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Bismuth manganite: A multiferroic with a large nonlinear optical response

Alok Sharan,1 James Lettieri,1 Yunfa Jia,1 Wei Tian,1 Xiaoqing Pan,2 Darrell G. Schlom,1 and Venkatraman Gopalan1

1Materials Research Institute and Department of Materials Science and Engineering, Pennsylvania State University,University Park, Pennsylvania, 16802, USA

2Department of Materials Science and Engineering, The University of Michigan, Ann Arbor, Michigan, USA�Received 16 October 2003; revised manuscript received 19 December 2003�

We report evidence for ferroelectricity in bismuth manganite epitaxial films from optical second-harmonicgeneration �SHG�. The change in the polar symmetry of SHG signals under external electric fields is correlatedto specific changes in the ferroelectric domain microstructures. We also observe giant enhancement of SHG by3 to 4 orders of magnitude with effective d f�193 pm/V under electric fields of �707 V/mm. The material alsoexhibits a large third-order nonlinear optical response with nonlinear absorption coefficient � I��0.08 cm/kW and nonlinear refractive index nI��0.53�10�9 cm2/W.

DOI: 10.1103/PhysRevB.69.1341XX PACS number�s�: 77.80.�e, 42.65.Ky

There is growing interest in multiferroic materials1–3 dis-playing simultaneous ferromagnetism, ferroelectricity, andferroelasticity, due to potential applications as ferroelectro-magnets and in spintronics, in addition to the inherent inter-est in the underlying physics of the coexistence of ferroelec-tricity and ferromagnetism. Bismuth manganite (BiMnO3), amaterial with the perovskite structure and predicted to bemultiferroic,3 has been previously shown to beferromagnetic4–7 below a transition temperature of �105 Kand a likely ferroelectric.4 Ferroelectricity has been difficultto prove because of the lack of single crystals and the lowresistance of BiMnO3 films, making it difficult to associatemeasured dielectric hysteresis loops to ferroelectricity in-stead of nonlinear dielectric losses. Bismuth manganite ismetastable at atmospheric pressure and has required pres-sures of at least 40 000 atm to synthesize in bulk form. Mor-eira et al.4 have reported ferroelectric hysteresis loops forpolycrystalline thin films and bulk powders of BiMnO3 ,which contained some unidentified impurities phases as well.A structural phase transition from monoclinic C2 to anorthorhombic Pbnm has been observed at a temperature of�770 °C,8 which is presently postulated to be a likely ferro-electric to paraelectric phase transition.

In this paper, we study phase pure, epitaxially grown thinfilms of BiMnO3 on SrTiO3 �111� substrates. We correlateobserved permanent changes in the magnitude and symmetryof optical second harmonic generation signals to changes inthe ferroelectric domain microstructure upon applying exter-nal electric fields to the film. The large nonlinear opticalresponses observed in this manuscript open up possibilitiesfor device applications exploiting all three features of ferro-electric, ferromagnetic, and optical nonlinearity.

The magnetic point group of BiMnO3 has been reportedto be 2, with lattice parameters of a�9.523 Å, b�5.6064 Å, and c�9.8536 Å, ����90°, and ��110.667°, at room temperature �Fig. 1�. Symmetry dictatesthat the ferroelectric polarization Ps if it exists, should bealong the twofold rotation axis, since this axis will destroyany polarization vector component Ps� perpendicular to it,by requiring an equal and opposite vector �Ps� . Recentneutron diffraction studies indicate that the magnetic polar-ization is also oriented along the twofold axis. Magnetic

measurements of an epitaxial BiMnO3 film grown in thesame way as the films in this study on a �100� SrTiO3 sub-strate reveal a ferromagnetic transition at Tc�97 K, slightlylower than the Tc�105 K value of bulk BiMnO3 samples.9

