Temperature dependence of electron spin resonance in CaCu3Ti4O12 substituted with transition metal elements

Solid State Sciences 11 (2009) 875–880

Contents lists available at ScienceDirect

Solid State Sciences journal homepage: www.elsevier.com/locate/ssscie

Temperature dependence of electron spin resonance in CaCu3Ti4O12 substituted with transition metal elements Virginie Brize´ a, *, Ce´cile Autret-Lambert a, Je´roˆme Wolfman a, Monique Gervais a, Patrick Simon b, c, François Gervais a a

Laboratoire d’e´lectrodynamique des mate´riaux avance´s (LEMA), UMR6157 CNRS/CEA, Faculte´ des Sciences & Techniques, Universite´ François Rabelais Tours, Parc de Grandmont, 37200 Tours, France CNRS UPR 3079 CEMHTI, Avenue de la Recherche Scientifique, 45071 Orle´ans Cedex 2, France c Universite´ d’Orle´ans, BP6749, 45067 Orle´ans Cedex 2, France b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 11 September 2008 Received in revised form 16 December 2008 Accepted 17 December 2008 Available online 3 January 2009

The temperature dependence of the electron spin resonance (ESR) spectrum of copper in CaCu3Ti4O12 (CCTO) polycrystalline samples doped with transition metal elements Mn, Fe, Ni is reported. The frequency dependence of the dielectric constant of the sample is also reported at room temperature. While the dielectric constant of undoped CCTO samples reaches w10,000, it is found one hundred times lower in samples doped with only 0.5 or 1% of Mn or Fe. Copper is confirmed to give a g ¼ 2.14 signal at room temperature for substituted and unsubstituted samples. Below the antiferromagnetic transition that occurs near 25 K, the signal is found shifted down to low fields for all samples. However the downshift is 10–20 times more important in Mn and Fe-doped samples compared to undoped or Nidoped CCTO. ESR results in an undoped CCTO thin film grown by pulse laser deposition are also reported. While in the low-temperature antiferromagnetic phase the spectrum is multi-line and magnetic-fieldorientation-dependent, it reduces to a narrow single line, independent of the orientation of the magnetic field, in the upper paramagnetic phase, similar to the undoped polycrystalline sample. All doped samples display much broader response in the upper phase. The results are discussed within the framework of the relationship between the high effective dielectric constant and the electrical conductivity of CCTO bulk. Ó 2009 Elsevier Masson SAS. All rights reserved.

Keywords: CaCu3Ti4O12 ESR Powder Thin film Dielectric

1. Introduction Ferroelectric titanates, with BaTiO3 as a typical example, are known for six decades to show high permittivity in the vicinity of the Curie temperature. In this context, the report of still higher permittivity in CaCu3Ti4O12 (CCTO) was puzzling since the temperature behaviour does not sign for any ferroelectric–paraelectric phase transition [1,2]. In addition, the dielectric properties of CCTO are promising for technological applications because, in addition to the very high dielectric constant – at least up to the megahertz range – it varies only smoothly near room temperature, contrary to other titanates showing a sharp dielectric constant peak at the paraelectric–ferroelectric phase transition. Therefore, CCTO seems to open the way to miniaturized high-value capacitances for electronic applications, and more specifically nomad telecommunications.

* Corresponding author. E-mail address: [email protected] (V. Brize´). 1293-2558/$ – see front matter Ó 2009 Elsevier Masson SAS. All rights reserved. doi:10.1016/j.solidstatesciences.2008.12.012

Recent experiments performed in a single crystal confirmed the high permittivity found in previous single crystal studies [3], and focused on the importance of surface effects understood in terms of a supposed insulating thin barrier sandwiched between the electrode and semiconducting CCTO [4,5]. Previous experiments enlightened the parallel role of insulating grain boundaries in polycrystalline samples as barriers separating semiconducting CCTO grains. These reports proposed extrinsic mechanism in terms of internal barrier layer capacitance (IBLC) effect [6–13]. In the brickwork layer model [11,13], the effective dielectric constant is related to the ratio of the grain size over the grain boundary thickness, times the dielectric constant of the grain boundary. With grains of a few tens of micrometers and grain boundaries a few nanometers thick, one may reach effective dielectric constants higher than 105, indeed found experimentally, provided the permittivity of the grain boundary is of the order of 100 or higher and that CCTO grains are conducting enough. Single crystal studies of Ref. [5] report a CCTO conductivity of 103 U1 cm1 at 1 kHz and 101 U1 cm1 at 1 GHz, at room temperature. However, thin films [14–17] hardly reproduce the high

