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