Worldwide research on relaxor ferroelectric (RFE) has been carried out since 1950s. There are several schools in the world who have defined the evolution and origin of relaxor properties in the ferroelectric materials in their own way. One common consensus among the scientists is the presence of polar nano regions (PNRs) i.e. self assembled domains of short range ordering typically of less than 20-50 nm in the ferroelectric relaxor materials which causes the dielectric dispersion near the phase transition temperature. Another common approach has been also believed among the relaxor ferroelectric scientists i.e. the existence of random field at nanoscale. Random field model is considered on the experimental and theoretical facts driven from the different dielectric dispersion response under zero field cooled (ZFC) and field cooled (FC) among the relaxors.
Overall relaxor ferroelectrics have been divided into two main categories such as (i) classical relaxors (only short range ordering), the most common example is PbMg1
This article deals with the historical development of the relaxor ferroelectrics, microstructural origin of RFE, strain mediated conversion of normal ferroelectric to relaxor ferroelectrics, superlattice relaxors, lead free classical relaxor ferroelectrics, distinction of classical relaxors and semiclassical ferroelectric relaxors based on the polarization study, and their potential applications in microelectronic industry.
Relaxor ferroelectric materials were discovered in complex perovskites by Smolenskii  in early fifties of twentieth centuries. Since then a vast scientific communities have been working on relaxor materials and related phenomena but the plethora of mesoscopic and microscopic heterogeneities over a range of lengths and timescales made difficult to systematic observations . The microscopic image and the dielectric response of relaxor are qualitatively different for that of normal ferroelectrics. The universal signature of RFE is as follows [3 - 18]: (i) the occurrence of broad frequency-dependent peak in the real and imaginary part of the temperature dependent dielectric susceptibility (χ') or permittivity (ε') which shifts to higher temperatures with increasing frequency, G. A. Smolenskii and A. I. Agranokskaya, Soviet Physics Solid State 1, 1429 (1959), (ii) Curie Weiss law is observed at temperatures far above dielectric maxima temperature (
As we know ferroelectric and related phenomenon are synonyms of ferromagnetism, antiferromagnetism, spin glass, and random field model which have been originally studied for magnetic materials. Relaxors ferroelectrics possess a random field state, as initially proposed by Westphal, Kleemann and Glinchuk [16-18]. Near Burns temperature, small polar nano regions start originating in different directions inside the crystal at mesoscopic scale; however, these polar nano regions are not static in nature at Burns temperature. At low temperature these polar nanoregions (PNRs) become static and developed a more defined regions called random field, the nature of these fields are short range order. The evidence of the existence of nanosized polar domains at temperatures well above the dynamic transition temperature comes for experimental observations. The presence of these polar nanoregions (PNRs) was established by measuring properties that depend on square of the polarization (
Electrostriction is a property which depends on
The existence of PNRs well above
3. Theory of relaxor ferroelectricity
The general formula of perovskite having A and B-site cations with different charge states can be written as A′xA′′1−xB′yB′′1−yO3. The randomness occupancy of A′,A′′ and B′,B′′ in A, B site respectively, depends on the ionic sizes, distribution of cations ordering at sub lattices and charge of cations. If the charges of cations at B-sites are same it is unlikely to have the polar randomness at nanoscale. Long range order (LRO) is defined as a continuous and ordered distribution of the B cations on the nearest neighbor sites. The short coherence length of LRO occurs when the size of the ordered domains are in a range of 20 to 800 Å in diameter. The long coherence range of LRO occur when the size of the ordered domains are much greater than 1000 Å. Randall et al. made a classification of complex lead perovskite and their solid solutions based on B-cation order studied by TEM and respective dielectric, X-rays and optical properties -. This classification divides the complex lead perovskites into three subgroups; random occupation or disordered, nanoscale or short coherent long-range order and long coherent long-range order of B-site cations.