876

V. Brize´ et al. / Solid State Sciences 11 (2009) 875–880

level of permittivity found in single crystals, and the more modest achievements temperate the promising character of potential applications. This is consistent with the suggestion of surface barrier layer capacitance (SBLC) effect in the single crystal, the thin thickness in the film then minimizing the effective permittivity of the system, compared to thick crystals. On the other hand, the need for large grains embedded in insulating grain boundaries of the IBLC scenario is expected to be accommodated in thin films with more difficulties. While some transmission electron microscopy studies failed to observe twins or anti-phase domains either in the single crystal or in polycrystalline CCTO [18], other studies reported a little tilt of domains possibly inducing polarization switching, but without firm conclusion [19]. Note that Ref. [12] emphasizes the possible role of depletion layers at the interface of electrodes. On the other hand, intrinsic scenarios, like frustrated ferroelectrics [3], have been little considered for lack of experimental evidence of a mechanism able to explain the increase of the dielectric constant between the farinfrared region where it hardly exceeds 100, up to the much higher values observed below 1 MHz (in semiconducting samples). Before considering one possible indication of such a mechanism, let us recall the situation in ferroelectric barium titanate. In this compound, a soft mode is observed but the soft mode does not explain the high value of the dielectric constant [20]. This is due to a displacive-order–disorder crossover effect [21] related to highly-correlated relaxational motion along (100) Ti–O–Ti chains, but decorrelated from one chain to another, consistent with early X-ray diffuse scattering reported by Comes, Lambert and Guinier [22]. Recently, Liu et al. [23] reported diffuse scattering by electron diffraction in CCTO single crystal interpreted in terms of correlated relaxational motion of Ti along (100) chains, thus suggesting support to intrinsic frustrated ferroelectrics scenario. The amplitude of Ti motions was found to be 0.04 Å along (100) and 0.07 Å along (111). However, such a mechanism is hardly compatible with the loss of permittivity at low temperature which is not expected within a scenario of highly-correlated relaxational motions. Large amplitude of Ti motions alternatively might be related to some phonon mode softening. This is the tendency confirmed in a recent report [24]. Within the context of extrinsic mechanism of giant permittivity, the semiconducting character of CCTO bulk appears central, either within the surface-effect mechanism (SBLC) for single crystals, or within IBLC mechanism for sintered ceramics. One possible reason which is invoked to explain the change from semiconducting to insulating character of CCTO is the oxygen stoichiometry. A rate of only 103 of oxygen deficiency might be sufficient to explain a change from semiconducting to insulating CCTO. The role of oxygen stoichiometry has been discarded [25]. But this view is still controversial [26]. Another way to change the semiconducting character is to use doping, in particular cationic substitutions at the rate of only 0.5%. This is the subject of the present paper. The ESR spectrum of copper in CCTO has been already reported to display some puzzling characteristics [27–30]. The role of oxygen nonstoichiometry on the ESR line width has been also studied [31]. Since both Mn2þ and Fe3þ ions display an 6S5/2 electronic configuration, which usually gives narrow electron spin resonance lines, CCTO has been doped with these elements and the study by ESR is reported here. The temperature dependence of the ESR response of a thin film of undoped CCTO grown by pulse laser deposition is also reported. The aim of the paper is to check if the sensitivity of ESR may add information about non-stoichiometry, its role on conductivity and on permittivity therefore via the IBLC model.

gel-assisted citrate process [32]. The CCTO thin film was grown on a lanthanum aluminate single crystal substrate using PLD (KrF laser with l ¼ 248 nm). During deposition, the laser repetition rate was 10 Hz, the substrate temperature was kept constant at 765  C. During deposition, the oxygen partial pressure was 0.3 mbar. The film is epitaxial and oriented (001) as shown by X-ray diffraction pattern in Fig. 1. Electron spin resonance measurements have been performed with a BRUKER EMX 6/1 in the X-band (9.5 GHz) and a BRUKER ER200 in the Q band (34 GHz). 3. Bonding character of Cu–O and Ti–O in CCTO Before showing the ESR results, it is interesting to exploit earlier infrared experiments to get further information about the chemical bonding in CCTO. The effective ionic charge carried by copper in CCTO has been calculated from the infrared reflectivity spectrum [33] using a relationship firstly derived by Kurosawa [34] and which has been exploited in many compounds later, mainly oxides [35]. Within the context of quasi-harmonic phonons, this relation shows that the effective ionic charge Ze is related to the transverse optical (TO) and longitudinal optical (LO) phonon frequencies via

