Primary ferroics

A hexagonal representation of proper and improper primary ferroics as proposed by Newnham Cross (1981) is given in Fig. 6.54. The order parameter for proper ferroics appears on the diagonals of the hexagon, while the sides of the hexagon represent improper ferroics. They indicate the cross-coupled origin of ferroic phenomena. An improper primary ferroic in this classification is distinguished from a true secondary... 

If the switching of a crystal from one orientational state to another can be performed by application of one kind of external field, the material belongs to the primary ferroics (e.g. ferroelectrics, ferromagnets). 

Fig. 1.1 Schematic view of order parameter hysteresis loops in the primary ferroics... 

It has already been indicated in the Sect. 1.1 that the primary, secondary and higher-order ferroics are defined by the number of external fields necessary to switch the ferroic from one orientational state to another. In particular, the primary ferroics can be switched under the application of one kind of physical fields (magnetic, electric, elastic). Besides three mentioned types of primary ferroics, there are six more types of secondary ones, where the difference between orientational (domain) states thermodynamic potential (free energy) Ag is proportional either to square or to the product of external fields as it is shown in the Table 1.1. 

The main difference between primary ferroics and those of the higher orders is related to the fact, that at least one pair of the domains in the primary ferroics has opposite direction of order parameter, while the same pair in the higher-order ferroics can be induced by corresponding set of external fields. For example, in ferrobielectric, the domain pairs have the same orientations of polarization P, so that field-induced domain reorientation can be represented via induced polarization difference as follows ... 

Short-Range Order Ousters in Primary Ferroic Glasses... 

The existence of ferroelectric phase in sufficiently thin antiferroelectric films had been revealed experimentally in several works [64-66]. In Ref. [64], the switchable ferroelectric polarization has been observed in PbZrOs antiferroelectric thin film on Si substrate. It has been revealed, that both in the latter film and in one more antiferroelectric BiNb04 one, the ferroelectric phase appears only if the film thickness is smaller then certain threshold value, which depends on material parameters. For instance, the ferroelectric hysteresis loop has been observed [65] in 100 nm thick PbZrOs/Si Alms, while those thicker than 400-500 nm revealed antiferroelectric behavior. Note, that the other primary ferroic demonstrates the same behavior. Namely, the films of antiferromagnetic BiFeOs on SrTiOs substrate reveal the emergence of ferromagnetism at the thicknesses less than 100 nm [67]. 

In this Chapter, contrary to Chaps. 2 and 3, where primary ferroics were considered, we are going to pay more attention to multiferroics with coexistence of ferroelectric and magnetic order. We will consider these multiferroics in the form of thin films on subsfrate [9, 10] or nanowires [11] on the example of quantum paraelectric EuTiOs. The necessity of detailed consideration of magnetoelectric effects in such systems is pretty obvious also. 

Ferroic domairts (or domairts in domain twin) differ in the orientation of sporrla-neous electric polarization, spontaneous magnetization or spontaneorrs strain in case of so-called primary ferroics. Magnitude of the sporrtaneoirs qirarrtity is typically the same in both domains btrilding domain twin, tensor components are different (i.e. vector components for polarization and magnetization and syrranetrical second-order tensor components for mechanical strain). Situation is more complicated for... 

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