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Ferroelectric domain states of a tetragonal BiFeO_{3} thin film investigated by second harmonic generation microscopy
Nanoscale Research Lettersvolume 12, Article number: 353 (2017)
Abstract
We investigate the ferroelectric state of a tetragonal BiFeO_{3} thin film grown on a LaAlO_{3} (001) substrate using an optical second harmonic generation (SHG) microscope. Whereas the ferroelectric state of this material hosts nanometersized domains which again form micrometersized domains of four different configurations, we could figure out the characteristic features of each domain from the SHG mapping with various sizes of the probe beam, i.e., from 0.7 to 3.9 μm in its diameter. In particular, we demonstrate that a single micrometersized domain contributes to the SHG as a coherent summation of the constituent nanometersized domains, and multimicrometersized domains contribute to the SHG as an incoherent summation of each microdomain.
Background
Ferroelectrics have a great importance in both fundamental research and technical applications. Among them, BiFeO_{3} (BFO) has attracted a large attention since it hosts, as a multiferroic material, both ferroelectric and antiferromagnetic properties at the same time; it undergoes a ferroelectric phase transition at 1103 K and antiferromagnetic phase transition at 643 K [1,2,3]. In particular, it exhibits a large magnetoelectric effect even at room temperature [3,4,5] and can be used for novel functional devices, for example, in a multistorage information technology. As in other ferroelectric materials, BFO is known to have several types of ferroelectric domains with a size ranging from nanometer to micrometer scale [6, 7]. Such a local ferroelectric domain distribution and the characteristics of individual domains have been characterized often by using piezoresponse force microscopy (PFM) with controls of temperature, electric field, and crystal strain, which revealed several intriguing phenomena, such as conducting domain wall, flexoelectric effect, and morphotropic phase boundaries [8,9,10].
As an alternative technique to investigate the ferroelectric properties, an optical second harmonic generation (SHG) also has been widely adopted [11,12,13,14]. The ferroelectric state with no inversion symmetry usually provides strong second harmonic signals which show specific anisotropic patterns depending on the symmetry of the material. As a noncontact optical method, this technique can be usefully exploited in the characterization of ferroelectric or polar systems with a large leakage current. Since the SHG process is allowed only when the spatial inversion symmetry is broken, it has been used also to examine the symmetry lowering at the (sub)nanometerscale surface or interfacial state of centrosymmetric bulk or thin films [15]. Furthermore, the nanometerscale domain distribution has been successfully demonstrated by using the SHG technique combined with a scanning probe microscope [16]. Nevertheless, it is usually difficult to investigate the individual domains by using the conventional SHG microscope as the spatial resolution is limited by a fundamental diffraction which is about several hundred nanometers in the visible spectral range [17]. SHG studies on BiFeO_{3} have been performed by several research groups who could provide detailed symmetry information of tetragonallike and rhombohedrallike phases, but it should be noted that most of the works have been done with assumptions of the homogeneous and coherent contributions of constituent domains [18, 19].
In this paper, we demonstrate that the distribution and characteristics of ferroelectric domains for the tetragonallike BiFeO_{3} (TBFO) can be investigated by using a conventional SHG microscope with proper adjustments of probe beam sizes with respect to the domain size. Since this TBFO hosts nanometersized domains which form specific patterns of micrometersized domains, it provides an excellent environment to address how the SHG responses are contributed to by each ferroelectric domain of different sizes and their mixtures. We mapped the sample with a probe beam of several sizes and found large positiondependent variations of the SHG signal which originate from distinct characteristics of the domain distribution. By considering the coherent and incoherent contributions of each domain to the SHG response, we could successfully explain such experimental results. We therefore expect that symmetry information of the individual nanometersized domain can be obtained even from the farfield microscopic measurement provided that the proper modeling can be chosen and applied between the incoherent and the coherent approaches.
Methods
The TBiFeO_{3} thin film is grown on a LaAlO_{3} (001) substrate by using a pulsed laser deposition technique of which details can be found elsewhere [4]. The thickness of TBFO film is about 30 nm. For the SHG experiment, fundamental light of 800 nm wavelength illuminates the sample in a normal incidence, and second harmonic light is detected in reflection geometry. We used laser pulses from the Ti:sapphire laser system for fundamental light which has a pulse width of about 30 fs and a repetition rate of 80 MHz. It has a power of about 20 mW and is focused down to the diffraction limit using an objective lens with a magnification of ×50 and a 0.75 numerical aperture. Polarization states of fundamental and second harmonic light are set to be parallel (XX) or orthogonal (XY) as shown in Fig. 1a.
