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PbTiO3 sandwich structural film
Solid State Communications 147 (2008) 433–435
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Solid State Communications journal homepage: www.elsevier.com/locate/ssc
Fast-track communication
Antiferroelectriclike hysteresis loops in PbTiO3 /BiFeO3 /PbTiO3 sandwich structural film Hongri Liu a,b,∗ , Xiuzhang Wang b a
Hubei Key Laboratory of Bioanalytical Technology, Hubei Normal University, Huangshi 435002, China
b
Department of Physics, Hubei Normal University, Huangshi 435002, China
article
info
Article history: Received 30 June 2008 Accepted 10 July 2008 by A.H. MacDonald Available online 16 July 2008 PACS: 77.55.+f 77.80.-e
a b s t r a c t PbTiO3 /BiFeO3 /PbTiO3 sandwich structure has been deposited on Pt/Ti/SiO2 /Si substrate by sol-gel method annealing at 600 ◦ C. X-ray diffraction analysis revealed that the film was fully crystallized with no impure phase. Antiferroelectriclike hysteresis loop was observed at room temperature under low applied field. Under high applied electric field, ferroelectric hysteresis loop was observed renew. Compared with the BiFeO3 film, the sandwich structural film showed reduced leakage. © 2008 Elsevier Ltd. All rights reserved.
Keywords: A. Ferroelectrics B. Sol-gel processing C. X-ray scattering D. Ferroelectricity
1. Introduction In recent years, ferroelectric superlattices and multilayers have attracted considerable interest due to their attractive properties and new opportunities they provide on engineering the ferroelectric materials for various applications [1]. In the point of fundamental physics, the properties of ferroelectric multilayers and superlattices such as polarization, susceptibility, and dielectric constant is also different from the homogeneous individual materials constituting the multilayers and superlattices [2]. It has been found that the physical properties of multilayers and superlattices are highly dependent on the interface among the layers and the dimensions of the individual layers present [3]. The influence of various interactions such as short range, long range, and the interfacial interaction among the dipoles present in bilayers, multilayers, and superlattices has been an interest of study from both the technological importance and the fundamental understanding of ferroelectric interactions [4]. There have been various studies on interlayer interaction and its dimensional dependence in the case of ferroelectric heterostructures [5–7]. The importance of the interfacial interaction in the case of FE
∗ Corresponding author at: Hubei Key Laboratory of Bioanalytical Technology, Hubei Normal University, Huangshi 435002, China. Tel.: +86 0714 6571339; fax: +86 0714 6571339. E-mail address: [email protected] (H. Liu). 0038-1098/$ – see front matter © 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssc.2008.07.009
heterostructures has been studied by various theoretical models [8,9]. In which, the influence of the interfacial coupling in the polarization behavior has been studied theoretically using a continuum model based on the Landau free energy of the system as a function of polarization [9] and a discrete Ising model [10,11]. More recently, Ranjith prepared (1 − x)Pb(Mg1/3 Nb2/3 )O3 –xPbTiO3 multilayers and observed antiferroelectriclike polarization behavior and transverse Ising model was used to simulated the results [12]. In multilayers structure films, sandwich structural film is a type of interesting structure and relative few attentions have been focused on which. BiFeO3 film is a kind of typical multiferroics and it has been prepared into bilayer film with PZT [13], and multilayer film with SrTiO3 to obtain better electric and magnetic properties, while there is seldom report on the sandwich structure of BiFeO3 with other ferroelectric material. To our best knowledge, the only report is from Xing et al. [14], they prepared Bi3.25 La0.75 Ti3 O12 /BiFeO3 /Bi3.25 La0.75 Ti3 O12 sandwich structural film and observed enhanced dielectric property and weakened magnetism. In the present work, PbTiO3 /BiFeO3 /PbTiO3 sandwich structural film (PBP film) has been prepared by sol-gel process on Pt/Ti/SiO2 /Si substrate. As an experimental evidence of antiferroelectric interface couple, antiferroelectriclike polarization behavior has been observed. 2. Experiment procedures PbTiO3 /BiFeO3 /PbTiO3 sandwich structural film was prepared by a sol-gel process. The preparation of BiFeO3 and PbTiO3
434
H. Liu, X. Wang / Solid State Communications 147 (2008) 433–435
