Identification and mechanical control of ferroelastic domain structure in rhombohedral CaMn 7 O 12
aa r X i v : . [ c ond - m a t . s t r- e l ] J a n Identification and mechanical control of ferroelastic domain structure inrhombohedral CaMn O Renliang Yuan, Lian Duan, Xinyu Du, and Yuan Li
1, 2, ∗ International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
We report on observation of ferroelastic domain structure in single crystals of multiferroicCaMn O at room temperature. Two types of ferroelastic domain wall are found, consistent withthe material’s rhombohedral symmetry that is reduced from cubic symmetry at higher tempera-tures. Using Raman spectroscopy along with other measurements, we develop a systematic methodto determine the microscopic domain orientation. Moreover, we find a switching behavior of thedomains, which allows us to detwin the crystals conveniently at room temperature using a mod-erate uniaxial compression. Our result paves the way for further spectroscopic study and domainengineering in CaMn O . PACS numbers: 75.85.+t, 77.80.Dj, 78.30.-j
I. INTRODUCTION
Ferroic (ferroelectric, ferromagnetic, ferroelastic) do-main walls have aroused persistent research interest dueto their significance in both fundamental research andpromising applications.
In so-called multiferroic ma-terials, different ferroic order parameters coexist and ex-hibit mutual coupling, hence allowing for the manipula-tion of one ferroic property through another. This co-existence gives rise to composite domain walls thatmight be a key to utilizing the mutual controllability offerroic properties in applications. Furthermore, domainwalls can exhibit distinctly different properties from thebulk, leading to the possibility of using the domainwalls as device. In addition to the intensively studiedsystem BiFeO , intriguing domain structures have beenobserved and tuned in manganites. CaMn O is a “type-II” multiferroic material withvery large ferroelectric polarization induced by mag-netic order, and has been the subject of considerablerecent research efforts. Unlike in many widely stud-ied ferroelectric materials, the occurrence of ferroelec-tricity in CaMn O is preceded by a ferroelastic struc-tural phase transition at higher temperatures, makingit an ideal platform to study the ferroelastic and ferro-electric domain structures separately. At high tempera-tures, CaMn O possesses the AC B O cubic struc-ture which is a derivative of simple perovskite ABO . Upon cooling, a first-order phase transition occurs at T s ≈
440 K. The four Mn . ions in each formula unitare charge-ordered into three Mn and one Mn ions.The body diagonal of the high-temperature cubic cellthat runs through the Mn ions shrinks a little bit, andbecomes the c -axis of the new rhombohedral unit cell inhexagonal basis. This hexagonal c -axis plays an im-portant role that not only determines the direction of theincommensurate orbital order established below T o = 250K, but also sets the direction of the giant improper fer-roelectric polarization that arises from the helical mag-netic order below T N = 90 K. The pseudo-cubic cell below T s , along with the shortened body diagonal,are denoted by yellow/blue cubes and magenta lines, re-spectively, in Figs. 1(a-b), omitting most details.Since current methods of growing single crystals ofCaMn O all take place at temperatures far above theferroelastic structural transition temperature T s , one can reasonably expect ferroelastic domains to formupon cooling the crystals to room temperature, as aresult of simultaneous nucleation from different partsin the crystal, just like those in YBa Cu O δ andBaFe As . In this paper, we focus on domain struc-tures in CaMn O at room temperature, where the com-pound is rhombohedral but not ferroelectric. We presentdirect observations of two types of stripe-like ferroelasticdomain structures in single crystals. By using polarized-light microscopy, Raman spectroscopy and stylus surfaceprofiler, we study the ferroelastic domain structures weobserve. We propose a method to uniquely determinesurface domain structures using Raman spectroscopy incombination with stylus profiler. Moreover, we identify aswitching behavior of the ferroelastic domains, and showthat the crystals can be mechanically detwinned by amoderate uniaxial compression. These findings are im-portant for further spectroscopic studies of CaMn O that require single-domain samples, and may facilitatefuture investigations of domain and domain-wall proper-ties in multifunctional oxides. II. EXPERIMENTAL METHODS
High-quality cube-shaped single crystals of CaMn O were grown with a flux-reaction method at a coolingrate of 5 ◦ C/h. Natural facets of the crystals are par-allel to crystallographic { } c planes, where the sub-script “c” denotes pseudo-cubic notation. The sampleswere characterized as described elsewhere. Optical im-ages of crystal surfaces were taken with a polarized-lightmicroscope Olympus BX51 with polarizer and analyzerset in an almost perpendicular configuration. Differentialinterference contrast apparatus was installed to enhanceimage contrast. Surface profiles of crystal facets weremeasured with a KLA-Tencor P-6 Stylus Profiler using acontact force of 0.5 mg. Raman scattering measurementswere performed in a back-scattering confocal geometryusing the 632.8 nm line of a He-Ne laser for excitation.The diameter of the focused laser spot is estimated tobe less than 5 microns. A Horiba Jobin Yvon LabRAMHR Evolution spectrometer, equipped with a 600 gr/mmgrating and a liquid-nitrogen-cooled CCD detector, wasused to analyze the Raman spectra.
