Effects of the randomly distributed magnetic field on the phase diagrams of the transverse Ising thin film

Abstract

The effect of the zero centered Gaussian random magnetic field distribution on the phase diagrams and ground state magnetizations of the transverse Ising thin film has been investigated. As a formulation, the differential operator technique and decoupling approximation within the effective field theory has been used. The variation of the phase diagrams with the Gaussian distribution width (σ) has been obtained and particular attention has been paid on the evolution of the special point coordinate with distribution parameter. In addition, the ground state longitudinal and transverse magnetization behaviors have been investigated in detail. IntroductionRecently there has been growing interest both theoretically and experimentally on the finite magnetic materials especially on semi-infinite systems and thin films, since the magnetic properties of free surfaces are drastically different from the bulk material, because the free surface breaks the translational symmetry, i.e. surface atoms are embedded in an environment of lower symmetry than that of the inner atoms [1,2]. If the surface exchange coupling is greater than a critical value, the surface region can exhibit an ordered phase even if the bulk is paramagnetic and it has a transition temperature higher than the bulk one. This fact has been observed experimentally [3,4,5].Also, the development of the molecular beam epitaxy technique and its application to the growth of thin metallic films has stimulated renewed interest in thin film magnetism. It was experimentally found that, the Curie temperature and the average magnetic moment per atom increases with the increasing thickness of the film [6,7]. Thin films can be modeled by Ising model due to the fact that, many ultrathin films do indeed exhibit a strong uniaxial anisotropy [8]. These systems have been widely studied in literature by means of several theoretical methods such as Monte Carlo (MC) simulations [9,10,11,12,13,14], mean field approximation (MFA) [15,16] and effective field theory (EFT) [17,18].But the study of ferroelectric films treated by transverse Ising model (TIM) are more common in the literature. Oxide thin films with perovskite-type structure (such as Barium titanate BaT iO 3 and Strontium titanate SrT iO 3 ) have been fabricated [19,20,21] and novel physical properties found in these ferroelectric thin films which have many application areas in technology [22], such as 1 umit.akinci@deu.edu.tr 1

Magnetic hysteresis, compensation behaviors, and phase diagrams of bilayer honeycomb lattices

“…The Ising model is a well-known pioneering theoretical model that is widely used in magnetic systems and which plays an important role in understanding in-depth the phase transitions and critical phenomena. Recently, thin films have been widely studied by means of Monte Carlo (MC) simulations, [36][37][38][39][40][41] mean-field approach (MFA), [42][43][44] and the effective-field theory (EFT) [45][46][47][48][49][50][51] along with well-known theoretical methods in equilibrium statistical physics in the liter-ature of Ising systems. Despite these studies, as far as we know, the hysteresis and compensation behaviors of BHL Ising system have not been investigated.…”

Random field distributed Heisenberg model on a thin film geometry

“…see references in Ref. [16]). Thin films which do not exhibit a strong uniaxial anisotropy requires to solve the Heisenberg model in the thin film geometry.…”

The Effect of Next Neareast Neighbor Ineraction on Thermodynamic Properties of Ultrathin Magnetic Films

“…Several models have been used to investigate the features of the films such as: Heisenberg model, transverse Ising model, XY model… Among them, the transverse Ising model (TIM) is often used because of its simplicity and usefulness. There are many works has applied TIM to investigate magnetic thin films within the framework of the mean field theory and effective field theory [4][5][6][7]. In a previous work [8], we investigated the dependence of the order-disorder phase transition temperature on the transversal field and obtained the explicit equation for this temperature.…”