X j



U2jLO  U2jTO ¼

1 X ðZk eÞ2 3v V mk k

where the summation in the right-hand side of the equation is over all atoms of mass mk contained in the unit cell volume V. 3v is the dielectric constant of vacuum and e is the electron charge. The problem in CCTO is that there are four unknowns ZCa, ZCu, ZTi, ZO but only two equations: the one written above and the electric neutrality. If one adopts the formal valence for calcium, ZCa ¼ 2, then the effective charge of the lightest atom that gives the major contribution to the right hand side of the above equation, is evaluated unambiguously and found equal to ZO ¼ 1.2. The absolute value of the oxygen charge is significantly lower than the one found in barium or strontium titanate via the same method, approximately 1.5 [35], pointing towards more covalent character of bonding in CCTO. There is a balance for ZTi and ZCu that satisfies the equations. For example, if the former is set equal to 2.4, then ZCu ¼ 1. If ZTi is increased up to 2.6, then ZCu is reduced to 0.6. To keep physically realistic values for the effective charge of copper, ZTi cannot be set in excess of 2.8. Again note that the average value of 2.5  0.3 found here for the titanium in CCTO focus to more covalent bonding than the one found in SrTiO3, 3  0.15 [35]. A more covalent character is here confirmed experimentally for the Cu–O

2. Experimental Undoped and Ni, Mn, Fe-doped CCTO powders and ceramic target for pulse laser deposition (PLD) were prepared by an organic

Fig. 1. X-ray diffraction pattern of the pulsed laser deposited CCTO film onto LaAlO3 substrate.

V. Brize´ et al. / Solid State Sciences 11 (2009) 875–880

bond, complemented by a partially hybridized character of the Ti–O bond [8] too. 4. ESR results and discussion 4.1. PLD undoped thin film The temperature dependence of the ESR response of the film in the X band is shown in Fig. 2. Above 25 K, it displays a single symmetric line at g ¼ 2.14, which is found independent of the orientation of the sample in the magnetic field. This g value is typical

877

of copper and is shifted with respect to free-electron value g ¼ 2 due to Jahn–Teller effect of copper ion. The response is very similar to that found in undoped polycrystalline sample. Note that small additional narrow lines observed in the spectrum are related to Fe3þ impurities in the lanthanum aluminate single crystal substrate. They shift with the orientation of the crystal with respect to the magnetic field, as expected for a fine structure spectrum in a single crystal sample. The single main line slightly broadens upon cooling. Below 25 K where a transition to an antiferromagnetic phase has been reported [8], the single line is splitted into a multi-line spectrum. Contrary to what is observed above 25 K, the spectrum in the antiferromagnetic phase depends on the orientation of the film with respect to the direction of the magnetic film (see e.g. spectra denoted (a) and (b) at 5 K in Fig. 2 obtained for two different random orientations of the thin film with respect to the magnetic field). 4.2. Undoped and doped polycrystalline samples

Fig. 2. Temperature dependence of X-band electron spin resonance spectrum of a CCTO thin film. Small additional narrow lines denoted by arrows are due to iron impurities in the lanthanum aluminate single crystal substrate. While the spectrum at 5 K denoted (a) is measured for a film orientation with respect to the magnetic field identical to the orientation used at higher temperature, the spectrum denoted (b) correspond to another orientation.

