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Frustration of ferroelectricity in epitaxial film of relaxor ferroelectric PbSc1/2Nb1/2O3
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 J. Phys.: Condens. Matter 26 325901 (http://iopscience.iop.org/0953-8984/26/32/325901) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 129.81.226.78 This content was downloaded on 22/08/2014 at 11:57
Please note that terms and conditions apply.
Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 26 (2014) 325901 (7pp)
doi:10.1088/0953-8984/26/32/325901
Frustration of ferroelectricity in epitaxial film of relaxor ferroelectric PbSc1/2Nb1/2O3 M Tyunina1, I Pintilie2, A Iuga2, M S Stratulat1 and L Pintilie2 1
Microelectronics and Materials Physics Laboratories, University of Oulu, PO Box 4500, FI-90014 Oulunyliopisto, Finland 2 National Institute of Materials Physics, PO Box MG 7, Bucharest - Magurele, 077125, Romania E-mail: [email protected] Received 7 May 2014, revised 12 June 2014 Accepted for publication 23 June 2014 Published 17 July 2014 Abstract
Relaxor-to-ferroelectric transformations induced by varying electric fields and temperatures are studied experimentally in acube-on-cubetype epitaxial PbSc1/2Nb1/2O3 film grown on La1/2Sr1/2CoO3/MgO(001). Dielectric response, quasi-static and dynamic polarization, and dynamic current–voltage characteristics evidence the absence of spontaneous relaxor-toferroelectric transition. The electricfield-induced transformation from a glass-like relaxor state to a new dynamic polar state is detected at low temperatures below 100 K only. The frustration of ferroelectricity is discussed in relation to orientational anisotropy of the dipolar system in the epitaxial (001) film. Keywords: relaxor ferroelectric, epitaxial, dipolar glass (Some figures may appear in colour only in the online journal)
1. Introduction
reorientation, or flips, of a dipole are activated thermally and/ or by an electric field. Although the microscopic nature of the polar entities is under research and debate, the dipolar approach can explain such features of RFEs as a broad dielectric peak ε(T) around temperature Tm with a strong frequency dispersion of ε and Tm, a Vogel-Fulcher relationship between the temperatures Tm and the dipolar relaxation times,divergence between static and dynamic responses, electric-field-induced transformations, and effects of high hydrostatic pressure [11]. Notice that the dielectric peak around Tm in RFEs is not related to a FE phase transition.Aphase transition from the R to FE state can take place spontaneously upon cooling to a certain temperature Ts crystal direction of the epitaxial (001) oriented PSN film. 3. Results and discussion 3.1. Microstructure of PSN
Room temperature XRD analysis of PSN/LSCO/MgO shows that both the LSCO and perovskite PSN layers are highly oriented, with (00l) planes parallel to the (001) surface of the MgO substrate (figure 1(a)). No pyrochlore phase is detected in PSN. The epitaxial relationship is of cube-on-cube-type PSN[100](001)‖LSCO[100](001)‖MgO[100](001). The out- of-plane lattice parameter of PSN is c = 4.089 Å, and the in-plane parameter is approximately a ≈ 4.080 Å. The parameters areclose to the lattice parameter a0 = 4.08(4) Å of the perovskite-structure pseudocubic cell of bulk PSN at room temperature [25–27]. The PSN film is slightly elongated 2
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J. Phys.: Condens. Matter 26 (2014) 325901
(a)
(c)
(b)
(d)
(a)
(b)
Figure 3. (a) Derivative ξ of inverse permittivity as a function of temperature determined at f = 30 kHz in the (a) PSN capacitor and (b) PMN capacitor [19].
where RF and REL are the resistances of the PSN film and the LSCO electrode layer, correspondingly, CH is the capacitance of the stack including the PSN film and the film-electrode interfacial layers, and ω = 2πf. As follows from (1), the measured loss factor tan D characterizes losses in the Pt/PSN/LSCO capacitor, and it is not equivalent to dielectric losses in the PSN film. Since the resistances and the interfacial capacitance are not known exactly, it is impossible to accurately determine and analyze the imaginary part of the permittivity in the PSN film. Both the real part of the dielectric permittivityε and the loss factor tan D determined in the heterostructureare affected by the capacitor design,whichmakes it difficult to conclude on the type of dielectric relaxation in PSN from the observed frequency dispersion of ε and tan D. However, the temperatures Tm of the maxima in ε(T, f ) are practically insensitive to extrinsic factors in thin-film capacitors. The Vogel-Fulcher relationship (2),which is accepted as an empirical proof of the RFE behavior, can be inspected in thin films directly:
Figure 2. (a, c) The real part of the dielectric permittivity ε and (b, d) loss factor tan D in the PSN heterostructure as a function (a, b) of temperature T at frequencies f = 200 Hz–1 MHz, and (c, d) of frequency at T = 400 K. Arrows show direction of frequency increase.
