Critical temperature studies of the anisotropic bilayer and multilayer Heisenberg ferromagnets in Pair Approximation

Abstract

The Pair Approximation method is applied to studies of the bilayer and multilayer magnetic systems with simple cubic structure. The method allows to take into account quantum effects related with non-Ising couplings. The paper adopts the anisotropic Heisenberg model for spin S = 1/2 and considers the phase transition temperatures as a function of the exchange integrals strength in line with the role of intra-and interplanar anisotropic interactions in the onset of low-dimensional magnetism. The compensation effect for the Curie temperature is found for asymmetric interactions within the neighbouring planes of the bilayer system. The paper predicts the saturation of the Curie temperature for strong interplanar interactions. However, such an effect for the multilayer system occurs only when the interplanar interactions are of purely isotropic character. Figure 1: (a) A schematic view of the bilayer composed of two layers, A and B. The intraplanar couplings are J AA x = J AA y = J AA ⊥ , J AA z and J BB x = J BB y = J BB ⊥ , J BB z , respectively. The interplanar coupling is J AB x = J AB y = J AB ⊥ , J AB z . (b) A schematic view of a multilayer, containing an infinite number of subsequent layers A and B.visible in Fig. 8 (b) this reduction of T c becomes less pronounced for the increasing coupling in the B plane. On the other hand, when J BB z is comparable with J AA z the behaviour of the critical temperature follows the trend presented in the Fig. 8(a). It is particularly interesting that at some value of J BB z /J AA z the critical temperature k B T c /J AA z = 1/2 ln 2 is restored for each curve, even though the disordering Heisenberg interplanar couplings are present. The value of J BB z /J AA z at which the compensation of the opposite influences of J AB ⊥ and J BB z takes place is very weakly sensitive to the strength of interplanar coupling. This is visible in the Fig. 8 (b) as an approximate interception point of all the curves plotted for various values of J AB z /J AA z . The insensitivity of the coupling ratio J BB z /J AA z * , for which T c has the constant value (characteristic of an uncoupled bilayer system), on the interplanar interaction is further illustrated in the Fig. 9. There, the values of J BB z /J AA z * are plotted as a function of the interplanar coupling J AB z /J AA z strength. The plot is prepared not only for isotropic

Magnetocaloric properties of a spin-1 anisotropic ferromagnetic Heisenberg system within the pair approximation

“…It is seen that T C is higher for z=6 (bulk system) for all J Ĵ // values and decreases gradually when J Ĵ // is increased, while the MFA predicts a linear decreasing [15]. Thus, our results are much closer to those obtained by field theory [16] or PA [17]. These results are equally in concordance with those obtained by Balcerzak et al [11] for S=1/2 and D=0.…”

Ordering phenomena in a heterostructure of frustrated and unfrustrated triangular-lattice Ising layers

“…The observation by Nienhuis et al [39] is crucial for explaining the BKT-like phenomena (η eff o ≈ 1/2 and its small temperature variation with η eff o 1/2) observed in the bilayer model. The standard procedure that we follow to describe this physics is to map the TLIA model (15) onto a height model, also known as the solid-on-solid model [39,45]. By working first on the GS manifold of the zero-field TLIA, namely, by excluding configurations that contain vortices for the moment, we assign an integer-valued height variable h i to each site i of the triangular lattice.…”

“…A number of previous studies focused on magnetic properties of simple Ising bilayers formed by two ferromagnetic (FM) layers coupled by an exchange interaction of varying strength [7][8][9][10][11][12][13][14][15][16]. Such bilayers have been shown to undergo phase transitions that belong to the 2D Ising universality class and their critical temperature is controlled by the shift exponent that depends on the interlayer to intralayer coupling ratio.…”

Critical behavior of a triangular lattice Ising AF/FM bilayer

“…Properties of Ising bilayers consisting of two different ferromagnetic layers coupled by either ferromagnetic (FM) or antiferromagnetic (AF) exchange interactions of varying strengths have been investigated in a number of studies [7][8][9][10][11][12][13][14][15][16]. Regarding their critical behavior, it has been found that they belong to the same universality class as a two-dimensional Ising model and their critical temperature is controlled by the so call shift exponents that depends on the interlayer to intralayer interaction ratio.…”