Domain Morphology, Electrocaloric Response, and Negative Capacitance States of Ferroelectric Nanowires Array

We analyzed the domain morphology, electrocaloric response, and negative capacitance states in a one-dimensional array of uniformly oriented, radial symmetric ferroelectric nanowires, whose spontaneous polarization is normal to their symmetry axis. The wires are densely packed between flat electrodes. Using finite element modeling based on the Landau-Ginzburg-Devonshire approach, electrostatics, and elasticity theory, we calculated the distributions of spontaneous polarization, domain structures, electric potential, electric field, dielectric permittivity, and electrocaloric response in the nanowires. Due to size and depolarization effects, the paraelectric and ferroelectric (poly-domain or single-domain) states of the wires can be stable, depending on their radius and the dielectric permittivity of the surrounding medium. It is demonstrated that dipole-dipole interaction between the nanowires determines the stability of the polar (or anti-polar) state in the array when the wire radius is significantly smaller than the critical size of the paraelectric transition in an isolated wire. We reveal that a large region of a mixed state, characterized by poly-domain ferroelectric states with nonzero average polarization inside each wire and zero average polarization of the whole array, can be stable. By selecting the dielectric permittivity of the surrounding medium and the nanowire radius, one can maximize the negative capacitance effect in the capacitor with densely packed wires. It is also possible to achieve maximal enhancement of the electrocaloric response due to size effects in the wires. The underlying physics of the predicted enhancement is the combined action of size effects and the long-range electrostatic interactions between the ferroelectric dipoles in the nanowires and the image charges in the electrodes

💡 Research Summary

This paper presents a comprehensive theoretical investigation of the domain morphology, electrocaloric (EC) response, and negative capacitance (NC) states in densely packed arrays of radially symmetric ferroelectric (FE) nanowires oriented normal to flat electrodes. Using finite‑element modeling (FEM) that couples the Landau‑Ginzburg‑Devonshire (LGD) free‑energy formalism with electrostatic and elasticity equations, the authors explore how the nanowire radius (R = 2–20 nm) and the relative dielectric permittivity of the surrounding medium (εₘ = 1–300) dictate the equilibrium polarization patterns and functional properties at room temperature (298 K).

The study adopts BaTiO₃ as the model ferroelectric material and assumes the wires are long enough that all fields are invariant along the wire axis (Y). The wires are placed almost in contact with the top and bottom electrodes, with an ultra‑thin gap (< one lattice constant) between neighboring wires, thereby maximizing dipole‑dipole interactions. A low‑frequency (≪ LK relaxation rate) sinusoidal voltage is applied across the electrodes to generate quasi‑static hysteresis loops and to probe the EC effect.

Key findings are summarized in a phase diagram in the (R, εₘ) plane. When εₘ ≪ ε_FE (≈200 for bulk BaTiO₃), the external field is expelled from the wires, leading to strong depolarization fields. In this regime, wires with R > R_c (critical radius) split into multiple domains (poly‑domain, PD) to reduce depolarization energy, whereas wires with R < R_c become paraelectric (PE). Conversely, for εₘ ≫ ε_FE the field concentrates inside the wires, suppressing depolarization; even very small wires (R ≈ 5–7 nm) can sustain a single‑domain (SD) state. Notably, at intermediate εₘ (≈30–100) and radii near the critical size (≈8–12 nm), a mixed “SD+PD” state emerges: each wire contains both single‑domain and poly‑domain regions, yielding a non‑zero average polarization per wire but zero net polarization for the whole array. This mixed state is a direct consequence of long‑range dipole‑dipole coupling that is only significant in the densely packed geometry.

Negative capacitance appears when the differential capacitance C = dQ/dV becomes negative due to a nonlinear reduction of the effective permittivity with increasing voltage. The simulations reveal that NC is maximized for moderate εₘ (≈30–100) combined with radii close to the transition region (≈8–12 nm). In this window the balance between depolarization suppression and inter‑wire electrostatic interaction yields the largest voltage‑induced charge reversal. For εₘ too low, depolarization dominates and prevents voltage amplification; for εₘ too high, the field is fully screened inside the wires and NC disappears.

The electrocaloric response, quantified as ΔT = –(T/Cₚ)(∂P/∂T)ΔE, is strongly enhanced by size effects. As R decreases below ~10 nm, the temperature derivative of polarization (∂P/∂T) grows sharply, leading to EC temperature changes up to 2–3 times larger than in bulk BaTiO₃. High εₘ further amplifies the EC effect by strengthening the interaction with image charges in the electrodes, which concentrates the field within the wires and increases the polarization’s temperature sensitivity. The optimal EC performance is predicted for R ≈ 6 nm and εₘ ≈ 200, where ΔT can exceed 1 K for modest field changes.

Overall, the work demonstrates that by judiciously selecting nanowire dimensions and the dielectric environment, one can simultaneously (i) tune the ferroelectric phase (PE ↔ PD ↔ SD), (ii) stabilize a unique SD+PD mixed state, (iii) achieve pronounced negative capacitance, and (iv) maximize the electrocaloric response. These insights provide concrete design guidelines for next‑generation high‑energy‑density capacitors, solid‑state EC coolers, and devices exploiting negative capacitance for voltage amplification in low‑power electronics.