Probing (sub)nanoscale ferrons in an electron microscope

Abstract

Ferrons are collective excitations of polarization fluctuations that can enable terahertz communications and quantum transduction due to long propagation lengths. Although ferrons have been experimentally demonstrated in van der Waals ferroelectrics and relaxor ferroelectrics, there is no direct (sub)nanoscale experimental evidence of ferrons in three-dimensional ferroelectrics. Here, we detect two types of ferrons, Higgs and pseudo-Goldstone, at the (sub)nanoscale in lead titanate by measuring vibrational signals due to polarization fluctuations. By harnessing momentum transfer in electron energy loss spectroscopy (EELS), we directly distinguish between soft-phonons and ferrons. We observe that the Higgs mode originates from the soft optical phonon parallel to the polar axis, whereas the pseudo-Goldstone mode originates from the soft optical phonon perpendicular to the polarization axis. Together with Landau theory, Raman spectroscopy measurements, and EELS, we observe that Higgs group velocities, in the bulk limit, are eight times greater than those of out-of-plane soft phonons and the pseudo-Goldstone ferrons have group velocities six times greater than in-plane soft phonons due to long-range dipole interactions. We further show that the domain size confinement effects lead to doubling of the respective bulk ferron group velocities, reaching up to approximately 15 km per second (almost 15 times higher than the out-of-plane soft phonon modes). Overall, this study opens a pathway to the detection of ferrons in three-dimensional ferroelectrics with domain engineering as a promising avenue for terahertz communication and transduction.