Epitaxial BiMnO3 thin films were synthesized by pulsedlaser deposition on �111� SrTiO3 substrates using a bismuth-rich target with composition Bi2.4MnOx . The parametersused to grow the samples studied were a substrate tempera-ture of 755–758 °C, an oxygen pressure of 150 mTorr, a laserfluence of 1.5–2 J/cm2, and a laser repetition rate of 4 Hzusing a 248 nm excimer laser. The samples were quenched atthe completion of growth in 1 atm of oxygen to minimizingbismuth desorption from the film during the coolingprocess. Additional details on the film deposition, struc-tural and magnetic characterization are being reportedelsewhere.9 The films studied here are phase-pure filmswith the following epitaxial orientation relationship:BiMnO3 (111)//SrTiO3 (111), with in-plane orientations of

� 110� BiMnO3 //�101�SrTiO3 �exact relation� and �112�

BiMnO3 //� 121� SrTiO3 �approximate relation�. Figure 2�a�

FIG. 1. A unit cell of BiMnO3 indicating the polarization direc-tion (Ps) and the growth plane for the films studied. The vector x�

is defined as x�� b� c . Various angles are defined, for example, as

A x��cos�1 lAx�

, where A x�is the angle between unit vectors A

and x� . These angles are A x��62.695°, B x�

�62.77°, �Cx�

�19.790° or Cx��160.209°, Da�30.46°, Db�59.538°, Dc

�72.288°, Dx��143.755° or l�Dx�

�36.245°, Ea�56.706°, Eb�0°, E c�53.96°, E x�

�36.039°, Fa�72.13°, Fb

�60.36°, F c�29.638°, F x��90°.

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shows a �-2� x-ray diffraction scan of one of the BiMnO3films studied. The scan reveals a phase-pure BiMnO3 filmwith its (111) plane parallel to the �111� plane of the SrTiO3substrate. The full width at half maximum �FWHM� of the222 reflection of BiMnO3 is 0.24° and 0.39° in 2 and �Fig. 2�b��, respectively. Figure 2�c� shows a � scan of the110 peak of the (111)-oriented BiMnO3 film with a FWHMin � of �1.7°. The Bragg angle obtained from the �-2�

scan for the 111 peak (2�19.39°) agrees well with thatobtained from the reported lattice parameter values (2�19.36°) of that of bulk BiMnO3 .

The microstructure of one of the same films whose opticalproperties were investigated was studied by cross-sectionaltransmission electron microscopy �TEM�. The results areshown in Fig. 3. Figure 3�a� shows a low-magnificationcross-sectional TEM image of the film. The TEM imagesrevealed no evidence of impurity or amorphous phases. Fig-

ures 3�b� and 3�c� are selected-area electron diffraction�SAED� patterns taken from the film and the substrate, re-spectively, with the incident electron beam along the samedirection. They are, respectively, identified to be the �101�zone axis SAED pattern of monoclinic BiMnO3 and the

�101� zone axis SAED pattern of SrTiO3 . The electron dif-fraction patterns observed were consistent with the film hav-ing the same monoclinic structure as bulk BiMnO3 samplesand the orientation relationship determined from TEM cor-roborated that deduced from the four-circle x-ray diffractionmeasurements. Figure 3�d� shows a high-resolution TEM�HRTEM� image of the film/substrate interface. The HRTEMimage reveals that the interface is clean.

Figure 4 shows the 12 types of ferroelectric domain vari-ants that can exist in these films. Both ferroelectricity andelectric-dipole second harmonic generation �SHG� occuronly in noncentrosymmetric media. Since the monoclinicspace group (C2) of BiMnO3 is noncentrosymmetric, onewould expect SHG signals due to the electric dipole. How-ever, to establish ferroelectricity one has to see the changesin the ferroelectric polarization direction with applied exter-nal fields. The consequent changes in the magnitude, and inparticular, symmetry of second harmonic response with ap-plied external fields can provide unique signatures of thepresence and rearrangement of ferroelectric domains.10–12

