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High-density switchable skyrmion-like polar nanodomains integrated on silicon


Topological domains in ferroelectrics1,2,3,4,5 have received much attention recently owing to their novel functionalities and potential applications6,7 in electronic devices. So far, however, such topological polar structures have been observed only in superlattices grown on oxide substrates, which limits their applications in silicon-based electronics. Here we report the realization of room-temperature skyrmion-like polar nanodomains in lead titanate/strontium titanate bilayers transferred onto silicon. Moreover, an external electric field can reversibly switch these nanodomains into the other type of polar texture, which substantially modifies their resistive behaviours. The polar-configuration-modulated resistance is ascribed to the distinct band bending and charge carrier distribution in the core of the two types of polar texture. The integration of high-density (more than 200 gigabits per square inch) switchable skyrmion-like polar nanodomains on silicon may enable non-volatile memory applications using topological polar structures in oxides.

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Fig. 1: High-density polar nanodomains in a PTO20/STO10 bilayer from PFM measurements.
Fig. 2: Polarization mapping of polar nanodomains in a PTO20/STO10 bilayer by vector PFM and 4D STEM.
Fig. 3: Effective Hamiltonian model simulations of skyrmion-like nanodomains in PTO/STO bilayers.
Fig. 4: Resistive behaviours of the polar nanodomains integrated on silicon.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.

Code availability

All the code or mathematical algorithm files within this paper are available from the corresponding authors upon reasonable request.


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We thank L. Chen for discussions, and H. Huyan at UCI for assisting with the TEM experiments. This work was supported by the National Natural Science Foundation of China (grant numbers 11774153, 11861161004, 51772143, 51725203, 51721001, 11874207 and U1932115), the National Key R&D Program of China (grant numbers 2021YFA1400400 and 2020YFA0711504) and the Fundamental Research Funds for the Central Universities (0213-14380198). Y. Nie is supported by High Level Entrepreneurial and Innovative Talents Introduction, Jiangsu Province; C.A., X.Y. and X.P. acknowledge funding from the Department of Energy (DOE) under grant DE-SC0014430, and the NSF under grant number DMR-2034738. The 4D STEM experiments was conducted using facilities and instrumentation at the UC Irvine Materials Research Institute (IMRI) supported in part by the National Science Foundation through the Materials Research Science and Engineering Center programme (DMR-2011967); Researchers at the University of Arkansas acknowledge DARPA grant number HR0011727183-D18AP00010 (TEE Program), the Vannevar Bush Faculty Fellowship (VBFF) grant number N00014-20-1-2834 from the Department of Defense, and ARO grant number W911NF-21-2-0162 (ETHOS). Computations were made possible thanks to the use of the Arkansas High Performance Computing Center, HPCC resources of Nanjing University and the Arkansas Economic Development Commission. S.C. acknowledges the support of startup grants from the Department of Applied Physics at the Hong Kong Polytechnic University, the General Research Fund (grant number 15306021) from the Hong Kong Research Grant Council, the National Natural Science Foundation of China (grant number 12104381) and the open subject of the National Laboratory of Solid State Microstructures, Nanjing University (M34001).

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Authors and Affiliations



Y. Nie conceived the idea and directed the project with X.P., Y.C. and D.W. L.H. synthesized the samples and characterized the crystalline structure with the help of Y.F., H.L., D.J. and W.G. under the supervision of Y. Nie, X.P. and Z.G. L.H. performed the PFM and CAFM measurements and data analysis with the help of H.F. under the supervision of D.W. and Y. Nie. C.A. performed 4D STEM measurements and data analysis with the help of X.Y. under the supervision of X.P. M.W. performed the selected area electron diffraction and S/TEM measurements with the help of S.C. under the supervision of P.W. and X.P. S.P., Y. Nahas and Y.Y. performed and discussed the effective Hamiltonian model simulations under the supervision of L.B. T.W. helped with the lithography processing. Y. Nie and L.H. wrote the manuscript. All authors discussed the data and contributed to the manuscript.

