The ancient Greek philosopher Democritus viewed swirling vortices of matter, along with atoms, as fundamental components of the Universe. Nowadays, vortices are seen at all scales — from spiral galaxies and whirlpools to microscopic examples in superconductors and quantum fluids. Moreover, vortices have been found to greatly affect the properties of many materials, including superconductors, ferromagnets (materials exhibiting the familiar form of magnetism found in iron) and ferroelectrics (the electrical counterparts of ferromagnets). In a paper in Nature, Li et al.1 report that vortices of electrical polarization in ferroelectrics can vibrate at terahertz-level frequencies (1 THz is 1012 Hz). The collective dynamics of such vortices potentially offer a platform for ultrafast data processing driven by electric fields.
Ferroelectrics have an intrinsic electrical polarization that is caused by a slight relative shift of positively and negatively charged ions in opposite directions. In nanometre-scale ferroelectrics, these ions not only interact with an applied electric field, but also produce a substantial internal electric field owing to charges arising at the material surfaces. The resulting self-interaction of the ions through this internal field generates a plethora of polarization patterns — such as vortices and intricate structures called skyrmions and hopfions. Until now, the dynamics of these polarization patterns had been conjectured2–5, but not demonstrated experimentally.
To address this lack, Li and colleagues used a structure called a ferroelectric superlattice, which consists of stacked alternating films of a ferroelectric and an electrical insulator. Since the dawn of solid-state physics6,7, it has been known that magnetic films harbour periodic domains of alternating oppositely oriented magnetization. But it was recognized only in the past few decades that similar polarization domains arise in ferroelectrics. The polarization pattern is more elaborate in ferroelectric superlattices than in isolated ferroelectrics, and gradually changes between domains8. Moreover, this pattern has been shown experimentally to evolve into a periodic system of vortices and antivortices (whirls that rotate in the opposite direction to vortices)9.
The authors used ultrashort pulses of terahertz radiation to generate vortex motion in the ferroelectric films of the superlattice. They then used a technique known as ultrafast X-ray diffraction to probe the dynamics of the periodic vortex–antivortex structure. These state-of-the-art experimental methods allowed Li et al. to induce and analyse the collective movement of the polarization vortices directly on picosecond timescales (1 ps is 10–12 s). The authors detected a single mode of vibration at 0.08 THz and a set of such modes at 0.3–0.4 THz.
In terms of dynamics, the vortex–antivortex system (Fig. 1a) resembles a linear chain of balls connected by elastic springs. The role of elastic forces is taken by electrostatic interactions between the ions that maintain vortex periodicity. The system can host two types of collective vibration, an up-and-down (transverse) motion (Fig. 1b) and a side-to-side (longitudinal) motion (Fig. 1c).
Li et al. attributed their detected 0.08-THz mode to transverse vibrations. This previously unseen vortex motion indicates that an instability accompanies a structural transition to a state in which the vortex centres form a zigzag chain. Compared with the 0.08-THz mode, those at 0.3–0.4 THz are associated with more-intricate vortex dynamics and can be less easily attributed to a particular type of vibration.
To unravel the full picture of vortex dynamics, future work needs to distinguish between inter-vortex motion, intra-vortex motion and vortex bending. Moreover, the longitudinal mode of vibration must be identified. This mode is associated with a sequence of alternating displacements of domain walls (the boundaries between domains) and has remarkable properties that arise from the associated dynamics of surface charges.
In metals, surface charges oscillate at frequencies corresponding to ultraviolet light (about 1015 Hz), and the collective oscillations are known as plasmons. Similarly, in a ferroelectric film, the longitudinal mode causes surface charges to oscillate at terahertz frequencies, and the collective oscillations can be thought of as polarization plasmons. In such a film, as in metals, a quantity called the dielectric constant is negative when the frequency of an applied electric field is lower than the plasmon oscillation frequency. Surprisingly, the dielectric constant in the ferroelectric film remains negative as the frequency of the applied field tends to zero, resulting in a negative-capacitance effect5 — a phenomenon that promises to reduce the power consumption of next-generation nanoscale electronic devices.
The past decade has seen remarkable progress in developing terahertz semiconductor devices, working in the frequency range between radio waves and infrared light. The potential applications of these devices span wireless transmission of vast amounts of data, detection of distant security threats, 6G wireless technology and opportunities for non-invasive medical imaging. Li and colleagues’ discovery that polarization vortices in nanoscale ferroelectric films can vibrate at terahertz-level frequencies could help to scale down terahertz devices to the nanoscale and achieve high-speed, high-density data processing driven by electric fields. Such advances might enable the development of terahertz optoelectronics and plasmonics (plasmon-based photonics), ultrafast data exchange and intra-chip communications in emerging computer circuits.
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