Self-assembly and properties of domain walls in BiFeO3 layers grown via molecular-beam epitaxy

Bismuth ferrite layers, ∼ 200-nm-thick, are deposited on SrRuO 3 -coated DyScO 3 (110) o substrates in a step-ﬂow growth regime via adsorption-controlled molecular-beam epitaxy. Structural characterization shows the ﬁlms to be phase pure with substrate-limited mosaicity (0.012 ○ x-ray diffraction ω -rocking curve widths). The ﬁlm surfaces are atomically smooth (0.2 nm root-mean-square height ﬂuctuations) and consist of 260-nm-wide [ 1¯11 ] o -oriented terraces and unit-cell-tall (0.4 nm) step edges. The combination of electrostatic and symmetry boundary conditions promotes two monoclinically distorted BiFeO 3 ferroelectric variants, which self-assemble into a pattern with unprecedentedly coherent periodicity, consisting of 145 ± 2-nm-wide stripe domains separated by [001] o -oriented 71 ○ domain walls. The walls exhibit


I. INTRODUCTION
The control of topological textures within the lattice, charge, and spin order parameters of multiferroic materials offers the possibility to realize emergent behaviors that transcend the functionality of any spatially uniform host material. Indeed, ferroelectric domain walls are already employed in various applications spanning nonlinear optics, 1,2 nanoelectronics, 3 and nonvolatile memories. 4,5 Epitaxial layers of the room-temperature multiferroic BiFeO 3 are a well-established material platform for hosting domain walls with functional properties. 6 To date, the overwhelming majority of BiFeO 3 films are produced using far-from-equilibrium growth techniques incorporating ion irradiation during film growth, including magnetron sputter deposition 7 and pulsed-laser deposition. 8 When uncontrolled, ions spawn unintended defects impacting domain wall morphology and properties. 9,10 Molecular-beam epitaxy, in contrast, provides an alternative synthesis approach which employs thermalized molecular fluxes. 11 Near-equilibrium growth regimes free from the bombardment of energetic ions 12 are expected to engender subtler defect profiles, 13 desirable for the fabrication of nonlinear optical elements as well as for understanding leakage mechanisms in nonvolatile ferroelectric-based memories.
In this letter, we employ molecular-beam epitaxy 11,14 to grow commensurately strained BiFeO 3 /SrRuO 3 /DyScO 3 (110)o epitaxial heterostructures (the o subscript designates orthorhombic indices in the nonstandard Pbnm setting) and demonstrate the self-assembly of The growths are carried out using molecular-beam epitaxy in an adsorption-controlled regime. Ts are substrate temperatures, estimated using a thermocouple in the vicinity of, but not in direct contact with, the growth surface. P are partial pressures during deposition of an oxidant comprised of approximately 20% O 2 and 80% O 3 , produced by controllably degassing ozoneinfused silica beads. J A=Bi,Sr and J B=Fe,Ru are molecular fluxes, measured using a calibrated quartz-crystal microbalance. T A=Bi,Sr and T B=Fe are effusion cell temperatures (Ru is supplied from an electron-beam source). R are film growth rates. ferroelectric BiFeO 3 domain walls with unprecedentedly long-range order. The walls exhibit the combination of enhanced conductivity and electrical rectification. We anticipate that the results discussed here may prove useful for improving the fabrication of nonlinear optical and nanoelectronic devices.

A. Film growth
BiFeO 3 /SrRuO 3 /DyScO 3 (110)o heterostructures are grown without breaking vacuum in a Veeco GEN10 molecular-beam epitaxy system with a chamber base pressure of 1 × 10 −8 Torr using deposition conditions summarized in Table I. For SrRuO 3 growths, ruthenium is supplied in abundance with a ruthenium-to-strontium flux ratio of J Ru /J Sr > 2. At a growth temperature of 780 ○ , the excess ruthenium oxidizes forming volatile RuOx species which continuously desorb from the growth surface resulting in single-phase SrRuO 3 layers. 15 BiFeO 3 is grown in an oxidant comprised chiefly of ozone (and 20% oxygen). This approach, which represents an evolution of increasing oxidation environments, 14,16-20 helps to suppress the formation of oxygen vacancies, responsible for engendering mobile electrons 21 and ensures the oxidation of bismuth. 14 Additionally, high bismuth-to-iron flux ratios (J Bi /J Fe ∼ 16) are employed to compensate the loss of volatile BiOx species at the high homologous growth temperature utilized (Ts ∼ 650); the desorption of bismuth oxides during BiFeO 3 deposition is analogous to that of ruthenium oxides during SrRuO 3 growth. Although multiple films were grown and all findings presented here (and in the supplementary material) are obtained from a single film, for which Rutherford back scattering spectrometry results yield a film bismuth-to-iron molar ratio equal to 0.98 ± 0.07. The deposition of stoichiometric layers, containing equal concentrations of bismuth and iron, combined with long diffusion lengths for surface adatoms promote films with long-ranged crystallographic and ferroic order.