Diffuse phase transition behavior is characteristic of the disordered structures. In these structures, random lattice disorder introduces dipolar impurities and defects that influence the static and dynamic properties of these materials. The presence of the dipolar entities on a lattice site of the highly polarizable FE structure, induced dipoles in a region determined by the correlation length (
These PNRs are dynamic and they experience a slowing down of their fluctuations at
The temperature dependence of the dielectric constant below
where γ and δ are parameters describing the degree of relaxation and diffuseness of the transition respectively. The parameter γ varies between 1 and 2, where values closer to 1 indicate normal ferroelectric behavior whereas values close to 2 indicate good relaxor behavior. Above
where C and Θ are the Curie constant and Curie temperature respectively.
Last sixty years of extensive research in the field of relaxor ferroelectrics, several models have been proposed to explain the unusual dielectric behavior of these materials. Some of these models are: statistical composition fluctuations [20, 21], superparaelectric model , dipolar glass model , random field model , spherical random field model  etc. These models can explain much of the experimental observed facts but a clear understanding of the relaxor nature or even a comprehensive theory is not available yet. Despite the absence of a comprehensive theory of relaxor ferroelectricity, the literature agree to define relaxor materials in terms of the existence of polar nano regions as motioned above, these ordered regions exist in a disordered environment.
4. Strain induced relaxor phenomenon
The influence of epitaxial clamping on ferroelectric properties of thin films to rigid substrates has been largely studied and successfully explained in a Landau-Ginzburg-Devonshire (LGD) framework [26-30]. However, when the same treatment was applied to RFE, discrepancies among the predicted values and those observed in experiments were found . For instance, a downward shift in
We have calculated shift in the peak position of the dielectric maxima of PSNT films compared to bulk values following the model developed by Catalan et.al. The model is as follow: In LGD formalism, the thermodynamical potential of a perovskite dielectric thin films is described as [27-28].
where α and β correspond to linear and nonlinear terms of the inverse permittivity, and
which directly leads to Curie-Weiss behavior, where C is the Curie constant. Substituting α into the above equation showing that the strain shifts the critical temperature for a ferroelectric by:
In case of PSNT films, we observed a quadratic temperature dependence of the permittivity:
Since the inverse of the dielectric constant is the second derivative of free energy with respect to polarization (Equation 5), the measured dielectric constant can be related to the appropriate coefficients in the LGD thermodynamical potential. For P=0 and
We substituted the values of α in Equation 5 and calculated the dielectric maxima temperature under strain . To calculate , we differentiated the inverse of permittivity with respect to temperature at .
where it is assumed that
We have used the above equation to calculate the shift in the position of dielectric maxima of PSNT films. Due to lack of experimental mechanical data in literature for PSNT films or ceramics, we have used the standard
5. Experimental observation of strain induced relaxor phenomenon
Fig. 2 shows the dielectric behavior and the microstructures of the PSNT thin films and their bulk matrix [31-33]. It has been shown that the two-dimensional (2D) clamping of films by the substrate may change profoundly the physical properties of ferroelectric heterostructure with respect to the bulk material. We observed a transfer and relaxing of epitaxial strain between the layers due to in-plane oriented heterostructure. However the mismatch strain due to different thermal expansion properties of each layer provokes a shift of 62 K in the temperature of the dielectric maxima.
Transmission electron microscopy (TEM) images of PSNT in bulk (Fig. 2(a)) and thin film (Fig. 2(b)) form are shown in Fig. 2. The interlayer of about 20 nm between MgO and LSCO and the fibril structures along a single direction in the film confirm the in-plane strain state of the film. TEM image of bulk shows well ordered nanoregions in the grain matrix that meet a basic ingredient to produces relaxor behavior: the existence of nano-ordered regions surrounding by a disordered structure, however, it is unable to produce it. It has been observed from the neutron diffraction data that if the ordered nanoregions are in the range of ~ 5-10 nm, then it is capable of yielding frequency dispersion in the dielectric spectra . But the relaxor state also depends on the coherency with what the dipoles respond to the probing field (and frequency). They can establish long range or short range coherent response. PSNT ceramic was incapable to produce the frequency dispersion behavior, but in thin films form the in plane strain and the breaking of long range ordering response, induced dielectric dispersion and shifting in dielectric maxima temperature towards lower temperature side. We have observed from the temperature evolution of the Raman spectra of bulk PSNT ceramic [31-33], the competitions between ordered domains of short and long-range order due to Nb- and Ta-rich regions respectively. The average disorder arrangement of Sc3+/Nb5+/Ta5+ ions in the B-site octahedra leads to the observed diffuse phase transition. In film only short range ordering in B'/B'' ions was developed within the disordered matrix. Although bulk matrix exhibited nano-ordered regions its average size must be higher than film. Stress effects change the ionic positions somehow favoring short-range ordering. These microstructural differences trigger the different observed dielectric responses. The microstructure-property relation of PSNT thin films and ceramics, one can build conclusions that perovskite with similar compositions have well defined relaxor behavior than their bulk matrix.