The temperature dependence of ESR response of undoped CCTO and samples doped with manganese, iron and nickel (sintered powders) is shown in Fig. 3. ESR spectra can be influenced by the grain-boundary chemistry and another group has shown the segregation of the impurities to the grain boundaries in CCTO [29]. ESR spectra in sintered powders (sintering at 1000  C during 20 h) are similar to those obtained in non-sintered powders (powder annealing at 900  C during 1 h). No signature of grain boundary effect, therefore, is observed in present ESR spectra. The dielectric response (see Ref. [32] for undoped CCTO) of the samples at room temperature is shown in Fig. 4. In the undoped sample (film and ceramic), while a single narrow line is observed above the antiferromagnetic (AFM) transition temperature TN, ESR spectra (Figs. 2 and 3) display a multi-line spectrum below the transition. The spectrum of the thin film depends in the AFM phase, upon the orientation of the sample in the magnetic field whereas in the polycrystalline sample it is integrated over all possible orientations of the grains. Note that the oxygen stoichiometry that has been shown to influence the ESR response [31], might be different in both samples. Crystal field calculations in Ref. [27] predict a single line, shifting from g ¼ 2 to g ¼ 4 depending on the orientation of the square planar oxygen neighbours in the magnetic field. The observed multi-line spectrum in the thin film with geff ranging from g ¼ 1.5 to g ¼ 7, and more than three lines (one expected per spin ½ for each of the three orientations of the square planar copper sites), does not fit this expectation. It means that what has to be considered is not the resonance of individual spins but rather the collective resonance of some magnetically-ordered features. While the room temperature ESR lines are narrow (35 G) for both undoped CCTO thin film and ceramic sample, they are conversely found much broader for all doped samples. The temperature dependence of the line width in each sample (main line below TN) is shown in Fig. 5. Results appear very contrasted. For undoped CCTO, the line width little evolves upon cooling in the PM phase and moderately starts increasing in the vicinity of TN. For the samples doped either with Fe or Mn, the line width little evolves upon cooling except right above TN where it starts increasing. The increase is strongly accelerated just below TN. For the sample doped with nickel, the line width conversely decreases upon cooling when approaching TN from above. An effective g factor geff estimated from the intercept of ESR signal with the magnetic field axis is plotted in Fig. 6 for the four samples. Again, the observations are highly contrasted. While the results for undoped and Ni doped samples show a modest downshift of the resonance line below TN (by comparison with both other samples), the downshift is so large for samples doped either with Fe or Mn that the resonance line is lost a few degrees below the temperature (assigned to TN) at which the

V. Brize´ et al. / Solid State Sciences 11 (2009) 875–880

878

CCTO_Fe

[50 K- RT]

30 K 25 K 20 K 10 K 15 K

0

1000

2000

3000

4000

5000

5K 31 K 30 K

0

1000

20 K

25 K

30 K 50 K

15 K

100 K RT

10 K

0

1000

2000

3000

2000

29 K

3000

4000

5000

Magnetic Field (G)

4000

5000

50 K 35 K

CCTO_Mn

ESR Signal (arb.units)

ESR Signal (arb.units)

Magnetic Field (G) CCTO_Ni

RT

100 K 50 K 35 K 32 K

ESR Signal (arb.units)

ESR Signal (arb.units)

CCTO

200 K RT

31 K 30 K

4K 25 K

29 K 28 K

0

1000

Magnetic Field (G)

2000

3000

4000

5000

Magnetic Field (G)

Fig. 3. Temperature dependence of ESR of undoped, Mn, Fe and Ni-doped CCTO ceramic samples.

downshift starts (Fig. 5). Another way to parameterize the contrasting behaviors is to emphasize that Dgeff/DT below TN is 10–20 times larger in samples doped with Mn and Fe, compared to undoped and Ni-doped samples. A downshift of geff usually signs for collective resonance of magnetic domains and is commonly observed in a ferromagnetic phase (effect of depolarizing field) [36]. Actually, as shown schematically in Fig. 7, the magnetic moments in the AFM phase are assumed to be aligned ferromagnetically in copper planes perpendicular to the (111) direction, and antiferromagnetically between the two symmetric copper planes with respect to the Ti ion. The spins may experience, therefore, a local magnetic field even if the sample is not ferromagnetic. Note that both Mn- and Fe-doped samples, showing large Dgeff/DT below TN, also display the lowest permittivity in Fig. 4. Conversely, undoped and Ni-doped samples show very high

permittivity at low frequency in Fig. 4. An unexpected correlation of low-frequency permittivity and Dgeff/DT below TN, therefore, is found. ESR line widths of the four samples have also been measured at room temperature in the Q band at 34 GHz, and found roughly similar to the values respectively measured in the X band at 9.5 GHz. Ref. [31], that focus upon the correlation of permittivity and oxygen stoichiometry, did not report any significant difference of X and Q band line widths either. The authors discussed the origin of the line widths. After discarding inhomogeneous broadening since the line width is not magnetic field dependent, they conclude that the most probable homogeneous broadening mechanism in CCTO is the dipolar interactions. They found a correlation of line broadening and the conditions that create oxygen vacancies (and possibly Ti3þ). However, no quantitative estimate of the actual role played by vacancies or trivalent titanium in the huge line width

