dropped. No noticeable change in c-axis was observed apart from the change due to thermal expansion, and the RC versus temperature curves indicate no noticeable effects. This leads to the conclusion that the energy gain obtained at lower temperature by eventually polarizing the STO is not enough to switch the regions of opposite polarization making the SL monodomain.
Satellite width
The width of the satellites provides information on the length over which the domains are coherentξ=0.9394·2πFWHM
Q
4. This value is actually a lower limit on the real coherence length due to all sorts of defects that would lead to a peak broadening. One may note that the coherence length measured on different order satellites might not be the same for all of them. This is certainly due to the disorder in the system but more investigation should be done in order to draw a definite conclusion.
5.3 Conclusion
In summary, this study has allowed us to distinguish between two response regimes which strongly depend upon the electrical history of the sample.
For small voltages applied to a virgin sample, the domain wall breath-ing scenario has been confirmed. Upon increasbreath-ing the field, irreversible changes take place, accompanied by the splitting of the SL Bragg peaks.
Having this in mind, in Chapter 7, we will focus our attention on the dielectric response of a polydomain system which is believed to be strongly affected by the breathing of its domain walls.
4The Scherrer equation relates the broadening of a peak (FWHM) to the size or co-herence (ξ) of that specific feature. When a scan is in angle, the equation is given by:
ξ=FWHM0.9394·λ
2θ·cos(θ), withλis the X-ray wavelength. SinceQ=4πsin(θ)λ andd(2θ)dQ =2πcos(θ)λ . Hence one can write: FWHMQ=FWHM2θ2πcos(θ)
λ givingξ=FWHM0.9394λ
2θcos(θ) =0.9394·2πFWHM
Q .
Chapter 6
Depolarization field: tuning and possible applications
At this point of the thesis we are convinced that heterostructures of fer-rolectric and dielectric layers are an interesting model system to study domain physics. In this chapter, we will show how the depolarization field can be controlled in order to tune the domain structure and discuss possi-ble future applications of 180◦ferroelectric domains.
6.1 Tuning of the depolarization field
One of the key points for the screening properties is the effective screening lengthλeff=λI/Iwhich is an intrinsic property of the metal-ferroelectric interface and can therefore be reduced by a suitable choice of the metallic electrode [21, 69, 70]. Nevertheless, sinceλI represents the physical dis-tance or spread of the charges away from the interface andIthe dielectric constant of the interface layer, the screening efficiency can be artificially tuned by inserting a dielectric spacer to modify the depolarization field in the ferroelectric layer. Such interface modification has previously been explored in the context of increasing the energy storage capacity of fer-roelectric capacitors [71] and modifying the built-in dipole at the metal-ferroelectric interfaces [31]. In this chapter, we present a way of increasing the depolarization field leading to nanodomains in thin PbTiO3films.
To do so, we consider oxide heterostructures made of 10-50-nm-thick
Figure 6.1: PFM phase and amplitude for four different samples with 50nm-thick PbTiO3 and A with no spacer, B with a bottom 2nm-thick SrTiO3 spacer, C with both top and bottom spacers and D with only a top spacer. All structures have a bottom 22nm-thick SrRuO3 electrode.
The top images are phase images showing the local orientation of the po-larization which is uniform for samplesAandDand with 180◦ domains forBandC. At the center are the amplitude images showing for samples B and Cdrops of intensity at the domain walls. The schematics of the heterostructures is shown in the bottom line.
PbTiO3 films with a 22nm-thick SrRuO3 electrode in situ grown by RF off-axis magnetron sputtering on TiO2terminated (001)-oriented SrTiO3. Some heterostructures have a thin SrTiO3 spacer whose thickness varies from 0 to 4 nm inserted in between the SrRuO3 and the PbTiO3 and/or on top of the ferroelectric.1 PFM and XRD at room temperature were used to characterize the samples. By doing PFM, we have access to the domain configuration: monodomain up, monodomain down or polydomain. With the XRD we gain information on the out-of-plane lattice parameter.
The very small lattice mismatch between the SrTiO3(a= 3.905Å) and
1See Chapter 3 for details on the growth conditions.
