4.3 Diffuse scattering study on relaxor ferroelectric Magnetite
Relaxor ferroelectrics relate to normal ferroelectrics similar as spin glasses relate to magnetically ordered phases. The relaxor behaviour normally originates from the compositionally induced disorder or frustration. This behavior was mostly observed and extensively studied in disordered ABO3 pervoskite ferroelectrics [133, 134]. However, the origin of the relaxor phase has been a subject of intense research over decades. At high temperature the non-polar paraelectric (PE) phase is similar to a PE phase of normal ferroelectric. As temperature decreases they transform into the relaxor state, in which polar clusters of nanometer size with randomly oriented direction of dipole moments appear. The formation of these nano-sized polar clusters below a characteristic temperature, known as Burn’s temperature (Td) gives rise to a characteristic dielectric dispersion [135, 136], strongly resembling ac-susceptibility on spin glasses, see figure 4.11. Near the Burns temperature these polar nano regions (PNR) are mobile and as temperature is lowered, their dynamics slow down and at a low enough temperature the PNR in the canonical relaxors become frozen into a nonergodic state. Freezing of these PNR or the dipoledynamics is associated with the wide peak in the temperature
Figure 4.11: Temperature dependencies of the real part of dielectric permittivity of 0.75PMN-0.25PT ceramics, taken from reference [129]
dependence of the dielectric constant with the characteristic dispersion and in contrast to normal ferroelectric it is highly diffuse and frequency dependent. Because of this
“diffuseness ”of the dielectric properties, relaxors are often called as “ferroelectric with diffuse phase transition”, even though an actual phase transition to a ferroelectric phase does not occur. Since these polar nano domains are randomly oriented the zero field polarization is significantly smaller. Temperature dependence of P(E) curves are shown in figure 4.12. It is possible to induce the large polarization in relaxor ferroelectrics with a sufficiently large electric field [137].
Figure 4.12: Dielectric hysteresis in PMN as a function of temperature, taken from reference [133]
Although there is still much debate about the cause and mechanism and even the exact nature of these PNRs and hence the relaxor behaviour, typical relaxors like potassium lithium tantalate (KLT) and lead magnesium niobate (PMN) show specific diffuse scattering at low temperature associated with PNR [138]. It has been observed that in these materials instead of long range ferroelectric order, the formation of diffuse scattering near the Burns temperature where the local polar regions are formed and the intensity of the diffuse scattering increases with decreasing temperature below Td. Several models have been proposed to describe the diffuse scattering in terms of phase-shifted polar nonoregions and the static stain fields [139–141]. However, all these models relate diffuse scattering to the presence of polar correlations in the relaxor ferroelectric material.
If magnetite is indeed a relaxor ferroelectric, it is expected that such diffuse scattering as observed in classical relaxors can be seen. In the past few decades there have been a number of diffuse scattering studies on magnetite [142–145]. However they almost exclusively focus on the strong diffuse scattering at and above Tv, which is not connected
4.3 Diffuse scattering study on relaxor ferroelectric Magnetite
to possible relaxor dynamics at much lower temperature.
Figure 4.13: Temperature dependent of Diffuse neutron scattering in(hhl) plane at (a) 4.2 K and (b) 250 K , (c) Specific heat, CP of the crystal measured at zero magnetic field (TV = 93 K).
In order to test the relaxor-hypothesis of Schrettle et al, we therefore performed a comprehensive study of diffuse scattering focusing on low T<<TV. The figure 4.13 is the neutron diffuse scattering in magnetite measured by mapping the reciprocal space in (hhl) plane of magnetite single crystal at the instrument DNS [section 2.6.4] MLZ. In panel (b) the observed diffuse scattering, well above the Verwey transition is well understood by polaron model by Yamuda. A polaron is a quasiparticle, which describes the interaction between a charge carrier (electrons or holes) and atoms in a solid material. This diffuse scattering was interpreted in terms of cooperative motion of molecular polarons [145] and these polarons describes the properties of valence fluctuations in magnetite above Verwey transition. At sufficiently high temperatures, the polarons are randomly distributed and are fluctuating independently by hopping through the crystals and each of these molecular polaron induces instantaneous strain field around it. Based on this model it was interpreted that the observed diffuse scattering should be Huang scattering [that is, the scattering induced by the an impurity introduced into an elastic medium], due to the strain field induced by independent molecular polarons. However our measurement in the very low temperature, below 4 K, suggested that a type of diffuse scattering unique to low temperature is present. The new result is shown in the fig 4.13 (a) and the figures are plotted in the cubic setting of the high temperature structure. This diffuse scattering is in the [111] direction and perpendicular to scattering at 250 K and also the intensity is very weak compared to the one at high temperature.
This result from first neutron measurement to study the relaxor ferroelectricity was
Figure 4.14: Experimental arrangement to reduce the number of domains. Crystal was tilted 40o to the c-axis. Incident and diffracted beams were in the plane of [001] and the orientation of the field H, as shown, removed the [a,b] twinning.
obtained on the non-stoichiometric sample. The Verwey transition temperature is 93 K and, accordingly, of second order as well visible in fig 4.13(c) . We performed a analogous measurement at DNS on a very high quality sample with TV = 123 K to check whether the previously observed diffuse scattering is sample specific or a real intrinsic property. Even after repeating the measurement we have observed the same diffuse scattering, although it is weaker 4.15 (a) [indicted by the white arrow]. However the observed extremely weak diffuse scattering could be because of the sample size as in the previous measurement the measured sample was with 10 grams and in the second measurement the sample size was 200 mg. Though there was large difference in the sample size we were able to reproduce the result, which confirmed the intrinsic properties of the crystal. To exclude any magnetic contribution, and to test the contribution from lattice part, we have performed a diffuse scattering experiment on a (much smaller) higher quality crystal with TV = 123 K by high energy X-rays at 6-ID-D (APS). Since magnetite has 24 structural domains in the low temperature monoclinic Cc structure, the crystal was cooled under the magnetic field of 1 T along a cubic [001]- direction. With magnetic field cooling through TV the number of domains will be reduced due to the magnetoelastic coupling, makes it low temperature c-axis [146]. We also tried to remove the [a,b] twinning by orienting the crystal 40o to the