Supporting Information for “Visualization and Manipulation of Meta-stable Polarization Variants in Multiferroic Materials” Moonkyu Park, Kwangsoo No* and Seungbum Hong* S1. In-/Out-of-plane PFM images of BiFeO3 thin films at the as-deposited state S2. Out-of-plane poling process using biased AFM tip S3. Calculation of polarization charges at the domain boundaries where the vertical domain switching initiated S4. In-/Out-of-plane PFM images of the BiFeO3 thin film at the vertically switched state S5. Retention characteristics of the vertically poled domains in BiFeO3 thin films S6. Formation mechanism of intermediate polarization variants S7. In-plane domain configurations with different sample rotation angles of 10 and 30 1 S1. In-/Out-of-plane PFM images of BiFeO3 thin films at the as-deposited state As discussed in the text, we obtained in-/out-of-plane PFM images of BiFeO3 (BFO) thin film at the as deposited state while rotating the sample from 0° to 180° with an interval of 30° between each image as shown in Figs. S1 and S2, respectively. The faceted islands that are seen in topography are the Fe2O3 phase as described in our previous work.1 In order to avoid any spurious effects caused by Fe2O3 phase and surface morphology, we chose to analyze a flat area (dashed box in the PFM images) when acquiring the domain configuration. The ac modulation voltage applied to Pt coated tip (Micromasch, NCS 14 tip) was 0.7 Vrms at 17 kHz. Scan area was 2 μm 2 μm. Fig. S1. Topography, in-plane PFM amplitude and phase images over the full scan area at each angular step from 0o to 180o in <001> BFO thin films at the as-deposited state. Scale bars in Fig. S1 represent 500 nm. 2 Fig. S2 shows the out-of-plane PFM images of the same area as that used for in-plane PFM images in Fig. S1. The PFM phase images showed a uniform bright contrast indicating downward polarization direction while rotating the sample from 0° to 180° as expected. Fig. S2. Topography, and out-of plane PFM amplitude and phase images over the full scan area at each angular step from 0° to 180° in <001> BFO thin films at the as-deposited state. Scale bars in Fig. S2 represent 500 nm. 3 S2. Out-of-plane poling process using biased AFM tip Fig. S3 (a) shows the out-of-plane PFM images of the same area as that used for domain configuration in the text with various external voltage steps (-2 V, -2.3 V, -2.5 V, -2.7 V and -3.5 V). The external voltages were applied to the conductive AFM tip. As shown in Fig. S3 (a), opposite domains were nucleated at the applied voltage of -2.3 V and domain growth occurred laterally with increasing the external voltage. Finally, at the applied voltage of -3.5 V, whole scan area was switched to the opposite direction. Figs. S3. (a) Out-of plane PFM images after poling with various external voltages and (b) graph of normalized switched area extracted from PFM phase images versus applied external voltage. 4 S3. Calculation of polarization charges at the domain boundaries where the vertical domain switching initiated We calculated the polarization charges of the domain boundaries where the vertical domain switching initiated. In our previous study, we could quantitatively calculate the amount of polarization charging at the charged domain boundary using the angle between polarization direction and boundary.2 In Fig. S4 (a), we denoted the 7 regions where vertical domain switching initiated. In Figs. S4 and S5, we showed the local in-plane domain map overlapped with vertically switched region (dark brown region in each figure), schematics of domain boundaries and polarization direction of the switched region and angle between boundary and polarization directions at each segment of domain boundaries. Figs. S4. (a) In-plane domain map of BFO thin film at the as deposited state. Local in-plane domain maps and collected segments of domain boundaries in the area where vertical domain switching initiated in regions (b) 1, (c) 2 and (d) 3 shown in (a). 5 Figs. S5. Local in-plane domain maps and collected segments of domain boundaries in the areas where vertical domain switching initiated in regions (a) 4, (b) 5, (c) 6 and (d) 7 shown in Fig. S4 (a). 6 In Table SI, we listed the calculated amount of polarization charges per unit length in the regions mentioned above. We found that the mean value of amount of polarization charges per unit length was +0.124 ± 0.304. Positive mean value indicates the boundaries are on average charged in positive state. Table SI. Amount of polarization charges per unit length at the each region Region Polarization charges per unit length 1 -0.088 2 0.683 3 0 4 0.08 5 0.389 6 -0.017 7 -0.177 Mean value +0.124 ± 0.304 7 S4. In-/Out-of-plane PFM images of the BiFeO3 thin film at the vertically switched state As discussed in the text, we obtained the in-/out-of-plane PFM images after the poling process while rotating the sample from 0° to 180° with an interval of 30° between each image as shown in Figs. S6 and S7, respectively. Fig. S6. In-plane PFM images over the full scan area at each angular step from 0° to 180° in <001> BFO thin films after the vertical poling process. Scale bars in Fig. S6 represent 500 nm. 8 Fig. S7. Out-of plane PFM