Observation of Electric-Field-Induced Structural Dislocations in a Ferroelectric Oxide

Dislocations are 1D topological defects with emergent electronic properties. Their low dimensionality and unique properties make them excellent candidates for innovative device concepts, ranging from dislocation-based neuromorphic memory to light emission from diodes. To date, dislocations are created in materials during synthesis via strain fields or flash sintering or retrospectively via deformation, for example, (nano)-indentation, limiting the technological possibilities. In this work, we demonstrate the creation of dislocations in the ferroelectric semiconductor Er(Mn,Ti)O3 with nanoscale spatial precision using electric fields. By combining high-resolution imaging techniques and density functional theory calculations, direct images of the dislocations are collected, and their impact on the local electric transport behavior is studied. Our approach enables local property control via dislocations without the need for external macroscopic strain fields, expanding the application opportunities into the realm of electric-field-driven phenomena.


■ INTRODUCTION
The presence of dislocations transcends condensed matter research and gives rise to a diverse range of emergent phenomena, 1−6 ranging from geological effects 7 to light emission from diodes. 8 Classically, dislocations have often been regarded as imperfections in otherwise perfectly ordered crystals that are detrimental to electronic functionality. 9,10 However, very recently, there has been growing interest in the properties of individual dislocations because they have different symmetries, and therefore different properties, from those of the surrounding material. 11 Examples of emergent functional physical properties include locally enhanced conductivity, 12 ferromagnetic order in antiferromagnets, 13 redox-based resistive switching behavior, 4 and trapping of light. 14 Because of the low dimensionality of dislocations, which makes them highly stackable, and their unique properties, dislocations are now perceived as promising atomic-scale entities for nextgeneration device applications. 10,11 Despite their exciting application potential, there are key limitations to the technological development of dislocations: The most critical is the control of their formation. Currently, dislocations are created by strain engineering, predominantly in one of two ways: either strain fields during growth, so that dislocations form to release the strain, 15−17 or postgrowth via applied stress, 18 for example, by nanoindentation. 19−22 Although strain engineering is a highly efficient tool for creating dislocations, it is challenging to alter the properties of a material exactly via strain fields on the local scale. This is particularly problematic after a material has been implemented into a device architecture. Aside from strain, flash sintering has been applied to produce defects, including structural dislocations. This approach is particularly promising regarding the production of defect-rich samples, but it lacks the nanoscale control required for technological applications. 23 Here we use electric fields to create partial dislocations in a ferroelectric material with nanoscale spatial precision, altering the structure and the electronic transport behavior where the field was applied. The hexagonal manganite Er(Mn,Ti)O 3 is chosen as the model system (see the Materials and Methods for details), 24,25 but similar behavior is expected in structurally equivalent systems such as hexagonal gallates, indates, and ferrites.
is shown in the piezoresponse force microscopy (PFM) image in Figure 1a. The PFM data demonstrate that the two possible 180°polarization domains, +P and −P, form six-fold meeting points that are characteristic of hexagonal manganites. 26,27 After mapping the domain structure of Er(Mn,Ti)O 3 , we apply −60 V (for 5 s) to the back electrode while keeping the probe tip static. Using a simple point-charge approximation (E = V/r tip ), the biased static tip generates an electric field of ∼6 MV/cm. 28,29 Subsequent conductive atomic force microscopy (cAFM) images (taken with +45 V) reveal a local modification of the transport behavior, manifesting as an ellipsoidal area of enhanced conductance (gold, in Figure 1b) with an insulating core: The core of reduced conductance occurs directly below the position of the AFM tip, that is, the position of the maximum electric field. A scanning electron microscopy (SEM) image of the same region as in Figure 1b is presented in Figure 1c, which demonstrates that the area of enhanced conductance in the cAFM scan correlates with bright contrast in SEM, associated with an increased yield of secondary electrons. A direct comparison of the SEM and cAFM images is given by the cross-sectional profiles in Figure  1d, showing a clear correlation. Figure 1 thus reveals that the electrically modified region displays two regimes: (i) a broader area with enhanced conductance due to anti-Frenkel defects, as reported in ref 30, and (ii) a highly localized area with reduced conductance. In contrast with the enhanced conductance in regime (i), the suppressed conductance in regime (ii) cannot be explained by the same defect formation process, 30 indicating a different microscopic origin.