III. RESULTS AND DISCUSSIONSA. Possible domain-wall orientations
Figures 1(c-d) display typical polarized-light opticalimages of multi-domain samples. Ferroelastic domainsmanifest themselves in a regular bright-and-dark stripepattern. While only the crystals’ top faces are shown, thedomain structures actually extend to span the entire crys-tals, i.e. , a consistent pattern is found on the side faces aswell. This is illustrated (with exaggerated rhombohedraldistortion of the domains) in Fig. 1(e) and Fig. 1(f), inwhich the slab-like domains are found to stack along thepseudo-cubic h i c and h i c directions, respectively.On slightly twinned samples, especially those grown at acooling rate slower than 5 ◦ C/h, we can occasionally findstripes near the edges of the faces that do not span theentire crystal.When the crystals are heated to temperatures above T s , the stripe patterns gradually disappear, consistentwith the recovery of a single-domain cubic structureabove T s . Cycling the temperature through T s can eachtime lead to a completely different stripe pattern in rhom-bohedral phase, which indicates that the domain forma-tion is not pinned by disorder or defects, and it in turnconfirms the high quality of our samples. On the otherhand, when the samples are cooled down to cryogenictemperatures, the stripe pattern remains even below T N = 90 K in the ferroelectric phase. Hence it is possible tocontrol low-temperature ferroelectric domain structuresby pre-setting a desired ferroelastic domain structure inthe paraelectric phase.Grown at temperatures far above T s and then cooledto room temperature, most crystals contain multiple fer-roelastic domains due to simultaneous rhombohedral dis-tortions that nucleates from different parts of the sam-ples. Even though as-grown crystals can occasionallybe found in a single-domain state, further manipula-tions may affect the domain structure. For example, toacquire pure A g Raman spectra in CaMn O , the prepa-ration of a polished surface is required, and the polish-ing process will inevitably exert mechanical stress ontothe sample, thus raising the risk of twinning it. We willdiscuss domain-switching behavior under external forcesand how to utilize it to detwin crystals later. (a) (b)(c) (d)(e) (f) AAB CD D xyz
FIG. 1. (Color online) (a), (b) Schematics of { } c and { } c type domain walls in CaMn O . The blue and yellowcubes indicate different domains with the magenta lines indi-cating the shortened body diagonals. Domain walls are de-noted by the planes separating the cubes. (c), (d) Polarized-light optical images of single crystals with { } c and { } c domain walls. In addition to the domain structures which ap-pear as regular bright-and-dark stripe patterns, growth ter-races are seen especially in (c), but they do not seem to affectthe domain distribution. (e), (f) Three-dimensional illustra-tions of the crystals in (c) and (d), respectively, with blueand yellow slabs indicating the two different domains. Sur-faces with four inequivalent domain structures are labeled asA, B, C, and D. Domain-wall orientations in ferroelastic materials canbe understood by the equilibrium boundary condition(strain compatibility), which can be written as thefollowing:
25 3 X i,j =1 [ S ij − S ′ ij ] x i x j = 0 , (1)where S and S ′ are the strain tensors of two adjacentdomains. Indices i and j = 1, 2, and 3 denote Cartesiancoordinates, and all possible ( x , x , x ) that satisfy theequation constitute permissible boundaries between thetwo domains.The rhombohedral phase of CaMn O belongs tothe ferroelastic species m3F3 with four possible domainvariants, which is the result of symmetry lowering fromIm3 to R3. The four different spontaneous strain ten-sors can be written in the form: S = d dd dd d , S = − d − d − d d − d d ,S = − d d − d − dd − d , S = d − dd − d − d − d , (2)with the corresponding shortened body diagonals lyingin direction [111] c , [111] c , [111] c , and [111] c , respectively.When any two of these four domain variants meet, thesolutions to Eq. 1 correspond to one of the equivalentcrystallographic planes { } c and { } c , which is inperfect agreement with our observations in Fig. 1. Thetwo different types of domain walls are illustrated inFigs. 1(a-b). Similar domain structures have been foundin BiFeO , BaTiO , LaAlO , etc. All of these per-ovskites have rhombohedrally distorted phase, the straintensors of which are in the same form as in our case.Additional domain variants may exist when ferroelectric-ity sets in, but the number of ferroelastic variants willremain to be four since 180 ◦ ferroelectric domain wallsare not ferroelastic. There are a total of four inequivalent surface domainstructures on any { } c face of a cube-shaped crystal.They are labeled as A, B, C, and D in the illustrations inFigs. 1(e-f). On an A-type face one finds h i c stripes inthe optical image, which continue onto adjacent faces as h i c stripes; a B-type face exhibits no stripes since it issingle-domain; a C-type face has h i c stripes; a D-typeface has h i c stripes, but unlike the A-type, the stripescontinue onto adjacent faces as h i c stripes. Therefore,for a given crystal with sufficiently large single-domainvolumes that span the entire crystal, one can obtain arough idea about its domain structure by visually in-specting all of its six faces under a polarized-light micro-scope. B. Identification of individual domain orientation
Optical images of crystal faces can only provide infor-mation about the relative orientations of the hexagonal c -axis in adjacent domains (Figs. 1(a-b)). Other methodsare required to reveal the absolute orientation of individ-ual domains. We reported in our previous work thatRaman scattering can detect A g and E g optical phononsseparately with parallel and perpendicular combinationsof incoming- and scattered-photon polarizations, respec-tively, when at least one of the polarizations is parallel tothe hexagonal c -axis. If none of the polarizations is alongthe hexagonal c -axis, the acquired Raman spectrum willbe a weighted combination of A g and E g signals. Therelative intensities of A g and E g phonon peaks dependon the exact scattering geometry. Figure 2 displays Ra-man spectra taken under “XX” and “YY” geometries on a single-domain crystal. Here, XX denotes that both theincoming- and scattered-photon polarizations are alongthe [110] c direction, whereas YY denotes that both po-larizations are along the [110] c direction; the hexagonal c -axis of the crystal is determined to be along the [111] c direction (see below). The measurement configurationsare illustrated in upper-left inset of Fig. 2. Comparingthe XX and YY spectra, one sees a clear difference inthe 380 to 500 cm − region, where four peaks can beattributed to A g and E g modes. The difference is dueto the fact that both the incoming- and scattered-photonpolarizations have a non-zero projection along the hexag-onal c -axis in the XX scattering geometry. This non-zeroprojection leads to a larger (smaller) weight of the A g ( E g ) signals in the Raman spectrum compared to thatobtained in the YY scattering geometry, in which thephoton polarizations are perpendicular to the hexagonal c -axis.By performing both XX and YY measurements on onlyone face of the cube and after obtaining the data shownin Fig. 2, we can only tell that the hexagonal c -axis isalong either the [111] c or the [111] c direction. In orderto unambiguously determine