in the out-of-plane direction, with the lattice strain s = (c/a0 − 1) × 100 ≈ 0.1%. The out-of-plane strain distribution (Δs/s) was evaluated using a Williamson-Hall analysis of perovskite (00l) XRD diffractions, whose full width at half maximum (FWHM) was determined by peak fitting (figure 1(b)). The obtained value is approximately (Δs/s) ≈ 0.17%, implying a negligibly small strain gradient. The theoretical misfit strain in a pseudomorphic PSN/ LSCO/MgO stack is very large [21, 31–33]. However, the misfit strain is efficiently relaxed in the grown epitaxial PSN/ LSCO/MgO heterostructures, as evidenced by XRD. Such a relaxation has been previously related to a three-dimensional island-type epitaxial growth leading to the formation of a nano-columnar microstructure without destroying the cube-on-cubetype epitaxy [33]. SEM analysis confirms the presence of nanocolumns with lateral dimensions of approximately 20–100 nm in the grown PSN films (figure 1(c)). Notice that the polarization and the dielectric response of the PSN/LSCO/MgO heterostructures are measured in the out-ofplane direction and they are not influenced directly by the inplane boundaries between nano-columns.
⎡ ⎤ TA ⎥ f = f0 exp⎢ − (2) ⎢⎣ (Tm − Tf ) ⎥⎦
where f0, TA, and Tf are fitting parameters.The temperature Tm is frequency independent (figure 2(a)), and the Vogel-Fulcher relationship is invalid in the PSN film. The frequency independent Tm ≈ 400 K indicates that the PSN film might experience FE transition. However, the FE or R-state below Tm cannot be unambiguously distinguished from the data in figure 2. As proven before [19 and references therein], the FE transitions and the RFE behavior in thin films can be identified clearly by analyzing the temperature dependence of the derivative ξ of inverse permittivity: ξ(T ) =
3.2. Dielectric response
∂ ⎛⎜ 1 ⎟⎞ ∂T ⎝ ε ⎠
For the low-temperature FE state with the Curie-Weiss-type behavior of permittivity, the derivative ξ is negative and independent of temperature: ξ = const T > 100 K. The loops start acquiring FE-like shape below 100 K only, i.e. by 300 K lower than Tm. The asymmetric shape of the loops can be related to Schottky barriers of different heights formed at the interfaces between PSN and electrodes made of materials with different work functions (Pt and LSCO [34]).
3.4. Current
The dynamic (I–V) loops in the PSN film differ significantly from the switching current behavior in the films of normal FEs (figure 7). The (I–V) curves exhibit four peaks resembling antiferroelectric-like (AFE) behavior. AFE-looking polarization loops have been reported for bulk RFEs at temperatures a few degrees higher than Ts, and they have been ascribed to the field-induced R-FE transition (see [8] and references therein). Contrary to the field-induced FE transition in bulk, the four-peaked (I–V) curves are found in the PSN film at all 4
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J. Phys.: Condens. Matter 26 (2014) 325901
(a)
(b)
Figure 8. Positive branches of the dynamic current-voltage loops measured at frequency f = 1 kHz and temperature T = (a) 200 K (curve 1), 100 K (curve (2), 50 K (curve 3), 20 K (curve 4), and (b) 50 K (open symbols). Lines in (b) show multi-peak fit.
(a)
Figure 10. Log-log plots of the voltages V1 and V2 of the current peaks as a function of the product (Vmf) determined at the temperature T = 150 K. Lines are fits.
(b)
Figure 11. Schematic illustration of dipoles in the epitaxial (001)
(c)
film. The electric field is applied along the out-of-plane ≪100 > crystal direction. The field increases from zero in (a) to higher ones in (b), (c), and (d). Red color indicates reorientation of dipoles.