Results and discussion
We first monitored a distribution of the ferroelectric domains by using a scanning probe microscope (Bruker, MultiModeV). PFM measurements were performed at a scan rate of 3 μm/s using Ptcoated Si conductive tips (MikroMasch, NSC35) with applying an ac driving voltage of 3 V_{pp} at a frequency of 12 kHz. Figure 1a displays the PFM image of TBFO obtained at room temperature. It shows that ferroelectric domains form stripe patterns in a submicron length scale and the larger micronscale areas are distributed with typical stripe orientations along 45° or 135°. In Fig. 1c, we schematically draw four types of such domain patterns. Owing to the monoclinic distortion, TBFO has an inplane component of the polarization as well as the polarization along the caxis [7]. As the normal incidence in SHG measurement, a configuration adopted in this work is not sensitive to the outofplane polarization component; we here restrict our interest only in the inplane component. We consider first a nanometersized domain with a polarization along the a or baxis, and their headtotail combination with a domain wall formed along the diagonal directions. Consistently with the PFM result, we hence consider four possible combinations of such domains as depicted in Fig. 1c. It should be noted that each stripe pattern is distributed over a few micrometers or even tens of micrometer scales as shown in Fig. 1a.
Before showing the experimental result, let us discuss the SHG response simulations of TBFO (C_{1h} point group) with a consideration of each domain configuration [20]. Intensity of second harmonic (SH) light I(2ω) is given in proportion to the induced SH polarization P(2ω) as I(2ω) ∝ P(2ω)^{2} = χ _{ ijk } E _{ j } E _{ k }^{2}, where χ _{ ijk } represents the nonlinear susceptibility of the material, E _{ i } is the electric field component of the fundamental light, and i, j, and k denote the crystallographic axes. The transverse coherence length L _{ T } is determined as L _{ T } = λR/2D [21]. Here, D is a size of the domain which acts as an SH light source and λ is a wavelength of SH light, i.e., 400 nm. R denotes a distance (0.38 mm) from the sample surface to the objective lens. Note that the coherence length is comparable to the objective lens size (625 μm in its diameter) when D is about 100 nm. Therefore, when we consider the contributions of multidomains to the SHG, it is reasonable to assume that each nanometersized domain having a size of about 50 nm contributes to the SHG responses coherently as I(2ω) ∝ (P _{1} + P _{2})^{2}, whereas microdomains contribute to I(2ω) incoherently as I(2ω) = P _{1} ^{2} + P _{2} ^{2}. Here, P _{1} and P _{2} imply the induced SH polarizations of each nano or microdomain when only two types of domains are considered.
Figure 1d shows the azimuthdependent I(2ω) obtained by considering such coherent and incoherent contributions of different domains. For the leftmost case, we consider the coherent summation of two nanometersized domains corresponding to the first configuration listed in Fig. 1c. The polarization direction of each nanometersized single domain is along the x and yaxes. We take χ _{xxx} = 0.35, χ _{xyy} = 1.0, and χ _{ yxy } = 0.4 for the domain with the xaxis polarization and χ _{yyy} = −0.35, χ _{yxx} = −1.0, and χ _{xyx} = −0.4 for the domain with the yaxis polarization. All other susceptibility components are assumed to be zero. For the rightmost case, we consider the fourth configuration of Fig. 1c with the same values of χ _{xxx}, χ _{xyy}, and χ _{yxy} with changes in the sign of χ _{yyy}, χ _{yxx}, and χ _{xyx}. The azimuthdependent I(2ω) for the former and latter cases are displayed in the first and fifth plots in Fig. 1d; the XX response in each configuration has maximum values along the direction perpendicular to the net polarization axis because χ _{xxx} < χ _{xyy} and χ _{yyy} < χ _{yxx}. With these two cases as end members, we consider coherent and incoherent summations with different portions f (0.0 < f < 1.0) or 1f of the contribution from each end member. In the intermediate cases with f = 0.75, 0.5, and 0.25, the incoherent summation leads to the finite value of the minimum I(2ω) and more swollen lobe shape compared to the coherent summation.