We have discussed the origin and functional properties of relaxor, in nutshell the basic characteristic of relaxors are the existence of ordered PNRs in a disordered matrix [37-42]. Similarly, relaxor ferromagnets (synonyms: “Mictomagnets”) are also known in the literature since the 1970s. A mictomagnet is described as having magnetic clusters (superparamagnetism) which form a spin glass and have a tendency to form short-range ordering [40, 41]. The materials hold both ferroelectric and magnetic orders at nanoscale are called “birelaxors”. Birelaxors are suppose to possess only short range order over the entire temperature range with broken symmetry such as “global spatial inversion” and “time reversal symmetry” at nanoscale. Nanoscale broken symmetries and length scale coherency make birelaxors difficult to investigate microscopically; it is advisable to use optical tools for proper probing. Birelaxors do not usually show linear ME coupling (
A single-phase perovskite PbZr0.53Ti0.47O3 (PZT) and PbFe2/3W1/3O3 (PFW), (40% PZT-60 % PFW) solid solutions thin film grown by pulsed laser deposition system have shown interesting birelaxor properties. Raman spectroscopy, dielectric spectroscopy and temperature-dependent zero- field magnetic susceptibility indicate the presence of both ferroic orders at nanoscale .
Dipolar glass and spin glass properties are confirmed from the dielectric and magnetic response of the PZT-PFW system, the micro Raman spectra of this system also revealed the presence of polar nanoregions. Dielectric constant and tangent loss show the dielectric dispersion near the dielectric maxima temperature that confirms near-room-temperature relaxor behavior. Magnetic irreversibility is defined as
7. Superlattice relaxors and high energy density capacitors
Material scientists are looking for a system or some novel materials that possess high power density and high energy density or both. Relaxors demonstrate high dielectric constant, low loss, non linear polarization under external electric field, high bipolar density, nano dipoles (polar nano regions (PNRs) and moderate dielectric saturation, these properties support their potential candidature for the high power as well as high energy devices. At present high-k dielectric (dielectric constant less than 100, with linear dielectric) dominates in the high energy, high power density capacitor market. The high-k dielectrics show very high electric breakdown strength (> 3 MV/cm to 12 MV/cm) but their dielectric constant is relatively very low which in turns offer 1-2 J/cm3 volume energy density. Recently, polymer ferroelectric, antiferroelectric, and relaxor ferroelectric have shown better potential and high energy density compare to the existing linear dielectrics [46-51].
BaTiO3/Ba0.30Sr0.70TiO3 (BT/BST) superlattices (SLs) with a constant modulation period of Λ= 80 Å were grown on (001) MgO substrate by pulsed laser deposition. The modulation periodicity Λ/2 was precisely maintained by controlling the number of laser shots; the total thickness of each SL film was ~6,000 Å = 0.6 μm. An excimer laser (KrF, 248 nm) with a laser energy density of 1.5 J/cm2, pulse repetition rate of 10 Hz, substrate temperature 830 °C, and oxygen pressure at 200 mTorr was used for SL growth. The detailed growth and characterization techniques are presented elsewhere .
