Depolarization field

K below Tc, the first-order satellites shift to smaller Ko, and peaks appear at the higher, odd-order satellite positions AK = nK0(n = 3,5,...). Finally, at about 400 K below Tc, the satellites disappear. This indicates that some alternative mechanism for neutralizing the depolarizing field is operative at low temperature. At a given temperature the positions and intensities of the satellites do not change with time, and are very reproducible provided that T is lowered monotonically from above Tc. 

Another factor that influences strongly the evolution of polarization reversal in fe bulk crystals is the limited minimization of the depolarization field by means of screening charges. In the case of the afm tip of R 50 nm the screening charge is limited both by the size of the tip and its non-ohmic contact with the sample surface. Such an effect is especially pronounced in the case of indirect electron beam exposure method described in this paper. The strong limitation of the screening phenomenon provides a necessary condition for the observed effect of fdb [13-15],... 

The domain energy W consists of the depolarization field energy W,i, the energy of the domain walls Ws, and the energy, Wt, of the interaction between the electric field of the tip and the spontaneous polarization of the domain. Following Landauer [63] hereafter we assume that the domain has a shape of an elongated half-ellipsoid in the polar direction. 

The expression for the domain wall energy and depolarization field energy of the elongated half-ellipsoidal domain has been obtained by Landauer [63] ... 

Let us show that under conditions of fdb the intrinsic depolarization field action may lead to the domain elongation. The driving force for a domain elongation, Ft, may be found from Equation (10.14)... 

To visualize the depolarization fields we may consider the following idea assume we find a molecule with its absorption dipole moment in the plane of the sample. We now adjust the polarization of the excitation beam such that the fluorescence is maximized. We may assume that this happens if the electric field vector in the focus is parallel to the dipole moment. Now, if we turn the incoming polarization by 90° the dominant electric field component will not be able to excite the molecule and the presence of other field components should become visible as weak, but distinctly non-circular spots. Figure 6 shows the result of such an experiment. In Fig. 6(b) the polarization has been turned by 90° as compared to (a) as indicated by the white arrows. The bright spots become dim and their symmetry changes to a four-lobed structure. These weak structures can be made visible if the excitation intensity is increased by a factor of five [see Figs. 6(c) and (d)]. 

An individual atom or ion in a dielectric is not subjected directly to an applied field but to a local field which has a very different value. Insight into this rather complex matter can be gained from the following analysis of an ellipsoidal solid located in an applied external field Ea, as shown in Fig. 2.28. The ellipsoid is chosen since it allows the depolarizing field Edp arising from the polarization charges on the external surfaces of the ellipsoid to be calculated exactly. The internal macroscopic field Em is the resultant of Ea and Edp, i.e. Ea — Edp. 

An immediate consequence of the onset of spontaneous polarization in a body is the appearance of an apparent surface charge density and an accompanying depolarizing field ED as shown in Fig. 2.43(a). The energy associated with the... 

After some distance from the surface, the fields of all dipoles of the interface are screened by the intervening water molecules. Hence, the spatial average of the field induced by the surface dipoles vanishes, since the depolarization field of the remote dipoles is no longer negligible compared to the polarization field of the nearest dipoles. 

Because the correction term in Eq. (6.40) is proportional to M, the development of a net dipole moment in the -direction leads to an increase in the total configurational potential energy. This is consistent with one s physical intuition if one recalls from elementary electrostatics that an infinitely extended slab polarized along the slab normal experiences a depolarizing field equal to acting against the polarization [242]. In fact,... 

The polarization induces a depolarization field Ei = —P/3eo which is the average electric field on the volume of a crystal unit cell. The local field is then ... 

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