From now on, we present the experimental SHG results and discuss them based on the coherent and incoherent analyses of the multidomain contribution. Before each SHG measurement, we characterized the beam size of fundamental light at the sample position using a knifeedge method [22]. Figure 2a shows an intensity (open symbols) obtained with a displacement of the knife edge by 1 μm. We fit the results assuming the Gaussian distribution of the beam intensity and estimate the beam size W, a width defined by two points having the 1/e ^{2} intensity of the maximum value as 0.7, 1.5, 2.1, and 3.9 μm.
Figure 2b displays a twodimensional distribution of I(2ω) obtained with W = 0.7 μm. The displacement for each step is 1 μm, and the mapping area is 25 × 25 μm^{2}. The sample azimuth Ф is fixed as 45° in the XX geometry. I(2ω) exhibits a large variation with no discernible pattern. These results clearly indicate that the domain size in the probed area is comparable to the beam size.
We can get a deeper insight into the ferroelectric domain by examining the azimuthdependent of I(2ω) at each sample position. Figure 2c displays the results obtained at five representative positions. Although each point is displaced by 1 μm from neighboring points, the SHG results vary quite drastically from a point to a point. Looking at the results of the XX geometry, although P _{1}, P _{3}, and P _{5} exhibit twofold symmetry, P _{2} and P _{4} show a fourfold symmetry. The behaviors in the XY geometry are relatively less distinct. Nevertheless, P _{1} and P _{3} have a main lobe at Ф = 135° (315°); P _{5} has the corresponding maximum at 45° (225°). These results strongly suggest that each measured point has distinct preferred planar orientations of the ferroelectric polarization. Actually, the patterns of the experimental result can be identified by the simulation results shown in Fig. 1d; P _{1} (P _{3}) and P _{5} correspond to the case f = 1.0 and 0.0, respectively. Also, P _{2} and P _{4} can be identified as the case f = 0.5 (incoherent). In other words, the results of P _{1} and P _{5} pick up the single configuration of four possible microdomains shown in Fig. 1c, and the measurement at P _{2} and P _{4} covers two (or more) microdomains. Considering the coherence length, it is expected that such microdomains contribute to the SHG response incoherently. From these results, we therefore confirm that nanodomains compose a single microdomain and contribute to the SH response coherently, whereas microdomains contribute to the SHG response incoherently. Furthermore, the part of symmetry information of a single nanosized domain can be obtained from the analysis of the single microdomain contribution; the simulation results in Fig. 1 give that χ _{xxx} = 0.35, χ _{xyy} = 1.0, and χ _{yxy} = 0.4 for the nanodomain with the xaxis polarization. (In the XY geometry, the relative intensity at Ф = 45° and 135° appears oppositely to the simulation results in Fig. 1d. This discrepancy requires further analysis.)
We increased the beam size and monitored how the SHG response varies depending on it. Figure 3a, b show the results of the twodimensional mapping obtained with W = 1.5 and 2.1 μm, respectively. Here, the interval between two neighboring points is kept as the same, i.e., Δx = 1 μm, and the power of fundamental light is also maintained. As the beam size increases from W = 0.7 to 1.5 and to 2.1 μm, I(2ω) decreases as expected from the smaller beam fluence. Also, the distribution of I(2ω) becomes to have a less position dependence.
Azimuthdependent SHG patterns also show systematic variations as the beam size increases. For W = 1.5 μm, we can still observe the strong position dependence; P _{1} and P _{4} reflect two distinct microdomains, and the other points can be considered as mixtures of such microdomains. Compared with the results for W = 0.7 μm, it is clear that the incoherent contributions become more discernible for W = 1.5 μm; the minimum value of the SHG intensity becomes nonzero, and it is much larger than for W = 0.7 μm. For W = 2.1 μm, such tendency becomes more pronounced; there is almost no position dependence as shown in Fig. 3d. This is probably due to the influence of the dominance of a single microdomain over the entire probing area. With W = 0.7 μm, a single microdomain can be probed, and hence, the SHG intensity is determined by the coherent contribution from the constituent nanosized domains. With W = 1.5 μm and 2.1 μm, on the other hand, several microdomains are probed together, and they contribute to the SHG intensity as an incoherent summation.