SHG experiments were performed using a tunable Ti-sapphire laser with 65 fs pulses of ��900 nm fundamentallight. The laser pulses were incident from the substrate sideat a repetition rate of 82 MHz with an average power of�400 mW over a probed beam with a 126 m diameterbeam incident on the film. The SHG signal was detected

FIG. 2. �a� �–2� x-ray diffraction scan of one of the BiMnO3

films used in this study grown on a SrTiO3 �111� substrate. The scan

reveals a nearly phase-pure (111) oriented BiMnO3 film. The full

width at half maximum �FWHM� of 222 reflection of BiMnO3 is

0.24° in 2. �b� Rocking curve of the 222 peak of this sameBiMnO3 film with a FWHM of 0.39° in . �c� Plot a � scan of the

110 peak at ��61.5° of the (111) oriented BiMnO3 film with aFWHM in � of �1.7°. (��90° aligns the diffraction vector to beperpendicular to the plane of the substrate�. ��0° is aligned to be

parallel to the SrTiO3� 121� in-plane orientation.

FIG. 3. �a� Low-magnification TEM image showing a cross-sectional view of one of the BiMnO3 films used in this study grownon a �111� SrTiO3 substrate. �b� and �c� The �101� zone axis SAED

pattern of BiMnO3 and the �101� zone axis SAED pattern ofSrTiO3 taken with the incident electron beam along the same direc-tion, respectively. Electron diffraction studies of the film and thesubstrate confirm the epitaxial orientation established by x-ray stud-ies. �d� HRTEM image of the BiMnO3 /SrTiO3 interface imaged by

the electron beam along the �101� zone axis of SrTiO3 . The HR-TEM image reveals a clean interface.

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using a line filter around 450 nm, and using a lock-in tech-nique. Under identical conditions, no SHG signals were ob-served from a bare SrTiO3(111) substrate with or withoutapplied fields. Electric fields were applied in situ while SHGmeasurements were performed. Since the film exhibited largedielectric losses at room temperature and above, Au elec-trode pads were applied to the backside of the SrTiO3 sub-strate, with a spacing of 2 mm, and voltages of up to �2 kVwere applied as shown in the inset of Fig. 7. Using a relativedielectric constant of 448 for the 0.87-mm-thick SrTiO3 sub-strate at room temperature, and not accounting for the pres-ence of the film, the actual fields at the interface between thefilm and the substrate were estimated to be of the order of707 V/mm parallel to the interface. We have not attempted toapply Au pads on the film side for measurement at lowertemperatures �82 K� where dielectric losses may be lower.

Figure 5 shows the polar plots at a temperature of 82 K,of the SHG intensity (��450 nm) polarized along either theSrTiO3 �101� direction „denoted as the x axis; intensity Ix in�Figs. 5�b�, 5�d��… or the SrTiO3 � 121� direction „denoted asthe y axis, intensity Iy in �Figs. 5�a�, 5�c��… as a function ofthe input polarization direction of the fundamental beam (��900 nm) at an angle to the x axis. The local nonlinearpolarization Pi

2 �i denotes local unit-cell coordinates� arecalculated for each domain variant in Fig. 4, and summed,taking their relative phases into account. The total nonlinearpolarization P j

2 ( j�x or y, which are global coordinates�,in the film created by the fundamental beam can thus bederived as

P j2��A I, j�A II, je

i�II, j�A III, jei�III, j�cos2

��B I, j�B II, jei�II, j�B III, je

i�III , j�sin2

��C I, j�C II, jei�II, j�C III, je

i�III, j�sin�2�, �1�

where, referring to Fig. 4, the terms AK , j , BK , j , and CK , j arethe net contributions from the domains set K(�I,II,III).They are listed in Table I. The terms � II, j and � III, j are rela-tive phase shifts of the SHG contribution from domain sets IIand III with respect to set I. The second harmonic intensity I jis obtained as