10000

4000

4000 CCTO

3500

2500

ΔHpp

εeff

CCTO_Ni

CCTO_Mn

ΔHpp

3000

CCTO

1000

CCTO_Fe

CCTO_Mn CCTO_Fe

2000

1000

2000 1500

100

CCTO_Ni

3000

0

20

25

30

35

40

45

50

Temperature (K)

1000 500 10

102

103

104

105

106

107

Frequency (Hz)

0

0

50

100

150

200

250

Temperature (K) Fig. 4. Room temperature frequency dependence of the permittivity of the samples of Fig. 3.

Fig. 5. Temperature dependence of the line width of the samples of Fig. 3.

V. Brize´ et al. / Solid State Sciences 11 (2009) 875–880

5,0

4,5

4,0

9

CCTO

geff

4,5

4,0

8 7

3,5 3,0

geff

geff

10

5,5

5,0

2,5

3,5

2,0

3,0

geff

5,5

0

10

20

30

50

40

6 5

10 9 8 7 6 5 4 3 2

CCTO_Fe

20

4

Temperature (K)

2,5

25

30

35

40

50

45

Temperature (K)

3

2,0

2

0

50

100

150

200

250

0

300

50

Temperature (K)

5,0 4,5

4,0

10 9

CCTO_Ni

geff

4,5

4,0

8 7

3,5

geff

3,0 2,5

3,5

2,0

3,0

0

10

20

30

40

50

Temperature (K)

2,5

150

200

250

300

Temperature (K)

5,5 5,0

100

geff

5,5

geff

879

6 5

10 9 8 7 6 5 4 3 2

CCTO_Mn

20

4

25

30

35

40

45

50

Temperature (K)

3

2,0

2

0

50

100

150

200

250

300

Temperature (K)

0

50

100

150

200

250

300

Temperature (K)

Fig. 6. Temperature dependence of geff of the samples of Fig. 3.

increase, was given in Ref. [31]. Based on the contrasting behaviours shown in Fig. 4, we suggest another possibility for the paramagnetic phase above TN. The relaxation time of copper d electron spins is assumed to be short due to the large spin–spin dipolar interactions, provided that electron remains localized at the copper site, viz. in insulating bulk or grains. This is consistent with broad ESR response observed in Mn-doped, Fe-doped and/or oxygen under stoichiometric samples. Indeed, the effective permittivity is

[111]

Ca

Cu

Ti

Cu

Ca Fig. 7. Schematic arrangement of cations in CCTO along the [111] direction. Arrows indicate the AFM order at low temperature.

found relatively low (w100) at low frequency in these samples. Such a low permittivity signs for a low electrical conductivity of the grains in the context of the IBLC model. Conversely, measurements of conductivity in an undoped single crystal of CCTO shows that the conductivity becomes much larger above 1 MHz, and in particular of the order of 101 S cm1 near 9.5 or 34 GHz [5]. Such a level of conductivity then suggests hopping motions of the copper d electrons from Cu site to Cu site. This is also made possible by the partial hybridisation of Cu–O bonding estimated in paragraph 3. Since the positions of the three copper sites are equivalent by symmetry with respect to the (111) direction (Fig. 7), we conjecture that the thermally-activated motions of the conducting electrons randomise the dipolar interactions of their spins and might induce line narrowing. The weak temperature dependence of the ESR line above TN might thus be the result of the balance of two competing contributions: the spin-lattice relaxation time that tends to increase the line width, and the thermal activation of the electron motions that would tend to narrow the line. The case of the nickel-doped sample where the ESR line remains large while the permittivity is also large opens an additional question. It also shows a different profile of temperature dependence of the line width in the paramagnetic phase. We suggest that nickel could be substituted at the copper site, instead of Ti site (assumed for other doping), and would break, therefore, the symmetry invoked for the randomisation of dipolar interactions. As a result, the line remains large with Ni doping at room temperature. Note that a recent paper [37] focuses on an alternative scenario. By analysing EXAFS experiment, it is concluded that part of copper ions seems to sit at the calcium site and hybridise with oxygen to form conducting islands embedded in an insulating matrix. More generally, one may imagine alternative scenarios based on the general concept of phase separation. Provided conducting domains are embedded in an insulating matrix, one keeps the ingredients that allow colossal effective permittivity. In any case, a sufficient level of grain conductivity is needed. Any method able to give