B. Film structural perfection
The structural perfection of BiFeO 3 layers deposited on SrRuO 3 -coated DyScO 3 (110) substrates is established using the combination of x-ray diffraction (XRD), atomic force microscopy (AFM), and scanning transmission electron microscopy (STEM). An XRD θ−2θ scan (see Fig. S1 of the supplementary material) collected between 10 ≤ 2θ ≤ 110 ○ using Cu Kα 1 radiation (wavelength λ = 0.154 06 nm) exhibits only 00lp film and hh0o substrate reflections (the p subscript refers to pseudocubic indices); the absence of additional reflections evince a phase-pure single crystalline film.   Fig. 1(a), insert]. The FWHM value measured for the BiFeO 3 reflection is the same as that for the underlying DyScO 3 and demonstrates that the film structural perfection is limited by the intrinsic mosaicity of the substrate. From lattice-resolution STEM images obtained along the 110 o zone axis near BiFeO 3 /SrRuO 3 [ Fig. 1(c)] and SrRuO 3 /DyScO 3 [ Fig. 1(d)], we find atomically abrupt heterostructure interfaces with commensurate pseudo cube-on-cube crystallographic stacking: AFM height images, including Fig. 1(b), evince smooth surfaces (0.2 nm root-mean-square height fluctuations) over macroscopic distances (≳20 µm) with motifs including unit-cell-tall (0.