Atomic-Scale Imaging of Defects. To investigate the underlying microscopic effect, we study the atomic structure in the electrically modified region using transmission electron microscopy (TEM) techniques on a focused ion beam (FIB) prepared lamella. (See the Materials and Methods.) A brightfield overview image of a lamella, prepared to cross-section the electrically modified region in Figure 1, is given in Figure 2a. The data show that the crystal structure has changed in a limited region around the position where the cAFM tip was placed (indicated schematically). This modified region has a lateral extension of ∼160 nm and protrudes ∼35 nm into the depth of the sample, whereas the rest of the crystal structure has remained in the as-grown state. To discern the differences between the modified region and the as-grown state, 26,30,31 high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) images of the two regions are presented in Figure 2b,c, respectively. In Figure 2b,c, the bright dots correspond to Er and Mn atomic columns; the heavier Er atoms give brighter dots than the lighter Mn atoms. The HAADF-STEM of Figure 2c shows that the Er layers are disrupted in several places and appear to be displaced, seemingly merging with the Mn layers in the projected image. This disruption of the lattice only occurs directly underneath the cAFM tip, and no such alterations of the lattice are seen in the wider crystal ( Figure 2a). To visualize associated local changes in the lattice periodicity, Fourier filtering is applied, as presented in Figure 2d. This treatment reveals discontinuities in the lattice periodicity and the presence of edge dislocations, marked by the green and red circles in Figure 2d. An enlarged section with a higher resolution of the feature in the red box in Figure 2c is shown in Figure 2e. On the left side of the dislocation in Figure 2e, the HAADF-STEM image shows the normal sequence of alternating Er and Mn layers, whereas the right side of the image shows Er columns that continuously merge into Mn columns and vice versa. We note that there is no clear interface where Er columns swap with Mn columns, as the interface is inclined to the [001] viewing direction. The general possibility to stabilize such stacking faults is not surprising, 32 as their growth-induced formation has been reported in hexagonal manganites and ferrites. 33−35 In contrast with previous work, however, the stacking faults in our system are generated postgrowth and with nanoscale spatial precision by the application of an electric field. We note that the sample used in this work has been cut from the same single crystal studied in, for example, refs 24 and 30 and discussed in, for example, refs 36 and 37. During the previous extensive high-resolution TEM investigations, no partial dislocations were observed in the ErMnO 3 crystal lattice, corroborating that such defects are not intrinsic to the lattice or generated by the applied preparation methods.
To evaluate the stability of the defect structure resolved in Figure 2e, we model the dislocated lattice using density functional theory (DFT), as illustrated in Figure 2f. To look for stable states, we consider the isostructural system YMnO 3 (refs 31 and 38), where multiple 240-atom 1 × 8 × 1 supercells were initialized in the high-symmetry P6 3 /mmc phase with different dislocation configurations and relaxed into the polar state P6 3 cm until the forces on all of the atoms were <0.01 eV Å −1 . The analysis of YMnO 3 instead of ErMnO 3 is standard Nano Letters pubs.acs.org/NanoLett Letter practice, as their structural and chemical properties are very similar (see Table S1 and Figure S1), but the absence of f electrons significantly reduces the computational cost. 31,38,39 The DFT calculations show that a stable dislocated structure exists when the lattice is displaced by c/4 and a/3 (or one of the six symmetry equivalent directions, perpendicular to the unique axis), as shown in Figure 2f. The calculated dislocation configuration is in excellent agreement with our HAADF-STEM data ( Figure S2 shows the dislocated structure viewed down the [110] direction, which is symmetry equivalent to [1̅ 00]), leading us to the conclusion that the merging features in Figure 2e correspond to a stacking fault between two partial dislocations.
