Two-Dimensional Ferroelectrics
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University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Stephen Ducharme Publications Research Papers in Physics and Astronomy 2000 Two-Dimensional Ferroelectrics L. M. Blinov Institute of Crystallography, Russian Academy of Sciences, Leninski|¯ prosp. 59, 117333 Moscow, Russian Federation V. M. Fridkin Institute of Crystallography, Russian Academy of Sciences, Leninski|¯ prosp. 59, 117333 Moscow, Russian Federation S.P. Palto Institute of Crystallography, Russian Academy of Sciences, Leninski|¯ prosp. 59, 117333 Moscow, Russian Federation A. V. Bune University of Nebraska - Lincoln Peter A. Dowben University of Nebraska-Lincoln, [email protected] See next page for additional authors Follow this and additional works at: https://digitalcommons.unl.edu/physicsducharme Part of the Physics Commons Blinov, L. M.; Fridkin, V. M.; Palto, S.P.; Bune, A. V.; Dowben, Peter A.; and Ducharme, Stephen, "Two- Dimensional Ferroelectrics" (2000). Stephen Ducharme Publications. 51. https://digitalcommons.unl.edu/physicsducharme/51 This Article is brought to you for free and open access by the Research Papers in Physics and Astronomy at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in Stephen Ducharme Publications by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. Authors L. M. Blinov, V. M. Fridkin, S.P. Palto, A. V. Bune, Peter A. Dowben, and Stephen Ducharme This article is available at DigitalCommons@University of Nebraska - Lincoln: https://digitalcommons.unl.edu/ physicsducharme/51 Physics ± Uspekhi 43 (3) 243 ± 257 (2000) # 2000 Uspekhi Fizicheskikh Nauk, Russian Academy of Sciences REVIEWS OF TOPICAL PROBLEMS PACS numbers: 75.70. ± i, 77.80. ± e Two-dimensional ferroelectrics L M Blinov, V M Fridkin, S P Palto, A V Bune, P A Dowben, S Ducharme DOI: 10.1070/PU2000v043n03ABEH000639 Contents 1. Introduction 243 2. Ferroelectricity and the ferroelectric phase transitions 244 3. Thin ferroelectric films and the finite-size effect 245 4. Ferroelectric polymers: vinylidene fluoride copolymers 247 5. Langmuir ± Blodgett ferroelectric films 249 6. Two-dimensional ferroelectric films 254 7. The surface phase transition in ferroelectric films 256 8. Conclusions 256 References 257 Abstract. The investigation of the finite-size effect in ferroelec- 1. Introduction tric crystals and films has been limited by the experimental conditions. The smallest demonstrated ferroelectric crystals Ultrathin crystalline films offer the possibility of exploring had a diameter of 200 A and the thinnest ferroelectric films phase transitions in the crossover region between two and were 200 A thick, macroscopic sizes on an atomic scale. three dimensions. Second-order ferromagnetic phase transi- Langmuir ± Blodgett deposition of films one monolayer at a tions have been observed in monolayer magnetic films [1, 2], time has produced high quality ferroelectric films as thin as where the surface anisotropy energy stabilizes the two- 10 A, made from polyvinylidene fluoride and its copolymers. dimensional ferromagnetic state at finite temperatures [3]. These ultrathin films permitted the ultimate investigation of Similarly, a number of magnetic materials have magnetic finite-size effects on the atomic thickness scale. Langmuir ± surface layers that show a second-order ferromagnetic ± Blodgett films also revealed the fundamental two-dimensional paramagnetic phase transition with an increased Curie character of ferroelectricity in these materials by demonstrat- temperature [4]. Ferroelectricity is in many ways analogous ing that there is no so-called critical thickness; films as thin as to ferromagnetism, and bulk ferroelectricity and finite-size two monolayers (1 nm) are ferroelectric, with a transition effects have been observed in nanocrystals as small as temperature near that of the bulk material. The films exhibit 200 A in diameter [5, 6], and in thin films as thin as 600 A all the main properties of ferroelectricity with a first-order [7] {. First-order ferroelectric ± paraelectric phase transitions ferroelectric ± paraelectric phase transition: polarization hys- in surface layers approximately 200 A thick have been teresis (switching); the jump in spontaneous polarization at the reported by Scott et al. [8] and found to have enhanced phase transition temperature; thermal hysteresis in the polar- transition temperatures. These results also can be interpreted ization; the increase in the transition temperature with applied as bulk ferroelectricity suppressed by the effects of surface field; double hysteresis above the phase transition temperature; energy and the depolarization field, and imply that the bulk and the existence of the ferroelectric critical point. The films ferroelectric state is associated with a minimum critical size also exhibit a new phase transition associated with the two- [8 ± 10]. Nevertheless, it is clear that the ferroelectric phase dimensional layers. transition in the two-dimensional lattice is possible even in the simplest two-dimensional Ising model, as shown by Onsager in 1944 [11]. L M Blinov, V M Fridkin, S P Palto Institute of Crystallography, Russian Academy of Sciences, Here, we present a review of investigations of the ferro- Leninski|¯ prosp. 