precursor solutions see our previous work [15]. Pt/Ti/SiO2 /Si was used as substrate. Before spin coating, the Pt/Ti/SiO2 /Si substrate was cleaned by ultrasonication in alcohol and acetone repeatedly. First, PbTiO3 film was deposited on the substrate by spin coating. The depositions were carried out by spin coating at 4000 rpm for 15 s and annealed at 600 ◦ C for 5 min in air. The spin coating and annealing process were repeated 2 times to obtain the bottom PbTiO3 layer. Then BiFeO3 film was deposited on the PbTiO3 layer with the same technology, the spin coating and annealing process were repeated 4 times to obtain the BiFeO3 layer. Last, a top layer of PbTiO3 film was deposited using the same technology to the BiFeO3 layer to obtain the sandwich structure. The structure of the film was investigated with an X-ray diffractometer. The surface and cross section morphology were analyzed by field emission scanning electric microscopy (SEM) under an operation voltage of 5 kV. For electrical measurements, Au dots of 0.0314 mm2 (with a radius of 0.1 mm) were deposited through a mask on the film by evaporation. Ferroelectric hysteresis loops and leakage current were obtained using a Precision Work Station (radiant technology). 3. Experimental results and discussions The XRD pattern of the PBP film was shown in Fig. 1. From which we can observe peaks of PbTiO3 and Pt, no peaks of BiFeO3 and other impure phase were observed. The peaks are from the top PbTiO3 layer of the PBP film. Moreover, the top PbTiO3 layer is identified as randomly oriented. The surface and cross section SEM photos were shown in Fig. 2. It can be seen that the film are well crystallized since even fine grains can be identified. From the cross section photo we can
Fig. 1. XRD pattern of PbTiO3 /BiFeO3 /PbTiO3 sandwich structure.
confirm the sandwich morphology and the thickness of the PBP film. The total thickness is about 1.5 µm and the thicknesses of the BiFeO3 layer and PbTiO3 layer are about 300 nm and 900 nm, respectively. Furthermore, compact integration between PbTiO3 layer and BiFeO3 layer can be observed since no gap and distinct interface can be observed. The electric hysteresis loops are shown in Fig. 3. The loops of PBP film under different applied field are shown in Fig. 3(a). For comparison, BiFeO3 film and PbTiO3 film of the same thickness to the PBP film were prepared with the same spin coating and annealing process and the loops were plotted in Fig. 3(b). Obviously, under higher applied electric field, a saturated ferroelectric hysteresis loop can be observed for the PBP film. The remanent polarization of the PBP film under higher applied field of 300 kV/cm is ∼45 µC/cm2 . While for the PbTiO3 film and BiFeO3 film, ferroelectric hysteresis loops are able to be obtained under a relative low applied field 160 kV/cm. Under such an electric field, the remanent polarization of the PbTiO3 and BiFeO3 films are 28.3 µC/cm2 and 35.9 µC/cm2 , respectively. Moreover, contribution from leakage can be observed in the loop of the BiFeO3 film. Under a low applied field same to the BiFeO3 and PbTiO3 of 160 kV/cm, antiferroelectriclike hysteresis loop is observed in the PBP sandwich film. To our best knowledge, there has no report on the direct evident of antiferroelectric coupling in ferroelectric sandwich structure till now. Although the influence of the interfacial coupling in the polarization behavior has been studied theoretically using a continuum model based on the Landau free energy of the system as a function of polarization and a discrete Ising model in the multilayer ferroelectric film heterostructures [9–12], very few experimental evidences on the appearance of antiferroelectriclike loops in the case of ferroelectric heterostructures have been reported. To our best knowledge, the only similar report is from Ranjith et al., they prepared compositionally varying multilayers of (1 − x)Pb(Mg1/3 Nb2/3 )O3 − (x)PbTiO3 using pulsed laser ablation technique and observed antiferroelectriclike polarization hysteresis in the relaxor based multilayer systems [13]. They thought that the competition among the intrinsic ferroelectric coupling in the relaxor ferroelectrics and the antiferroelectriclike coupling among the dipoles at the interface gives rise to an antiferroelectriclike polarization behavior. Similar to the results of Ranjith, we suggest that the antiferroelectriclike polarization behavior of the PBP sandwich film under low applied field is caused by the interface antiferroelectric coupling between the BiFeO3 layer and PbTiO3 layer. Relative to the antiferroelectrics such as PbZrO3 , the antiferroelectric interaction by the interface is weak, therefore it can be removed by high applied field. According to Fig. 3(a), under high applied field of 300 kV/cm, the interface antiferroelectric couple is removed and the PBP film shows ferroelectric behavior.