the hexagonal c -axis, oneneeds to perform additional measurements on adjacentfaces of the cube. To verify the validity of our method,we have performed six pairs of XX and YY measurementson all faces of several single-domain crystals, all yieldingconsistent results supporting the aforementioned picture.This gives us confidence on how to identify and orientsingle-domain crystals. Moreover, it suggests the possi-bility to determine the orientations of individual domainsin multi-domain samples using Raman spectroscopy.For simplicity, here we use the relative inten-sity ratio between 390 and 425 cm − , R = I (390 cm − ) /I (425 cm − ), to represent the key charac-teristics of the XX and YY Raman spectra in Figs. 2.As can be seen from the upper-right inset, R capturesthe most significant difference between the two types ofspectra: it is approximately 0.8 or 0.5, respectively, whenthe photon polarizations are perpendicular to or partiallyalong the hexagonal c -axis. To demonstrate how R canbe used to characterize surface-domain structures, wehave performed space-resolved Raman scattering mea-surements on each of the four types of crystal faces thatare labeled as A, B, C, and D in Figs. 1(e-f). The dataare displayed in Figs. 3(a2-d2), along with polarized-lightoptical images of the surfaces in the top panels (a1-d1).In the optical images a horizontal white line indicates thetrajectory on which the Raman spectra were taken. Inthese Raman measurements, the incident and scatteredphoton polarizations are always kept to be parallel, alongone of the two perpendicular face diagonals ([110] c and[110] c , labeled as “XX” and “YY”, respectively) on thesurface.Indeed, on A-type (Figs. 3(a1-a2)) and D-type(Figs. 3(d1-d2)) faces, R is found to switch between 0.5and 0.8 every time the scanning position crosses a bound-ary between the stripes, and whenever R XX is around
100 200 300 400 500 600 700 800 900Raman shiftω (cm -1 ) I n t en s i t y ( a r b . un i t s ) E g A g A g E g XXYY I ( a . u . ) ω (cm -1 )0.8350 400 4500.51 FIG. 2. (Color online) Polarized Raman spectra obtained atroom temperature, offset for clarity. Data curves are color-coded with arrows in the upper-left inset that indicate thepolarization geometries with respect to the hexagonal c -axis(magenta body diagonal of the cube). Vertical dashed linesindicate A g and E g phonon peaks. Upper-right inset, XXand YY spectra in the 350 to 450 cm − region, normalized at425 cm − . R YY is around 0.8 (and vise versa). The resultsare in perfect agreement with our expectations based onthe model illustrated in Fig. 1. On the other hand, R is found to remain roughly constant in a given scatter-ing geometry across the entire B-type (Figs. 3(b1-b2))and C-type (Figs. 3(c1-c2)) faces, for different reasons:the B-type surfaces are single-domain, whereas on the C-type surfaces the hexagonal c -axes in different domainshave the same projection onto the surface plane. Theseresults render Raman spectroscopy, when used alone, un-able to distinguish between A-type and D-type, and be-tween B-type and C-type surfaces. In combination withpolarized-light microscopy one can easily tell them apart,but neither optical inspection nor Raman spectroscopy isable to distinguish, e.g. , between hexagonal c -axis orien-tations of [111] c and [111] c , where the degeneracy is dueto the fact that light is propagating along the [001] c di-rection.A feasible way to completely determine the domainstructure by looking at only one surface is to measurealternating inclinations, or wrinkles, on the surface. Fig-ures 3(a3-d3) display surface profiles measured roughlyalong the same trajectory on which we took the Ramanspectra. We find that the A-type and C-type surfaces