Study of Phase Transition Properties in Epitaxial Ferroelectric Film

Based on the transverse Ising model and using decoupling approximation to the Fermi-type Green's function, we study the phase transition properties of the epitaxial ferroelectric film with one substrate. A general recursive equation of the ferroelectric thin film with two n-layer materials is obtained, which enables us to study the phase transition properties for any number layers forepitaxial ferroelectric thin film. With the help of this equation, we analyze the effect of the exchange interaction and the transverse field in the phase diagram, the influence to the polarizations and Curie temperature numerically. The results show that epitaxial ferroelectric film are able to induce a strong increase or decrease of Curie temperature to different exchange interactions and transverse fields within the epitaxial film layers. The theoreticalresults are in reasonable accordance with experimental data of different ferroelectric thin film.     

Properties of ferroelectric thin films with a first-order phase transitions

A Green's function technique is used to investigate the properties of ferroelectric thin films with a first-order phase transitions on the basis of the transverse Ising model. Taking into account the four-spin interactions beside the two-spin interactions the dependence of the polarization on film thickness and temperature and the thickness dependence of the Curie temperature become more complicated.     

Spin-Polarization of Ferroelectric Supperlattice with Spin-1/2 Transverse Ising Model

By using the simple decoupling approximation to Fermi-type Green's functionfor the transverse Ising model under pseudospin theory, we systemicallystudy the influence of different exchange interactions (transverse fields)of the two distinct materials on the polarization and Curie temperature offinite alternating superlattice. Meanwhile, we analyze the effect of thewhole parameters of the top surface, present their influence on thepolarization of each layer (including the mean polarization of the wholeferroelectric superlattice) and on the Curie temperature. The results showthe ratio of the exchange interactions (the transverse fields), which are ofthe two alternating materials have deeply impact on the polarization andCurie temperature of the supperlattice. Moreover, the top surface also hasgreat influence on the whole ferroelectric superlattice.     

Epitaxy surface effect on the first-order phase transition properties in a ferroelectric thin film

By modifying the interchange interactions and the transverse fields on the epitaxy surface layer,this paper studies the phase transition properties of an n-layer ferroelectric thin film by the Fermi-type Green’s function technique based on the transverse Ising model with a four-spin interaction.The special attention is given to the effect of the epitaxy surface layer on the first-order phase transition properties in the parameter space constructed by the ratios of the bulk transverse field and the bulk four-spin interaction to the bulk two-spin interaction with the framework of the higher-order decoupling approximation to the Fermi-type Green’s function.The results show that the first-order phase transition properties will be changed significantly due to the modification of interchange interaction and transverse field parameters on the epitaxy surface layer.The dependence of the first-order phase transition properties on the thickness of ferroelectric thin films is also discussed.     

Investigation of the seeding-layer effect for a ferroelectric thin film with the transverse Ising model

The transition feature of a ferroelectric thin film with a seeding layer is studied based on the transverse Ising model. The influence of the seeding layer on the transition behavior of a ferroelectric thin film is investigated systemically, and the effect of the interaction parameters for the seeding layer on the phase diagram is also obtained. Meanwhile, the polarization and Curie temperature of the ferroelectric thin film are calculated for different seeding-layer structures. The results show that the polarization and Curie temperature of the film will be obviously modified on adding a seeding layer.     

Influence of Surface Transition Layers on Phase Transformation and Pyroelectric Properties of Ferroelectric Thin Film

Taking into account surface transition layers （STLs）, we study the phase transformation and pyroelectric properties of ferroelectric thin films by employing the transverse Ising model （TIM） in the framework of the mean field approximation. The distribution functions representing the intra-layer and inter-layer couplings between the two nearest neighbour pseudo-spins are introduced to characterize STLs. Compared with the results obtained by the traditional treatments for the thin films using only the single surface transition layer （SSL）, it is shown that the STL model reflects a more realistic and comprehensive situation of films. The effects of various parameters on the phase transformation properties have shown that STL can make the Curie temperature of the film higher or lower than that of the corresponding Sulk material, and the thickness of STL is a key factor influencing the film properties. For a film with definite thickness, there exists a critical STL thickness at which ferroelectricity will disappear when the intra-layer and inter-layer interactions are weak.     