I j��m ,n

�Am , j cos2 �Bm , j sin2 �Cm , j sin 2��An , j cos2

�Bn , j sin2 �Cn , j sin 2�cos��m , j��n , j�, �2�

where m, n�I, II, III refer to the three domain sets I, II, andIII, respectively, and we are free to choose the arbitraryphase � I, j�0 according to Eq. �1�. If we assume, for simpli-fication, that all �m , j�0, then Eq. �2� simplifies to

I j��A j cos2 �B j sin2 �C j sin 2�2, �3�

where A j��mAm , j and similarly for B j and C j . Theoreticalfits based on Eq. �3� are shown in Fig. 5 as solid lines. Asshown in Figs. 5�c� and 5�d�, one also observes that, at 82 K,these polar plots show permanent changes when an externalstep voltage of �2 kV is applied along the �y direction fora period of 30 min and then shut off. These permanentchanges are discussed below.

We emphasize the qualitative physical implications of fit-ting parameters in Eq. �3� and Table I from a domain micro-structure perspective. Within a two-dimensional microstruc-ture assumption for the thin film, and within the probe areaof the beam, let us define f k as the area fraction of any one ofk�1 – 12 domain variants in Fig. 4. Abbreviated notationsuch as f 1�3�2�4� f 1� f 3� f 2� f 4 is adopted. The con-

FIG. 4. Plan view of the growth plane with 12 different possibledomain variants in an epitaxial thin film of BiMnO3 . The brokenlines are the projection of the a, b, and c unit-cell axes on thegrowth plane. Arrows indicate the projection of Ps on the growthplane. At room temperature, the ferroelectric polarization �b axis� istilted at an angle of �54.88°, and a and c axes at �34.69° and�32.80°, respectively, from the growth plane.

FIG. 5. Polar plots at 82 K of the SHG intensity polarized along

either the SrTiO3 �101� �denoted as the x axis; intensity Ix �b� and

�d�� or � 121� �denoted as the y axis, intensity Iy �a� and �c�� as afunction of the input polarization direction of the fundamental beamat an angle to the x axis. Plots �a� and �b� correspond to beforeapplication of any voltage, and plots �c� and �d� correspond to afterapplication and removal of a voltage of �2 kV. Circles are experi-mental points and solid lines are theoretical fits based on Eq. �3�.Double-headed arrows in �a� indicate the projection of possibleferroelectric polarization directions Ps shown in Fig. 1 on to thefilm growth plane, also the plane of the plots.

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stants F in Table I are linear functions of nonlinear coeffi-cients d34 , d21 , d22 , d23 , d16 and cosines of various geo-metric angles. The constants G in Table I are linear functionsof nonlinear-coefficients d36 , d25 , d14 , and cosines of vari-ous geometric angles. These dependencies are explicitlyshown in Tables II and III. None of the nonlinear coeffi-cients, and hence F and G, are known. However, as shownbelow, the explicit expressions for F and G are unimportant

for the qualitative conclusions drawn here, except to notethat they are material constants and do not change with ex-ternal fields. The external fields only change the area frac-tions f k , and hence the fitting parameters A j , B j , and C j inTable I. The following general conclusions can be drawn.

We begin by observing that in Fig. 4, for an applied elec-tric field along the �y direction, as in our experiments, theelectric field would be expected to increase the fraction f k ,

TABLE I. The parameters in Eq. �3� as a function of domain fractions f k(k�1 – 12) shown in Fig. 4 Theconstants F are linear functions of nonlinear coefficients d34 , d21 , d22 , d23 , d16 and cosines of variousgeometric angles. The constants G are linear functions of nonlinear coefficients d36 , d25 , d14 and cosines ofvarious geometric angles. Subscripts and superscripts accompanying F and G refer to the specific parametersthey are associated with in column 1. These functions are listed in Tables II and III.