ex-hibit clear zigzag profiles, whereas the B-type and D-typesurfaces are essentially flat. Moreover, the angles of thezigzag profiles on the A-type ( ≈ . ◦ ) and C-type( ≈ . ◦ ) surfaces are slightly different. To under-stand these results, we refer to the schematics in Fig. 1. For crystals with { } c domain walls (Figs. 1(a, e)), thestrain tensors of the two domains are S and S (Eq. 2);when they are contracted with the vector (1 , , S and S ((0 , d, d ) and (0 , − d, − d ),respectively) have opposite projections along both the[010] c and [001] c directions. These are the normal direc-tions of the A-type surfaces, and thus the surfaces arewrinkled. A similar argument can be used to explainthe wrinkles on C-type surfaces (Figs. 1(b, f)), where thestrain tensors can be taken as S and S , which are to becontracted with the vector (1 , − ,
0) and then projectedalong [001] c . For D-type surfaces, we should instead use(1 , ,
0) (or (0 , , S and S , but here the outcomes have the same pro-jection along the [010] c (or [100] c ) direction, hence theD-type surfaces are not wrinkled despite the presenceof domain walls. No wrinkles are expected on single-domain B-type surfaces. Using the room-temperaturelattice constants of CaMn O , the angles of wrinkleson A- and C-type surfaces are calculated to be 0.75 ◦ and1.05 ◦ , respectively, which are in good agreement with oursurface-profile data.Taking the above results altogether, we suggest anew method to determine ferroelastic domain structuresbased on measurements of only one pseudo-cubic samplesurface. The most reliable way is to use Raman spec-troscopy combined with surface profile measurements,with polarized-light microscopy being a complementarybut not necessary method. First, one needs to find theorientation of the domain walls by scanning in differentdirections and rotating photon polarizations in the Ra-man scattering measurement, aiming to maximize thecontrast in both the Raman and surface profile data.Second, the surface domain structure can be know bycomparing the data with the results shown in Fig. 3.Third, from the surface profile data one can further tellapart the aforementioned [111] c and [111] c degeneratedsituations on A- and C-type surfaces, using the fact thatshortened hexagonal c -axis always connects the valleysof the wrinkles. Our method is particularly useful whenthe sample is in thin-film form, or when the edges ofcrystals are not along a high-symmetry direction. Whilepiezoresponse force microscopy is most commonly usedto study ferroelectric domain structures, our method pro-vides a route to monitoring the ferroelastic domains bothabove and below the ferroelectric transition temperature,which may help improve our understanding of the inter-play between different ferroic order parameters in multi-ferroics. To detect nano-scale domains, tip-enhanced Ra-man spectroscopy can be used to enhance the spatialresolution of our method. C. Domain switching and detwinning effect
In addition to methods for characterizing the domains,we found that domain structure in CaMn O single crys- XY (a1) R e l a t i v e I n t en s i t y XXYY (a2)
Position ( µ m) H e i gh t ( n m ) ° (a3) XY (b1) XXYY (b2)
Position ( µ m) (b3) XY (c1) XXYY (c2)
Position ( µ m) ° (c3) XY (d1) XXYY (d2)
