Size and doping effects on the coercive field of ferroelectric nanoparticles: A microscopic model

Abstract

A microscopic model for describing ferroelectric nanoparticles is proposed which allows us to calculate the polarization as a function of an external electric field, the temperature, the defect concentration and the particle size. The interaction of the constituents of the material, arranged in layers, depends on both the coupling strength at the surface and that of defect shells in addition to the bulk values. The analysis is based on an Ising model in a transverse field, modified in such a manner to study the influence of size and doping effects on the hysteresis loop of the nanoparticles.Using a Green's function technique in real space we find the coercive field, the remanent polarization and the critical temperature which differ significantly from the bulk behavior. Depending on the varying coupling strength due to the kind of doping ions and the surface configuration, the coercive field and the remanent polarization can either increase or decrease in comparison to the bulk behavior. The theoretical results are compared with a variety of different experimental data. 5, 6 ). In particular, we analyze the behavior of spherical FE particles, which are depicted in Fig. 1. In case of BTO the bulk interaction parameter is J b = 150 K and the transverse field is Ω b = 10 K. Due to the different numbers of next nearest neighbors on the surface the interaction strength J can take different values for the surface, denoted by J s , and for the bulk, labeled as J b , compare also [21]. Firstly, let us consider the hysteresis loop for different surface configurations represented by the interaction constant J s at a fixed temperature T = 300 K and fixed N. The results for a particle with N = 8 shells are shown in Fig. 2.One observes that the coercive field E c is sensitive to variations of the interaction parameter J. If the coupling at the surface is smaller J s = 50K as that in the bulk J b = 150 K (dashed line), the coercive field E c and the remanent polarization σ r are reduced in comparison to the case for J s = J b (solid line). With other words, the coercive field is lowered when the critical temperature of the system is decreased due to the smaller J s value. In the opposite case J s > J b (dotted line) both, the coercive field E c and the remanent polarization σ r increase compared to J s = J b . Because of the enlarged value of J s the phase transition temperature

Synthesis and characterization of nanostructured (Pb1−xSrx)TiO3thin films by a modified chemical route

“…Figure 4c shows the calculated lattice parameters and tetragonality (c/a) of PST films, which is consistent with the report by Chu et al [18] for pure PbTiO 3 . The significant reduction in the value of c/a with Sr concentration is due to the closely matched ionic radii of both Pb (1.33 Å ) and Sr (1.32 Å ), which can slow down the diffusion rate of Sr 2 þ and Pb 2 þ ions, resulting in small grains and consequent low growth along the c-axis [22]. The average grain size was obtained from the Scherer relation and their mean values are given in Table 1.…”

Light transmission through metallic two-dimensional arrays of compound coaxial structures with central and annular apertures: A charge oscillation picture

“…16,17 For subwavelength apertures, the basic twodimensional ͑2D͒ TE 1,0 mode plays an important role in the process of extraordinary transmission. 18 For coaxial apertures, many theoretical [19][20][21][22] and experimental [23][24][25] studies of their transmission properties have been reported. It has been found that some transmission peaks in annular circular apertures are attributed to the resonances of TE m,1 guide modes.…”

Phase transformation properties of finite size ferroelectric thin film with structural transition zones

“…1 In view of the sustained trend toward further miniaturization of electronic devices, the investigation of surface and size effects in ferroelectric thin films is practically important. There have been a lot of experimental [2][3][4][5][6][7][8][9][10] and theoretical [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] efforts devoted to study these important effects.…”