In situ observation of the ferroelectric-paraelectric phase transition in a triglycine sulfate single crystal by variable-temperature electrostatic force microscopy E. Z. Luo,* Z. Xie, J. B. Xu, and I. H. Wilson Department of Electronic Engineering and the Materials Science & Technology Research Center, The Chinese University of Hong Kong, New Territories, Hong Kong, People’s Republic of China L. H. Zhao Applied Physics Department, Hunan University, Changsha 410082, People’s Republic of China Received 15 June 1999 The ferroelectric-paraelectric phase transition of triglycine sulfate single crystal was investigated by variable-temperature electrostatic force microscopy. Near the Curie temperature T C , the evolution of ferro- electric domains with temperature was observed in situ. We have found that the domain structures are not thermally reversible until T C -2 °CT T C , within which the domain density N diverges reversibly via ( T C -T ) - , with =0.540.05, larger than is predicted by mean-field theory. The spontaneous polarization P in individual domains decreases continuously and reversibly to zero and eventually vanishes at T C . Quan- titative analysis reveals that P 2 ( T C -T ). I. INTRODUCTION Triglycine sulfate TGS:NH 2 CH 2 COOH 3 H 2 SO 4 is a well-known ferroelectric material and is of special interest because it is one of the few ferroelectric crystals having typi- cally a second-order phase transition ferroelectric- paraelectricat its Curie point T C 49 °C. 1–4 Below the Cu- rie point TGS exists as a typical uniaxial ferroelectric phase, the spontaneous polarization P is along the crystallographic b axis with antiparallel 180° configurations. The most inter- esting issue in a second-order phase transition is the critical phenomena near T C . 1–4 Macroscopic measurements have proved that the material can be well described by Landau’s mean-field theory. 5,6 The critical behavior of the order pa- rameter is Landau type with the critical exponent = 1 2 , i.e., P T T C , 1 where =( T C -T )/ T C is the reduced temperature. Another interesting phenomenon in a second-order phase transition is domain evolution with temperature. The critical behavior of the equilibrium domain density N can be written as 1–4 N - = 1 4 , T T C . 2 The exponent = 1 4 has rarely been measured. By using nematic liquid-crystal method, Nakatani measured the tem- perature dependence of domain width, which is the inverse of N, in TGS during cooling down from above T C . 7 The thermodynamic reversibility was not studied in Ref. 7. From the data presented in Ref. 7, one can calculate that is close to 1 when T is very close to T C . Similar results have also been observed by Wang et al. in La 1 -x Nd x P 5 O 14 LNPP single crystals, 8 which exhibit a strong thermal hyteresis ef- fect in domain density. However, it decreases rapidly as T deviates from T C . Therefore, from both experimental and theoretical points of view, it is highly desirable to visualize in situ the domain evolution during the phase transition on a nanometer scale. It is also of great interest to experimentally verify the phenomenological mean-field theory at the single domain scale. This demands a technique with capability of imaging ferroelectric domains with high resolution and in an environment with high-temperature stability and accuracy. Significant progress has been achieved in imaging do- mains in ferroelectric single crystals and thin films by using various forms of scanning force microscopes SPM’s, 9 in- cluding conventional atomic force microscopy AFM, 10 lat- eral force microscopy LFM, 11,12 and electrostatic force mi- croscopy EFMin contact and noncontact mode. 13–16 Recently, Hong and co-workers pointed out that EFM work- ing in dynamic contact mode they term it DC-EFMhas superior domain contrast to that by noncontact EFM. 17,18 There have been some observations of domain evolution in TGS. 11,13,17 However, little attention has been paid to ther- modynamics. In this paper, we present a study of the ferroelectric-paraelectric phase transition of TGS by using DC-EFM. For this purpose, we have designed a special heat- ing stage with high-temperature stability and accuracy. 19 By controlling the sample temperature carefully, the temperature dependence of domain configuration, as well as of the spon- taneous polarization P in domains, has been studied. II. EXPERIMENT The experiments were carried out in a commercial AFM Nanoscope III, Digital Instruments. A TiN coated tip was used. Here the basic principle of DC-EFM is introduced be- low. An ac modulation V =V ac cos(t) was applied between the conducting tip and the bottom electrode of the sample. The component of electrostatic force F e induced by the surface charge is given by 18 F e = b C /2 0 V ac cos t , 3 where b is the bounded surface charge density, in the case of ferroelectric domains b = P , 0 is the dielectric constant in vacuum, and C is the tip-sample capacitance. The EFM works in contact mode. Therefore the electrostatic force is proportional to b and V ac . The electrostatic force is de- tected by a lock-in amplifier and imaged simultaneously with PHYSICAL REVIEW B 1 JANUARY 2000-I VOLUME 61, NUMBER 1 PRB 61 0163-1829/2000/611/2034/$15.00 203 ©2000 The American Physical Society