(c)
mastercurves for the voltage V1 are of different type than for the voltage V2 at all temperatures. The scaling of the voltage log(V2) resembles the behavior found in the epitaxial PMN film [22]. The two scaling regions of log(V2) can be distinguished. A tendency to a linear relationship [log(V2) ∞ log(Vmf)] can be seen for the larger products (Vmf) (figure 10). Additionally to this linear high-field region, a non-linear low-field region exists. The two electric fieldinduced processes corresponding to the two scaling regimes have been suggested to be dipolar flips and flow of a phaseboundary [22]. The thermally and electric field-activated flips determine dynamic response at high temperatures and low fields (the non-linear regime). The contribution of the flips becomes weaker upon cooling, while that of the boundary flow is enhanced. The boundary flow can be mainly responsible for the high-field (linear) regime, especially at lower temperatures. Importantly, the two scaling regions for the voltage V2 differ clearly from the two linear scaling regions for the coercive field resulting from a dynamic crossover between the creep and flow regimes of the FE domain wall in epitaxial FE films [35]. Besides the voltage V2, whose behavior is consistent with the earlier observations in the PMN film, there is a smaller voltage V1 in the PSN film. The voltage V1 exhibits a tendency toward high-field linear scaling [log(V1) ∞ log(Vmf)], similar to the behavior of V2 (figure 10). Moreover, the difference between the voltages V1 and V2 decreases at high fields. Considering dipolar flips and boundary flow, the coexistence of V1 and V2 may be ascribed to the presence of two types of dipoles, with the major difference between these types being in reorientation barriers. The phase boundary motion makes the dipolar contributions less distinguishable at high fields.
Figure 9. Log-log plots of the voltages V1 and V2 of the current peaks as a function of the product (Vmf) determined at the temperature T = (a) 150 K, (b) 300 K, and (c, d) T = 100–350 K. Arrows in (c, d) show direction of temperature increase.
temperatures (figure 8), including the higher temperatures at which the quasi-static (Pqs–V) loops evidence the absence of FE transition. Moreover, the constituent peaks are better separated at higher temperatures, and the voltages of the current peaks depend on temperature, frequency and maximum applied voltage Vm. A more accurate analysis of the dynamic (I–V) curves was performed. In particular, the voltages of the current peaks were found by fitting of the positive and negative branches of the (I–V) curves (figure 8(b)). Although the (I–V) loops are slightly biased due to different electrodes [34], the behavior of the peak voltages is similar for the positive and negative branches. The voltages V1 and V2 of the positive branches of the (I–V) loops, where V1 crystal direction (solid arrows in figure 11(a)) due to the cube-on-cubetype epitaxial growth of metrically tetragonal PSN. Additionally to the ≪100 > dipoles, the dipoles with component(s) of polarization parallel to the (001) plane (corresponding to the in-plane directions in the films) may also still exist (open arrows in figure 11(a)) as discussed before [20]. Compared to the ≪100 > -type dipoles, the ≪111 > or ≪110 > -type dipoles may have lower barriers for flips under an electric field applied along the ≪100 > direction (figure 11(b)). The voltage V1 may be ascribed to ‘easier’ reorientation of the ≪111 > or ≪110 > directed dipoles, and the larger voltage V2 to flips of the ≪100 > dipoles (figures 11(b) and (c)). The dipolar systems in epitaxial RFE films may be orientationallyanisotropic, with thedipolarmoments aligned along only a certain crystal direction. This is principally different from the model isotropic random dipolar system in bulk RFEs [11]. (Notice that atomistic anisotropy of correlations between the local cation displacements has been analyzed in the work [36]. Here we discuss anisotropy of dipolar system on a larger scale.) A theoretical analysis of such an orientationally anisotropic dipolarglass-like system is desirable. We believe, however, that orientational anisotropy may lead to frustration of the long-range ferroelectric order and to stabilization of the glass-like R-state in epitaxial RFE films. The in-plane biaxial compression enhances tetragonality of the unit celland, correspondingly, preferential alignment of the dipolar moments along the ≪100 > direction in cube-on-cube type epitaxial (001) oriented films. Thus in contrast to enhancement of FE polarization in films of normal FEs, epitaxial strain may enhance orientational anisotropy and, as a consequence, also stability of a glass-like state in RFE films.
