Ferroic Structures

Ferromagnetic and ferroelectric materials are only two examples of a wider group that contains domains built up from switchable units. Such solids, which are called ferroic materials, exhibit domain boundaries in the normal state. These include ferroelastic crystals whose domain structure can be switched by the application of mechanical stress. In all such materials, domain walls act as planar defects running throughout the solid. 

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Some of the well-known ferroelectric materials are perovskite oxides. No ferroelectric oxide of K2NiF4 structure has been reported until now similarly, other ferroic properties 87) are yet to be explored. 

Main group oxides with three-dimensional structures or transition metal oxides with d or d configurations are wideband gap materials and are colorless when pure. As such they may serve as transparent optical materials or hosts for such applications as lasers or luminescent materials when properly doped. Others that lack a center of symmetry may have ferroelectric or ferroic properties that make them useful for a variety of device applications. Some of these may have nonlinear optical properties so important to modern communication networks (see Sections 6.3 and 6.5 and see Luminescence and see Ferroelectiicit. ... 

Figure 11.16. The number of different domains that are found in an actual crystal will depend on the number of different displacement directions that are possible. This is generally greater than two, and domain structures can be complicated. In general, crystals that exhibit a domain structure are called ferroic materials.

Ferroic is a generic term for crystals that have an internal structure that can be switched from one stable orientation to another that is equally stable, by the application of a suitable driving force along an appropriate direction. Multiferroics are... 

Characteristic feature of ferroics is the existence of at least two equivalent states which differ only in their orientations (either of some structural units or spontaneous electric/magnetic moment, or both) called orientation states. The term prototype phase means real or hypothetical phase of crystal where all of the orientational states are the same. It is clear that the prototype phase has higher point symmetry group, than real ferroic. Therefore there is a phase transition in a ferroic if [2] ... 

Another important feature of the ferroics is the possibility to control the domain structure by external fields. This basic feature has been introduced by Aizu [4,5], who coined the term ferroic . He defined ferroic as a material, which has two or more orientation states in the absence of magnetic field, electric field, and mechanical stress, and can shift from one to another of these states by means of magnetic field, an electric field, a mechanical stress or a combination of these . It is obvious, that when orientation states (domains) are converted to each other under the action of external fields, the interfaces (domain walls) separating them are transferred accordingly. 

In low-temperature phase, the order parameter is a sum of field-induced and spontaneous parts so that it becomes nonlinear function of external field due to domain structure influence. As a result, the field dependence of order parameters in the ferroics is described by hysteresis loops, schematically depicted in Fig. 1.1. The shape of these loops is close to those observed in specially prepared (e.g. by application of external field during the crystal growth) monodomain ferroics. One can see from Fig. 1.1 that order parameter in the ferroics contains spontaneous part (at zero field, where two opposite values of order parameter exist) and field-induced one, that saturates at large fields. Under the field decrease, order parameter first decreases and at some field called coercive, it becomes zero and then changes sign (so-called switching phenomenon) accompanied by strong nonlinearity. 

Besides above four types of ferroics, a large number of multiferroics with other structures is known. The information can be found in Refs. [2, 13, 14]. In the next section we discuss an important (both for fundamental science and applications) question about magnetoelectic coupling in the secondary ferroics with coexistence of magnetization and electric polarization (ferromagnetoelectrics in Table 1.1). 

The materials with ME effect consist of about 50 % composites and 25 % single phase systems, which are the secondary ferroics. The other 25 % include solid solutions, laminar structures consisting of several layers with thickness about one millimeter as well as nanostructures in the form of thin films, nanorods etc. 

We write Gibbs free energy for multicomponent order parameter t) (which are the components of magnetization, polarization or strain) for the case of monodomain ferroic. The latter is valid for small enough sizes (<100 nm), where the domain structure disappears [1-3]. For the materials with inversion center in paraphrase, the bulk (Gy) and surface (Gs) parts of free energy can be written as [4] ... 

Figure 3.13a shows the structure of orthorhombic V2O5 comer-shared paired chains of distorted VOs octahedra parallel to the c-axis share edges to create c-axis zigzag chains. Ferroic c-axis displacements of V atoms in the paired chains create asymmetric c-axis bonds 0. .. V = O, which places the V atoms in square-pyramidal sites. These chains share comers in the a—b planes with antiferroelectric coupling across shared edges to create the a—b layers of Fig. 3.13a. Li" ions can be inserted reversibly into the 6-axis tuimels to form 8-LiV205 via an intermediate 8-Li cV205 phase.

If the adaptronic structure requires temperature stability, active functional materials must be used since they can have a flat temperature response away from the phase transition and are controllable with external fields. Most materials in this category are ferroic materials, i. e., ferroelectric, ferromagnetic and ferroelastic materials. 

In contrast to polycrystaUine ceramic materials with ferroic properties, there exist nonferroic single crystal piezoelectrics such as a-quartz or materials with a calcium gaUium germanate (CGG) structure, as well as single crystal pyroelectrics with perovskite structure such as lithium tantalate (IiTa03). 

As shown in Table 8.1, the piezoelectric effect causes the creation of charges in a dielectric and ferroic materiaL respectively, in response to an applied stress field. The opposite effect-that is, the induction of strain (deformation) by applying an outside electric field-is called the inverse piezoelectric effect. Piezoelectricity requires that no symmetry center exists in the crystal structure. The piezoelectric properties of ceramic materials are described by four parameters (i) the dielectric displacement D (ii) the electric field strength E (iii) the applied stress X and (iv) the strain (deformation) x. These are related by two equations that apply to the (direct) piezoelectric effect D = e x and E = h x, and two equations that apply to the inverse piezoelectric effect x = g D and x = d E. The four coefficients e, h, g, and d are termed the piezoelectric coefficients. 

These materials have the ilMnOs R = Sc or small, rare earth cation) stoichiometry,and have been erroneously referred to as hexagonal perovskites. The compounds do not exhibit the perovskite structure. The Mn cations are not octahedrally coordinated, rather the cation is surrounded by five oxide anions in a trigonal prismatic coordination environment. Also the R cations are not 12-coordinate, as would be the case in a perovskite, but are in seven-fold coordination. The materials are multi-ferroic, with anti-ferromagnetic and ferroelectric properties.The nature of the polarity and therefore the ferroelectric behaviour was only recently described. Careful structural studies indicated that although the dipole moments are attributable to the R-O bonds and not the Mn-O bonds, the R-cations are not directly responsible for the ferroelectric behaviour. The noncentrosymmetry is attributable to the tilting of the MnOs polyhedra, which in conjunction with the dipole moments in the R-O bonds results in ferroelectric behaviour. Thus the ferroelectric behaviour in these materials is termed improper " and occurs by a much different mechanism than BaTiOs or even BiFeOs. 

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