GUO Changqing; YANG Letao; WANG Jing; HUANG Houbing

doi:10.7498/aps.74.20250334

Abstract

Flexible ferroelectric materials possess considerable potentials for wearable electronics and bio-inspired devices, yet their mechano-electric coupling mechanisms under dynamic bending conditions remain incompletely understood. In his work, the effects of bending deformation on domain structures and macroscopic ferroelectric responses in (SrTiO₃)₁₀/(PbTiO₃)₁₀/(SrTiO₃)₁₀ flexible ferroelectric trilayer films are systematically investigated using phase-field simulations. By constructing computational models for upward-concave (U-shaped) and downward-concave (N-shaped) bending configurations, the strain distribution and its regulation mechanism on polarization patterns under different curvature radii are analyzed. The results reveal distinct strain gradients across bending modes: U-shaped bending induces compressive strain in the upper layer and tensile strain in the lower layer, generating a negative out-of-plane strain gradient. Conversely, N-shaped bending reverses this strain distribution. Such inhomogeneous strains drive significant polarization reconfiguration within the PTO layer. At a moderate curvature (large R), the system retains stable vortex-antivortex pairs. Reducing bending radius (smaller R) promotes divergent topological transitions—U-shaped bending facilitates vortex pair transformation into zigzag-like domains, while N-shaped bending drives vortex-to-out-of-plane c-domain evolution. Notably, bending-induced strain gradients impose transverse flexoelectric fields that markedly change trilayer hysteresis loops. U-shaped bending introduces a negative flexoelectric field, shifting loops rightward with maximum polarization (P_max) decreasing. In contrast, N-shaped bending generates a positive field, enhancing P_max via leftward loop shifting. The polarization switching analysis under electric field further demonstrates bending-mediated control of domain evolution pathway and reversal dynamics. These findings not only elucidate profound bending effects on flexible ferroelectrics’ domain architectures and functional properties but also provide theoretical guidance for designing strain-programmable ferroelectric memories, adaptive sensors, and neuromorphic electronics.

Keywords:

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Corresponding author: HUANG Houbing, hbhuang@bit.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 92463306, 52372100, 52472119) and the Natural Science Foundation of Beijing, China (Grant No. 2242057).