As a final test, we further increased the probe beam size up to W = 3.9 μm of which result is displayed as closed circles in Fig. 4. Also shown are the results for smaller Ws which are averaged over several points around the beam central position for W = 3.9 μm. Interestingly, such averaged results for W = 0.7, 1.5, and 2.1 μm appear quite similarly in both XX and XY geometry with the single measurement results for W = 3.9 μm. As this average process of the measured SH intensity is identical to the incoherent summation of each microdomain contribution, this agreement confirms our understanding of the incoherent contribution to the SHG responses of multimicrodomains.
Conclusions
We investigated the ferroelectric domains of a tetragonal BiFeO_{3} film by using a second harmonic generation (SHG) technique. Whereas the normal incidence SHG measurement provides us with clear information about the inplane component of the ferroelectric polarization, we found large variations of the SHG responses from a point to a point of the sample. This clearly indicates the inhomogeneity of the domain distribution. By reducing the beam size down to 0.7 μm, we demonstrated that the observed SHG results could reveal the symmetry characteristic of individual micrometersized domains which is determined by types of constituent nanometersized domains. By increasing the beam size up to 3.9 μm, we found the SHG response with a much less position dependence. Actually, we could reproduce this SHG result obtained with a 3.9 μm beam size with averages of several results obtained with smaller beam sizes and confirmed that each microdomain contributes to the SHG responses incoherently. Therefore, we can have a chance to retrieve symmetry information of the individual nanometersized or even micrometersized domain if we can apply a proper model between coherent and incoherent analysis of the SHG results.
Abbreviations
 BFO:

BiFeO3
 PFM:

Piezoresponse force microscopy
 SH:

Second harmonic
 SHG:

Second harmonic generation
 TBFO:

Tetragonal BiFeO_{3}
 XX:

Parallel
 XY:

Orthogonal
References
 1.
Roginska YE, Tomashpo YY, Venevtse YN, Petrov VM, Zhdanov GS (1966) Nature of dielectric and magnetic properties of BiFeO_{3}. Sov Phys JETP 23:47
 2.
Sosnowska I, Loewenhaupt M, David WIF, Ibberson RM (1992) Investigation of the unusual magnetic spiral arrangement in BiFeO_{3}. Physica B 180–181:117
 3.
Wang J, Neaton JB, Zheng H, Nagarajan V, Ogale SB, Liu B, Viehland D, Vaithyanathan V, Schlom DG, Waghmare UV, Spaldin NA, Rabe KM, Wuttig M, Ramesh R (2003) Epitaxial BiFeO_{3} multiferroic thin film heterostructures. Science 299:1719
 4.
Ko KT, Jung MH, He Q, Lee JH, Woo CS, Chu KH, Seidel J, Jeon BG, Oh YS, Kim KH, Liang WI, Chen HJ, Chu YH, Jeong YH, Ramesh R, Park JH, Yang CH (2011) Concurrent transition of ferroelectric and magnetic ordering near room temperature. Nat Commun 2:567.
 5.
Chu YH, Martin LW, Holcomb MB, Gajek M, Han SJ, He Q, Balke N, Yang CH, Lee D, Hu W, Zhan Q, Yang PL, FraileRodriguez A, Scholl A, Wang SX, Ramesh R (2008) Electricfield control of local ferromagnetism using a magnetoelectric multiferroic. Nat Mater 7:478.
 6.
Zhao T, Scholl A, Zavaliche F, Lee K, Barry M, Doran A, Cruz MP, Chu YH, Ederer C, Spaldin NA, Das RR, Kim DM, Baek SH, Eom CB, Ramesh R (2006) Electric control of antiferromagnetic domains in multiferroic BiFeO_{3} films at room temperature. Nat Mater 5:823
 7.
Chen Z, Luo Z, Huang C, Qi Y, Yang P, Lu Y, Hu C, Wu T, Wang J, Gao C, Sritharan T, Chen L (2011) Lowsymmetry monoclinic phases and polarization rotation path mediated by epitaxial strain in multiferroic BiFeO_{3} thin films. Adv Funct Mater 21:133
 8.
Zeches RJ, Rossell MD, Zhang JX, Hatt AJ, He Q, Yang CH, Kumar A, Wang CH, Melville A, Adamo C, Sheng G, Chu YH, Ihlefeld JF, Erni R, Ederer C, Gopalan V, Chen LQ, Schlom DG, Spaldin NA, Martin LW, Ramesh R (2009) A straindriven morphotropic phase boundary in BiFeO_{3}. Science 326:977
 9.