EFFECTS OF LONG-RANGE INTERACTIONS ON THE FERROELECTRIC FILM

The effect of long-range interactions on the spontaneous polarization and the Curie temperature of the ferroelectric film is investigated by use of the Landau theory. On the assumption that the nearest-neighbour interaction remains constant, we find that the spontaneous polarization and the phase transition temperature increase with the enhancement of the long-range interactions. In the case of positive extrapolation length, the critical thickness of the ferroelectric film, in which a size-driven phase transition occurs, decreases with the enhancement of the long-range interactions.     

High-temperature dynamics of surface magnetism in iron thin films

Finite-temperature magnetic properties of iron thin films are investigated by computer simulation over a broad range of temperatures up to the point of the ferromagnetic–paramagnetic phase transition. The coupled dynamics of atoms and magnetic moments is treated using the large-scale spin–lattice dynamics (SLD) algorithm. We investigate surface and bulk magnetic properties of iron, and how these properties vary as a function of temperature, film thickness and surface crystallography. We find that magnetization at surfaces is enhanced at low temperatures and suppressed at higher temperatures, in agreement with experimental observations. The effective Curie temperature of a film decreases as a function of thickness. Short-range magnetic order and non-vanishing spin–spin spatial correlations are found above the Curie temperature. The spin autocorrelation functions exhibit slower oscillations with longer decoherence times near the surface. We also find that the directional spin disorder has a significant effect on the surface strain.     

Exchange Interactions and Curie Temperatures of 3D- and 2D-Ferromagnets

Effective exchange interactions in bulk ferromagnets as well as in magnetic overlayers on Cu(001) covered by a Cu-cap layer of varying thickness were determined from first principles by mapping of corresponding total energies onto the effective Heisenberg model in the framework of the adiabatic approximation and magnetic force theorem. The effective Heisenberg model is then used to determine spin-wave stiffness constants and Curie temperatures evaluated in the framework of the random-phase approximation. Calculations are in a fair agreement with available experimental data for bulk ferromagnets and reproduce an oscillatory Curie temperature of magnetic overlayers as a function of Cu-cap thickness in a qualitative agreement with recent experiments.     

Oscillatory curie temperature of two-dimensional ferromagnets

The effective exchange interactions of magnetic overlayers Fe/Cu(001) and Co/Cu(001) covered by a Cu-cap layer of varying thickness were calculated in real space from first principles. The effective two-dimensional Heisenberg Hamiltonian was constructed and used to estimate magnon dispersion laws, spin-wave stiffness constants, and overlayer Curie temperatures within the mean-field and random-phase approximations. Overlayer Curie temperature oscillates as a function of the cap-layer thickness in a qualitative agreement with a recent experiment.     

Curie temperatures of CoPt ultrathin continuous films

The effects of layer thickness and thermal annealing on Curie temperature have been studied for CoPt ultrathin continuous layers in AlN/CoPt multilayer structures. It is found that there exists a critical thickness below which Curie temperature rapidly decreases due to the loss of spin-spin interactions in the vicinity of interface. After high temperature annealing, the in-plane lattice constant of CoPt film is increased and the exchange coupling parameter is decreased. Consequently, Curie temperatures decrease for some films with large thickness, compared with as-deposited state. Upon annealing at 600?^°C, CoPt undergoes ordering transformation, which also contributes to the degradation of the Curie temperature. However, when the CoPt film thickness is below 2?nm, the Curie temperature is increased after annealing. Especially for 1?nm thick film, the Curie temperature is strikingly increased from 173?^°C to 343?^°C after annealing at 600?^°C. This effect is attributed to the out-of-plane lattice deformation of CoPt thin layers in AlN/CoPt multilayer structures.     

Study of Defect-Layers Effect in Ferroelectric Thin Film with TransverseIsing Model

By taking into account the two-spin interaction in the transverse Ising model (TIM), the influence of the defect layers (including J_B andΩ_B on the polarization and Curie temperature are calculated numerically, within the framework of the decoupling approximation under Green's function. The numerical results show that the polarization and Curie temperature will both become large sensitively due to the large values ofJ_B and the small value of Ω_B of the defect layers. Meanwhile, the dependence of the crossover values of the exchange interaction J_A, the transverse field Ω_Aof the bulk material on the exchange
interaction J_B and the transverse fieldΩ_B of the defect layers are shown in 3-Dimensional (3-D) figures for the first time. Moreover, the transition features of the ferroelectric thin film with defect layers are presented.     

