SUPPLEMENTARY INFORMATION

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1 SUPPLEMENTARY INFORMATION Insulating Interlocked Ferroelectric and Structural Antiphase Domain Walls in Multiferroic YMnO 3 T. Choi 1, Y. Horibe 1, H. T. Yi 1,2, Y. J. Choi 1, Weida. Wu 1, and S.-W. Cheong 1,2,* 1 Rutgers Center for Emergent Materials and Dept. of Physics and Astronomy, Rutgers University, Piscataway, NJ 08854, USA 2 Dept. of Electrical and Computer Engineering, Rutgers University, Piscataway, NJ 08854, USA * sangc@physics.rutgers.edu 1. Ferroelectric characterization of a YMnO 3 single crystal. The ferroelectric polarization-electric field (P-E) loops of a ~15 µm-thick YMnO 3 single crystal were obtained using a Radiant Technology precision premier II with a virtual ground method. For P-E measurements Au electrodes on both sides of the YMnO 3 crystal were deposited with shadow masks by using magnetron sputtering. The standard P-E hysteresis measurement is an effective way to show the total polarization response to the external electric field, as shown in Fig. S1a. This response consists of a number of contributions including parasitic linear elements (i.e. non- remanent polarization) due to linear capacitance and leakage current along with the nonlinear ferroelectric component (remanent polarization). In order to obtain the precise intrinsic ferroelectric polarization, a pulsed positive-upnegative-down (PUND) polarization measurement on the same YMnO 3 crystal was performed at low temperatures (e.g. 100 K) and various frequencies (e.g. 1 khz). We extracted remanent polarization from the difference between switched polarization and nonswitched polarization. Fig. S1b shows a fully-saturated remanent P-E loop of the crystal displaying a remanent polarization of ~5 µc/cm 2. We found that the remanent polarization exhibits little frequency dependence in the range of 10 Hz-2 khz. These results indicate that the ferroelectric polarization switching is due to the intrinsic ferroelectric property of the YMnO 3 single crystal. 2. High-resolution TEM image of an antiphase domain boundary in YMnO 3. Fig. S2 shows a high-resolution TEM image of an antiphase domain boundary in YMnO 3. nature materials 1

2 supplementary information Periodic contrast indicates the presence of the superstructure associated with Mn trimerization. Red lines and blue lines do not match near the green dotted line, demonstrating the presence of an antiphase domain boundary near the green line. 3. Determination of polarization orientations in ferroelectric domains. To determine polarization orientations in ferroelectric domains, we applied large bias voltages to derive the domain growth of YMnO 3 single crystals through the switching of ferroelectric polarization. The domain growth was mapped with CAFM before and after applying large bias voltages. We used a conductive Pt/Ir-coated Si cantilever as a movable top electrode for our CAFM measurements (tip radius of ~30 nm, force constant of ~5.5 N/m, and a resonant frequency of ~150 khz). We performed a DC voltage sweep to induce polarization switching. We applied voltage to the CAFM tip on local spots in the c surface of a ~10 µm-thick YMnO 3 crystal with a grounded Ag back electrode. The voltage of CAFM tip was swept from 0 V to +10 V with the ramping speed of 0.1 V/s. Note that a positive tip voltage corresponds to a reverse bias. Fig. S3a shows a cloverleaf domain pattern in a 6 5 μm 2 area obtained from CAFM with a -4 V bias before any polarization switching. The blue outlines indicate domain boundaries. Fig. S3b displays a CAFM image (reading at -4 V) of the same area obtained after the +10 V sweep on the initially-bright spots (indicated by red circles). Fig. S3 demonstrates that the +10 V induces the growth of bright domains. Particularly, two-initially-bright domains (denoted as α-) merge into one conductive domain. These results indicate that the bright domains correspond to downward polarization orientation and the polarization in the dark domains is upward. Note that the initially-bright spots (red circles) became non-conductive after applying the +10 V sweep. This suggests possible damage of the local spots by the +10 V voltage sweep. Indeed, we found that AFM topography images show rough surfaces at the non-conducting spots after the +10 V sweep, confirming the local damage by the +10 V sweep. 4. Local distortions at the domain boundaries (APB+FEB) for the [α+, β-, γ+, α-, β+, γ-] cloverleaf configuration. Fig. S4 displays the local lattice distortions at the domain boundaries in the [α+, β-, γ+, α-, β +, γ-] cloverleaf configuration. The [α+, β-], [β+, γ-], [γ+, α-] boundaries are of the simultaneous APB I +FEB type, while the [α-, β+], [β-, γ+], [γ-, α+] boundaries are of the simultaneous APB II +FEB type. 2 nature MATERIALS