The authors are grateful to J Levoska for valuable discussions. The research has been supported by the Academy of Finland (Project No. 264961), Tekes (Project No. 400.31.2013), and through the Idea-Complex Research Grant (PN-II-IDPCCE-2011-2-0006, No. 3/2012) of the Romanian Ministry of Education (MEN-UEFISCDI). References [1] Smolenskii G A, Bokov V A, Isupov V A, Krainik N N, Pasynkov R E and Sokolov A I Ferroelectrics and Related Materials (New York: Gordon and Breach) [2] Ye Z G (ed) 2008 Handbook of Advanced Dielectric, Piezoelectric and Ferroelectric Materials – Synthesis, Properties and Applications (Cambridge: Woodhead Publishing) [3] Blinc R 2011 Advanced Ferroelectricity (Oxford: Oxford University Press) [4] Baek S H et al 2011 Science 334 958 [5] Xu G, Wen J, Stock C and Gehring P M 2008 Nat. Mater. 7 562 [6] Phelan D et al 2014 Proc. Natl Acad. Sci. 111 1754 [7] Manley M E, Lynn J W, Abernathy D L, Specht E D, Delaire O, Bishop A R, Sahul R and Budai J D 2014 Nat. Commun. 5 3683 [8] Aktas O, Salje E K H,Crossley S, Lampronti G I, Whatmore R W, Mathur N D and CarpenterM A 2013 Phys. Rev. B 88 174112 [9] Cowley R A, Gvasaliya S N, Lushnikov S G, Roessli B and Rotaru G M 2011 Adv. Phys. 60 229 [10] Vakhrushev S B, Naberezhnov A A, Okuneva N M and Savenko B N 1995 Phys. Solid State 37 1993 [11] Pirc R and Blinc R 1999 Phys. Rev. B 60 13470 [12] Blinc R, Dolinšek J, Gregorovič A, Zalar B, Filipič C, Kutnjak Z, Levstik A and Pirc R 1999 Phys. Rev. Lett. 83 424 [13] Pirc R, Blinc R, Bobnar V and Gregorovič A 2005 Phys. Rev. B 72 014202 [14] Pirc R and Blinc R 2007 Phys. Rev. B 76 020101 [15] Dawber M, Rabe K M and Scott J F 2005 Rev. Mod. Phys. 77 1083 [16] Schlom D G, Chen L Q, Eom C B, Rabe K M, Streiffer S K and Triscone J M 2007 Ann. Rev. Mater. Res. 37 589 [17] Rondinelli J M and Spaldin N A 2011 Adv. Mater. 23 3363 [18] Pertsev N A, Zembilgotov A G and Tagantsev A K 1998 Phys. Rev. Lett. 80 1988 [19] Tyunina M, Plekh M and Levoska J 2009 Phys. Rev. B 79 054105 [20] Lynnyk A, Chvostova D, Pacherova O, Kocourek T, Jelinek M, Dejneka A and Tyunina M 2013 Appl. Phys. Lett. 103 132901 [21] Tyunina M, Levoska J, Janolin P E and Dejneka A 2013 Phys. Rev. B 87 224107 [22] Tyunina M, Pintilie I, Iuga A and Pintilie L 2014 Phys. Rev. B 89 094106 [23] Prosandeev S, Wang D and Bellaiche L 2013 Phys. Rev. Lett. 111 247602 [24] Chu F, Reaney I M and Setter N 1995 J. Appl. Phys. 77 1671 [25] Malibert C, Dkhil B, Kiat J M, Durand D, Berar J F and Spasojevic-de Bire A 1997 J. Phys.: Condens. Matter 9 7485 [26] Perrin C, Menguy N, Suard E, Muller Ch, Caranoni C and Stepanov A 2000 J. Phys.: Condens. Matter 12 7523 [27] Abdulvakhidov K G, Mardasova I V, Myasnikova T P, Kogan V A, Spinko R I and Kupriyanov M F 2001 Phys. Solid State 43 508 [28] Bidault O, Perrin C, Caranoni C and Menguy N 2001 J. Appl. Phys. 90 4115
4. Conclusions Electricfield-induced transformations are studied experimentally in cube-on-cube-type epitaxial (001) oriented RFE PSN film grown on LSCO/MgO(001). The dielectric response, quasi-static and dynamic polarization, and dynamic current– voltage characteristics are analyzed as a function of temperature, frequency and applied field. In contrast to spontaneous FE transition in bulk PSN, the studies evidence the absence of FE transition in the PSN film. The low temperature R-state is stable in a broad range of electric fields and temperatures. The current analysis indicates two electric field-induced processes that are ascribed to dipolar flips and flow of a phase boundary. An electric-field-induced transformation to a new dynamic polar state is detected at low temperatures below 100 K only. The stability and robustness of the R-state may be related to orientational anisotropy of the dipolar glass-like system in the epitaxial (001) PSN film. 6
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[33] Tyunina M, Yao L, Plekh M, Levoska J and van Dijken S 2013 Adv. Funct. Mater. 23 467 [34] Pintilie L and Alexe M 2005 J. Appl. Phys. 98 124103 [35] Yang S M, Jo J Y, Kim T H, Yoon J G, Song T K, Lee H N, Marton Z, Park S, Jo Y and Noh T W 2010 Phys. Rev. B 82 174125 [36] Takenaka H, Grinberg I and Rappe A M 2013 Phys. Rev. Lett. 110 147602
[29] Raevskii I P, Eremkin V V, Smotrakov V G, Gagarina E S and Malitskaya M A 2000 Phys. Solid State 42 161 [30] Perrin C, Menguy N, Bidault O, Zahra C Y, Zahra A M, Caranoni C, Hilczer B and Stepanov A 2001 J. Phys.: Condens. Matter 13 10231 [31] Levoska J and Tyunina M 2003 Ferroelecrics 291 11 [32] Tyunina M, Levoska J and Leppävuori S 2002 J. Appl. Phys. 91 9277
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Frustration of ferroelectricity in epitaxial film of relaxor ferroelectric PbSc1/2Nb1/2O3
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 J. Phys.: Condens. Matter 26 325901 (http://iopscience.iop.org/0953-8984/26/32/325901) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 129.81.226.78 This content was downloaded on 22/08/2014 at 11:57
Please note that terms and conditions apply.
Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 26 (2014) 325901 (7pp)
doi:10.1088/0953-8984/26/32/325901
Frustration of ferroelectricity in epitaxial film of relaxor ferroelectric PbSc1/2Nb1/2O3 M Tyunina1, I Pintilie2, A Iuga2, M S Stratulat1 and L Pintilie2 1
Microelectronics and Materials Physics Laboratories, University of Oulu, PO Box 4500, FI-90014 Oulunyliopisto, Finland 2 National Institute of Materials Physics, PO Box MG 7, Bucharest - Magurele, 077125, Romania E-mail: [email protected] Received 7 May 2014, revised 12 June 2014 Accepted for publication 23 June 2014 Published 17 July 2014 Abstract
Relaxor-to-ferroelectric transformations induced by varying electric fields and temperatures are studied experimentally in acube-on-cubetype epitaxial PbSc1/2Nb1/2O3 film grown on La1/2Sr1/2CoO3/MgO(001). Dielectric response, quasi-static and dynamic polarization, and dynamic current–voltage characteristics evidence the absence of spontaneous relaxor-toferroelectric transition. The electricfield-induced transformation from a glass-like relaxor state to a new dynamic polar state is detected at low temperatures below 100 K only. The frustration of ferroelectricity is discussed in relation to orientational anisotropy of the dipolar system in the epitaxial (001) film. Keywords: relaxor ferroelectric, epitaxial, dipolar glass (Some figures may appear in colour only in the online journal)
1. Introduction
reorientation, or flips, of a dipole are activated thermally and/ or by an electric field. Although the microscopic nature of the polar entities is under research and debate, the dipolar approach can explain such features of RFEs as a broad dielectric peak ε(T) around temperature Tm with a strong frequency dispersion of ε and Tm, a Vogel-Fulcher relationship between the temperatures Tm and the dipolar relaxation times,divergence between static and dynamic responses, electric-field-induced transformations, and effects of high hydrostatic pressure [11]. Notice that the dielectric peak around Tm in RFEs is not related to a FE phase transition.Aphase transition from the R to FE state can take place spontaneously upon cooling to a certain temperature Ts crystal direction of the epitaxial (001) oriented PSN film. 3. Results and discussion 3.1. Microstructure of PSN
Room temperature XRD analysis of PSN/LSCO/MgO shows that both the LSCO and perovskite PSN layers are highly oriented, with (00l) planes parallel to the (001) surface of the MgO substrate (figure 1(a)). No pyrochlore phase is detected in PSN. The epitaxial relationship is of cube-on-cube-type PSN[100](001)‖LSCO[100](001)‖MgO[100](001). The out- of-plane lattice parameter of PSN is c = 4.089 Å, and the in-plane parameter is approximately a ≈ 4.080 Å. The parameters areclose to the lattice parameter a0 = 4.08(4) Å of the perovskite-structure pseudocubic cell of bulk PSN at room temperature [25–27]. The PSN film is slightly elongated 2
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J. Phys.: Condens. Matter 26 (2014) 325901
(a)
(c)
(b)
(d)
(a)
(b)
Figure 3. (a) Derivative ξ of inverse permittivity as a function of temperature determined at f = 30 kHz in the (a) PSN capacitor and (b) PMN capacitor [19].
