[Paper Review] Terahertz Electrodynamics of $180^\circ$ Domain Walls in Thin Ferroelectric Films

Igor Lukyanchuk, Alexey Pakhomov+3 more|arXiv (Cornell University)|Oct 12, 2014

Acoustic Wave Resonator Technologies3 citations

TL;DR

This paper proposes that periodic 180° domain walls in ultrathin ferroelectric films, such as PbTiO₃/SrTiO₃, support a collective resonance mode in the sub- and low-terahertz range (0.3–3 THz), which can be detected via reflection-absorption spectroscopy. The dynamic permittivity of the domain structure enables tunable, compact THz devices with resonance frequencies adjustable via film thickness and composition.

ABSTRACT

We investigate oscillation dynamics of a periodic structure of the $180^\circ$ domain walls in nanometricaly thin substrate-deposited ferroelectric films and superlattices. We calculate dynamic permittivity of such structures and reveal a collective resonance mode, which in the typical ferroelectric compounds, PbTiO3/SrTiO3, lies in the sub- and low THz frequency range of 0.3-3THz. We propose the reflection-absorbtion spectroscopy experiments to observe this mode.

Motivation & Objective

• To investigate the dynamic electrodynamics of periodic 180° domain walls in ultrathin ferroelectric films and superlattices.
• To calculate the dynamic permittivity of such domain structures and identify collective vibrational modes in the sub- and low-THz range.
• To propose a feasible experimental method—reflection-absorption spectroscopy—for detecting the predicted resonance mode.
• To optimize resonance frequency and damping by tuning film thickness and material composition (e.g., PTO vs. PZT).
• To demonstrate the potential of these systems for compact, tunable THz devices in the 0.3–3 THz window.

Proposed method

• Theoretical modeling of the dynamic permittivity εf(ω) of a ferroelectric film with periodic 180° domain walls using effective medium theory and dielectric response functions.
• Derivation of the effective oscillator frequency ω₀′ using the Lyddane-Sachs-Teller relation and the dielectric response of the system.
• Application of the transfer matrix method to calculate the reflectivity R(p) of p-polarized THz radiation from a film-on-substrate structure.
• Use of the reflectivity formula R(p) ≈ R₀(p) |1 - (2af/λ)(8π cosθ sin²θ / (cosθ - εp⁻¹/² sinθ)²) Im[1/εf(ω)]| to detect domain-induced reflectivity enhancements.
• Numerical simulation of reflectivity as a function of frequency and incidence angle θ, with focus on Brewster angle (θB ≈ 86°) and resonance at ωr/2π ≈ 0.75 THz.
• Comparison of monolayer PTO films with PTO/STO superlattices to show enhanced reflectivity proportional to the number of PTO layers.

Experimental results

Research questions

• RQ1 Can collective vibrational modes of 180° domain walls in ferroelectric thin films produce resonant responses in the 0.3–3 THz range?
• RQ2 How does the resonance frequency and damping of these modes depend on film thickness and material composition?
• RQ3 Can reflection-absorption spectroscopy detect the dynamic response of domain walls in the sub- and low-THz region?
• RQ4 What is the role of the paraelectric substrate and film geometry in enhancing the detectability of the resonance?
• RQ5 How does the reflectivity of p-polarized THz radiation change due to the presence of domain walls, and can this be used as a detection mechanism?

Key findings

• The collective vibrational mode of 180° domain walls in PbTiO₃/SrTiO₃ films exhibits a resonance frequency in the 0.3–3 THz range, with a peak at ωr/2π ≈ 0.75 THz for a 30 nm PTO film.
• The resonance is detectable via reflection-absorption spectroscopy, with a reflectivity enhancement ΔR/R ≈ 0.1 at the Brewster angle θB ≈ 86°.
• The resonance frequency increases with decreasing film thickness, and the mode can be tuned across the 0.3–3 THz window by adjusting film thickness and composition.
• The reflectivity enhancement is proportional to the number of PTO layers in superlattices, enabling giant responses in multilayer structures.
• The dynamic permittivity εf(ω) is calculated using effective medium theory and the Lyddane-Sachs-Teller relation, enabling accurate prediction of the resonance frequency and damping.
• The theoretical framework applies generally to ferroelectric films and superlattices, with PZT films showing similar behavior at sub-THz frequencies (0.3–1 THz) as confirmed by ab initio simulations.