Dielectric responses of BT/BST SLs display the similar response as for normal relaxor ferroelectric which can be seen in Figure 4. It follows the non linear Vogel- Fulcher relationship (inset Figure. 4 (a)), frequency dispersion near and below the dielectric maxima temperature (
BT/BST SLs demonstrate a “in-built” field in as grown samples at low probe frequency (<1 kHz), whereas it becomes more symmetric and centered with increase in probe frequency system (>1 kHz) that ruled out the effect of any space charge and interfacial polarization. Energy density were calculated for the polarization-electric field (P-E) loops provide ~ 12.24 J/cm3 energy density within the experimental limit, but extrapolation of this data in the energy density as function of applied field graph for different frequencies (see inset in Figure 4) suggests huge potential in the system such as it can hold and release more than 40 J/cm3 energy density.
Experimental limitations restrict to proof the extrapolated data, however the current density versus applied electric field indicates exceptionally high breakdown field (5.8 to 6.0 MV/cm) and low current density (~ 10-25 mA/cm2) near the breakdown voltage. Both direct and indirect measurements of the energy density indicate that it has ability to store very high energy density storage capacity (~ 46 J/cm3).
The above experimental facts suggest the relaxor nature of BT/BST ferroelectric superlattices. It also indicates their potential to store and fast release of energy density which is comparable to that of high-k (<100) dielectrics, hopefully in the coming years it might be suitable for high power energy applications. These functional properties of relaxor superlattices make it plausible high energy density dielectrics capable of both high power and energy density applications.
Extensive studies on the relaxor ferroelectrics suggest the presence of localized nano size ordered regions in the disordered matrix or static random field are responsible for the dielectric dispersion near
This work was partially supported by NSF-EFRI-RPI-1038272 and DOE-DE-FG02-08ER46526 grants.
G. A. Smolenskii and A. I. Agranokskaya, Soviet Physics Solid State 1, 1429 (1959)
R. E. Cohen, Nature, 441, 941 (2006)
Eric Cross, Ferroelectrics, 151, 305, (1994)
G. A. Samara, J. Phys.: Condens. Matter 15, R367, (2003)
G. Burns and F. H. Dacol, Solid State Communications, 48, 853, (1983)
G. A. Samara, Solid State Physics, vol. 56, Edited by H. Ehrenreich, and R. Spaepen, New York: Academic, New York (2001)
B. Krause, J. M. Cowley, and J. Wheatly, Acta Cryst. A35, 1015 (1979)
C.A. Randall, D. J. Barber, and R. W. Whatmore, J. Micro. 145, 235 (1987)
J. Chen, H. Chen, and M. A. Harmer, J. Am. Ceram. Soc. 72, 593 (1989)
I. M. Brunskill, H. schmid, and P. Tissot, Ferroelectrics 37, 547 (1984)
C. A. Randall, A. S. Bhalla, T. R. Shrout, and L. E. Cross, J. Mater. Res., 5, 829 (1990)
C. A. Randall and A. S. Bhalla, Japanese Journal of Applied Physics, 29, 327 (1990)
Ferroelectrics and Related Materials, G. A. Smolenskii (Ed.), V. A. Bokov, V. A. Isupov, N. N. Krainik, R. E. Pasynkov and A. I. Sokolov, Gordon & Breach Science Publisher, New York (1984)
Z.-G Ye, Key Engineering Materials, 155-156, 81 (1998)
H. Vogel. Z. Phys. 22, 645 (1921). G. Fulcher. J. Am. Ceram. Soc. 8, 339 (1925)
V.Westphal,W. Kleeman, and M.D. Glinchuk, Phys. Rev. Lett. 68, 847 (1992).
R. Pirc and R. Blinc, Phys. Rev. B. 60, 13470 (1999).
R. Blinc, J. Dolinsek, A. Gregorovic, B. Zalar, C. Filipic, Z. Kutnjak, A. Levstik, and R. Pirc, Phys. Rev. Lett. 83, 424 (1999).
H.T. Martirena and J.C. Burfoot. Ferroelectrics, 7, 151 (1974)
G. A. Smolenskii, V. A. Isupov, A. I. Agranovskaya and S. N. Popov, Soviet Phys.-Solid State. 2, 2584 (1961).
G. A. Smolenskii, J. Phys. Soc. Jpn. 28, Suppl. 26 (1970).
L.E. Cross, Ferroelectrics 76, 241 (1987).