Position ( µ m) (d3) FIG. 3. (Color online) (a1)-(d1) Optical images of A-, B-, C-, and D-type crystal faces (Figs. 1(e-f)). Horizontal white lineindicates the trajectory along which the measurements in (a2)-(d2) and (a3)-(d3) are performed. Half-solid-half-dashed lineindicates the orientation of the hexagonal c -axis (along one of the h i c directions) in each domain, with the solid end pointingat the top face. (a2)-(d2) Raman intensity ratio R (see text) measured along the trajectories indicated in (a1)-(d1), respectively,with different photon polarizations. The data are color-coded with the arrows indicating polarization directions in (a1)-(d1).(a3)-(d3) Surface profiles along the trajectories indicated in (a1)-(d1). tals can be altered at room temperature under moderateuniaxial compression. Figure 4 displays the same face ofa crystal at different times. Initially, the surface exhibitsa stripe pattern indicative of presence of { } c domainwalls (Fig. 4(a)). When a compressive force of about 1.5N is applied along the direction shown by the arrows inFig. 4(b), the stripe pattern is rotated by 45 ◦ , which indi-cates the formation of new { } c domain walls and thedisappearance of the old ones. The magnitude of the ap-plied force amounts to a uniaxial stress of about 30 MPainside the crystal, and the new stripe pattern persistsafter the force was removed. Similarly, when a compres-sion is applied along the direction in Fig. 4(c), the stripepattern is found to rotate again by 90 ◦ . This domain-switching behavior can be understood as the following:when a uniaxial compression is applied, the ferroelas-tic domains rearrange themselves to minimize the lengthalong the direction of compression. In the case of com-pression in the [110] c direction, domains with hexagonal c -axes along [111] c and [111] c are energetically favored.According to the analysis in Section III A, this may re-sult in the formation of either (001) c or (110) c domainwalls, but the former would also generate wrinkles on the(100) c and (010) c faces which are incompatible with theapplied compression. Hence the resulting domain wallsare parallel to (110) c . For the same reason, one can rea- sonably expect that a h i c domain can be exclusivelyselected if the compression is primarily along a body di-agonal of the cube, as is indeed shown to be the case inFig. 4(d). Apart from taking optical images, we have per-formed Raman scattering measurements on all six facesof the sample in Fig. 4(d), which consistently show thatthe crystal is highly detwinned.This switching behavior of ferroelastic domains inCaMn O stems from the fact that the rhombohedraldistortion is characterized by the shortening rather theelongation of a body diagonal, which makes the detwin-ning operations simple. Among other rhombohedrallydistorted perovskites, LaAlO is similar to CaMn O ,whereas the distortion in BiFeO features an elongatedbody diagonal, making it rather tricky to prepare certaintypes of domain structure. IV. CONCLUSIONS
In summary, we have observed and investigated ferroe-lastic domain structures in single crystals of CaMn O .For cube-shaped single crystals with multiple domains,we can determine the orientation of individual domainsby measurements either on two adjacent faces with Ra-man spectroscopy alone, or on only one face using both (a) (b)(c) (d) FIG. 4. (Color online) Optical images of the same face ofa crystal: (a) initial state, (b) after compression was appliedalong the face diagonal indicated by the arrows, (c) after com-pression was applied along the other face diagonal, and (d)detwinned state after compressed primarily along a body di-agonal.
Raman spectroscopy and stylus surface profiler. The lat-ter method is also suitable for determining domain struc-tures in thin-film samples, where only one surface is avail-able. In addition, polarized-light microscopy provides acomplementary and convenient way to observe the do-main structure. Finally, we find that the domain struc-ture can be altered by moderate uniaxial compression atroom temperature, which allows for a simple method toobtain twin-free samples with a controlled orientation ofthe hexagonal c -axis. Our results offer the opportunity toprepare well-defined CaMn O samples, e.g. , for spec-troscopic studies that require single-domain crystals, andthe methods we use can be readily transferred to stud-ies of thin-film samples as well as other rhombohedrallydistorted cubic compounds. Acknowledgments