Christen HM, Nam JH, Kim HS, Hatt AJ, Spaldin NA (2011) Stressinduced RM_{A}M_{C}T symmetry changes in BiFeO_{3} films. Phys Rev B 83:144107
 10.
Lummen TTA, Gu Y, Wang J, Lei S, Xue F, Kumar A, Barnes AT, Barnes E, Denev S, Belianinov A, Holt M, Morozovska AN, Kalinin SV, Chen LQ, Gopalan V (2014) Thermotropic phase boundaries in classic ferroelectrics. Nat Commun 5:3172.
 11.
Sharan A, Lettieri J, Jia Y, Tian W, Pan X, Schlom DG, Gopalan V (2014) Bismuth manganite: a multiferroic with a large nonlinear optical response. Phys Rev B 69:214109.
 12.
Yokota H, Haumont R, Kiat JM, Matsuura H, Uesu Y (2009) Second harmonic generation microscopic observations of a multiferroic BiFeO_{3} single crystal. Appl Phys Lett 95:082904
 13.
Barad V, Lettieri J, Theis CD, Schlom DG, Gopalan V, Jiang JC, Pan XQ (2001) Probing domain microstructure in ferroelectric Bi_{4}Ti_{3}O_{12} thin films by optical second harmonic generation. J Appl Phys 89:1387
 14.
Wang J, Jin K, Guo H, Gu J, Wan Q, He X, Li X, Xu X, Yang G (2016) Evolution of structural distortion in BiFeO_{3} thin films probed by second harmonic generation. Sci Rep 6:38268
 15.
Hamh SY, Park SH, Jerng SK, Jeon JH, Chun SH, Jeon JH, Kahng SJ, Yu K, Choi EJ, Kim S, Choi SH, Bansal N, Oh S, Joonbum P, ByungWoo K, Jun Sung K, Lee JS (2016) Surface and interface states of Bi_{2}Se_{3} thin films investigated by optical secondharmonic generation and terahertz emission. Appl Phys Lett 108:051609
 16.
Neacsu CC, Van Aken BB, Fiebig M, Raschke MB (2013) Secondharmonic nearfield imaging of ferroelectric domain structure of YMnO_{3}. Phys Rev B 79:100107(R)
 17.
Sänger I, Pavlov VV, Bayer M, Fiebig M (2006) Distribution of antiferromagnetic spin and twin domains in NiO. Phys Rev B 74:144401
 18.
Trassin M, De Luca G, Manz S, Fiebig M (2015) Probing ferroelectric domain engineering in BiFeO_{3} tin films by second harmonic generation. Adv Mater 27:4871
 19.
Lofland SE, McDonald KF, Metting CJ, Knoesel E, Murakami M, Aronova MA, Fujino S, Wutting M, Takeuchi I (2006) Epitaxy, texturing, and secondharmonic generation in BiFeO_{3} thin films. Phys Rev B 73:092408
 20.
Nonlinear optics, edited by Robert W. Boyd. (Academic press, Iic, 2008), Chaps. I.
 21.
Elements of modern Xray physics, edited by Jens AN, and MacMorrow DF. (Wiley, 2010), Chaps. I.
 22.
De Araujo MAC, Silva R, De Lima E, Pereira DP, De Oliveira PC (2009) Measurement of Gaussian laser beam radius using the knifeedge technique: improvement on data analysis. Appl Opt 48:393
Acknowledgements
We acknowledge Y. G. Choi for the technical support in performing the second harmonic measurements. This work was supported in part by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (Nos. 2015R1A5A1009962, 2015R1A1A1A05001560). The work at KAIST was supported by the NRF via the Center for Quantum Coherence in Condensed Matter (2016R1A5A1008184).
Authors’ contributions
CJR and SYH carried out the second harmonic generation experiment and analyzed the results. CSW, KEK, and CHY prepared the BiFeO_{3} thin films and carried out the piezoelectric force microscope experiment. CJR and JSL wrote the manuscript. JSL supervised the research. All authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
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Keywords
 Ferroelectrics
 BiFeO_{3}
 Thin film
 Second harmonic generation
 Multidomain
PACS
 77.84.s
 77.55.Nv
 78.20.e