Multiferroic Domain Dynamics in Strained Strontium Titanate

A. Vasudevarao,1 A. Kumar,1 L. Tian,1 J. H. Haeni,1 Y. L. Li,1,2 C.-J. Eklund,4 Q. X. Jia,2 R. Uecker,3 P. Reiche,3

K. M. Rabe,4 L. Q. Chen,1 D. G. Schlom,1 and Venkatraman Gopalan1,*1Department of Materials Science and Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, USA

2MPA-STC, Los Alamos National Lab, Los Alamos, New Mexico 87545, USA3Institut fur Kristallzuchtung, Max-Born-Straße 2, 12489 Berlin (Adlershof), Germany4Department of Physics and Astronomy, Rutgers University, New Jersey 08854, USA

(Received 19 June 2006; published 21 December 2006)

Multiferroicity can be induced in strontium titanate by applying biaxial strain. Using optical secondharmonic generation, we report a transition from 4=mmm to the ferroelectric mm2 phase, followed by atransition to a ferroelastic-ferroelectric mm2 phase in a strontium titanate thin film. Piezoelectric forcemicroscopy is used to study ferroelectric domain switching. Second harmonic generation, combined withphase-field modeling, is used to reveal the mechanism of coupled ferroelectric-ferroelastic domain wallmotion. These studies have relevance to multiferroics with coupled polar and axial phenomena.

DOI: 10.1103/PhysRevLett.97.257602 PACS numbers: 77.84.Dy, 42.70.Mp, 77.80.Dj, 77.80.Fm

Multiferroic materials with multiple order parametersare attracting significant interest due to the possibility of arich array of coupled phenomena such as ferroelastic-electric-magnetic, piezoelectric-magnetic, andelectromagneto-optic effects [1–3]. At first glance, stron-tium titanate would appear an unlikely candidate for amultiferroic. Bulk SrTiO3 is a cubic (m�3m) centrosymmet-ric perovskite at room temperature; it undergoes a nonpolarantiferrodistortive (AFD) phase transformation to a te-tragonal point group 4=mmm at �105 K and exhibitsindications of a frustrated ferroelectric (FE) transition at�20 K, which it never completes [4]. First principlescalculations [5] and thermodynamic analysis [6,7] havesuggested, however, that external strain can induce ferro-electricity. This prediction has been experimentally con-firmed recently in a SrTiO3 thin film strained in biaxialtension [8]. The multiferroic nature of strained strontiumtitanate, i.e., the coexistence of ferroelectric and ferroelas-tic domains, is unique in many respects. It is induced byexternal strain. Further, unlike other ferroelectric-ferroelastics, two independent primary order parametersexist: a polar ferroelectric order parameter p and an axialantiferrodistortive rotation order parameter q [7,9–11].Hence, depending on the strain, the ferroelectric transitiontemperature can precede or succeed the ferroelastic tran-sition temperature [7]. From a symmetry perspective, theSrTiO3 multiferroic domain structure has striking similar-ities with, and, hence, of broader relevance to, other multi-ferroics with coexisting polar and axial phenomena, suchas materials that exhibit coexisting ferroelectricity (polarproperty) and antiferromagnetism (axial property) [3,12].

This Letter focuses on the domain structure and phasetransitions in a 500 �A thick SrTiO3 thin film grown on a(110) DyScO3 substrate with a 0.94% uniform in-planebiaxial tensile strain in the growth plane [8]. (This is thesame film that was studied by Haeni et al. in Ref. [8].)Thermodynamic calculations predict a FE transition tem-