We thank W. H. Yang and X. B. Wang for technicalassistance in the use of polarized-light microscope andstylus profiler. This work is supported by the NSF ofChina (No. 11374024) and the NBRP of China (No.2013CB921903). ∗ [email protected] G. Catalan, J. Seidel, R. Ramesh, and J. F. Scott, Rev.Mod. Phys. , 119 (2012). E. K. Salje, Annu. Rev. Mater. Res. , 265 (2012). J. Yang, Y. Huang, Q. He, and Y. Chu, J. Appl. Phys. , 066801 (2014). M. Fiebig, T. Lottermoser, D. Fr¨ohlich, A. Goltsev, andR. Pisarev, Nature , 818 (2002). Y. Tokunaga, N. Furukawa, H. Sakai, Y. Taguchi, T.-h.Arima, and Y. Tokura, Nature Mater. , 558 (2009). T. Choi, Y. Horibe, H. Yi, Y. Choi, W. Wu, and S.-W.Cheong, Nature Mater. , 253 (2010). A. Aird and E. K. Salje, J. Phys. Condens. Matter ,L377 (1998). J. Seidel, L. W. Martin, Q. He, Q. Zhan, Y.-H. Chu,A. Rother, M. Hawkridge, P. Maksymovych, P. Yu,M. Gajek, et al. , Nature Mater. , 229 (2009). Q. He, C.-H. Yeh, J.-C. Yang, G. Singh-Bhalla, C.-W.Liang, P.-W. Chiu, G. Catalan, L. Martin, Y.-H. Chu,J. Scott, et al. , Phys. Rev. Lett. , 067203 (2012). G. Catalan and J. F. Scott, Adv. Mater. , 2463 (2009). D. Meier, J. Seidel, A. Cano, K. Delaney, Y. Kumagai,M. Mostovoy, N. A. Spaldin, R. Ramesh, and M. Fiebig,Nature Mater. , 284 (2012). T. Jungk, ´A. Hoffmann, M. Fiebig, and E. Soergel, Appl.Phys. Lett. , 012904 (2010). S. Chae, N. Lee, Y. Horibe, M. Tanimura, S. Mori, B. Gao,S. Carr, and S.-W. Cheong, Phys. Rev. Lett. , 167603(2012). D. Khomskii, Physics , 20 (2009). R. Johnson, L. Chapon, D. Khalyavin, P. Manuel,P. Radaelli, and C. Martin, Phys. Rev. Lett. , 067201 (2012). N. Perks, R. Johnson, C. Martin, L. Chapon, andP. Radaelli, Nat. Commun. , 1277 (2012). X. Lu, M.-H. Whangbo, S. Dong, X. Gong, and H. Xiang,Phys. Rev. Lett. , 187204 (2012). M. Iliev, V. Hadjiev, M. Gospodinov, R. Nikolova, andM. Abrashev, Phys. Rev. B. , 214302 (2014). X. Du, R. Yuan, L. Duan, C. Wang, Y. Hu, and Y. Li,Phys. Rev. B. , 104414 (2014). A. Vasilev and O. Volkova, Low Temp. Phys. , 895(2007). B. Bochu, J. Buevoz, J. Chenavas, A. Collomb, J. Joubert,and M. Marezio, Solid State Commun. , 133 (1980). R. Przenioslo, I. Sosnowska, E. Suard, A. Hewat, andA. Fitch, J. Phys.: Condens. Matter , 5747 (2002). H. Schmid, E. Burkhardt, E. Walker, W. Brixel, M. Clin,J.-P. Rivera, J.-L. Jorda, M. Francois, and K. Yvon, Z.Phys. B: Condens. Matter , 305 (1988). M. Tanatar, A. Kreyssig, S. Nandi, N. Ni, S. Budko,P. Canfield, A. Goldman, and R. Prozorov, Phys. Rev.B , 180508 (2009). J. Sapriel, Phys. Rev. B , 5128 (1975). K. Aizu, J. Phys. Soc. Jpn. , 387 (1969). K. Aizu, J. Phys. Soc. Jpn. , 706 (1970). F. Zavaliche, S. Yang, T. Zhao, Y. Chu, M. Cruz, C. Eom,and R. Ramesh, Phase Transitions , 991 (2006). P. Marton, I. Rychetsky, and J. Hlinka, Phys. Rev. B ,144125 (2010). S. Bueble, K. Knorr, E. Brecht, and W. W. Schmahl, Surf.Sci. , 345 (1998). J. Fousek and V. Janovec, J. Appl. Phys. , 135 (1969). R. Przenios lo, I. Sosnowska, E. Suard, A. Hewat, andA. Fitch, Physica B , 358 (2004). N. Balke, I. Bdikin, S. V. Kalinin, and A. L. Kholkin, J.Am. Ceram. Soc. , 1629 (2009). J. M. Atkin, S. Berweger, A. C. Jones, and M. B. Raschke,Adv. Phys. , 745 (2012). K. F. Domke and B. Pettinger, ChemPhysChem , 1365(2010). H. Fay and C. Brandle, J. Appl. Phys. , 3405 (1967). F. Kubel and H. Schmid, J. Cryst. Growth , 515 (1993). Y.-H. Chu, Q. He, C.-H. Yang, P. Yu, L. W. Martin,P. Shafer, and R. Ramesh, Nano Lett.9