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	变量	数值	变量	数值
PTO	$ {\alpha _1}/({10^8}{\text{ }}{\mathrm{J}} {\cdot} m {\cdot} {{\mathrm{C}}^{ - 2}}) $	$ - 1.706 $	$ {{{Q}}_{11}}/({{\mathrm{m}}^4} {\cdot} {{\mathrm{C}}^{ - 2}}) $	0.089
	$ {\alpha _{11}}/({10^7}{\text{ }}{\mathrm{J}} {\cdot} {{\mathrm{m}}^5} {\cdot} {{\mathrm{C}}^{ - 4}}) $	$ - 7.3 $	$ {{{Q}}_{12}}/({{\mathrm{m}}^4} {\cdot} {{\mathrm{C}}^{ - 2}}) $	–0.026
	$ {\alpha _{12}}/({10^8}{\text{ }}{\mathrm{J}} {\cdot} {{\mathrm{m}}^5} {\cdot} {{\mathrm{C}}^{ - 4}}) $	$ 7.5 $	$ {{{Q}}_{44}}/({{\mathrm{m}}^4} {\cdot} {{\mathrm{C}}^{ - 2}}) $	0.0675
	$ {\alpha _{111}}/({10^8}{\text{ }}{\mathrm{J}} {\cdot} {{\mathrm{m}}^9} {\cdot} {{\mathrm{C}}^{ - 6}}) $	$ 2.6 $	$ {{{G}}_{11}}/({10^{ - 10}}{\text{ }}{\mathrm{N}} {\cdot} {{\mathrm{m}}^4} {\cdot} {{\mathrm{C}}^{ - 2}}) $	$ 1.44 $
	$ {\alpha _{112}}/({10^8}{\text{ }}{\mathrm{J}} {\cdot} {{\mathrm{m}}^9} {\cdot} {{\mathrm{C}}^{ - 6}}) $	$ 6.1 $	$ {{{G}}_{12}}/({\mathrm{N}} {\cdot} {{\mathrm{m}}^4} {\cdot} {{\mathrm{C}}^{ - 2}}) $	0
	$ {\alpha _{123}}/({10^8}{\text{ }}{\mathrm{J}} {\cdot} {{\mathrm{m}}^9} {\cdot} {{\mathrm{C}}^{ - 6}}) $	$ - 3.7 $	$ G_{44},G_{44}'/(10^{-11}\text{ }\mathrm{N}{\cdot}\mathrm{m}^4{\cdot}\mathrm{C}^{-2}) $	$ 7.2 $
	$ {{c}_{11}}/({10^{11}}{\text{ }}{\mathrm{J}} {\cdot} {{\mathrm{m}}^{ - 3}}) $	$ 2.3 $	$ {{f}_{11}}/{\mathrm{V}} $	1.6
	$ {{c}_{12}}/({10^{11}}{\text{ }}{\mathrm{J}} {\cdot} {{\mathrm{m}}^{ - 3}}) $	$ 1 $	$ {{f}_{12}}/{\mathrm{V}} $	–0.8
	$ {{c}_{44}}/({10^{10}}{\text{ }}{\mathrm{J}} {\cdot} {{\mathrm{m}}^{ - 3}}) $	$ 7 $	$ {{f}_{44}}/{\mathrm{V}} $	0.15
STO	$ {\alpha _1}/({10^8}{\text{ }}{\mathrm{J}} {\cdot} {\mathrm{m}} {\cdot} {{\mathrm{C}}^{ - 2}}) $	$ 2.017 $	$ {{{Q}}_{44}}/({{\mathrm{m}}^4} {\cdot} {{\mathrm{C}}^{ - 2}}) $	0.00957
	$ {\alpha _{11}}/({10^9}{\text{ }}{\mathrm{J}} {\cdot} {{\mathrm{m}}^5} {\cdot} {{\mathrm{C}}^{ - 4}}) $	$ 1.7 $	$ {{{G}}_{11}}/({10^{ - 10}}{\text{ }}{\mathrm{N}} {\cdot} {{\mathrm{m}}^4} {\cdot} {{\mathrm{C}}^{ - 2}}) $	$ 1.44 $
	$ {\alpha _{12}}/({10^9}{\text{ }}{\mathrm{J}} {\cdot} {{\mathrm{m}}^5} {\cdot} {{\mathrm{C}}^{ - 4}}) $	$ 4.45 $	$ {{{G}}_{12}}/({\mathrm{N}} {\cdot} {{\mathrm{m}}^4} {\cdot} {{\mathrm{C}}^{ - 2}}) $	0
	$ {{c}_{11}}/({10^{11}}{\text{ }}{\mathrm{J}} {\cdot} {{\mathrm{m}}^{ - 3}}) $	$ 3.3 $	$ {{{G}}_{44}}, {{G}}_{44}'/({10^{ - 11}}{\text{ }}{\mathrm{N}} {\cdot} {{\mathrm{m}}^4} {\cdot} {{\mathrm{C}}^{ - 2}}) $	$ 7.2 $
	$ {{c}_{12}}/({10^{11}}{\text{ }}{\mathrm{J}} {\cdot} {{\mathrm{m}}^{ - 3}}) $	$ 1 $	$ {{f}_{11}}/{\mathrm{V}} $	–3.21
	$ {{c}_{44}}/({10^{11}}{\text{ }}{\mathrm{J}} {\cdot} {{\mathrm{m}}^{ - 3}}) $	$ 1.25 $	$ {{f}_{12}}/{\mathrm{V}} $	1.47
	$ {{{Q}}_{11}}/({{\mathrm{m}}^4} {\cdot} {{\mathrm{C}}^{ - 2}}) $	0.0457	$ {{f}_{44}}/{\mathrm{V}} $	1.07
	$ {{{Q}}_{12}}/({{\mathrm{m}}^4} {\cdot} {{\mathrm{C}}^{ - 2}}) $	–0.0135	ε_r (PTO/STO)	20

DownLoad: CSV

U型弯曲- R/nm	ε_xx,z/ (10⁶ m^–1)	E_c/ (kV·cm^–1)	P_max/ (μC·cm^–2)	P_r/ (μC·cm^–2)
未弯曲	0	0	43.90	0
1200	–0.61	2.78	43.72	–0.29
937	–0.77	2.78	43.64	–0.31
600	–1.14	5.56	43.52	–0.46
400	–1.82	11.11	43.30	–0.57
300	–2.42	13.89	43.05	–0.64
240	–3.03	16.67	42.86	–0.69

DownLoad: CSV

N型弯曲- R/nm	ε_xx,z/ (10⁶ m^–1)	E_c/ (kV·cm^–1)	P_max/ (μC·cm^–2)	P_r/ (μC·cm^–2)
未弯曲	0	0	43.90	0
1200	0.61	–2.78	44.13	0.21
600	1.14	–5.56	44.33	0.43
400	1.82	–8.33	44.53	0.67
300	2.42	–13.89	44.78	0.93
240	3.03	–16.67	44.88	1.18
200	3.61	–19.44	45.15	1.42

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Vol. 74, Issue 12 - 2025-06-20

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