Parameters j�x , SrTiO3 �101� j�y , SrTiO3 � 121�

A I, j f 1�4�2�3F I,xA � f 1�2�3�4G I,x

A f 1�3�2�4F I,yA � f 1�2�3�4G I,y

A

A II, j f 5�8�6�7G II,xA f 5�7�6�8F II,y

A � f 5�6�7�8G II,yA

A III, j f 10�11�9�12F III,xA f 9�11�10�12F III,y

A

B I,x f 1�4�2�3F I,xB � f 1�2�3�4G I,x

B f 1�3�2�4F I,yB � f 1�2�3�4G I,y

B

B II, j f 5�8�6�7F II,xB � f 5�6�7�8G II,x

B f 5�7�6�8F II,yB � f 5�6�7�8G II,y

B

B III, j f 10�11�9�12F III,xB � f 11�12�9�10G III,x

B f 9�11�10�12F III,yB � f 9�10�11�12G III,y

B

C I, j f 1�3�2�4F I,xC � f 1�2�3�4G I,x

C f 1�4�2�3F I,yC � f 1�2�3�4G I,y

C

C II, j f 5�7�6�8F II,xC � f 5�6�7�8G II,x

C f 5�8�6�7F II,yC � f 5�6�7�8G II,y

C

C III, j f 9�11�10�12F III,xC � f 9�10�11�12G III,x

C f 10�11�9�12F III,yC � f 11�12�9�10G III,y

C

TABLE II.

K j FK , j

K�I j�x F I,xA �l Db�d34l Dc

2�(d21�d16)l

�Dx�

2�d22l Db

2�d23l Dc

2�

F I,xB �d34l Dcl Acl Ab�l Db(d21l Ax�

2�d22l Ab

2�d23l Ac

2)�d16l�Dx�

l Abl Ax�

F I,xC �1/2��d34(l

Dc

2l Ab�l Acl Dbl Dc)�l Db(2d21l Ax�

l�Dx��2d22l Dbl Ab�2d23l Dcl Ac)

�d16l�Dx�(l Dbl Ax�

�l Abl�Dx�)�

j�y F I,yA ��d34l Dcl Dbl Ac�l Ab(d21l�Dx�

2�d22l Db

2�d23l Dc

2)�d16l Dbl�Dx�

l Ax�

F I,yB ��d34l Ac

2l Ab�l Ab(d21l Ax�

2�d22l Ab

2�d23l Ac

2)�d16l Ax�

2l Ab

F I,yC �1/2�d34(l Acl Abl Dc�l

Ac

2l Db)�l Ab(2d12l�Dx�

l Ax��2d22l Dbl Ab�2d23l Dcl Ac)

�d16l Ax�(l Dbl Ax�

�l Abl�Dx�)�

K�II j�x F II,xA �0

F II,xB �d34l Ecl�B cl�Bb�d16l Ex�

l�Bbl Bx�

F II,xC �1/2�d34l Ec

2l�Bb�d16l�Bbl

Ex�

2�

j�y F II,yA �l�Bb(d21l Ec�

2�d23l�B c

2)

F II,yB �d34l�B c

2l�Bb�l�Bb(d21l Bx�

2�d22l�Bb

2�d23l�B c

2)�d16l Bx�

2l�Bb

F II,yC �1/2�l�Bb�d34l�B cl Ec�(2d21l Ex�

l Bx��2d23l Ecl�B c)�d16l Bx�

l Ex���

K�III j�x F III,xA �l Fb(d22l Fb

2�d23l Fc

2)�d34l Fc

2l Fb

F III,xB ���d34l Fcl�Ccl Cb�l�Fb(d22l Cb

2�d21l�Cx�

2�d23l�Cc

2)�

F III,xC �1/2�l�Fb(�2d22l Fbl Cb�2d33l Fcl Cc)