3 supplementary information 5. Temperature dependence of the electronic transport properties of a YMnO 3 single crystal. Fig. S5 shows the temperature dependence of resistivity (ρ(t)) near the ferroelectric transition temperature and the activation energy, dln(ρ(t))/d(1/t), estimated from the resistivity behavior of a YMnO 3 single crystal. ρ(t) was measured upon heating first, and then cooling after quenching (Q) or slow-cooling (SC) from 1,100 K. It is evident that the ferroelectric state is more conducting than the paraelectric state, and the activation energy decreases below the ferroelectric transition temperature of 880 K. The large resistivity after quenching is consistent with the increase of the number of insulating ferroelectric domain walls. 6. The polarization-orientation dependence of the charge conduction of ferroelectric domains. Fig. S6 represents the schematic energy diagrams for the conduction variation in different ferroelectric domains. In terms of general theories for metal-semiconductor rectifying contacts, the ferroelectric polarization may induce an infinite sheet of surface charge placed at a finite distance from the interface. It is assumed that the polarization bound charges are compensated with trapped charges or ionized shallow impurities in the space charge region. We consider the influence of the polarization on the potential barrier and the maximum electric field at the interface between the tip and YMnO 3. The maximum electric field at the interface is enhanced with downward polarization and reduced with upward polarization. Consequently, the Schottky barrier height and the apparent built-in voltage are small for downward polarization and large for upward polarization, as illustrated in Fig S6. In addition, for forward bias voltages, the hole carriers diffuse readily from the semiconducting YMnO 3 to the tip with a reduced band bending of YMnO 3 at the interface. Conversely, only small current flows to YMnO 3 in the reserve bias case because the diffusing-hole density is significantly reduced by increased band bending. As a result, the ferroelectric domains exhibit the overall rectification effect. nature materials 3

4 supplementary information Figure S1. Ferroelectric characterization of a YMnO 3 single crystal. a, Standard P-E hysteresis loops of a Au/YMnO 3 (15 µm)/au structure at 100 K and 1 khz. b, Remanent P-E hysteresis loop obtained using a PUND measurement at the same temperature and frequency. Figure S2. High-resolution TEM image of an antiphase domain boundary in YMnO 3. The green dotted line indicates an antiphase domain boundary. 4 nature MATERIALS

5 supplementary information Figure S3. The growth of conductive domains in a YMnO 3 single crystals with large bias voltages. a three-winged cloverleaf conductive domain pattern of YMnO 3 before (a) and after (b) a large positive bias voltage sweep. Figure S4. Local distortions at the simultaneous APB + FEB for the [α+, β-, γ+, α-, β+, γ-] cloverleaf configuration. Yellow, brown and blue circles represent the Y, Mn, and O ions, respectively. Light blue and dark blue circles indicate the top and bottom apical oxygen ions of MnO 5 polyhedra. Arrows depict the directions of atomic displacements. Triangles with green bars correspond to the Mn trimers. nature materials 5

6 supplementary information Figure S5. Temperature dependence of resistivity of a YMnO 3 single crystal. The temperature dependence of resistivity, ρ(t), (left) along the c axis and the in-plane near the ferroelectric transition temperature and the activation energy, dln(ρ(t))/d(1/t), (right) estimated from the resistivity behavior of a YMnO 3 single crystal. ρ(t) was measured upon heating first, and then cooling after quenching (Q) or slow-cooling (SC) from 1,100 K. Arrows indicate the heating and cooling cycles. Figure S6. The schematic energy diagrams for the conduction variation in different ferroelectric domains. Schematic energy diagrams of band alignment at the interface between a metal (tip) and a ferroelectric semiconductor (YMnO 3 ) in forward bias (left) and reverse bias (right) for two-different polarization orientations (red; downward, and blue; upward). 6 nature MATERIALS