi (b)

Phase diagram of a thin Heisenberg antiferromagnetic film

J. Cabral Neto, J. Ricardo de Sousa

Published Jun 14, 2007• 1 citation
Publisher

Abstract

Abstract 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 TN(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 TN(H, ℓ) of the film is smaller than the corresponding bulk critical temperature $ T^{\rm b}_{\rm N} $ (H) ≡ TN(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, TN(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: Hc(ℓ) = 6.224 for ℓ ≥ 3 (three‐dimensional regime), Hc(ℓ = 2) = 5.210 (intermediate regime) for ℓ = 2 and, finally, the two‐dimensional regime at ℓ = 1 with Hc(ℓ = 1) = 4.194. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

DOI
10.1002/pssb.200642388

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Abstract 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 TN(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 TN(H, ℓ) of the film is smaller than the corresponding bulk critical temperature TNbT^{\rm b}_{\rm N}TNb​ (H) ≡ TN(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, TN(H, ℓ) also increases and approaches TNbT^{\rm b}_{\rm N}TNb​ (H) for large values of ℓ. We have, also, studied the quantum phase transition where three critical fields were found: Hc(ℓ) = 6.224 for ℓ ≥ 3 (three‐dimensional regime), Hc(ℓ = 2) = 5.210 (intermediate regime) for ℓ = 2 and, finally, the two‐dimensional regime at ℓ = 1 with Hc(ℓ = 1) = 4.194. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Within the framework of the effective field theory, with a probability distribution technique that accounts for the single-site spin correlations, we examine the critical behavior of a diluted spin-1/2 Ising film. The critical temperature of the system is studied as a function of the thickness of the film, the concentration of magnetic atoms, the strength of the transverse field and the couplings. It is shown that for the ratio of the surface couplings to the bulk ones R = Js/J less than a critical value R,, the critical temperature of the film Tc/J is smaller than the bulk critical temperature Tc^B/J and for R ≥ Rc, Tc/J is larger than the bulk critical temperature Tc^B/J and Tc^S/J of the corresponding semi-infinite system. As the film thickness L is increased further Tc/J increases for R ≤ Rc (decreases for R 2 R,) and approaches asymptotically for large values of L the bulk critical temperature Tc^B/J (the surface critical temperature Tc^S/J) of the corresponding semi-infinite system.
Within the framework of the effective-field theory, we examine the phase transitions of a transverse spin-12\frac{1}{2}21​ Ising film. The critical temperatures of the film as a function of the interactions, transverse fields, and film thickness are studied. It is found that for the ratio of the surface interactions to the bulk ones R=Js/J{R=J}_{s}/JR=Js​/J less than a critical value Rc,{R}_{c},Rc​, the critical temperature Tc/J{T}_{c}/JTc​/J of the film is smaller than the bulk critical temperature TcB/J{T}_{c}^{B}/JTcB​/J and as the film thickness L is increased further, Tc/J{T}_{c}/JTc​/J increases and approaches asymptotically TcB/J{T}_{c}^{B}/JTcB​/J for large values of L. However, for R>Rc,Tc/JR>{R}_{c}, {T}_{c}/JR>Rc​,Tc​/J is larger both than the bulk TcB/J{T}_{c}^{B}/JTcB​/J and the surface TcS/J{T}_{c}^{S}/JTcS​/J critical temperatures of the corresponding semi-infinite system and as the film thickness L is increased further, Tc/J{T}_{c}/JTc​/J decreases and approaches asymptotically, for large values of L, the surface magnetic transition TcS/J{T}_{c}^{S}/JTcS​/J observed in the corresponding semi-infinite system. We calculate also some magnetic properties of the film such as the layer magnetizations, their averages and their profiles and the longitudinal susceptibility of the film. The film longitudinal susceptibility still diverges at the film critical temperature as does the bulk longitudinal susceptibility, but its magnitude is reduced. Also there is a rounded peak at the bulk critical temperature when R>Rc.R>{R}_{c}.R>Rc​. The bulk related character of the susceptibility is more pronounced and the surface related character is less pronounced when the film thickness is large.
Abstract By the use of both the standard mean field theory and the effective field theory with correlations the phase transition of the transverse Ising thin films is investigated with special emphasis to the behavior of the susceptibility χ(T) outside the critical regime. The exchange interaction and transverse field at the surfaces of the thin film take values different from those in the bulk. Various non‐monotonic temperature dependences of the effective exponent γ(T) introduced by Kouvel and Fisher are found, depending on the ratios of these properties between the surfaces and the bulk as well as the value of film thickness L. They are clearly different from the behavior in the bulk. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Within the framework of the effective field theory, we examine the phase transitions of the spin-12 Ising film in a transverse field. We study the critical temperature of the film as a function of the exchange interactions, the transverse field and the film thickness. We find that, if the ratio of the surface exchange interactions to the bulk ones R=Js/J is smaller than a critical value Rc, the critical temperature Tc/J of the film is smaller than the bulk critical temperature TcB/J and as R is increased further, Tc/J approaches TcB/J. On the other hand, if R>Rc, Tc/J is larger than the bulk TcB/J and the surface TcS/J critical temperatures of the corresponding semi-infinite system and as R is increased further, Tc/J approaches the surface critical temperature Tcs/J.
We have used Monte Carlo simulations and mean-field analysis to observe the magnetic behavior of Ising thin films with cubic lattice structures as a function of temperature and thickness, especially in the critical region. Magnetization and magnetic susceptibility, including layer variation, are investigated. We find that the magnetic behavior changes from two-dimensional to three-dimensional character with increasing film thickness. Both the crossover of the critical temperature from a two-dimensional to a bulk value and the shift exponent are observed. Nevertheless, with support from a scaling function, the simulations show that the effective critical exponents for films with large enough layer extents only vary a little from their two-dimensional values. This, in particular, provides an indication of two-dimensional universality in the thin films.
Abstract In this work we use numerical Monte Carlo techniques to study the phase diagram of the three‐dimensional classical Heisenberg anti‐ferromagnetic (AF) model with single‐ion anisotropy model with an uniform magnetic field applied along the easy axis. Early experimental as well as theoretical calculations have shown that the phase diagram of the model is quite rich. We simulated the model on a simple cubic lattices using the Wang–Landau sampling and Metropolis algorithm. Finite size scaling theory is used to obtain the phase diagram. At low field and low temperature the system exhibits AF order separated from a spin‐flop (SF) phase by a first‐order line. As temperature grows a paramagnetic phase is reached by crossing a second‐order line both from the AF phase and from the SF phase. The critical exponents are obtained for each transition line. Contrary to early works we find that the line separating the SF phase from the paramagnetic phase is in the Ising class of universality.