Antiferroelectric hysteresis loop

It could be expected, that built-in electric field (acting like external field) could transform antiferroelectric film into ferroelectric one. In bulk antiferroelectrics such transformation takes place when external field is higher than critical fields Ei and En, which define the position and width of antiferroelectric hysteresis loop [61,71]. The absolute values of these fields can be written in the form [70] ... 

Rg.ft.5-2 Antiferroelectric hysteresis loop. crit, critical field... 

PbZrO-i (LB Number 1A-15). This crystal is antiferro-electric below about 230 °C (Fig. 4.5-27), exhibiting a typical antiferroelectric hysteresis loop (Fig. 4.5-28). Solid solutions of this substance are very important in technological applications (see PZT and PLZT below). 

Fig. 4.5-28 PbZrOs. Rent versus T. Rent is the critical field of the antiferroelectric hysteresis loop...

MHPOBC, ii--(l-methylheptyl oxycarbony )phenyl 4 -octyloxybiphenyl-k-carboxylate (LB Number 71B-1 (A)) (Liquid Crystai). Seven phases are known for this liquid crystal. It exhibits an antiferroelectric hysteresis loop at low frequency, as shown in Fig. 4.5-96a, between... 

In detailed studies of this mixture, strong evidence was obtained suggesting that the new achiral smectic phase is antiferroelectric. This consisted mainly of the observation of a double hysteresis loop in the polarization vs. applied electric field curve for the material.30 In addition, it was shown that the mixture is a... 

P, which can be switched by an electric field, E, as illustrated in the P vs. E hysteresis loops in Figure 2) in favor of the non-ferroelectric cubic and antiferroelectric (AFE) phases. At a 65/35 ratio of PbZr03 to PbTi03, a concentration of 9.5% lanthanum is sufficient to reduce the rhombohedral-cubic phase transi-... 

An 8.2/70/30 composition is antiferroelectric at zero field but becomes ferroelectric when fields greater than lMVm-1 are applied. As a consequence the hysteresis loop has a narrow region at low fields which develops into a normal saturating characteristic at higher fields (Fig. 8.13). This behaviour is temperature sensitive but occurs to a sufficient extent for practical application between 0 and 40 °C. 

Figure 6.16 (a) Typical double hysteresis loop for an antiferroelectric perovskite... 

In some materials the antiferroelectric state is barely stable or metastable. In such materials, application of an electric field will convert the phase to ferroelectric, as described, but removal of the field leaves the phase in a ferroelectric state. This material then behaves like a typical ferroelectric and displays a conventional hysteresis loop. Heating the material to a high temperature so as to form the paraelectric structure, followed by cooling, can reform the original antiferroelectric state. 

Finally we can note that the ferroelectric state of relaxors is characterised by an extremely narrow hysteresis loop with a low value for the remanent polarisation (Figure 6.19a). This sort of hysteresis loop can be considered to fall into the continuum described previously (Figure 6.9) and suggests that the microsttucture of the phases is at an even more reduced scale than the fine-grained ceramic samples. Indeed, the behaviour when the materials are either cooled in or without an external electric field (FC or ZFC) is also taken as indicative of a complex microstructure. The strain versus applied electric field loop has a U shape, rather like the central portion of the strain curve for an antiferroelectric (Figure 6.19b). 

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]. 

At high frequencies of the a.c. field, the total polarisation of the entire sample is switched very fast and the ground, antiferroelectric state may be bypassed. Then the switching occurs between the two ferroelectric states as in an SSFLC cell. With increasing frequency (for example, from 100 Hz to 10 kHz) the double hysteresis loop is substituted by a single loop typical of ferroelectrics as shown in Fig. 13.16 by the solid and the dashed curves. 

Fig. 13.27 Achiral antiferroelectric. Voltage dependence of pyroelectric coefficient describing the double hysteresis loop (a) and dependence of the field-induced polarization on the content of a monomer in the polymer-monomer mixtures (b)...

Figure 27. A double hysteresis loop typical of the electro-optical switching of the antiferroelectric phase [212].

At the limit where the hysteresis loops shrink to thin lines, as in the diagram at the bottom, we get the response from a material where the dipoles are ordered in a helical fashion. Thus this state is ordered but has no macroscopic polarization and therefore belongs to the category of antiferroelectrics. It is called helical antiferroelectric or heliec-tric for short. If an electric field is applied perpendicular to the helical axis, the helix will be deformed as dipoles with a direction almost along the field start to line up, and the response P-E is linear. As in the normal antiferroelectric case, the induced P value will be relatively modest until we approach a certain value of E at which complete unwinding of the helix takes place rather rapidly. Although the helielectric is a very special case, it shares the two characteristics of normal antiferroelectrics to have an ordered distribution of dipoles (in... 

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