�d34l�F c(�l Fbl�Cc�l Cbl Fc)�j�y F III,y

A ��l Cb(d22l Fb

2�d23l Fc

2)�d34l Ccl Fcl Fb

F III,yB ���d16l�Cx�

2l Cb�l Cb�d22l Cb

2�(d23�d34)l

�Cc

2�d21l�Cx�

2��

F III,yC �1/2�d16l�Cx�

2l Fb�l�Cb(�2d22l Fbl Cb�2d33l Fcl Cc)

�d34l�Cc(�l Fbl�Cc�l Cbl Fc)�

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(k�2,4,6,8,10) of variants with ferroelectric domain polar-ization components pointing parallel to the field, and de-crease the fraction f k , (k�1,3,5,7,9) of those variants withpolarization components opposite to the field. The reversewould be true for a field along the �y direction. Thereforeelectric fields �y would systematically increase or decreaseterms of the sort f 1�3�2�4 , f 5�7�6�8 and f 9�11�10�12 .The changes to the remaining domain fraction sums underelectric fields �e.g., f 1�4�2�3 , and f 5�8�6�7 , etc., in TableI�, which we label here as ‘‘mixed terms’’ would, on theaverage be expected to be negligible. The terms f 1�2�3�4 ,f 5�6�7�8 and f 9�10�11�12 are precisely constants with noexpected changes under fields, since these sums are con-served, and the electric fields cannot transform the structuraldomains I, II, and III into each other.

This discussion in conjunction with Table I, would sug-gest that for electric-field-induced microstructural bias, theterms Ay

2 and By2 would dominate Iy , and terms Cx

2 woulddominate Ix . This is indeed seen in Fig. 5 where sin2(2)�associated with Cx

2) dominates the intensity patterns Ix .Similarly, sin2 and cos2 terms �associated with Ax

2 andBx

2) dominate the SHG signal Iy in Fig. 4.Let us now focus on the changes in the SHG signal Iy(0°)

and Iy(90°) due to electric fields �from Figs. 5�a� and 5�c��.From Eq. �3�, for fundamental polarizations at �0° or 90°,the terms that contribute to the SHG signal Iy are Ay

2 or By2,

respectively. The changes in Iy(0°) and Iy(90°) observedhere, therefore, corresponds to a net change in the area frac-tion of the domain set �1,3,5,7,9,11� with respect to the do-

main set �2,4,6,8,10,12� in Fig. 3, which is precisely what anelectric field along the �y axis is expected to do.

Similarly, the change in the experimental intensity Ix withapplied field �in Figs. 5�b� and 5�d�� is seen to increase thecontribution of the sin 2 term, which in turn indicates anincreased contribution from the Cx term. This again is pre-cisely what is expected when there is a net change in domainset �1,3,5,7,9,11� with respect to the domain set�2,4,6,8,10,12� in Fig. 1, with an electric field along the �yaxis. Hence we conclude that these permanent changes in theSHG signal with external electric fields are consistent withthe presence of ferroelectric domains in BiMnO3 films at82 K.

We note two more important aspects at 82 K. First, theabsolute changes in the SHG signal with the application of�2 kV appear to be of the order of 1. Second, when theassumption of �m , j�0 in Eq. �3� is lifted, the minima in thepolar plots of Figs. 5�c� and 5�d� can be accurately fit. Thissuggests that a phase change due to optical index differencesbetween different variant classes is finite.

We now turn to field effects at room temperature �296 K�.Polar plots similar to Figs. 5�a� and 5�b� are obtained at roomtemperature as well. Figure 6�a� shows an example of a hys-teresis loop of the SHG intensity Iy(90°) as a function of theapplied voltage �parallel to the �y axis� at room tempera-ture, which corresponds to a net change in area fractionsbetween the odd-numbered and the even-numbered domainsets in Fig. 4, as discussed above. �Actual SHG signalsshown in Fig. 6 are nonzero at all fields�. Highly asymmetrichysteresis loops are observed, with giant enhancements in

TABLE III.