6.1 Tuning of the depolarization field
thea = b = 3.9045Å [72] axes of the tetragonal bulk PbTiO3 allows all the films to be epitaxially strained to the substrate forcing the tetragonal long axis to point out-of-plane. This enforces the sample polarization to be either pointing away from the surface, up, or toward the surface, down.
To better understand the role played by the dielectric spacer, hetero-structures with 50nm-thick PbTiO3with and without spacer are compared.
Results of the PFM studies are summarized in Fig. 6.1. SampleAwhich is of the form PbTiO3/SrRuO3//SrTiO3is found to be monodomain up. This result is consistent with previously reported work of Nagarajan etal.[29]
showing a monodomain up PbZr0.2Ti0.8O3 grown on SrRuO3 electrodes.
Other works have also reported monodomain down configuration states of PbTiO3 on Nb-SrTiO3[74]. This preferential polarization direction im-plies the presence of a built-in field, which is most likely related to the differences in band alignments at the interfaces of our asymmetric struc-ture. This has been confirmed in our next work [73] where we have shown by the means of spectroscopic PFM loops that monodomain sam-ples have a larger imprint compared to the polydomain ones. Results are shown in Fig. 6.2.
Interestingly, if a 2-nm-thin SrTiO3 spacer is inserted in between the electrode and the ferrolectric (sample B), a polydomain structure is ob-served with a preferential up orientation matrix. Note that direction of the matrix is the same as without the spacer. The effect of the SrTiO3spacer is to increase the distance between the screening charges from the bottom electrode and the ferroelectric polarization making the screening less ef-fective and thus increasing the depolarization field inside the ferroelectric film. As a result, the polarization in the ferroelectric film is destabilized and domains of opposite polarization form in order to reduce the energy cost associated with this larger depolarization field. Therefore, without changing the thickness of the film, it is possible to tune the depolarization field and induce different domain configurations by adjusting the thick-ness of the insulating spacer. To go one step further in the understanding of what is being observed, it is important to compare the change in effec-tive screening length that is induced by the SrTiO3spacer with respect to what it would be without. From first-principles calculations, the intrinsic screening length for PbTiO3-SrRuO3and SrTiO3-SrRuO3interfaces is 0.15 Å [21, 23]. The effective screening length λeff = λI/I, for a 2nm-thick of SrTiO3 with I = 300gives λeff = 0.07 Å. The dielectric constant of SrTiO3has been measured in thin films and in PbTiO3-SrTiO3polydomain superlattices grown in the same conditions and is found to be close to 300.
Therefore, by adding the SrTiO3spacer in between the SrRuO3electrode
SrTiO3
Figure 6.2: Figure representing PFM, switching spectroscopy loops by the use of the AFM and XRD measurements. The top panel displays the schematics of the samples and their phase PFM signals showing the intrin-sic domains configuration. For the four samples, local switching loops are shown (using a B-doped diamond tip). SamplesAandDshow a larger built-in field than the polydomainB andCsamples. Bottom left shows θ-2θX-ray specular scans (shifted for clarity) around the (001) reflection.
The data was fitted to obtain thec-axis lattice parameter of the thin films of PbTiO3. Thec-axis of the PbTiO3varies depending on the intrinsic do-main configuration. Bottom right summarizes both measurements by plot-ting the built-in voltage averaged values (see for more details Ref. [73]) as a function of thec-axis. Both built-in voltage andc-axis vary depending on the intrinsic domain configuration, with larger values for the monodomain samples compared to the polydomain ones.
6.1 Tuning of the depolarization field
and the PbTiO3film, the resulting effective screening length becomes the sum of the effective screening length of the SrTiO3-SrRuO3interface and that of the SrTiO3spacer. Hence, the addition of the 2 nm spacer of SrTiO3 is expected to increase the screening length by 50% compared to the case without the spacer. Note that this simple argument does not take into account the field-induced reduction of the SrTiO3 permittivity due to any built-in fields and fields induced by the ferroelectric layer.2Therefore, the above simple calculation may underestimate the increase in the effective screening length of the added spacer.
PFM measurements were also performed for samples with a top spacer and the measurements are summarized in Fig. 6.1 for sample Cand D.
Their polarization pattern is very similar to that of the same heterostruc-tures without any top SrTiO3indicating that the bottom spacer has a much larger effect than the top one. Further investigation is needed to establish the origin of this effect.
