Multiferrons: lattice excitations with finite polarization and magnetization

TL;DR

The paper introduces multiferrons, a new class of lattice excitations in ferroelectrics that carry both electric polarization and magnetization, accessible without magnetic order. Using first-principles calculations on LiNbO$_3$, it shows that multiferrons have a net polarization perpendicular to the static ferroelectric polarization and a magnetization parallel to it, and they host higher-order multipoles (multipolons). The dynamics are captured with a Landau-Devonshire-type potential for degenerate E-mode phonons, where anharmonic cubic terms and tailored laser pulses generate linearly, elliptically, or circularly polarized responses, yielding controllable polarization, magnetization, and radial multipoles. The work reveals a rich multipolar landscape (quadrupoles and octupoles) tied to coherent phonon dynamics, suggesting new routes to couple and transport electric and magnetic multipoles and to probe them with neutron scattering or in altermagnetic contexts. These findings point to broad applicability across ferroelectrics and potential applications in ultrafast, multipole-based information technologies.

Abstract

Ferrons are a type of quasiparticle corresponding to elementary excitations of the ferroelectric order. Analogously to how magnons modulate and transport magnetization, ferrons modulate and transport electric polarization. Here, we introduce multiferrons as elementary excitations with both electric and magnetic character. Multiferrons lead to a tilt and elliptical precession of the polarization and at the same time create a magnetization through the mechanism of dynamical multiferroicity. Using first-principles calculations for LiNbO$_3$, we show that the electric polarization of multiferrons is perpendicular to the equilibrium ferroelectric polarization, whereas the magnetization is parallel to it. Our calculations further demonstrate that multiferrons carry net electric and magnetic quadrupole and octupole moments, which we term multipolons. These multipolons could couple to internal multipolar degrees of freedom, for example in altermagnets, or to external probes such as neutrons, leading to potentially experimentally observable phenomena following coherent or thermal excitation of multiferrons.

Figures (4)

• Figure 1: Ferrons in LiNbO$_3$. (a) Excitation of $A_1$ modes leads to anharmonic oscillations of the electric polarization $\mathbf{P}_\mathrm{ph}$, generating ferrons with a net polarization $\overline{\mathbf{P}}$, reducing the magnitude of the ferroelectric polarization $\mathbf{P}_0$. (b) Linear excitation of anharmonic $E$ modes produces in-plane ferrons with a net polarization perpendicular to the ferroelectric polarization, $\overline{\mathbf{P}}\perp\mathbf{P}_0$, leading to a tilting and increase of the total polarization (dashed line). (c) Elliptical excitation of anharmonic $E$ modes yields multiferrons, in which the total polarization precesses, leading to a net in-plane polarization and a net out-of-plane magnetization $\overline{\mathbf{M}}$. Polarization dynamics are shown in blue, net ferron polarization in red, and magnetization in orange.
• Figure 2: Magnetization induced by circular and elliptical excitation of the $E$ modes in LiNbO$_3$. (a) Superposition between the static ferroelectric polarization $\mathbf{P}_{0}$ and rotating phonon polarization $\partial_{t} \mathbf{P}_\mathrm{ph}$. (b) Resulting radial magnetization $\mathbf{M}_{\mathrm{rad}}$.
• Figure 3: Electric polarization and magnetization dynamics induced by resonant excitation of degenerate $E$ modes at 4.32 in LiNbO$_3$. (a,b) Side and top views of the unit cell of LiNbO$_3$. (c-e) Polarization dynamics driven by linearly ($\phi = 0$), elliptically ($\phi = \pi / 4$), and circularly ($\phi = \pi / 2$) polarized pulses in the time window from $-1.0$ to $0.75$. Equipotential lines representing the symmetry of the polarization are shown in gray. (f,g) Time evolution of the radial polarization $| \mathbf{P}_{\mathrm{ph}} |$ and net polarization $| \overline{\mathbf{P}} |$. (h,i) Corresponding time evolution of the radial magnetization $|\mathbf{M}_{\mathrm{rad}}|$ and net magnetization $|\overline{\mathbf{M}}|$.
• Figure 4: Time-averaged quadrupole tensors of radial polarization and magnetization for linearly ($\phi = 0$), elliptically ($\phi = \pi / 4$), and circularly ($\phi = \pi / 2$) polarized pulses. (a,b) Off-diagonal quadrupole tensor contributions to radial polarization $\mathbf{P}_{\mathrm{ph}}$. (c,d) Diagonal and off-diagonal quadrupole tensor contributions to radial magnetization $\mathbf{M}_{\mathrm{rad}}$.