On the basis of the DFT calculations, we can predict the expected atomic pattern when we image along other crystallographic directions, allowing us to conduct an independent test experiment. The calculated crystal structure viewed along different directions, with and without the dislocated structure, is presented in Figure S3, including the superposition of the dislocated structure and the unperturbed Er(Mn,Ti)O 3 structure with space group symmetry P6 3 cm. 40 This superposition accounts for the depth convolution present within TEM lamellas with finite thickness. A representative HAADF-STEM image recorded along the [001] direction of an Er(Mn,Ti)O 3 lamella with electrically modified regions (analogous to Figure 1) is presented in Figure 3a. As in Figure 2, the modification of the lattice only occurs in the area exposed to the high electric field. The HAADF-STEM image shows the Er atoms as bright dots, reflecting the characteristic pattern associated with the P6 3 cm space group symmetry of the crystal sketched in Figure S3. The latter is confirmed by the high-resolution HAADF-STEM image in Figure 3b, taken from the area represented in red in Figure 3a. On closer inspection, however, local deviations from the ideal structure are observed, as shown by the HAADF-STEM image in Figure 3c (obtained in the area represented in green in Figure 3a). Here the Er atoms are found to form a close-packed honeycomb-like structure, as illustrated by the schematic overlay, in accordance with the DFT-predicted structure. (See Figure S3; blue and gold dots in the overlay represent Er atoms from volumes on either side of the stacking fault.)  Nano Letters pubs.acs.org/NanoLett Letter Calculated Defect Properties. After establishing the presence of the structural defects in the region of reduced conductance, we calculate the associated formation energy. Note that because of the thermal stability of the structural ground state and the ferroelectric polarization, 41−43 finite temperature effects would be subtle at room temperature and would not change the results qualitatively, and hence they are not considered. For the partially dislocated structure in Figure  2f, we find a formation energy of ∼755 mJ m −2 , which is only about seven times higher than for the charged domain walls, which naturally occur in the hexagonal manganites. 44 The DFT calculations further show that the dislocated structure significantly alters the electrostatic potential. To quantify this, we calculate the planar average across the supercell in Figure 4a, which shows a decrease in the potential energy of ∼0.75 eV (∼1/2E g ) compared with the bulk, corresponding to bound negative charges associated with the stacking fault. However, in contrast with the negatively charged tail-to-tail domain walls in hexagonal manganites, 44 neither calculated Bader charges nor Mn magnetic moments reveal any inherent electronic charge transfer between the dislocated structure and the bulk. This is because the magnitude of the band bending (visualized in Figure S4) does not fulfill the Zener-like breakdown criterion, 44 meaning that our defects are not compensated by electronic charge carriers.
However, the bound negative charges associated with the dislocated structure in Figure 4a can attract mobile ionic defects with a relative positive charge, such as oxygen vacancies (v O •• ). In fact, we find that the v O •• formation energy is reduced by ∼0.15 eV compared with the bulk (Figure 4b), demonstrating a significant defect segregation enthalpy. To contextualize the strength of this driving force, it is five times higher than the attraction of oxygen interstitials (O i ″) to neutral domain walls in the hexagonal manganites (∼0.03 eV), which are experimentally well documented to have enhanced conductance. 45 (Figure 4c). The DOSs are qualitatively similar, but the v O •• DOS has a strongly localized state within the band gap and a higher Fermi energy. This increase in Fermi energy at the interface gives a variation in electronic charge carrier concentration andin a p-type system with holes as the majority carriers 38 is expected to cause a diffusion current, leading to a local reduction in the number of available electronic charge carriers. As a consequence, the dislocation-induced structural changes enhance the resistivity relative to the bulk, which is consistent with the lower conductance observed in the cAFM data in Figure 1b.