perature range of 277� 100 K and an AFD transition at�111–150 K [7,13]. First principles calculations wereperformed for this strain value with an Amm2 space groupsymmetry in the FE phase and an Ima2 (No. 46) symmetryin the multiferroic (FE� AFD) phase. In the multiferroicphase, the optimized ground state structure has a ferroelec-tric polarization of p� 0:18 C=m2 in the h110ip directionin the growth plane and a corresponding antiferrodistortiverotation of the oxygen octahedra by 5.9� about the vectorqh110ip, where the subscript p refers to the pseudocubicMiller index, showing that the combination of the twodistortions is lower in energy than either distortion alone.In this phase, there are 8 types of coexisting FE� AFDdomains [see Fig. 1(d)], which we classify into 4 types ofdomain classes: x� , x� , y� , and y� , each comprisedof two types of domains. Denoting the directions x ��110�p, y � �1�10�p, and z � �001�p, the order parametersin the 4 types of domain classes are x� : px; 0; 0; qx; 0; 0and px; 0; 0;�qx; 0; 0; x� : �px; 0; 0;�qx; 0; 0 and�px; 0; 0; qx; 0; 0; y� : 0; py; 0; 0; qy; 0 and0; py; 0; 0;�qy; 0; and y� : 0;�py; 0; 0; qy; 0 and0;�py; 0; 0;�qy; 0. These domains are separated by180� AFD (FE) domain walls across which p (q) remainsthe same, but q (p) rotates by 180�, and 90� (180�) FE�AFD domain walls across which both p and q rotate by 90�

(180�). In the pure FE phase, the order parameter q dis-appears, resulting in 4 types of domains and 2 types (90�

and 180�) of ferroelectric domain walls.We employ optical second harmonic generation (SHG)

to study domain structures and phase transitions [14,15].SHG involves the conversion of light (electric field E!) at afrequency ! into an optical signal at a frequency 2! by anonlinear medium, through the creation of a nonlinearpolarization P2!

i / dijkE!j E

!k [16]. The light source for

SHG experiment was a Ti:sapphire laser with a pulse widthof 140 femtoseconds, repetition rate of 1 kHz, and a

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wavelength of 800 nm. A fundamental wave of 800 nm wasincident from the substrate side in normal geometry. Itspolarization direction, at an angle � from the y axis, wasrotated continuously within the plane of the film [seeFig. 1(a)]. The intensity I2!

j of the output SHG signal at400 nm wavelength from the film was detected along eitherj � x; y polarization directions by a photomultiplier tube.The resulting polar plots of the SHG intensity at 123 K areshown in Fig. 2. A reference study of a bare (110) DyScO3

substrate without any film yielded no SHG intensity withinthe detection limits. Using SHG, the point group of thisfilm at 223 K (ferroelectric phase) was determined to bemm2, and the ferroelectric polarization p was found to bealong the h110ip axes in the film plane [7], consistent withfirst principles calculations. A theoretical analysis of thisfilm system yields the following expression for the SHGintensity [17]:

I2!j � K1;jsin22�� K2;jsin2�� K3;jcos2�2

� K4;jsin2�� K3;jcos2� sin2�; (1)

where Ki;j are constants given by:

K3;x �1

K3;y�d310

d33; (2)

�1

K3;y

�2�K1;x

K2;x

K1;y

K2;y

��

�d150

d33

�4; (3)

�K1;xK2;y

K2;xK1;y

�K2

3;y �

��Ay�Ax

�4; (4)

where d310 � d31 � d32=2 and d15

0 � d15 � d24=2.Two of these are ratios of nonlinear coefficients [d31

0=d33

(including its sign) and d150=d33 (absolute value only)] that

are independent of domain microstructure. The third quan-tity, �Ax=�Ay, is a microstructural quantity, where �Ax �Ax� � Ax� and �Ay � Ay� � Ay� are the net area frac-tional biases in the x and y directions, respectively. Theinverse relation between K3;x and K3;y, stipulated byEq. (2), can be seen to hold at all temperatures studied[Fig. 2(c)], showing that the symmetry is mm2 and thepolarization is oriented along h110ip directions in the 80–298 K range studied. These properties also show an anom-aly in the range of Tmax � 250–273 K, consistent with thepeak in the dielectric response � reported in Ref. [8].Noncentrosymmetry and polarization Ps exist well up toat least Tb � 323–328 K, where finally the SHG signal isbelow our detection limit. The SHG signal in Fig. 1(c) also

FIG. 2 (color online). (a),(b) Polar plots of SHG intensity[I2!j �[ at T � 123 K. (a) I2!

y and (b) I2!x , where directions x �

�110�p and y � �1�10�p are defined in the inset. The circles arethe measured data, and the solid curves are the theoretical fitsbased on Eq. (1). (c) I2!

y � � 0� vs T where the dark (hollow)squares are the cooling (heating) cycle. The anomaly around 148and 173 K are highlighted with spline curves. The variation ofratios of nonlinear optical coefficients with temperature is shownon the right axis. The circles (diamonds) represent K3;y (K�1

3;x ).

