Ferrimagnetism in the Heisenberg–Ising bilayer with magnetically non-equivalent planes

Abstract

The Pair Approximation method is applied to the antiferromagnetic Heisenberg-Ising spin-1/2 bilayer with a simple cubic crystalline structure. The method allows for self-consistent calculations of thermodynamic quantities, based on the determination of Gibbs free-energy. In the paper the phase diagrams and planar magnetizations are calculated for the system in question. Special attention is paid to the case of magnetically non-equivalent planes, one of which is additionally randomly diluted. The occurrence of a compensation phenomenon is found and the compensation temperature is discussed for such a system. The characteristic concentration of magnetic atoms p , below which the compensation phenomenon vanishes, is examined as a function of the Hamiltonian parameters.

Compensation temperature in spin-1∕2 Ising trilayers: A Monte Carlo study

“…These diagrams show that, in both trilayer types, there is always a compensation temperature for a sufficiently small J AA /J BB irrespective of the value of J AB /J BB , although the range of values of J AA /J BB for which the phenomenon occurs increases as the A-B interplanar coupling gets weaker. This behavior is consistent for MC, EFA, and MFA approaches and similar to what is reported for the diluted bilayer [41,45] and multilayer [47,49] systems for sufficiently small dilutions.…”

“…53. We see the same behavior when we contrast the PA [45] and MC [41] results for the Ising bilayer, in which case the smaller area is also obtained through Monte Carlo simulations, i.e., the area seems to decrease as we use more accurate approximations. Thus, we expect that if the pair approximation were applied to the trilayer systems, the line separating the phases with and without compensation would fall in between the dashed (EFA) and solid (MC) lines in both Figs.…”

“…We present phase diagrams and a detailed discussion about the conditions for the occurrence of the compensation phenomenon. For instance, we see that the phenomenon is only possible if J AA < J BB and that the range of values of J AA /J BB for which there is compensation increases as |J AB /J BB | gets smaller, as it is also the case for similar systems containing a mixture of ferromagnetic and antiferromagnetic bonds [41,45,47]. The summary of the results is presented in a convenient way on J AB × J AA diagrams which separate the Hamiltonian parameter-space in two distinct regions: one corresponding to a ferrimagnetic phase where the system has a compensation point and the other is a ferrimagnetic phase without compensation.…”

“…Since the effective-field approach still takes into account short-range correlations, which are entirely neglected by a standard MFA, the EFA temperatures should still be closer to the MC values than the MFA ones. It is worth stressing that the same occurs when we contrast pair approximation (PA) [45] and Monte Carlo [41] results for a site-diluted Ising bilayer, in which case the PA temperatures are higher than the MC ones. Although the PA takes into account longer-range correlations than both EFA and MFA, it still systematically overestimates the temperatures since it is a mean-field-like approximation.…”

The dynamic magnetic behaviors of the Blume–Capel Ising bilayer system

“…Research on magnetic bilayers has received much interest both from the experimental and theoretical point of view in recent years [1][2][3][4][5][6][7][8][9][10]. Experimentally, several works have been published on the properties of the magnetic bilayer such as FePt/Fe [11], FM/TbFe (FM=Fe, Py-permalloy, FeCo) [12], SiGe, SiC and GeC [13], Ni/Au [14], Fe/Ni and Fe/Co [15].…”