59, 117333 Moscow, Russian Federation electric phase transition in crystalline films of a random Tel. (7-095) 135 15 00. Fax (7-095) 135 10 11 copolymer of vinylidene fluoride and trifluoroethylene as E-mail: [email protected] thin as 10 A (two monolayers) prepared by Langmuir ± A V Bune, P A Dowben, S Ducharme Department of Physics and Blodgett (LB) deposition. The first-order ferroelectric phase Astronomy, Behlen Laboratory of Physics, Center for Materials Research transition with a Curie temperature nearly equal to the bulk and Analysis, University of Nebraska ± Lincoln, value was observed even in these essentially two-dimensional Lincoln, NE 68588-0111, USA Tel. 402-472-8590. Fax 402-472-2879 films. In addition, we observed a second phase transition at a E-mail: [email protected] lower temperature, which seems to have a surface nature. The absence of finite-size effects on the bulk transition implies Received 8 August 1999 Uspekhi Fizicheskikh Nauk 170 (3) 247 ± 262 (2000) Translated by V M Fridkin; edited by S N Gorin { And possibly as thin as 100 A, see Karasawa J et al. Integrated Ferroelectrics 12 105 (1996). (Authors' note for English Edition.) 244 L M Blinov, V M Fridkin, S P Palto, A V Bune, P A Dowben, S Ducharme Physics ± Uspekhi 43 (3) that these films must be considered as two-dimensional The equilibrium temperature of transition from para- ferroelectrics. electric to ferroelectric phase is Tc T0; all properties are dependent on the difference between the crystal temperature 2. Ferroelectricity and the ferroelectric phase T and the phase transition temperature Tc. The Æ signs transitions indicate that the polarization can point in either direction along the symmetry axis (recall that this is the uniaxial Ferroelectric materials have fascinated scientists since their case), and correspond to the two energetically equivalent discovery in 1920 [12 ± 15]. In analogy with ferromagnets, the states of the ferroelectric crystal at zero electric field. characteristic properties of ferroelectrics include spontaneous Equation (2.4) shows the typical result that at the second- electric polarization, polarization reversal (switching), and order ferroelectric phase transition there is no jump in the disappearance of the polarization above a ferroelectric phase order parameter (the magnitude Ps in this case) and in the transition temperature Tc. Ferroelectric materials have been a latent heat of transition. However, there is a jump in the fertile field for the study of phase transitions, electron ± heat capacity. phonon interactions, polaritons, and other optical and The dielectric polarizability w in the paraelectric phase is electrical phenomena in condensed matter. built-in to the definition of a and calculated from the free From the time of the first reports of Valasek in the early energy density expansion (2.1) and equilibrium conditions 1920s [12, 16], many books and reviews have been devoted to (2.2): the problem of ferroelectricity [14, 15, 17 ± 19]. V L Ginzburg q2F 1 T T developed the first phenomenological theory of ferroelectri- 0 : 2 city in the 1940s [20, 21] based on the Landau theory of qP w e0C second-order phase transitions [22 ± 24] and a similar treat- ment was developed by Devonshire shortly thereafter [13, 25, The dielectric constant of the medium e e1 w=e0 26]. Later, many phenomenological aspects of the problem contains contributions from the background polarizability were developed by E M Lifshitz, V L Ginzburg, A P Levanyuk, and the ferroelectric polarizability (2.5). D G Sannikov, V L Indenbom, and others. Here, we are The general first-order phase transition is accompanied by giving only a short summary of the Landau ± Ginzburg a small but finite jump of the order parameter P and enthalpy. phenomenological treatment of the ferroelectric phase transi- Many ferroelectric materials exhibit a special kind of first- tions. order phase transition with a change of symmetry from a Presuming that the order parameter in the Landau theory group to subgroup, which is close to the situation in the has the same transformation properties as the polarization second-order transition, and can be described by the free- vector P, we can in the uniaxial case express the Gibbs free