FIG. 1 (color online). Schematic showing Sr, O, and Ti atomicpositions and order parameters p and q in various phases ofstrained SrTiO3. (a) Paraelectric 4=mmm phase, (b) ferroelectricmm2 phase, (c) FE and AFD mm2 phase. Circles with crosses(dashes) are oxygen ions moving into the plane of the Letter (inthe dash direction). (d) Domains in the FE� AFD phase show-ing an AFD and coupled FE� AFD domain wall.

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shows a reproducible anomaly at TAFD � 148 K (cooling)to TAFD � 173 K (heating). This corresponds to the anti-ferrodistortive phase transition in SrTiO3, consistent withthermodynamic predictions [7,12]. The slight drop in theSHG intensity at the AFD transition could arise fromdoubling of the domain variants from 4 to 8 in the multi-ferroic phase or a change in the magnitude of d33 across thephase transition. The symmetry is observed to remainmm2across the AFD transition, as predicted.

The difference in the temperatures at which the peak inthe dielectric constant and the peak in the d33=d31

0 ratiooccurs (Tmax � 250 K) versus where noncentrosymmetrywas lost (Tb � 323 K) can arise from ferroelectric relaxorbehavior as recently reported [18], as well as inhomoge-neously strained regions. The Tb � 323–328 K transitionmay then be the Burns temperature [19]. Between Tmax andTb, polarization in a relaxor ferroelectric is normally ex-pected to exist as glassy nanopolar regions without well-defined domains or domain walls. This is consistent withpiezoelectric force microscopy (PFM) at room temperature(298 K), which reveals that the majority of the film isfeatureless with low piezoelectric signals. In the lateralPFM mode, x� and y� domains can be imaged as shownin Fig. 3(b). A shear strain "5 arising from the d15 coeffi-cient will give lateral displacements in the x-z (y-z) planesin the x� (y� ) domains, giving different lateral contrastsbetween these domains [20]. Some localized regions (esti-mated to be in �5% of the film area), however, revealferroelectric domains at room temperature as seen inFig. 3(b), indicating slight inhomogenity in strain. Uponheating, the piezoelectric response starts to disappear par-tially at 40 �C [Fig. 3(c)] and completely at 60 �C[Fig. 3(d)], and the domain features reappear on cooling[Fig. 3(e)] back to room temperature. The domains arepartly bounded by �5 nm high surface ridgelike featuresseen in topography [see Fig. 3(h)], within which theyreappear after cooling [Fig. 3(e)]. Although these filmshave the narrowest dielectric constant versus temperature

FIG. 3 (color online). Lateral PFM images of the same strainedSrTiO3 thin film. (a) Topography of the film surface. PFM imageof the film (b) at room temperature, 298 K, (c) heated to 313 K,(d) heated to 333 K, and (e) cooled from 333 K back to roomtemperature. PFM response as the film was poled along �110�pwith (f) �1 kV=mm and (g) �1 kV=mm. (h) PFM image of thefilm at room temperature. The white lines highlight the cracks inthe film as seen from the topographic image. The color bar [inset(b)] applies to images [(b)–(g)] and the length scale [inset (c)],and the directions [inset (f)] apply to all panels.

ppp

-2 -1 0 1 24.0

4.2

4.4

4.6

4.8

5.0

5.2

1.9

2.0

2.1

2.2

2.3

2.4A

y2(a

.u.)

Ax2

(a.u

.)

-1.0 -0.5 0.0 0.5 1.00.50

0.75

1.00

1.25

1.50

0.75

1.00

1.25

1.50

1.75

Ay2

(a.u

.)

Ax2

(a.u

.)

olt

(b)

p]101[

q q q

(c) (d) (e)

(f) (g) (h)

p]110[

(a)

ppp

-2 -1 0 1 24.0

4.2

4.4

4.6

4.8

5.0

5.2

1.9

2.0

2.1

2.2

2.3

2.4A

y2(a

.u.)

Ax2

(a.u

.)

-1.0 -0.5 0.0 0.5 1.00.50

0.75

1.00

1.25

1.50

0.75

1.00

1.25

1.50

1.75

Ay2

(a.u

.)

