Improper ferroelectrics

Bousquet E, Dawber M, Stucki N, Lichtensteiger C, Hermet P, Gariglio S, Triscone J-M, Ghosez P (2008) Improper ferroelectricity in perovskite oxide artificial superlattices. Nature (Lond) 452 732... 

Ferroelectricity can arise in a number of ways other than that described previously, in which dipoles are generated in a crystal structure and combine to give a spontaneous polarisation if the crystal symmetry permits. These alternatives have been called improper ferroelectricity (perhaps better extrinsic ferroelectricity, see Lines and Glass 2001). In essence, improper ferroelectricity is ferroelectricity which is not due to the normal polarisation of the stmcture but arises from other interactions. Improper ferroelectricity has been considered to be rare in bulk materials and is a weak effect, usually rather difficult to detect, but the creation of artificial superlat-fices and studies of layered perovskites have changed this and now improper ferro-electrics are becoming widely studied. 

In the layered Ruddlesden-Popper and Dion-Jacobson phases, improper ferroelectricity can also arise in a form termed hybrid improper ferroelectricity. Here, the ferroelectricity arises when two non-polar rotations of BO octahedra combine to produce a polar stmcture. The same effect may well also occur in the Aurivillius phases although this has not yet been proven. The creation of improper ferroelectric polarisation due to magnetic interactions in multiferroic perovskites is described in Section 7.10. 

In this section we consider a new mechanism of the Unear homogeneous magnetoelectrics or multiferroics (improper ferroelectrics-(anti)ferromagnets) creation with the help of the flexomagnetic effect. The ferroelectric-(anti)ferromagnetic... 

In this section we show the emergence of improper ferroelectric phase. The physical reason for such emergence is either the application of external stresses to the bulk (with or without domain structure) ferromagnets or action of internal stresses existing in geometrically confined ones with flexomagnetic effect. These stresses, due to FME coupling, can induce the electric polarization and hence the improper ferroelectricity. 

The improper ferroelectricity origin can be roughly explained in the following way, see Fig. 4.31a. Elastic strain induces the polarization vector F, dil]uki via the flexoelectric and piezoelectric effects. Since the strain... 

Table 4.4 Ferromagnets-improper ferroelectrics due to the flexomagnetic effect (multiferroics of the type II)...

It is rather important that the FME effect (4.56b) can induce the spontaneous polarization (i.e. improper ferroelectricity) in the antiferromagnets. Equation of state for polarization vector follows from the variation of the free energy (4.33) 8Fp/8P, — 0. Variation of the Eq. (4.56) leads to the built-in field appearance in the right-hand side of the equation for polarization... 

One can find all the symmetry groups of antiferromagnets, which can be improper ferroelectrics due to nonzero flexomagnetic effect (in some instances Qij / 7 0) in the paper [96]. Note that seven of the groups have no conventional linear ME effect. So, the linear FME coupling gives rise to the size-dependent linear magnetoelectricity in the type-II multiferroic nanosystems. 

Research to obtain further improvements in the performance of pyroelectric imaging systems is proceeding in several directions. Some further improvement in the spatial resolution obtainable with the vidicon will be obtainable with the reticulated targets which are now being fabricated [8.64]. Improper ferroelectrics offer improved materials [8.64a]. However, another approach is to develop smaller and more rugged tubes with lower power consumption aimed at providing cheaper and more convenient tubes for those applications for which the present performance is adequate [8.65, 66]. 

In the proper ferroelectrics, the spontaneous polarisation appears as a result of the polarisation catastrophe or, in other words, due to electric dipole-dipole interactions. There are also improper ferroelectrics, in particular, liquid crystalline ones, in which a structural transition into a polar phase occurs due to other interactions and, consequently, appears as a secondary phenomenon. We shall discuss this case later. For simplicity, the square of spontaneous polarisation vector can be taken as a scalar order parameter for the transition from the higher symmetry paraelectric phase to the lower symmetry ferroelectric phase. Therefore, in the absence of an external field, we can expand the free energy density in a series over P (T) and this expansion for ferroelectrics is called Landau-Ginzburg expansion ... 

However, the FLCs are improper ferroelectrics as the primary order parameter is the tilt angle and not the polarization. " Nevertheless, both these quantities are roughly proportional except the vicinity of the Sm C -Sm A phase transition, " which in most cases is of the second-order one. 

In the absence of any constraints, the direction of Ps rotates from one smectic layer to the next, with a period equal to the smectic C pitch, and so the average polarization for a sample would be zero. However, surface treatment or application of a field can cause the helix to untwist, resulting in a permanently polarized sample. The spontaneous polarization arises from a preferred alignment of molecular dipole components which are perpendicular to the molecular long axis, but it behaves differently from the ferroelectric and ferromagnetic polarization characterised for crystals. The liquid crystalline ferroelectric phases identified so far are improper ferroelectrics, since the spontaneous polarization results from a symmetry constraint, whereas in proper ferroelectrics the polarization results from dipole -dipole interactions. The Curie-Weiss law for proper ferroelectrics predicts a second order phase transition at the Curie temperature from the high temperature paraelectric state to a permanently polarized ferroelectric state ... 

Ferroelectrics in which the polarization P is not the primary order parameter are called improper ferroelectrics. The concept was introduced by Dvofak [88] in 1974. As we have seen in the last example, improper ferroelectrics may behave very differently from proper ferroelectrics. The differences are related to the nature of the coupling. If we write the coupling term -Xq P, our first example showed that for n = 1, the behavior may, however, be very similar to that of proper ferroelectrics. This class of improper ferroelectrics for which = 1 is called pseudoproper ferroelectrics. Ferroelectric liquid crystals belong to this class. 

I phases, smectics 16 Idemitsu polymer FLC 651 irainomethyl, spacers 846 iminopyridine complexes, metallomesogens 905 improper ferroelectrics 537 f improved Alt-Pleshko addressing technique (lAPT) 207... 

In the SmC liquid crystals, the primary order parameter is the director tilt and not the spontaneous polarization. The polarization, therefore, is often called secondary-order parameter, and the SmC materials are called improper ferroelectrics. The main reason for this is the weakness of the dipole-dipole interactions in the molecules. The polar order can be estimated by the ratio of the actual spontaneous polarization and which is the value that would appear when complete polar order is assumed. From its definition, the polarization is the density of the molecular dipoles. Assuming molecular dipoles of 3 Debye ( 10 Cm) and typical molecular weight of 300 g, density of about 1 g/cm = 10 kg/m, we get that in 1 m we have 6 10 molecules, which would give Po 2 W C/m = 2000nC/cm. For a SmC with Pg <100 nC/cnP, this means that less than 5% of the dipoles are ordered in one direction. For this reason, in the first approximation the polarization is proportional to the tilt angle. This relation, indeed, is found to be true for materials with moderate or low polarization. However, for materials with large polarization, like Pg 500 nC/cm, the dipole-dipole interaction becomes considerable, and the proportionality is not true. The deviation is more pronounced at lower temperatures, when the dipole-dipole... 

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