Corresponding authors

Correspondence to Di Wu, Yuefeng Nie or Xiaoqing Pan.

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Nature thanks Matthew Dawber, Si-Young Choi and Anna Morozovska for their contribution to the peer review of this work.

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Extended data figures and tables

Extended Data Fig. 1 Growth and transfer of freestanding PTO/STO bilayers.

a, Schematic illustration of the process of heterostructure growth and membrane lift-off. The PTO/STO heterostructure is first grown on TiO2-terminated (001) STO substrates with a SAO water-soluble sacrificial layer (left) and then the bilayer is attached to a supporting polymer and released from the substrate by dissolving away the SAO layer by water (middle). Finally, the bilayer is transferred onto the desired substrate (right). b, The Reflection High Energy Electron Diffraction (RHEED) patterns for as-grown PTO(16 u.c.)/STO(10 u.c.)/SAO(6 u.c.) film on (001) STO substrate. c, Atomic force microscopy characterization of (001) STO substrate (left) and as-grown films (right) showing an atomically smooth surface with unit cell step terraces. Scale bar, 1 µm. d, Low-magnification planar-view HADDF image of the freestanding (PbTiO3)20/(SrTiO3)10 bilayer transferred to a holey carbon TEM grid and selected area electron diffraction (SAED) taken along [001] zone axis (inset), showing the single-crystal structure of the bilayer. Scale bar, 1 µm.

Extended Data Fig. 2 Simulation of vector fields for two distinct divergent domains.

a, Simulation of vector fields for a quad divergent domain. b, Simulation of vector fields for a skyrmion-like bubble domain. c, Calculation of the divergence from vector PFM image.

Extended Data Fig. 3 Direct visualization of topological polar textures by vector piezoelectric force microscope (PFM).

a, Schematic of angle-resolved lateral PFM. In-plane (IP) PFM real part signal was collected experimentally as a function of tip orientation angle φ and then the amplitude and the phase delay were determined by trigonometric curve fitting, i.e. A and θ in Acos(φ-θ+π/2). Piezoresponse vector field can be constructed by finding IP vector components (Acosθ, Asinθ) as a function of position. b, IP piezoresponse vector map for a centre-divergent domain showing the centre-divergent nanodomain. c, The trigonometric curve fitting for four representative points that are denoted as red spots in b.

Extended Data Fig. 4 Characterization of a centre-convergent type nanodomain.

a, Polarization mapping by 4D-STEM. b, The projected electric field calculated from the (000) diffraction peak. c, The projected charge density calculated from the electric field based on Gauss’s law. Scale bar, 5 nm. d, Atomically resolved plane-view HADDF-STEM image of the PTO20/STO10 bilayer. Scale bar, 2 nm. e, The PACBED pattern extracted from the region of the centre-convergent domain shown in ac.

Extended Data Fig. 5 Spatial resolution in PFM.

a, i) SEM image of an unused spherelike PFM tip. Scale bar, 500 nm. ii) The radius r of the contact circle for a weak indentation (h ~ 1–2 nm) is used to characterize the radius r of the tip. Scale bar, 50 nm. b, Electric field distribution at the tip simulated by finite element modelling (FEM). Labels near the curves designate potential values. Scale bar, 10 nm. c, Schematic image of the PFM tip scanning across a nanodomain. The measured size is proportional to the tip radius.

Extended Data Fig. 6 Topological characterization of the centre-divergent domains and interfacial skyrmion-like nanodomain (polar Bobber) obtained computationally (via the effective Hamiltonian).

a, (001)-plane resolved polar structure of the centre divergent domains in the vicinity of the STO/PTO interface. The first, second and third PTO layers counting from the interface are indicated with labels z = 1,2, and 3, respectively. b, The in-plane projected polar structure superimposed with the distribution of the Pontryagin topological charge density. The arrows correspond to the in-plane-projected dipoles coloured according to their out-of-plane component; red and purple colours correspond to [001] and [00–1] oriented dipoles, respectively. c, Dependence of the interpolated polar angle θ between the local dipole and [001] axis on the distance R from the central axis of the domain. d, The dependence of the interpolated Pontryagin charge density \({\rho }_{{Sk}}\) on the distance R from the central axis of the domain. e, The plane-resolved Skyrmion number of a single centre-divergent domain as a function of the distance from the domain centre. f, Schematic illustration of the topology of centre-divergent domains (left). Each z ≥ 2 cross section of the domain reveals a 2D Néel skyrmion-like structure characterized by an integer Skyrmion number. The domain tip at the PTO/STO interface pins an anti-hedgehog-like Bloch point.