where RF and REL are the resistances of the PSN film and the LSCO electrode layer, correspondingly, CH is the capacitance of the stack including the PSN film and the film-electrode interfacial layers, and ω = 2πf. As follows from (1), the measured loss factor tan D characterizes losses in the Pt/PSN/LSCO capacitor, and it is not equivalent to dielectric losses in the PSN film. Since the resistances and the interfacial capacitance are not known exactly, it is impossible to accurately determine and analyze the imaginary part of the permittivity in the PSN film. Both the real part of the dielectric permittivityε and the loss factor tan D determined in the heterostructureare affected by the capacitor design,whichmakes it difficult to conclude on the type of dielectric relaxation in PSN from the observed frequency dispersion of ε and tan D. However, the temperatures Tm of the maxima in ε(T, f ) are practically insensitive to extrinsic factors in thin-film capacitors. The Vogel-Fulcher relationship (2),which is accepted as an empirical proof of the RFE behavior, can be inspected in thin films directly:
Figure 2. (a, c) The real part of the dielectric permittivity ε and (b, d) loss factor tan D in the PSN heterostructure as a function (a, b) of temperature T at frequencies f = 200 Hz–1 MHz, and (c, d) of frequency at T = 400 K. Arrows show direction of frequency increase.
in the out-of-plane direction, with the lattice strain s = (c/a0 − 1) × 100 ≈ 0.1%. The out-of-plane strain distribution (Δs/s) was evaluated using a Williamson-Hall analysis of perovskite (00l) XRD diffractions, whose full width at half maximum (FWHM) was determined by peak fitting (figure 1(b)). The obtained value is approximately (Δs/s) ≈ 0.17%, implying a negligibly small strain gradient. The theoretical misfit strain in a pseudomorphic PSN/ LSCO/MgO stack is very large [21, 31–33]. However, the misfit strain is efficiently relaxed in the grown epitaxial PSN/ LSCO/MgO heterostructures, as evidenced by XRD. Such a relaxation has been previously related to a three-dimensional island-type epitaxial growth leading to the formation of a nano-columnar microstructure without destroying the cube-on-cubetype epitaxy [33]. SEM analysis confirms the presence of nanocolumns with lateral dimensions of approximately 20–100 nm in the grown PSN films (figure 1(c)). Notice that the polarization and the dielectric response of the PSN/LSCO/MgO heterostructures are measured in the out-ofplane direction and they are not influenced directly by the inplane boundaries between nano-columns.
⎡ ⎤ TA ⎥ f = f0 exp⎢ − (2) ⎢⎣ (Tm − Tf ) ⎥⎦
where f0, TA, and Tf are fitting parameters.The temperature Tm is frequency independent (figure 2(a)), and the Vogel-Fulcher relationship is invalid in the PSN film. The frequency independent Tm ≈ 400 K indicates that the PSN film might experience FE transition. However, the FE or R-state below Tm cannot be unambiguously distinguished from the data in figure 2. As proven before [19 and references therein], the FE transitions and the RFE behavior in thin films can be identified clearly by analyzing the temperature dependence of the derivative ξ of inverse permittivity: ξ(T ) =
3.2. Dielectric response
∂ ⎛⎜ 1 ⎟⎞ ∂T ⎝ ε ⎠
For the low-temperature FE state with the Curie-Weiss-type behavior of permittivity, the derivative ξ is negative and independent of temperature: ξ = const T > 100 K. The loops start acquiring FE-like shape below 100 K only, i.e. by 300 K lower than Tm. The asymmetric shape of the loops can be related to Schottky barriers of different heights formed at the interfaces between PSN and electrodes made of materials with different work functions (Pt and LSCO [34]).
3.4. Current
The dynamic (I–V) loops in the PSN film differ significantly from the switching current behavior in the films of normal FEs (figure 7). The (I–V) curves exhibit four peaks resembling antiferroelectric-like (AFE) behavior. AFE-looking polarization loops have been reported for bulk RFEs at temperatures a few degrees higher than Ts, and they have been ascribed to the field-induced R-FE transition (see [8] and references therein). Contrary to the field-induced FE transition in bulk, the four-peaked (I–V) curves are found in the PSN film at all 4
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J. Phys.: Condens. Matter 26 (2014) 325901
(a)
(b)
Figure 8. Positive branches of the dynamic current-voltage loops measured at frequency f = 1 kHz and temperature T = (a) 200 K (curve 1), 100 K (curve (2), 50 K (curve 3), 20 K (curve 4), and (b) 50 K (open symbols). Lines in (b) show multi-peak fit.
(a)
Figure 10. Log-log plots of the voltages V1 and V2 of the current peaks as a function of the product (Vmf) determined at the temperature T = 150 K. Lines are fits.
(b)
Figure 11. Schematic illustration of dipoles in the epitaxial (001)
(c)
film. The electric field is applied along the out-of-plane ≪100 > crystal direction. The field increases from zero in (a) to higher ones in (b), (c), and (d). Red color indicates reorientation of dipoles.