C. Symmetry breaking and wall self-assembly
To investigate the breaking of cubic symmetries and the emergence of topological features within BiFeO 3 , we perform XRD reciprocal space maps (RSM), lateral (LPFM), and vertical (VPFM) piezoforce microscopy (PFM), and bright-field transmission electron microscopy (BF-TEM). 53 RSM analyses carried out about film peaks reveal that the BiFeO 3 103p and 113p family of reflections are split into doublets and triplets [ Fig. 2(a)], consistent with monoclinically distorted pseudocubic unit cells that have been sheared along ⟨110⟩ p . 26 The descent in symmetry from the cubic perovskite to the monoclinic structure is accompanied by polar ⟨111⟩ p cation displacements and antiferrodistortive a − a − a − antiphase FeO 6 octahedral rotations. 27 The symmetry-breaking process engenders four structural and eight ferroelectric variants, represented by r ± ψ , in which the subscript ψ identifies the azimuthal orientation of the in-plane polarization component and the superscript ± selects the out-of-plane component. Analyzing the intensity variation of the 103p and 113p family of peaks [see Fig. 2(a)] reveals that the BiFeO 3 layer consists primarily of two structural variants, r +45 ○ and r −45 ○ , which develop due to the orthorhombic symmetry of the DyScO 3 substrate. 28 The volume fraction occupied by the dominant vs secondary structural variants is estimated from ratios of RSM peak integrals to be ≳0.99. These findings are corroborated by PFM analyses [e.g., Fig. 2(b)], which exhibit a two-level contrast.
To determine the out-of-plane polarization orientation, ferroelectric domains are locally poled by applying ±15 V tip biases to a conductive probe while rastering it across the sample surface. Plan-view VPFM images (see Fig. S3 of the supplementary material) demonstrate that in regions where the tip is negatively biased, changes in contrast are observed due to the polarization being poled toward the tip. That the out-of-plane polarization component of as-deposited layers is homogeneously aligned toward the substrate is consistent with the A-site termination of our SrRuO 3 electrode, which encourages the BiFeO 3 polarization to orient in such a way that a depolarization field develops to counteract a built-in field associated with the valence states of each perovskite layer. 29 Between regions of uniform polarization are domain walls, two-dimensional topological field excitations that emerge when the potential energy describing the order parameter consists of deep valleys and disconnected ground states. 30 Plan-view LPFM [ Fig. 2(b)], cross-sectional VPFM [ Fig. 2(c)], and cross-sectional BF-TEM micrographs [Figs. 2(d) and 2(e)] show that the domain walls in our as-grown BiFeO 3 layers self-assemble into a periodic quasi-one-dimensional stripe array along DyScO 3 [001]o with interwall separations measuring 145 ± 2 nm. The walls are found to be inclined ∼45 ○ relative to the surface normal [Figs. 2(c)-2(e)], in agreement with geometric considerations for 71 ○ walls (the wall type is labeled based on the angle formed between polarization vectors in adjacent domains) residing on {110}p planes. 31,32 In previous work, it was shown that the inclination angle and the wall type can be controlled by changing boundary conditions 28 and film thicknesses; 33 similarly, the wall orientation can be tuned through the application of biaxial in-plane strain 34,35 from ⟨100⟩ p for 1.5% ≲ m ≲ 0.3% to ⟨110⟩ p for m ≈ 3.6%, in which m is the lattice mismatch between the BiFeO 3 film and the underlying substrate. [35][36][37][38][39] The stripe domains are occasionally seen to terminate within the film, giving rise to one-dimensional topological defects analogous to dislocations [the dotted circle in Fig. 2(b)]. Despite the one ARTICLE scitation.org/journal/apm defect that we observe in a ≳ 20 µm field of view, the structural perfection of the pattern realized here represents the most wellordered self-assembled array of ferroelastic domain walls produced to date. 33,35,36,[40][41][42][43][44][45][46] D. Electrical properties of walls The electrical properties of the BiFeO 3 /SrRuO 3 /DyScO 3 (110)o heterostructure are investigated using conductive AFM (c-AFM), by grounding the bottom SrRuO 3 electrode and rastering a biased tip in contact with the sample surface while recording through-layer currents. Typical results, shown in Figs. 3(a)-3(d), establish that no current flows for biases V b ≤ 1 V (detectable current limit ∼1pA). In the 2 ≤ V b ≤ 3 V regime, the current is preferentially emitted at domain walls, where the conductivity is two to ten times higher than at domains [see the current histogram in Fig. 3(e)]. At a bias of V b = 4 V, the corresponding electric field across the film, 180 kV/cm, exceeds the coercive field of bismuth ferrite, ∼170 kV/cm. 44 As a consequence, c-AFM images acquired under these conditions, including Fig. 3(d), contain contributions from both resistive and displacement currents as a result of domains being locally poled.
Macroscopic current-voltage I(V) measurements, obtained by integrating the c-AFM measurements over a 5 × 5 µm 2 area, Fig. 3(f), highlight the existence of rectifying behavior, agreeing with previous reports. 9,10 The enhanced conduction at 71 ○ domain walls can be understood to result from a combination of effects which include a reduction in the BiFeO 3 conduction band energy and an accumulation of intrinsic defects, 10,47 including double-donor 21 oxygen vacancy states, near the walls. The asymmetric response, which produces the rectifying behavior, is attributed to the combination of dissimilar emission barrier heights across the film/electrode and film/tip interface as well as to the presence of an out-of-plane film polarization which breaks up/down symmetry. 48 For the measurement conditions employed, Joule heating is estimated 49,51,52 to cause a temperature rise of only ∼0.03 K; for reference, electric fields are expected to trigger breakdown in perovskite oxides only above ∼2000 kV/cm, 50 five to ten times larger than the largest values applied here.

III. CONCLUSIONS
The ability to produce ordered walls with well-ordered periodicity, as demonstrated here, could have immediate technological implications. For example, domain walls are already lithographically introduced into commercial nonlinear crystals to help satisfy momentum conservation in three-photon interactions. These processes, which include sum frequency generation and parametric down conversion, are essential for up-converting laser frequencies as well as entangling photons for quantum computation. Being able to produce arrays of walls which self-assemble into high-fidelity patterns could provide a bottom-up alternative for the fabrication of such nonlinear optical elements. Additionally, the perfection of the patterns realized here reflects an intrinsically low concentration of defects. The realization of films with low defect density are necessary to produce energy efficient memories with ferroic orders that can be easily switched at low coercive fields without wall pinning. Finally, the 71 ○ domain walls are shown to simultaneously exhibit enhanced conductivity and electrical rectification-attributes which are desirable for emerging nanoelectronic applications, including domain wall memories. 4

SUPPLEMENTARY MATERIAL
Additional film characterization, including XRD θ−2θ, RHEED, and VPFM, is provided in the supplementary material.