■ DISCUSSION
Our experimental observations and DFT results reveal two important criteria for the formation of dislocations in ferroelectric oxides under locally applied voltage, promoting their injection postgrowth and with nanoscale spatial precision: (i) The cation has access to a new (meta-)stable cation configuration and (ii) the applied electric field generates enough energy to overcome the barrier toward the new ( meta-)stable state without leading to amorphization from leakage currents. A possible driving force for the spontaneous dislocation of the lattice observed in Er(Mn,Ti)O 3 is electricfield gradients that act on the uniaxial polarization (F = P·∇E). At present, however, no microscopic model exists that can capture the emergence of dislocations in electric fields, and theoretical in-depth studies are highly desirable.

■ CONCLUSIONS
Our work demonstrates that electric fields can be used to create partial dislocations in a complex oxide to engineer the local structure and electronic response, bypassing the necessity of applied strain fields. The ability to induce such changes postgrowth, on demand, and with nanometer spatial precision Nano Letters pubs.acs.org/NanoLett Letter provides a conceptually different approach to local property engineering, as exemplified by the enhanced resistance in hexagonal manganites. Our approach is expected to be generally applicable to dielectric materials close to a structural instability, where a sufficiently large electric field can build up. Because the electric-field-driven dislocation injection is applicable after a material has been synthesized or integrated into a device, it presents an opportunity for engineering functional materials via low-dimensional structural defects.

■ MATERIALS AND METHODS
Samples. Single crystals of Er(Mn 1−x ,Ti x )O 3+δ with x = 0.002 were grown using the pressurized floating zone method (ref 25). From this, we prepared samples with the ferroelectric polarization parallel to the sample surface (in-plane P). The crystals were orientated by Laue diffraction, cut to have thicknesses of ∼0.5 mm, and electromechanically polished to give a root-mean-square (RMS) surface roughness of ∼1 nm.
Focused Ion Beam. TEM specimen preparation was carried out using a Thermo Fisher Scientific Helios G4 UX DualBeam FIB. Lamellas were prepared "flipped" with in situ lift-out and backside milling. Final polishing was carried out at 2 kV. High-resolution Pt markers were used in conjunction with C protection layers to ensure that the final lamellas were centered on the region with suppressed conductance.
Transmission Electron Microscopy. TEM analysis was performed using a double-Cs aberration-corrected cold field emission gun JEOL ARM 200FC apparatus operated at 200 kV. STEM imaging was performed with a 27 mrad semiconvergence angle.
Atomic Force Microscopy. The lateral DART−PFM was performed on a Cypher ES Environmental AFM using an Oxford Instruments Asylec-01-R2 Pt/Ir tip. The remaining scanning probe microscopy (SPM) measurements were performed on an NT-MDT NTEGRA SPM using a TipsNano DCP20 tip. The voltage was applied to the sample backelectrode with the tip connected to ground.
Density Functional Theory. Calculations on isostructural YMnO 3 (isostructural and electronically similar to ErMnO 3 but without complicating f electrons) were carried out using the projector augmented wave (PAW) method, as implemented in the Vienna Ab initio Simulation Package (VASP), 46−48 using the Y_sv Mn_sv and standard O pseudopotentials supplied with VASP. PBEsol+U 49,50 with U = 5 eV on Mn 3d states, combined with a collinear frustrated antiferromagnetic order on the Mn sublattice, was used to reproduce the experimental lattice parameters 43 and the electronic band gap. 51 The energy cutoff of the plane-waves was set to 550 eV. The Brillouin zone was sampled with a Γcentered 4 × 1 × 2 k-point grid for geometry optimization and a 6 × 1 × 3 grid for DOS and electrostatic potential calculations. 240-atom 1 × 8 × 1 supercells were initialized in the high-symmetry P6 3 /mmc phase with different dislocation configurations and relaxed until the forces on all atoms were <0.01 eV Å −1 . Ferroelectric polarizations were calculated from a simple point-charge model using formal charges. 52 The dislocation formation energy was calculated as

Notes
The authors declare no competing financial interest.

■ ACKNOWLEDGMENTS
We thank Knut Marthinsen and Jan Schultheiß for helpful and insightful discussions about dislocations.