Fig. 2. SEM photos of PbTiO3 /BiFeO3 /PbTiO3 sandwich structural film (a) surface, (b) cross section.
H. Liu, X. Wang / Solid State Communications 147 (2008) 433–435
435
Fig. 3. Electric hysteresis loops of (a) PBP film under different applied field (b) BiFeO3 and PbTiO3 films.
Fig. 4. Current density-Applied electric fields characteristics of PbTiO3 /BiFeO3 /PbTiO3 film.
We also studied the leakage current characteristic of the BPB film. Positive bias electric fields were applied to the top electrodes and the J–E curves were recorded. Fig. 4(a) shows J–E characteristics of the BPB films annealed at 600 ◦ C. It can be seen from Fig. 4(a) that under an applied field of 100 kV/cm, the leakage current density is 3.5 × 10−6 A/cm2 and it is much lower than the films of the pure BiFeO3 [16,17]. Therefore the leakage conduction was reduced effectively in the PBP film. To clarify the conduction mechanism, the Log(E) vs. Log(J) relation was plotted in Fig. 4(b) and simple linear fit was carried. Under low applied field, the slope is fitted to be 1.23. The value is approach to 1, which is considered to be from the linear ohmic conduction. While under higher applied field, the slope value hops to 5.38 and it is suggested to the contribution of nonlinear ohmic conduction [18]. 4. Conclusion PbTiO3 /BiFeO3 /PbTiO3 sandwich structure has been deposited on a Pt/Ti/SiO2 /Si substrate by the sol-gel method and annealed at 600 ◦ C. X-ray diffraction analysis revealed that the film was fully crystallized with no impure phase. Antiferroelectriclike hysteresis loops were observed at room temperature under a low applied field and it is attributed to the antiferroelectric couple between the PbTiO3 layer and BiFeO3 layer. Under a high applied field, the antiferroelectric couple is removed and ferroelectric hysteresis
loop was observed renew. Compared with the BiFeO3 film and PbTiO3 film, the sandwich structural film showed reduced leakage. Acknowledgement The work is supported by the Young People Program of Hubei Province Education Committee under Grant No Q200722002. References [1] G. Rijnders, D.H.A. Blank, Nature (London) 433 (2005) 369. [2] J.B. Neaton, K.M. Rabe, Appl. Phys. Lett. 82 (2003) 1586. [3] D.P. Norton, B.C. Chakoumakos, J.D. Budai, D.H. Loundes, B.C. Sales, J.R. Thompson, D.K. Christen, Science 265 (1994) 2074. [4] J.M. Gregg, J. Phys.: Condens. Matter 15 (2003) 11. [5] B.D. Qu, W.L. Zhong, R.H. Prince, Phys. Rev. B 55 (1997) 11218. [6] J.B. Neaton, K.M. Rabe, Appl. Phys. Lett. 82 (2003) 1586. [7] C. Bungaro, K.M. Rabe, Phys. Rev. B 69 (2004) 184101. [8] J. Shen, Y.Q. Ma, Phys. Rev. B 61 (2000) 14279. [9] K.H. Chow, L.H. Ong, J. Osman, D.R. Tilley, Appl. Phys. Lett. 77 (2000) 2755. [10] Y.Z. Wu, P.L. Yu, Z.Y. Li, J. Appl. Phys. 91 (2002) 1482. [11] H.M. Christen, E.D. Specht, S.S. Silliman, K.S. Harshavardhan, Phys. Rev. B 68 (2003) 020101. [12] R. Ranjith, S.B. Krupanidhi, Appl. Phys. Lett. 91 (2007) 082907. [13] Y.W. Li, J.L. Sun, J. Chen, X.J. Meng, J.H. Chu, Appl. Phys. Lett. 87 (2005) 182902. [14] X.J. Xing, Y.P. Yu, L.M. Xu, Y.L. Zhang, S.W. Li, Mater. Sci. Eng. B 147 (2008) 95. [15] H. Liu, Y. Sun, X. Wang, J. Phys. D: Appl. Phys. 41 (2008) 095302. [16] M.A.H. Gonzalez, A.Z. Simões, L.S. Cavalcante, E. Longo, J.A. Varela, C.S. Riccardi, Appl. Phys. Lett. 90 (2007) 052906. [17] Y. Wang, C.W. Nan, Appl. Phys. Lett. 89 (2006) 052903. [18] G.R. Fox, S.B. Krupanidhi, J. Appl. Phys. 74 (1993) 1949.