Ax2

(a.u

.)

olt

-2 -1 0 1 24.0

4.2

4.4

4.6

4.8

5.0

5.2

1.9

2.0

2.1

2.2

2.3

2.4A

y2(a

.u.)

Ax2

(a.u

.)

olt-1.0 -0.5 0.0 0.5 1.0

0.50

0.75

1.00

1.25

1.50

0.75

1.00

1.25

1.50

1.75

Ay2

(a.u

.)

Ax2

(a.u

.)

olt

(b)

p]101[

q q q

(c) (d) (e)

(f) (g) (h)

p]110[

(a)

FIG. 4 (color online). Domain area fractions [I2!x 0

� / �A2x;

I2!y 0

� / �A2y] as a function of applied voltage along the

�x�110�p direction at (a) T � 123 K and (b) T � 223 K.Phase-field modeling of the evolution of FE [(c)–(e)] and AFD[(f)–(h)] domain morphologies with electric field alongx�110�p.

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peaks reported for SrTiO3 or Ba;SrTiO3 films [18], thewidths are still about 3 times broader than Ba; SrTiO3

single crystals [21]; hence, local inhomogeneous strainsand domains can arise.

The bright and dark regions of the PFM signal inFig. 3(b) can be attributed to the y� and x� domains,respectively. The domain walls [not related to topography;see Fig. 3(h)] separating these bright and dark domains areparallel to the h100ip direction, which correspond to 90�

domain walls. These walls can be influenced by externalelectric fields. Figure 3(e) shows that cooling has producedpredominantly y� domains. Two gold pads, 1000 �A thickand 1.3 mm apart, were sputtered on the film in its planesuch that an external electric field could be applied alongthe �x�110�p direction. When an electric field of�1 kV=mm is applied along the �x direction, they trans-form to predominantly x� domains [Fig. 3(f)] and thenpartially reverse back to y� domains after applying�1 kV=mm along the �x direction [Fig. 3(g)]. Theseresults indicate 90-degree ferroelectric domain wall mo-tion. Figures 4(a) and 4(b) show that both �A2

x and �A2y

change in response to an electric field of �1 kV appliedacross the gap. This indicates that the electric field alongthe �x direction switches domains along the �y directionas well, indicating motion of 90� domain walls that couplex� domains to the y� domains. This mechanism is op-erative at all temperatures including the multiferroic phase,where SHG indicates the motion of coupled 90�

ferroelectric-ferroelastic domain walls.Phase-field simulations [7] in the multiferroic phase

[Figs. 4(c)–4(h)] clearly show that, under an electric field,the area fraction of x� domains increases, while that of x�domains decreases through a motion of coupled 90�

ferroelectric-ferroelastic domain walls. The pure 180�

AFD walls [see Fig. 1(d)] within a single polarizationdomain state are degenerate in energy even under anelectric field and remain with statistically equal popula-tions [Figs. 4(f)– 4(h)]. The pure AFD domain walls withinthe polarization domain states not favored by the externalfield disappear, however, primarily as the 90� walls sweepthrough that domain state.

In conclusion, a unique form of multiferroicity, namely,an induced ferroelectric-antiferrodistortive phase instrained SrTiO3, is reported. For the first time, ferroelectricdomains were directly imaged at room temperature andabove in this material using PFM. In situ SHG underexternal fields show evidence for the movement of coupledferroelectric-ferroelastic 90� domain walls in the multi-ferroic phase, in agreement with phase-field modeling.From a symmetry perspective, the domain structure and

dynamics in this ferroelectric-antiferrodistortive systemcould have relevance to expected domain structures in aferroelectric-(anti)ferromagnetic system with two phasetransitions.

We thank C. Fennie for his help in performing firstprinciples calculations. The financial support from NSFunder Grants No. DMR-0122638, No. DMR-0507146,No. DMR-0512165, and No. DMR-0349632 and NSF-MRSEC center at Penn State is gratefully acknowledged.L. Q. C. also acknowledges support from the GuggenheimFoundation and Los Alamos National Labs. This work waspartially supported as a Laboratory Directed Research andDevelopment Project at Los Alamos National Laboratoryunder the United States Department of Energy.

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