(c)
mastercurves for the voltage V1 are of different type than for the voltage V2 at all temperatures. The scaling of the voltage log(V2) resembles the behavior found in the epitaxial PMN film [22]. The two scaling regions of log(V2) can be distinguished. A tendency to a linear relationship [log(V2) ∞ log(Vmf)] can be seen for the larger products (Vmf) (figure 10). Additionally to this linear high-field region, a non-linear low-field region exists. The two electric fieldinduced processes corresponding to the two scaling regimes have been suggested to be dipolar flips and flow of a phaseboundary [22]. The thermally and electric field-activated flips determine dynamic response at high temperatures and low fields (the non-linear regime). The contribution of the flips becomes weaker upon cooling, while that of the boundary flow is enhanced. The boundary flow can be mainly responsible for the high-field (linear) regime, especially at lower temperatures. Importantly, the two scaling regions for the voltage V2 differ clearly from the two linear scaling regions for the coercive field resulting from a dynamic crossover between the creep and flow regimes of the FE domain wall in epitaxial FE films [35]. Besides the voltage V2, whose behavior is consistent with the earlier observations in the PMN film, there is a smaller voltage V1 in the PSN film. The voltage V1 exhibits a tendency toward high-field linear scaling [log(V1) ∞ log(Vmf)], similar to the behavior of V2 (figure 10). Moreover, the difference between the voltages V1 and V2 decreases at high fields. Considering dipolar flips and boundary flow, the coexistence of V1 and V2 may be ascribed to the presence of two types of dipoles, with the major difference between these types being in reorientation barriers. The phase boundary motion makes the dipolar contributions less distinguishable at high fields.
Figure 9. Log-log plots of the voltages V1 and V2 of the current peaks as a function of the product (Vmf) determined at the temperature T = (a) 150 K, (b) 300 K, and (c, d) T = 100–350 K. Arrows in (c, d) show direction of temperature increase.
temperatures (figure 8), including the higher temperatures at which the quasi-static (Pqs–V) loops evidence the absence of FE transition. Moreover, the constituent peaks are better separated at higher temperatures, and the voltages of the current peaks depend on temperature, frequency and maximum applied voltage Vm. A more accurate analysis of the dynamic (I–V) curves was performed. In particular, the voltages of the current peaks were found by fitting of the positive and negative branches of the (I–V) curves (figure 8(b)). Although the (I–V) loops are slightly biased due to different electrodes [34], the behavior of the peak voltages is similar for the positive and negative branches. The voltages V1 and V2 of the positive branches of the (I–V) loops, where V1 crystal direction (solid arrows in figure 11(a)) due to the cube-on-cubetype epitaxial growth of metrically tetragonal PSN. Additionally to the ≪100 > dipoles, the dipoles with component(s) of polarization parallel to the (001) plane (corresponding to the in-plane directions in the films) may also still exist (open arrows in figure 11(a)) as discussed before [20]. Compared to the ≪100 > -type dipoles, the ≪111 > or ≪110 > -type dipoles may have lower barriers for flips under an electric field applied along the ≪100 > direction (figure 11(b)). The voltage V1 may be ascribed to ‘easier’ reorientation of the ≪111 > or ≪110 > directed dipoles, and the larger voltage V2 to flips of the ≪100 > dipoles (figures 11(b) and (c)). The dipolar systems in epitaxial RFE films may be orientationallyanisotropic, with thedipolarmoments aligned along only a certain crystal direction. This is principally different from the model isotropic random dipolar system in bulk RFEs [11]. (Notice that atomistic anisotropy of correlations between the local cation displacements has been analyzed in the work [36]. Here we discuss anisotropy of dipolar system on a larger scale.) A theoretical analysis of such an orientationally anisotropic dipolarglass-like system is desirable. We believe, however, that orientational anisotropy may lead to frustration of the long-range ferroelectric order and to stabilization of the glass-like R-state in epitaxial RFE films. The in-plane biaxial compression enhances tetragonality of the unit celland, correspondingly, preferential alignment of the dipolar moments along the ≪100 > direction in cube-on-cube type epitaxial (001) oriented films. Thus in contrast to enhancement of FE polarization in films of normal FEs, epitaxial strain may enhance orientational anisotropy and, as a consequence, also stability of a glass-like state in RFE films.