Contents lists available at ScienceDirect
Solid State Communications journal homepage: www.elsevier.com/locate/ssc
Fast-track communication
Antiferroelectriclike hysteresis loops in PbTiO3 /BiFeO3 /PbTiO3 sandwich structural film Hongri Liu a,b,∗ , Xiuzhang Wang b a
Hubei Key Laboratory of Bioanalytical Technology, Hubei Normal University, Huangshi 435002, China
b
Department of Physics, Hubei Normal University, Huangshi 435002, China
article
info
Article history: Received 30 June 2008 Accepted 10 July 2008 by A.H. MacDonald Available online 16 July 2008 PACS: 77.55.+f 77.80.-e
a b s t r a c t PbTiO3 /BiFeO3 /PbTiO3 sandwich structure has been deposited on Pt/Ti/SiO2 /Si substrate by sol-gel method annealing at 600 ◦ C. X-ray diffraction analysis revealed that the film was fully crystallized with no impure phase. Antiferroelectriclike hysteresis loop was observed at room temperature under low applied field. Under high applied electric field, ferroelectric hysteresis loop was observed renew. Compared with the BiFeO3 film, the sandwich structural film showed reduced leakage. © 2008 Elsevier Ltd. All rights reserved.
Keywords: A. Ferroelectrics B. Sol-gel processing C. X-ray scattering D. Ferroelectricity
1. Introduction In recent years, ferroelectric superlattices and multilayers have attracted considerable interest due to their attractive properties and new opportunities they provide on engineering the ferroelectric materials for various applications [1]. In the point of fundamental physics, the properties of ferroelectric multilayers and superlattices such as polarization, susceptibility, and dielectric constant is also different from the homogeneous individual materials constituting the multilayers and superlattices [2]. It has been found that the physical properties of multilayers and superlattices are highly dependent on the interface among the layers and the dimensions of the individual layers present [3]. The influence of various interactions such as short range, long range, and the interfacial interaction among the dipoles present in bilayers, multilayers, and superlattices has been an interest of study from both the technological importance and the fundamental understanding of ferroelectric interactions [4]. There have been various studies on interlayer interaction and its dimensional dependence in the case of ferroelectric heterostructures [5–7]. The importance of the interfacial interaction in the case of FE
∗ Corresponding author at: Hubei Key Laboratory of Bioanalytical Technology, Hubei Normal University, Huangshi 435002, China. Tel.: +86 0714 6571339; fax: +86 0714 6571339. E-mail address: [email protected] (H. Liu). 0038-1098/$ – see front matter © 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssc.2008.07.009
heterostructures has been studied by various theoretical models [8,9]. In which, the influence of the interfacial coupling in the polarization behavior has been studied theoretically using a continuum model based on the Landau free energy of the system as a function of polarization [9] and a discrete Ising model [10,11]. More recently, Ranjith prepared (1 − x)Pb(Mg1/3 Nb2/3 )O3 –xPbTiO3 multilayers and observed antiferroelectriclike polarization behavior and transverse Ising model was used to simulated the results [12]. In multilayers structure films, sandwich structural film is a type of interesting structure and relative few attentions have been focused on which. BiFeO3 film is a kind of typical multiferroics and it has been prepared into bilayer film with PZT [13], and multilayer film with SrTiO3 to obtain better electric and magnetic properties, while there is seldom report on the sandwich structure of BiFeO3 with other ferroelectric material. To our best knowledge, the only report is from Xing et al. [14], they prepared Bi3.25 La0.75 Ti3 O12 /BiFeO3 /Bi3.25 La0.75 Ti3 O12 sandwich structural film and observed enhanced dielectric property and weakened magnetism. In the present work, PbTiO3 /BiFeO3 /PbTiO3 sandwich structural film (PBP film) has been prepared by sol-gel process on Pt/Ti/SiO2 /Si substrate. As an experimental evidence of antiferroelectric interface couple, antiferroelectriclike polarization behavior has been observed. 2. Experiment procedures PbTiO3 /BiFeO3 /PbTiO3 sandwich structural film was prepared by a sol-gel process. The preparation of BiFeO3 and PbTiO3
434
H. Liu, X. Wang / Solid State Communications 147 (2008) 433–435