images over the full scan area at each angular step from 0° to 180° in <001> oriented BFO thin films after the vertical poling process. Scale bars in Fig. S7 represent 500 nm. 9 S5. Retention characteristics of vertically poled domains in BiFeO3 thin films We performed the retention experiments on the vertically switched BFO thin films to check the stability of the switched domains. We obtained the out-of-plane PFM images with elapsed time after the domain switching. Figs. S8 shows the out-of-plane PFM images at the as deposited state (Fig. S8(a)), just after the vertically switched state by applying external voltage of -7 V to tip (Fig. S8(b)), and the evolution of out-of-plane PFM amplitude and phase images as a function of elapsed time at room temperature (Fig. S8(c)). As shown in Fig. S8, BFO underwent insignificant retention loss, indicative of excellent retention properties. No domain reversal was found in the region of interest until 6,685 minutes after the poling. Fig. S8. Out-of-plane PFM images (a) at the as deposited state, (b) just after vertically switched state. (c) The evolution of out-of-plane PFM amplitude and phase images as a function of elapsed time. 10 Fig. S9 shows normalized domain area extracted from out-of-plane PFM phase images (red box region in Fig. S8 (c)) and out-of-plane PFM amplitude values (white box region in Fig. S8 (c)) with the elapsed time. We found that normalized domain area and amplitude values were almost constant with elapsed time. We believe that excellent retention properties of vertically switched state might be associated with the simple and electrostatically stable domain structure of the BFO thin film as described in the text. Fig. S9. (a) Normalized domain area extracted from out-of-plane PFM phase signals versus elapsed time graph and (b) out-of-plane PFM amplitude values versus elapsed time graph 11 S6. Formation mechanism of intermediate polarization variants Fig. S10 illustrates formation mechanism of intermediate polarization in epitaxially grown BFO thin films. Since BFO has a Curie temperature (1100 K) above the films growth temperature (953 K), BFO nuclei formed during the initial stages in film growth (stage 1 in Fig. S10), larger than the critical size to exhibit spontaneous polarization, will have their own ferroelectric polarization variants when they are deposited on the SRO/STO substrate. As the film grows first in an island mode, each island with its polarization variant will not interact with the neighboring ones and grow independently, preserving their polarization variants, until they touch each other. It is highly likely that in this process many of the polarization directions in the coalesced islands will not be able to fully switch to form a neutral boundary with the adjacent regions and so charged domain boundary will form (Stage 3 to Stage 6 in Fig. S10). We believe that the intermediate polarization variants, which deviate from the ferroelectric easy axes imposed by the rhombohedral crystal symmetry, are formed to act as mitigating regions to decrease the electrostatic energy at the charged domain boundaries. Fig. S10. Schematics of intermediate polarization variants formation during film growth; Stages 1 and 2: Initial film growth, Stages 3, 4 and 5: Emergence of charged domain boundaries and stage 6: Formation of intermediate polarization variants. 12 S7. In-plane domain configurations with different sample rotation angle of 10 and 30 Fig. S11 shows the in-plane polarization directions obtained by AR-PFM method with different angular resolutions, i.e. sample rotation angle. We identified the in-plane polarization directions with the angular resolution of 30° (Fig. S11(a)) and 10° (Fig. S11(b)) in the same region. More elaborated in-plane domain configuration was obtained with high angular resolution (small sample rotation angle). However, the fact that we can observe the intermediate polarization variants different from the well-defined crystallographic axis remained the same regardless of the angular resolution. Fig. S11. In-plane domain direction of BFO thin film obtained by AR-PFM method with angular resolution of (a) 30° and (b) 10°. Regarding the concern whether we can measure the ferroelectric domains smaller than the tip radius, we believe that AR-PFM and conventional PFM can resolve domains smaller than the tip radius because the ferroelectric materials show the piezoresponse at the extremely confined area under the tip. There have been studies about high resolution imaging of ferroelectric domains smaller than tip radius. Rodriguez et al., reported the high resolution ferroelectric domain imaging (~3 nm resolution) of ferroelectric materials in liquid condition.3 In addition, Ko et al., also observed that 25 nm sized ferroelectric domain using the wedge shaped probe with 300 nm in length,4 which implies that tip radius is the important factor to determine the spatial resolution, but not the only one. 13 14 References 1 M. Park et al., Appl. Phys. Lett. 97, 112907 (2010). M. Park, S. Hong, J. Kim, J. Hong, K. No, Appl. Phys. Lett. 99, 142909 (2011). 3 B. Rodriguez et al., Phys. Rev. Lett. 96, 237602 (2006). 4 H. Ko et al., Nano Lett. 11, 1428 (2011). 2 15