D. Viehland, J. F. Li, S. J. Jang, and L. E. Cross and M. Wuttig. Phys. Rev. B. 43, 8316 (1991).
R. Fisch. Phys. Rev. B. 67, 094110 (2003).
R. Pirc and R. Blinc, Phys. Rev. B. 60, 13470 (1999)
F. Devonshire, Philos. Mag. 40, 1040, (1949); 42, 1065, (1951)
G.A. Rossetti Jr., L.E. Cross, and K. Kushida, Appl. Phys. Lett., 59, 2504 (1991)
N.A. Perstev, A.G. Zembilgotov, and A. K. Tagantsev, Phys. Rev. Lett., 80, 1988 (1998)
M. Dawber, K.M. Rabe, and J.F. Scott, Reviews of Modern Physics, 77, 1083, (2005)
G. Catalan, M. H. Corbett, R. M. Bowman, and J. M. Gregg, J. App. Phys., 91,  2295 (2002).
Margarita Correa, A. Kumar and R.S. Katiyar, J. Am. Cer. Soc. 91 (6) 1788 (2008).
Margarita Correa, Ashok Kumar, and R. S. Katiyar, Applied Physic Letters, 91, 082905 (2007).
Margarita Correa, Ashok Kumar, and R. S. Katiyar, Integrated Ferroelectrics, 100, 297 (2008)
K. Brinkman, A. Tagantsev, P. Muralt, and N. Setter, Jpn. J. App. Phys., 45, [9B] 7288 (2006)
Q.M. Zhang and J. Zhao, Appl. Phys. Lett., 71, 1649 (1997)
D. L. Orauttapong, J. Toulouse, J. L. Robertson, and Z. G. Ye, Physical Rev. B , 64, 212101 (2001).
A. Kumar, N. M. Murari, and R. S. Katiyar, Appl. Phys. Lett. 90, 162903 (2007).
A. Levstik, V. Bobnar, C. Filipič, J. Holc, M. Kosec, R. Blinc, Z. Trontelj, and Z. Jagličič, Appl. Phys. Lett. 91, 012905, (2007).
V. V. Shvartsman, S. Bedanta, P. Borisov, W. Kleemann, A. Tkach, and P. M. Vilarinho, Phys. Rev. Lett. 101, 165704 (2008).
G. A. Samara, in Solid State Physics, edited by H. Ehrenreich and R. Spaepen Academic, New York, 2001, Vol. 56, p. 239.
J. Dho, W. S. Kim, and N. H. Hur, Phys. Rev. Lett. 89, 027202 (2002).
R. Pirc and R. Blinc, Phys. Rev. B 76, 020101R (2007).
A. Kumar, G. L. Sharma, R. S. Katiyar, R. Pirc, R. Blinc, and J. F. Scott, J. Phys.: Condens. Matter 21, 382204 (2009).
R. Pirc, R. Blinc, and J. F. Scott, Phys. Rev. B 79, 214114 (2009).
A. Kumar, G. L. Sharma, R. S. Katiyar, Appl. Phys. Lett. 99, 042907 (2011).
J. H. Tortai, N. Bonifaci, A. Denat, J. Appl. Phys. 97, 053304 (2005).
M. Rabuffi, G. Picci, IEEE Trans. Plasma Sci. 30, 1939 (2002).
X. Hao, J. Zhai, and, X. Yao, J. Am. Ceram. Soc., 92, 1133 (2009).
J. Parui, S. B. Krupannidhi, Appl. Phys. Lett., 92, 192901 (2008).
R. M. Wallace, G. Wilk, MRS Bulletin. 27, 186 (2002).
G. D. Wilk, R. M. Wallace, J. M. Anthony, J. Appl. Phys. 89, 5243 (2001).
N. Ortega, A Kumar, J. F. Scott, Douglas B. Chrisey, M. Tomazawa, Shalini Kumari, D. G. B. Diestra and R. S. Katiyar. J. Phys.: Condens. Matter. 24 445901 (2012).