Additionally to the PFM data, thec-axis has been measured for all the heterostructures (A,B, CandD) and compared in Fig. 6.2. Because all these samples have the same PbTiO3 thickness, the changes observed in theirc-axis values are directly related to the different electrostatic envi-ronment. Results show that both samples with a bottom spacer which are polydomain have a lower c-axis than the ones which are monodomain.
Those results are in line with the work of Takahashi etal.[35], who ob-serve an increase of the c-axis lattice parameter of PbTiO3 films grown on Nb-SrTiO3substrates when using photochemical switching to induce a monodomain state from an originally polydomain state. For samples with a top spacer, no difference was observed compared to the same samples without it.
Effect of the SrTiO3spacers on written domains
In order to test the effect of the SrTiO3 spacers and its influence on the depolarization field, a series of 20nm-thick PbTiO3samples with top and bottom SrTiO3 of varying thicknesses (0, 1, 2, 5 and 10 unit cells) were grown. One elegant way of determining the as-grown state is to write
2It is of great interest to note that the fields induced by the ferroelecrtic sample with small domains into the SrTiO3 spacer, are smaller than for samples with larger domains.
It has been pointed out in Ref. [32], that for 10nm-thick polydomain PbTiO3films there is little interaction between the domain structure with the metallic electrode compared to the 50nm-thick polydomain samples which by having larger domains, have a stronger coupling between the ferroelectric and the metallic electrode mediated by the stronger electric field induced in the SrTiO3spacer.
stripes with alternating DC voltages -/+/-/+/- (values applied to the bot-tom electrode) with a grounded AFM tip and then scan a larger area. In this way one can really confirm whether the as-grown state is monodomain up or down or if it is polydomain. Since all samples are revealed to have a preferential up polarization, the next step is to look at the time evolution of two written squares with up and down polarization. Results are shown in Fig. 6.3.3For the two monodomain samples, namely with 0 and 1 uc of SrTiO3spacer, only the regions written with down polarization are visible in the monodomain up background. The written squares slowly disappear with time as the domain wall surrounding the written region gradually becomes rougher, reducing the size of the written region through domain wall motionpredominantly driven by the built-in field. For the sample with 1 uc of SrTiO3, in addition to the roughening of the domain wall, we can notice that both the phase contrast and the amplitude decrease with time within the written region. This indicates that small up domains (below the tip resolution) start to appear in the down written region, resulting in a decrease of the locally averaged phase and amplitude. For the sam-ples with thicker spacers which are polydomain, the thicker the spacer, the faster is the polarization relaxation of the written squares back to its original polydomain state. Such process is driven by the depolarization field[75]. This conclusion is well in line with Ref. [75] where the strong impact of the depolarization field in the relaxation of the polarization has been demonstrated and has once more proved that the depolarization field is an intrinsic property of the interface. The different behaviors and times scales for the relaxation of the written domains indicate again that the depolarization field increases with the SrTiO3layer thickness.
Conclusion
We have demonstrated that by introducing a thin SrTiO3spacer we were able to tune the effective screening length and control the depolarization field in ferroelectric heterostructures. This offers the possibility to choose the polarization state of PbTiO3 thin films to be monodomain or polydo-main. Such nanodomains offer the possibility to enhance the dielectric properties via their large domain wall contribution or to engineer mate-rials whose properties are dominated by exotic functionalities that have recently been discovered at ferroic domain walls [20].
3Note that we did not perform scans continuously since the process of reading itself seams to influence the relaxation process.
6.1 Tuning of the depolarization field
Figure 6.3: PFM phase (right) and amplitude (left) images obtained for four samples with 20nm-thick PbTiO3 and with both top and bottom SrTiO3spacers with varying thicknesses of 1, 2, 5 and 10 unit cells. Images were taken at different times after writing two 500 ×500 nm2 squares with up and down polarization. Such images and their time evolution reveal different relaxation rates of the polarization for different samples.
The relaxation is found to be faster for samples with thicker spacers. In addition the relaxation process is found to have different origins depend-ing on the thickness of the spacer. For 0 and 1 uc of SrTiO3, the relaxation is predominantly driven by the built-in field. For thicker spacers, the de-polarization field is the main actor. For intermediate sizes, there is most probably a combination of both fields.