880

V. Brize´ et al. / Solid State Sciences 11 (2009) 875–880

information on the conductivity of the grain, therefore, is acknowledged. ESR experiments which can be easily performed on single crystal, sintered ceramics, thin films, and powders, may help to characterize this property by simply checking the line width at room temperature. A thin film of Mn-doped and another of Fe-doped [38] CCTO have also been grown by PLD for comparison with undoped thin film sample, but the resonance line is so broad that no ESR signal was observable. It might be important to note that the ESR spectra of all our polycrystalline samples systematically show a single line assigned to copper. The starting hypothesis to exploit the response of dopants like Mn or Fe actually failed. Since the response of these ions are expected at g ¼ 2 outside the range of the resonance of copper line, it seems that the expected lines are too broad to be observed probably due to strong spin–spin interactions. Other groups reported ESR line attributed to grain boundaries. The absence of additional lines in our samples suggests that grains only are observed in this study. 5. Summary The temperature dependence of the ESR response of an oriented thin film of CCTO deposited by laser ablation has been reported. Contrary to the multi-line spectrum observed in the low-temperature antiferromagnetic phase below 25 K, the spectrum merges into a single line above TN whereas there is no change of structure and no change of crystal field at the phase transition. This crossover from paramagnetic (T > TN) to internal-magnetic-field-dependent resonance is related to the onset of magnetic order including ferromagnetic-type spin interactions within the planes perpendicular to the (111) direction, AFM-type interactions between adjacent planes, below TN. Unexpectedly large Dgeff/DT has been found below TN in samples doped with Mn and Fe. A correlation has also been found between the ESR line width in the paramagnetic phase, and the sample conductivity (deduced from the effective permittivity). A line narrowing phenomenon related to the thermally-activated motion of Cu d electrons in conducting grains, is suggested. This line narrowing which is dependent on the grain conductivity allows a fast characterization of this property even in powders where it could not be checked easily by other methods. Even if this study doesn’t bring direct evidence on colossal permittivity, the sensitivity of the ESR copper response experiences the change of copper environment. In particular the interactions with mobile electric charges that themselves play a decisive role on grain permittivity via IBLC mechanism. Acknowledgments Some of the authors have benefited of valuable discussions with partners of the program STREP NUOTO of the European Commission.