precursor solutions see our previous work [15]. Pt/Ti/SiO2 /Si was used as substrate. Before spin coating, the Pt/Ti/SiO2 /Si substrate was cleaned by ultrasonication in alcohol and acetone repeatedly. First, PbTiO3 film was deposited on the substrate by spin coating. The depositions were carried out by spin coating at 4000 rpm for 15 s and annealed at 600 ◦ C for 5 min in air. The spin coating and annealing process were repeated 2 times to obtain the bottom PbTiO3 layer. Then BiFeO3 film was deposited on the PbTiO3 layer with the same technology, the spin coating and annealing process were repeated 4 times to obtain the BiFeO3 layer. Last, a top layer of PbTiO3 film was deposited using the same technology to the BiFeO3 layer to obtain the sandwich structure. The structure of the film was investigated with an X-ray diffractometer. The surface and cross section morphology were analyzed by field emission scanning electric microscopy (SEM) under an operation voltage of 5 kV. For electrical measurements, Au dots of 0.0314 mm2 (with a radius of 0.1 mm) were deposited through a mask on the film by evaporation. Ferroelectric hysteresis loops and leakage current were obtained using a Precision Work Station (radiant technology). 3. Experimental results and discussions The XRD pattern of the PBP film was shown in Fig. 1. From which we can observe peaks of PbTiO3 and Pt, no peaks of BiFeO3 and other impure phase were observed. The peaks are from the top PbTiO3 layer of the PBP film. Moreover, the top PbTiO3 layer is identified as randomly oriented. The surface and cross section SEM photos were shown in Fig. 2. It can be seen that the film are well crystallized since even fine grains can be identified. From the cross section photo we can
Fig. 1. XRD pattern of PbTiO3 /BiFeO3 /PbTiO3 sandwich structure.
confirm the sandwich morphology and the thickness of the PBP film. The total thickness is about 1.5 µm and the thicknesses of the BiFeO3 layer and PbTiO3 layer are about 300 nm and 900 nm, respectively. Furthermore, compact integration between PbTiO3 layer and BiFeO3 layer can be observed since no gap and distinct interface can be observed. The electric hysteresis loops are shown in Fig. 3. The loops of PBP film under different applied field are shown in Fig. 3(a). For comparison, BiFeO3 film and PbTiO3 film of the same thickness to the PBP film were prepared with the same spin coating and annealing process and the loops were plotted in Fig. 3(b). Obviously, under higher applied electric field, a saturated ferroelectric hysteresis loop can be observed for the PBP film. The remanent polarization of the PBP film under higher applied field of 300 kV/cm is ∼45 µC/cm2 . While for the PbTiO3 film and BiFeO3 film, ferroelectric hysteresis loops are able to be obtained under a relative low applied field 160 kV/cm. Under such an electric field, the remanent polarization of the PbTiO3 and BiFeO3 films are 28.3 µC/cm2 and 35.9 µC/cm2 , respectively. Moreover, contribution from leakage can be observed in the loop of the BiFeO3 film. Under a low applied field same to the BiFeO3 and PbTiO3 of 160 kV/cm, antiferroelectriclike hysteresis loop is observed in the PBP sandwich film. To our best knowledge, there has no report on the direct evident of antiferroelectric coupling in ferroelectric sandwich structure till now. Although the influence of the interfacial coupling in the polarization behavior has been studied theoretically using a continuum model based on the Landau free energy of the system as a function of polarization and a discrete Ising model in the multilayer ferroelectric film heterostructures [9–12], very few experimental evidences on the appearance of antiferroelectriclike loops in the case of ferroelectric heterostructures have been reported. To our best knowledge, the only similar report is from Ranjith et al., they prepared compositionally varying multilayers of (1 − x)Pb(Mg1/3 Nb2/3 )O3 − (x)PbTiO3 using pulsed laser ablation technique and observed antiferroelectriclike polarization hysteresis in the relaxor based multilayer systems [13]. They thought that the competition among the intrinsic ferroelectric coupling in the relaxor ferroelectrics and the antiferroelectriclike coupling among the dipoles at the interface gives rise to an antiferroelectriclike polarization behavior. Similar to the results of Ranjith, we suggest that the antiferroelectriclike polarization behavior of the PBP sandwich film under low applied field is caused by the interface antiferroelectric coupling between the BiFeO3 layer and PbTiO3 layer. Relative to the antiferroelectrics such as PbZrO3 , the antiferroelectric interaction by the interface is weak, therefore it can be removed by high applied field. According to Fig. 3(a), under high applied field of 300 kV/cm, the interface antiferroelectric couple is removed and the PBP film shows ferroelectric behavior.
