Ferrons: Magnetic Polarons & Ferroelectric Excitations

• Ferrons are quasiparticles representing collective excitations in magnetic and ferroelectric materials, defined by self-consistent regions or polarization waves.
• They exhibit distinct dispersion and transport properties, with nonlinear and hybrid coupling that pave the way for efficient THz and energy conversion devices.
• Experimental studies demonstrate their detection via ultrafast optics and device-level ferronics, highlighting applications in thermal management and quantum interconnects.

Ferrons are quasiparticles whose meaning depends on the research context. In older magnetic-transport and correlated-electron literature, the term denoted magnetic polarons or spin-polarized droplets. In recent ferroelectric research, ferrons are defined as quanta of collective electric-polarization waves, i.e. excitations of ferroelectric order that carry electric dipoles and are repeatedly presented as the electric analogue of magnons. Across these usages, the common element is a collective or self-consistent excitation tied to an ordered background—magnetic, ferroelectric, or paired—rather than a generic lattice vibration or band carrier (Polubotko, 2011, Tüzemen et al., 2019, Tang et al., 2022, Bauer et al., 2023).

1. Terminology and historical scope

The older usage goes back to the magnetic-polaron concept associated with E. L. Nagaev. In that formulation, “the conductivity electron creates ferromagnetic region around itself by orientation of the spins of neighbor atoms parallel to its spin,” so a ferron is a conduction electron or hole together with a self-created ferromagnetic region embedded in a paramagnetic or antiferromagnetic background (Polubotko, 2011).

A distinct modern usage emerged in ferroelectric theory. “Excitations of the ferroelectric order” defined ferrons as “the bosonic excitations in ferroelectrics that carry electric dipoles,” generated by the concerted action of anharmonicity and broken inversion symmetry (Tang et al., 2022). “A Perspective on Ferrons” then gave a compact thermodynamic definition: a ferron in state $i$ carries a finite dipole

$$\mathbf{p}_i=-\frac{\partial \omega_i}{\partial \mathbf{E}},$$

and explicitly framed ferrons as the ferroelectric counterparts of magnons (Bauer et al., 2023).

Other literatures retained the older naming convention for localized magnetic or spin-polarized objects. In the unitary Fermi gas, a ferron was introduced as a spin-polarized impurity bounded by a closed nodal surface of the pairing field with a $\pi$ phase shift across that surface (Tüzemen et al., 2019). In CeB$_6$, ferrons were identified with nanoscale spin droplets or spin polarons inside the antiferroquadrupolar phase (Azarevich et al., 2024). This suggests that “ferron” now labels at least two stable technical families: magnetic-polaron-like objects and ferroelectric polarization-wave quasiparticles.

2. Ferrons as localized magnetic or spin-polarized objects

In CuFeSe$_2$, ferrons were used to explain charge transport in a magnetic chalcogenide with p-type, metal-like conductivity. In the paramagnetic interval $70\,\mathrm{K}\le T\le100\,\mathrm{K}$, the observed $\rho\propto T$ together with approximately temperature-independent carrier density implied $\mu(T)\propto 1/T$, which was identified with Mott-type diffusion by small-radius ferrons. At very low temperature, where $\rho(T)$ becomes constant below $T\le10\,\mathrm{K}$, the same work invoked large-radius ferrons with approximately temperature-independent mobility (Polubotko, 2011). In that paper the relevant mobilities were written as

$$\mathbf{p}_i=-\frac{\partial \omega_i}{\partial \mathbf{E}},$$0

for small- and large-radius ferrons, respectively (Polubotko, 2011).

In CeB$$\mathbf{p}_i=-\frac{\partial \omega_i}{\partial \mathbf{E}},$$1, ferrons were not polarization waves but spin droplets in a heavy-fermion metal with dynamic charge stripes. Resistivity, inverse thermal conductivity, and specific heat in the antiferroquadrupolar phase exhibited exponential field dependences of the form

$$\mathbf{p}_i=-\frac{\partial \omega_i}{\partial \mathbf{E}},$$2

with $$\mathbf{p}_i=-\frac{\partial \omega_i}{\partial \mathbf{E}},$$3 from magnetoresistance and $$\mathbf{p}_i=-\frac{\partial \omega_i}{\partial \mathbf{E}},$$4 from relaxation-time analysis. The inferred ferron size was $$\mathbf{p}_i=-\frac{\partial \omega_i}{\partial \mathbf{E}},$$5, consistent with a Ce–Ce pair or small cluster embedded in the AFQ matrix (Azarevich et al., 2024).

