Random field effects on the anisotropic quantum Heisenberg model with Gaussian random magnetic field distribution

Abstract

Effect of Gaussian random magnetic field distribution which is centered at zero on the phase transition properties of isotropic quantum Heisenberg model has been investigated on two (2D) and three dimensional (3D) lattices within the framework of effective field theory (EFT) for a two spin cluster (which is abbreviated as EFT-2). Beside the phase diagrams and the evolution of the magnetization versus temperature curves with the Gaussian magnetic field distribution width, critical Gaussian distribution width values, which make the critical temperature zero, have been obtained for several lattices. Moreover, it has been concluded that all critical temperatures are of the second order and reentrant behavior does not exist in the phase diagrams.Keywords: Quantum isotropic Heisenberg model; Random magnetic field; Gaussian magnetic distribution IntroductionRecently, there has been growing theoretical interest in the random field lattice spin models. The model was introduced for the first time by Larkin [1] for superconductors and later generalized by Imry and Ma [2]. Ising model which is the most basic lattice spin model with quenched random field (RFIM) has been studied over three decades, since this model can be used to describe a wide variety of disordered systems. Diluted antiferromagnets (such as F e x Zn 1−x F 2 , Rb 2 Co x M g 1−x F 4 and Co x Zn 1−x F 2 ) in a homogenous magnetic field behave like ferromagnetic systems in the presence of random fields [3,4]. Structural phase transitions in random alloys, commensurate chargedensity-wave systems with impurity pinning, binary fluid mixtures in random porous media, and the melting of intercalates in layered compounds, such as T iS 2 [5] are the examples of the experimentally accessible disordered systems which can be described by RFIM. Besides, RFIM can mimic the phase transitions and interfaces in random media [6,7], e.g pre-wetting transition on a disordered substrate can be mapped onto a 2D RFIM problem [8]. RFIM has also been applied to describe critical surface behavior of amorphous semi-infinite systems [9,10].RFIM has been widely studied in the literature with discrete [11,12,13,14,15], as well as continous [16,17,18,19,20,21] distributions. Random distribution of the magnetic field may produce drastic effects on the phase diagrams and related magnetic properties of the system. It has been shown that Ising systems under the influence of discrete symmetric distributions, like bimodal [11] and trimodal [12] distributions, exhibit tricritical behavior, while continuous symmetric distributions like Gaussian distribution [16] lead to only second order transitions.Although the results of the RFIM have been reported for both discrete and continuous distributions, there has been less attention paid on the random field effects on the Heisenberg model. Since Heisenberg model is more realistic model than the Ising model for the spin systems, it is important to investigate this model in the presence of quenched random fields. Albuquerque and Arruda [22] studi...

Investigation of stabilization and survival of skyrmion vortices in the presence of magnetic field disorder in two-dimensional lattices: a case study for Janus dichalcogenides

“…It is also a crucial task to understand and clarify the influence of randomness on the stabilization of the skyrmion phase in ML magnets exhibiting the lack of inversion symmetry for the spintronic systems which have potential in practical applications. To the best of our knowledge, the magnetic properties of 2D FM lattices with random disorders have been scarcely studied in the literature [53][54][55][56][57][58][59][60][61]. Moreover, the problem in the non-zero DMI case still remains as an open problem, which is the primary objective of the present work.…”