The authors are grateful to J Levoska for valuable discussions. The research has been supported by the Academy of Finland (Project No. 264961), Tekes (Project No. 400.31.2013), and through the Idea-Complex Research Grant (PN-II-IDPCCE-2011-2-0006, No. 3/2012) of the Romanian Ministry of Education (MEN-UEFISCDI). References [1] Smolenskii G A, Bokov V A, Isupov V A, Krainik N N, Pasynkov R E and Sokolov A I Ferroelectrics and Related Materials (New York: Gordon and Breach) [2] Ye Z G (ed) 2008 Handbook of Advanced Dielectric, Piezoelectric and Ferroelectric Materials – Synthesis, Properties and Applications (Cambridge: Woodhead Publishing) [3] Blinc R 2011 Advanced Ferroelectricity (Oxford: Oxford University Press) [4] Baek S H et al 2011 Science 334 958 [5] Xu G, Wen J, Stock C and Gehring P M 2008 Nat. Mater. 7 562 [6] Phelan D et al 2014 Proc. Natl Acad. Sci. 111 1754 [7] Manley M E, Lynn J W, Abernathy D L, Specht E D, Delaire O, Bishop A R, Sahul R and Budai J D 2014 Nat. Commun. 5 3683 [8] Aktas O, Salje E K H,Crossley S, Lampronti G I, Whatmore R W, Mathur N D and CarpenterM A 2013 Phys. Rev. B 88 174112 [9] Cowley R A, Gvasaliya S N, Lushnikov S G, Roessli B and Rotaru G M 2011 Adv. Phys. 60 229 [10] Vakhrushev S B, Naberezhnov A A, Okuneva N M and Savenko B N 1995 Phys. Solid State 37 1993 [11] Pirc R and Blinc R 1999 Phys. Rev. B 60 13470 [12] Blinc R, Dolinšek J, Gregorovič A, Zalar B, Filipič C, Kutnjak Z, Levstik A and Pirc R 1999 Phys. Rev. Lett. 83 424 [13] Pirc R, Blinc R, Bobnar V and Gregorovič A 2005 Phys. Rev. B 72 014202 [14] Pirc R and Blinc R 2007 Phys. Rev. B 76 020101 [15] Dawber M, Rabe K M and Scott J F 2005 Rev. Mod. Phys. 77 1083 [16] Schlom D G, Chen L Q, Eom C B, Rabe K M, Streiffer S K and Triscone J M 2007 Ann. Rev. Mater. Res. 37 589 [17] Rondinelli J M and Spaldin N A 2011 Adv. Mater. 23 3363 [18] Pertsev N A, Zembilgotov A G and Tagantsev A K 1998 Phys. Rev. Lett. 80 1988 [19] Tyunina M, Plekh M and Levoska J 2009 Phys. Rev. B 79 054105 [20] Lynnyk A, Chvostova D, Pacherova O, Kocourek T, Jelinek M, Dejneka A and Tyunina M 2013 Appl. Phys. Lett. 103 132901 [21] Tyunina M, Levoska J, Janolin P E and Dejneka A 2013 Phys. Rev. B 87 224107 [22] Tyunina M, Pintilie I, Iuga A and Pintilie L 2014 Phys. Rev. B 89 094106 [23] Prosandeev S, Wang D and Bellaiche L 2013 Phys. Rev. Lett. 111 247602 [24] Chu F, Reaney I M and Setter N 1995 J. Appl. Phys. 77 1671 [25] Malibert C, Dkhil B, Kiat J M, Durand D, Berar J F and Spasojevic-de Bire A 1997 J. Phys.: Condens. Matter 9 7485 [26] Perrin C, Menguy N, Suard E, Muller Ch, Caranoni C and Stepanov A 2000 J. Phys.: Condens. Matter 12 7523 [27] Abdulvakhidov K G, Mardasova I V, Myasnikova T P, Kogan V A, Spinko R I and Kupriyanov M F 2001 Phys. Solid State 43 508 [28] Bidault O, Perrin C, Caranoni C and Menguy N 2001 J. Appl. Phys. 90 4115
4. Conclusions Electricfield-induced transformations are studied experimentally in cube-on-cube-type epitaxial (001) oriented RFE PSN film grown on LSCO/MgO(001). The dielectric response, quasi-static and dynamic polarization, and dynamic current– voltage characteristics are analyzed as a function of temperature, frequency and applied field. In contrast to spontaneous FE transition in bulk PSN, the studies evidence the absence of FE transition in the PSN film. The low temperature R-state is stable in a broad range of electric fields and temperatures. The current analysis indicates two electric field-induced processes that are ascribed to dipolar flips and flow of a phase boundary. An electric-field-induced transformation to a new dynamic polar state is detected at low temperatures below 100 K only. The stability and robustness of the R-state may be related to orientational anisotropy of the dipolar glass-like system in the epitaxial (001) PSN film. 6
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