References [1] A.P. Ramirez, M.A. Subramanian, M. Gardel, G. Blumberg, D. Li, T. Vogt, S.M. Shapiro, Solid State Commun. 115 (2000) 217. [2] M.A. Subramanian, D. Li, N. Duan, B.A. Reisner, A.W. Sleight, J. Solid State Chem. 151 (2000) 323. [3] C. Homes, T. Vogt, S.M. Shapiro, S. Wakimoto, A.P. Ramirez, Science 293 (2001) 673. [4] P. Lunkenheimer, V. Bobnar, A.V. Pronin, A.I. Ritus, A.A. Volkov, A. Loidl, Phys. Rev. B 66 (2002) 052105. [5] S. Krohns, P. Lunkenheimer, S.G. Ebbinghaus, A. Loidl, Appl. Phys. Lett. 91 (2007) 022910. [6] M.A. Subramanian, A.W. Sleight, Solid State Sci. 4 (2002) 347. [7] Y.J. Kim, S. Wakimoto, S.M. Shapiro, P.M. Gehring, A.P. Ramirez, Solid State Commun. 121 (2002) 625. [8] A. Koitzsch, G. Blumberg, A. Gozar, B. Dennis, A.P. Ramirez, S. Trebst, S. Wakimoto, Phys. Rev. B 65 (2002) 524061. [9] L. He, J.B. Neaton, M.H. Cohen, D. Vanderbilt, Phys. Rev. B 65 (2002) 2141121. [10] N. Kolev, R.P. Bontchev, A.J. Jacobson, V.N. Popov, V.G. Hadjiev, A.P. Litvinchuk, M.N. Iliev, Phys. Rev. B 66 (2002) 1321021. [11] D.C. Sinclair, T.B. Adams, F.D. Morrison, A.R. West, Appl. Phys. Lett. 80 (2002) 2153. [12] M.H. Cohen, J.B. Neaton, L. He, D. Vanderbilt, J. Appl. Phys. 94 (2003) 3299. [13] A.R. West, T.B. Adams, F.D. Morrison, D.C. Sinclair, J. Eur. Ceram. Soc. 24 (2004) 1439. [14] L. Fang, M. Shen, Thin Solid Films 440 (2003) 60. [15] Y.L. Zhao, G.W. Pan, Q.B. Ren, Y.G. Cao, L.X. Feng, Z.K. Jiao, Thin Solid Films 445 (2003) 7. [16] A. Tselev, C.M. Brooks, S.M. Anlage, H. Zheng, L. Salamanca-Riba, R. Ramesh, M.A. Subramanian, Phys. Rev. B 70 (2004) 144101. [17] L. Fang, M. Shen, W. Cao, J. Appl. Phys. 95 (2004) 6483. [18] L. Wu, Y. Zhu, S. Park, S. Shapiro, G. Shirane, J. Tafto, Phys. Rev. B 71 (2005) 014118. [19] S.Y. Chung, Appl. Phys. Lett. 87 (2005) 052901. [20] Y. Luspin, J.L. Servoin, F. Gervais, J. Phys. C 13 (1980) 3761. [21] K.A. Mu¨ller, Y. Luspin, J.L. Servoin, F. Gervais, J. Phys. Lett. 43 (1982) 537. [22] R. Comes, M. Lambert, A. Guinier, Solid State Commun. 6 (1968) 715. [23] Y. Liu, R.L. Withers, X.Y. Wei, Phys. Rev. B 72 (2005) 1. [24] C.H. Kant, T. Rudolf, F. Mayr, S. Krohns, P. Lunkenheimer, S.G. Ebbinghaus, A. Loidl, Phys. Rev. B 77 (2008) 045131. [25] T.B. Adams, D.C. Sinclair, A.R. West, J. Am. Ceram. Soc. 89 (2006) 3129. [26] M. Wang, K.S. Kao, S.Y. Lin, Y.C. Chen, S.C. Weng, J. Phys. Chem. Solids 69 (2008) 608. [27] M.C. Mozzati, C.B. Azzoni, D. Capsoni, M. Bini, V. Massarotti, J. Phys. C 15 (2003) 7365. [28] G. Chiodelli, V. Massarotti, D. Capsoni, M. Bini, C.B. Azzoni, M.C. Mozzati, P. Lupotto, Solid State Commun. 132 (2004) 241. [29] D. Capsoni, M. Bini, V. Massarotti, G. Chiodelli, M.C. Mozzatic, C.B. Azzoni, J. Solid State Chem. 177 (2004) 4494. [30] M.C. Giulloto, C.B. Mozzati, V. Azzoni, Massarotti, M. Bini, Ferroelectrics 298 (2004) 61. [31] M.A. Pires, C. Israel, W. Iwamoto, R.R. Urbano, O. Agu¨ero, I. Torriani, C. Rettori, P.G. Pagliuso, L. Walmsley, Z. Le, J.L. Cohn, S.B. Oseroff, Phys. Rev. B 73 (2006) 224404. [32] V. Brize´, G. Gruener, J. Wolfman, K. Fatyeyeva, M. Tabellout, M. Gervais, F. Gervais, Mater. Sci. Eng. B 129 (2006) 135. [33] A. Hassini, M. Gervais, J. Coulon, V.T. Phuoc, F. Gervais, Mater. Sci. Eng. B 87 (2001) 164. [34] T. Kurosawa, J. Phys. Soc. Jpn. 16 (1961) 1298. [35] F. Gervais, Solid State Commun. 18 (1976) 191. [36] C. Autret, M. Gervais, F. Gervais, N. Raimboux, P. Simon, Solid State Sci. 6 (2004) 815. [37] Y. Zhu, J.C. Zheng, L. Wu, A.I. Frenkel, J. Hanson, P. Northrup, W. Ku, Phys. Rev. Lett. 99 (2007) 037602. [38] R.K. Grubbs, E.L. Venturini, P.G. Clem, J.J. Richardson, B.A. Tuttle, G.A. Samara, Phys. Rev. B 72 (2005) 104111.