K j GK , j

K�I j�x G I,xA �l Dcl�Dx�

��(d36�d25)l Db�d14l�Dx��

G I,xB �l Ax�

�d36l Abl Dc�l Ac(d25l Db�d14l�Dx�)�

G I,xC �1/2���d36l Dc(l Dbl Ax�

�l Abl�Dx�)��d25l Db(l�Dx�

l Ac�l Ax�l Dc)

�d14l�Dx�(l�Dx�

l Ac�l Ax�l Dc)�

j�y G I,yA �l�Dx�

�d36l Dbl Ac�l Dc(d25l Ab�d14l Ax�)�

G I,yB �l Acl Ax�

��(d36�d25)l Ab�d14l Ax��

G I,yC �1/2��d36l Ac(l Dbl Ax�

�l Abl Dx�)��d25l Ab(l�Dx�

l Ac�l Ax�l Dc)

�d14l Ax�(l�Dx�

l Ac�l Ax�l Dc)�

K�II j�x G II,xA �d14l Ex�

2l Bc

G II,xB �l Bx�

(�d36l�Bbl Ec�d14l Ex�l�B c)

G II,xC �1/2�l Ex�

�d36l Ecl�Bb�d14(l Ex�l�B c�l Bx�

l Ec)��j�y G II,y

A �l Bx�(d25l�Bbl Ec�d14l Bx�

l Ec)

G II,yB ��l Bc(d36l�Bbl Bx�

�d25l�Bbl Bx��d14l Bx�

2)

G II,yC �1/2��d36l Ex�

l�B cl�Bb�d25l�Bb(l Ex�l�B c�l Ecl Bx�

)�d14l Bx�

(l Ex�l�B c�l Bx�

l Ec)]�

K�III j�x G III,xA �0

G II,yA �l�Cx�

(d36l Fcl Cb�d25l Fbl�Cc)G III,x

C �1/2�l Fcl�Cx�l Fb(d25�d36)�

j�y G III,yA �0

G III,yB ��l�Cx�

(d14l�Cx�l�Cc�d25l Cbl�Cc�d36l Ccl Cb)

G III,yC �1/2��l Cx�

(d14l�Cx�l Fc�d25l Cbl Fc�d36l�Ccl Fb)�

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one direction as compared to the other direction, indicating astrong internal microstructural bias in the film consistentwith poled ferroelectric domain microstructures. This biascan be reversed by the application of a steady electric field inthe opposite direction, as shown in Fig. 6�b�. Figure 7 showsthe time evolution of the SHG signal after a step voltage of�2 kV was applied to the sample, parallel to the �y axis. Inorder to quantify the SHG enhancement, we compare themaximum signal with that for a z-cut LiTaO3 reference, us-ing the d22�1.672 pm/V coefficient in the following equa-tion:

d f2�dr

2� P f2

Pr2� � Pr

P f

Tr

T f� 2 A f

Ar� n f

nr� 2 n f

2

nr2 � lc ,r

lc , f� 2 e��r

2lc ,r

e�� f2lc , f

,

�4�

where the subscripts r and f refer to the reference and thefilm, respectively, P2(P) are the second harmonic �funda-mental� signal powers measured, T is the transmission coef-ficient of the fundamental, A is the area of the probed beamdiameters, n are the indices of refraction, lc the coherencelengths, and � the absorption coefficient of the film at 2.Using spectroscopic ellipsometry, the refractive indices ofthe film were determined as n f

2�1.88�0.8j and n f

�2.217�0.56j . The beam areas were A f��(63 m)2 and

Ar��(57 m)2 and the powers were P f�580 mW, Pr

�27 mW. Since the calculated coherence length lc

�1.33 m for BiMnO3 is much larger than the film thick-ness (l f�110�29 nm), we assume lc , f�l f�110 nm in theabove relation. Even without accounting for film absorptionat 2 through the last ratio in Eq. �4�, the effectived f exp(�r

2lc,r��f2lf)�16.5 pm/V. Taking the absorption

into account, the estimated d f�193 pm/V. As a comparison,the d33 for well-known nonlinear material LiNbO3 is �36pm/V.13 Such giant dc field (E0) induced second harmonicresponse can arise from ferroelectric domain alignment, aswell as third order nonlinear optical process, where nonlinearpolarization Pi

2�� i jkl( , ,0)EEE0 is created in thefilm, and the superscripts indicate the frequencies.