Extended Data Fig. 7 Simulated dipolar structure of the centre-convergent domains.

a, The [100]–[001] cross-section of the simulated centre-divergent domain (Néel skyrmion). b, Artificially prepared partially switched dipolar configuration. c, Cross-section of the relaxed dipolar structure of the centre-convergent domain (submerged Néel bubble). d, Above and below the bubble (grey circle), the local dipoles are inclined (yellow arrows) towards and away from the central revolution axis (grey line), respectively. Red (purple) arrows indicate the polarization within (above) the bubble at its axis. e, The in-plane distribution of the thickness-averaged polarization. f, In-plane projection of the thickness averaged polarization.

Extended Data Fig. 8 Thickness dependence of the polar texture in PTOn/STO10 (n = 12, 16, 20) bilayers transferred on silicon and crystal structures of pure freestanding PTO and PTO/STO bilayer.

The surface morphology, in-plane PFM amplitude and phase images of (a) n = 20, (b) n = 16, (c) n = 12 bilayer films. Only the 20 u.c. PTO/10 u.c. STO shows circular shape polar textures. Scale bar, 30 nm. X-ray diffraction 2θ-ω scans around (002) (left) and (101) (right) diffraction peaks for (d) freestanding 20 u.c. PTO film and (e) freestanding (PbTiO3)20/(SrTiO3)10 bilayer. Schematic images showing the crystal structures of (f) freestanding 20 u.c. PTO film and (g) freestanding (PbTiO3)20/(SrTiO3)10 bilayer.

Extended Data Fig. 9 Reversible switching of topological nanodomains.

a, Schematic images illustrating the reversible switching of the topological domains by external electric field: The coexistence of two types of nanodomains in pristine bilayer (i) were first switched into all centre-divergent nanodomains by a scan with +5 V bias voltage (ii) and then further switched to all centre-convergent nanodomains by a scan with −5 V bias voltage (iii). bd, Vertical PFM amplitude (VPFM-amp.), vertical phase (VPFM-pha.), lateral PFM amplitude (LPFM-amp.) and lateral phase (LPFM-pha.) images for three corresponding cases shown in (a). The centre-divergent (centre-convergent) domains are marked by red (blue) circles. Scale bar, 100 nm. e, VPFM-amp. (upper left), VPFM-pha. (bottom left), LPFM-amp. (upper right) and LPFM-pha. (bottom right) images taken under an a.c. amplitude of 500 mV for one single skyrmion-like polar nanodomain after applying the 0 V, −1 V, −4 V, −2 V, +1 V and +4 V DC voltage. Scale bar, 20 nm. f, Hysteresis loop of the skyrmion-like polar nanodomain.

Extended Data Fig. 10 Domain structures and switching behaviour in a PTO/STO bilayer transferred on a P-doped silicon wafer after a standard electron beam lithography process.

a, Schematic images showing standard lithography process on the ferroelectric bilayer transferred on a P-doped silicon wafer. b, Quadrate patterns on a P-doped silicon wafer, inset shows the topography of a single piece. Scale bar, 10 μm. c, Vertical PFM amplitude (VPFM-amp.) and phase (VPFM-pha.), lateral PFM amplitude (LPFM-amp.) and phase (LPFM-pha.) images for the freestanding PTO20/STO10 bilayers transferred on P-doped silicon substrate. Scale bar, 100 nm.

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Han, L., Addiego, C., Prokhorenko, S. et al. High-density switchable skyrmion-like polar nanodomains integrated on silicon. Nature 603, 63–67 (2022).

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