A Thin Liquid Film and Its Effects in an Atomic Force Microscopy Measurement

Recently, it has been observed that a liquid film spreading on a sample surface will significantly distort atomic force microscopy （AFM） measurements. In order to elaborate on the effect, we establish an equation governing the deformation of liquid film under its interaction with the AFM tip and substrate. A key issue is the critical liquid bump height yoc, at which the liquid film jumps to contact the AFM tip. It is found that there are three distinct regimes in the variation of yoc with film thickness H, depending on Hamaker constants of tip, sample and liquid. Noticeably, there is a characteristic thickness H^＊ physically defining what a thin film is; namely, once the film thickness H is the same order as H^＊, the effect of film thickness should be taken into account. The value of H^＊ is dependent on Hamaker constants and liquid surface tension as well as tip radius.     

Investigation of the crossover properties for the interaction parameters of a ferroelectric thin film

The crossover feature, from the ferroelectric-dominant phase diagram (FPD) to the paraelectric-dominant phase diagram (PPD), for the interaction parameters of a ferroelectric thin film described by the transverse Ising model have been calculated in detail by the use of the mean-field approximation. The crossover values of the exchange interactions and the transverse fields for a thin film with certain layers are displayed as a curved surface in the three-dimensional parameter space. The numerical results show that for thin films with different numbers of layers there exists a common intersection line for the curved surfaces of the crossover values. Meanwhile the layer-independent equation for the intersection line is obtained for the first time.     

Curie temperature of a spin-one bethe lattice

The exact expression for the Curie temperature of a spin-1 Bethe lattice with dipolar and quadrupolar interactions is derived and the nature of variation of the Curie temperature with quadrupolar interaction constant is studied.     

用横场伊辛模型研究应力对铁电薄膜的热力学性质的影响

用横场伊辛模型研究了铁电薄膜的热力学性质.在体系的哈密顿量中引入一个两维的在平面内的应力，并假设应力从基底材料和薄膜材料之间的界面层到薄膜的表面层是呈指数形式衰减的.结果显示：压应力有利于极化，使居里温度向高温区移动，而张应力对极化和居里温度的影响正好相反.扩散长度对铁电薄膜的热力学性质有很大的影响. 关键词： 铁电薄膜 应力 横场伊辛模型     

Ultrathin Co/Cu(110) film as a lattice of ferromagnetic grains with dipolar interaction

The well-known fact of magnetic ordering in ultrathin Co films (with an effective thickness of several monoatomic layers) on a single-crystal Cu(110) substrate is described quantitatively using the model according to which the thin film is a lattice of three-dimensional ferromagnetic grains with dipole-dipole interactions. The critical film thickness corresponding to the ferromagnetic transition and the corresponding Curie temperature were calculated.     

X-ray study of the wetting behaviour of CCl4 on Si/SiO2 surfaces

The complete wetting of an uncoated silicon wafer covered with a native oxide layer by saturated vapour of carbon tetrachloride was studied by using the x-ray reflectivity-technique. Differential heating of the substrate relative to a liquid reservoir was used to examine the disjoining pressure as a function of film thickness. The measurements were done at the temperaturesT=308K andT=318K of the reservoir. The observed film thicknesses varied between 26Å and 345Å depending on the temperature difference. A model for explaining the measured film thickness as a function of the temperature difference in terms of van der Waals forces is presented. It is based on the non-retarded interaction and includes terms of higher order in the film thickness. Microscopic constants like the Hamaker constant were determined and compared with reported values.     

Ferrimagnetic magnetizations of transverse Ising thin films with diluted surfaces

The temperature dependences of longitudinal and transverse magnetizations in transverse Ising thin films with diluted surfaces which are coupled antiferromagnetically to the bulk are studied by the use of the effective-field theory (EFT) with correlations. Novel features are obtained for the thermal variations of longitudinal magnetization, being different from those of the bulk ferrimagnetic materials, such as the possibility of two compensation points. They are depending on the thickness of a film and the surface dilution. These characteristic phenomena come from the competition between the surfaces and the bulk when the ratios of the physical parameters (transverse field and exchange interaction) between the surfaces and the bulk are selected as some large values.     

Thickness-dependent Curie temperatures of ultrathin magnetic films: effect of the range of spin-spin interactions

We present a simple model of spin-spin coupling which provides insight into the nature of the rapid decrease in the Curie temperature with decreasing thin film thickness n (number of monolayers). The shift of Curie temperature t(n) = 1-T(c)(n)/T(c)(infinity) follows the usual power law t(n) approximately n(-lambda) in thin films crossing over to linear behavior t(n) approximately n in the ultrathin film thickness limit. Experimental results for ferromagnetic thin films are compared, and shown to follow curves of t(n) with lambda values dependent on the nature of the spin-spin interactions.