A related third-order optical nonlinearity is � i jkl( ,� ,), giving rise to intensity �I� dependent index change�n�nII and absorption change ���� II . These coefficientswere measured using the single beam z-scan technique14 at900 nm with 140 fs pulses with peak intensity at focus of 1.3GW/cm2. Both closed and open aperture scans were per-formed on BiMnO3 films to extract the nonlinear optical co-efficients. At room temperature �296 K� the nonlinear ab-sorption coefficient was measured to be � I��0.08 cm/kWand nonlinear refractive index as nI��0.53�10�9 cm2/W. These values did not change with the fre-quency of the chopping of the incident beam from 97 Hz to3.24 kHz, suggesting that the origin is not thermal in nature.These are large values as compared to films such as Rh:BaTiO3 deposited on SrTiO3 �Ref. 13� and SrBi2Ta2O9 onquartz,15–17 but smaller than Bi films on glass.16

There are many plausible explanations for the observednonlinear optical behavior. Domains of different variantsprobed by the beam contribute to SHG signal. Under theinfluence of external electric fields, the ferroelectric domainsrealign and the radiated SHG signals from these domainsinterfere constructively to enhance the SHG signal.12 This isone explanation for the pronounced dependence of SHG sig-nal on the applied electric field. Another mechanism for theSHG enhancement with applied fields may be a result ofcompetition between charge transfer and electron correlationsimilar to that discussed in Refs. 18–21. The large nonlinearresponse observed at room temperature and above is accom-panied by dielectric losses in the films. There could be acorrelation between the two, with some contribution fromfree-carrier absorption. In such a case, a plausible charge

FIG. 6. Hysteresis loops of theSHG intensity Iy(90°) as a func-tion of applied voltage �parallel tothe �y axis� at 23 °C �a� after ap-plying a steady voltage of �1 kVfor 30 min and �b� after �2 kVwas applied for 30 min. Arrowsindicate the direction of voltagecycling.

FIG. 7. Time evolution of the SHG signal after a �2 kV voltagestep is applied at 23 °C. The inset shows the geometry of SHGmeasurement and of voltage application across a 2 mm electrodegap. The peak enhancement of the SHG signal is around 35 000times.

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transfer mechanism may be between a 6p orbital of Bi and a3d orbital of Mn via a 2p orbital of O2 .19–21 A third possi-bility is that the material may be an electronic ferroelectric,22

where polarization arises from a condensation of an excitonelectron-hole pair �plausibly an itinerant Bi-6p electron anda localized Mn-3d hole�. This third possibility has been pre-dicted to result in giant second harmonic enhancement atspecific resonance frequencies.22

To conclude, we observe electric-field-induced permanentchanges in the second harmonic response from a BiMnO3thin film. These changes are shown to be consistent with thepresence of ferroelectricity in BiMnO3 films using external

electric fields. Three-to-four orders of magnitude enhance-ment in optical second harmonic response from a 900 nmincident light was observed at room temperature under exter-nal fields of �707 V/mm. Large nonlinear refraction (nI)and absorption coefficients (� I) were measured as well. Fur-ther investigations are presently underway in understandingthe origin of these nonlinear optical effects.

We would like to acknowledge valuable discussions withDr. Nicola Spaldin, and the help of Dr. Isli An and Chi Chenwith ellipsometry. This work was supported by a grant fromthe National Science Foundation through Grant Nos. DMR-9984691 and DMR-0103354.

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Cheetham, and C. N. R. Rao, Solid State Commun. 122, 49�2002�.

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