Fig. 2. SEM photos of PbTiO3 /BiFeO3 /PbTiO3 sandwich structural film (a) surface, (b) cross section.
H. Liu, X. Wang / Solid State Communications 147 (2008) 433–435
435
Fig. 3. Electric hysteresis loops of (a) PBP film under different applied field (b) BiFeO3 and PbTiO3 films.
Fig. 4. Current density-Applied electric fields characteristics of PbTiO3 /BiFeO3 /PbTiO3 film.
We also studied the leakage current characteristic of the BPB film. Positive bias electric fields were applied to the top electrodes and the J–E curves were recorded. Fig. 4(a) shows J–E characteristics of the BPB films annealed at 600 ◦ C. It can be seen from Fig. 4(a) that under an applied field of 100 kV/cm, the leakage current density is 3.5 × 10−6 A/cm2 and it is much lower than the films of the pure BiFeO3 [16,17]. Therefore the leakage conduction was reduced effectively in the PBP film. To clarify the conduction mechanism, the Log(E) vs. Log(J) relation was plotted in Fig. 4(b) and simple linear fit was carried. Under low applied field, the slope is fitted to be 1.23. The value is approach to 1, which is considered to be from the linear ohmic conduction. While under higher applied field, the slope value hops to 5.38 and it is suggested to the contribution of nonlinear ohmic conduction [18]. 4. Conclusion PbTiO3 /BiFeO3 /PbTiO3 sandwich structure has been deposited on a Pt/Ti/SiO2 /Si substrate by the sol-gel method and annealed at 600 ◦ C. X-ray diffraction analysis revealed that the film was fully crystallized with no impure phase. Antiferroelectriclike hysteresis loops were observed at room temperature under a low applied field and it is attributed to the antiferroelectric couple between the PbTiO3 layer and BiFeO3 layer. Under a high applied field, the antiferroelectric couple is removed and ferroelectric hysteresis
loop was observed renew. Compared with the BiFeO3 film and PbTiO3 film, the sandwich structural film showed reduced leakage. Acknowledgement The work is supported by the Young People Program of Hubei Province Education Committee under Grant No Q200722002. References [1] G. Rijnders, D.H.A. Blank, Nature (London) 433 (2005) 369. [2] J.B. Neaton, K.M. Rabe, Appl. Phys. Lett. 82 (2003) 1586. [3] D.P. Norton, B.C. Chakoumakos, J.D. Budai, D.H. Loundes, B.C. Sales, J.R. Thompson, D.K. Christen, Science 265 (1994) 2074. [4] J.M. Gregg, J. Phys.: Condens. Matter 15 (2003) 11. [5] B.D. Qu, W.L. Zhong, R.H. Prince, Phys. Rev. B 55 (1997) 11218. [6] J.B. Neaton, K.M. Rabe, Appl. Phys. Lett. 82 (2003) 1586. [7] C. Bungaro, K.M. Rabe, Phys. Rev. B 69 (2004) 184101. [8] J. Shen, Y.Q. Ma, Phys. Rev. B 61 (2000) 14279. [9] K.H. Chow, L.H. Ong, J. Osman, D.R. Tilley, Appl. Phys. Lett. 77 (2000) 2755. [10] Y.Z. Wu, P.L. Yu, Z.Y. Li, J. Appl. Phys. 91 (2002) 1482. [11] H.M. Christen, E.D. Specht, S.S. Silliman, K.S. Harshavardhan, Phys. Rev. B 68 (2003) 020101. [12] R. Ranjith, S.B. Krupanidhi, Appl. Phys. Lett. 91 (2007) 082907. [13] Y.W. Li, J.L. Sun, J. Chen, X.J. Meng, J.H. Chu, Appl. Phys. Lett. 87 (2005) 182902. [14] X.J. Xing, Y.P. Yu, L.M. Xu, Y.L. Zhang, S.W. Li, Mater. Sci. Eng. B 147 (2008) 95. [15] H. Liu, Y. Sun, X. Wang, J. Phys. D: Appl. Phys. 41 (2008) 095302. [16] M.A.H. Gonzalez, A.Z. Simões, L.S. Cavalcante, E. Longo, J.A. Varela, C.S. Riccardi, Appl. Phys. Lett. 90 (2007) 052906. [17] Y. Wang, C.W. Nan, Appl. Phys. Lett. 89 (2006) 052903. [18] G.R. Fox, S.B. Krupanidhi, J. Appl. Phys. 74 (1993) 1949.