In the unitary Fermi gas, ferrons are self-sustained spin-polarized droplets inside a superfluid background. Their defining signature is a closed nodal surface of the pairing field $$\mathbf{p}_i=-\frac{\partial \omega_i}{\partial \mathbf{E}},$$6 surrounding a partially spin-polarized superfluid region, with the phase of $$\mathbf{p}_i=-\frac{\partial \omega_i}{\partial \mathbf{E}},$$7 differing by $$\mathbf{p}_i=-\frac{\partial \omega_i}{\partial \mathbf{E}},$$8 across the nodal surface. The excess polarized particles occupy Andreev bound states localized near that surface, and the object survives after the spin-polarizing potential is removed (Tüzemen et al., 2019).

3. Ferrons as excitations of ferroelectric order

In the ferroelectric literature, ferrons are collective excitations of the polarization order parameter. For a uniaxial displacive ferroelectric described by a Landau–Ginzburg–Devonshire functional,

$$\mathbf{p}_i=-\frac{\partial \omega_i}{\partial \mathbf{E}},$$9

small fluctuations around the ordered state $\pi$0 obey Landau–Khalatnikov–Tani dynamics and have dispersion

$\pi$1

In this uniaxial displacive setting, the ferron is the longitudinal amplitude mode of the polarization, and the dipole per ferron can be written as

$\pi$2

(Tang et al., 2022).

A broader vector formulation appears in the Landau–Khalatnikov–Tani treatment of uniaxial ferroelectrics with $\pi$3. Linearization around $\pi$4 yields three bulk ferron eigenmodes with polarizations along $\pi$5: $\pi$6 with corresponding eigenvectors $\pi$7, $\pi$8, and $\pi$9 (Nursagatov et al., 5 Feb 2026). In this formulation, ferrons are quantized polarization waves, i.e. bosons associated with fluctuations $_6$0 of the macroscopic polarization field.

The perspective literature makes an additional distinction: not all phonons are ferrons. A mode qualifies as a ferron only if its energy changes linearly with electric field, equivalently if it carries a finite dipole in the sense of $_6$1 (Bauer et al., 2023). In LiNbO$_6$2, recent first-principles work further described ferrons as electric-dipole-carrying phonons in an anharmonic double-well potential, including $_6$3 amplitude modes along $_6$4 and in-plane $_6$5-mode ferrons that tilt the polarization (Pols et al., 17 Oct 2025).

4. Dispersion, transport, and collective response

Ferron transport theory was formulated in close analogy with spin caloritronics. In one dimension, polarization and heat currents were written as

$_6$6

introducing polarization conductivity, a ferroelectric Seebeck coefficient, and a ferroelectric Peltier coefficient (Bauer et al., 2023). In the displacive LGD treatment, ferrons were predicted to contribute to low-temperature pyroelectricity, electrocaloric response, and electric-field-tunable heat and polarization transport (Tang et al., 2022).

The role of ferrons in thermal properties was revisited for PbTiO$_6$7. There the ferron was explicitly identified as the collective amplitude mode of the ferroelectric order parameter with temperature-dependent dispersion

$_6$8

The work argued that ferron softening near $_6$9 is essential for reproducing the measured temperature and electric-field dependence of specific heat and thermal conductivity, in contrast to models that attribute thermal properties solely to acoustic phonons (Zhao et al., 29 Jan 2025).

Long-range dipolar interactions also produce distinctive surface ferrons. For a uniaxial ferroelectric slab, the predicted low-frequency surface branch lies at $_2$0, is strongly anisotropic, and has in-plane polarization transverse to its wave vector, while its evanescent stray electric field is circularly polarized and momentum-locked. A focused THz beam can therefore launch four narrow ferron beams, enabling directional routing in the surface plane (Zhou et al., 2022).

Transverse transport has now been extended to the Hall geometry. In BaTiO$_2$1, atomistic lattice dynamics with a magnetic-field-induced gyroscopic term predicted a ferron Hall effect: a longitudinal thermal gradient produces a transverse accumulation of polarization at the sample edges because the Hall-deflected soft-mode excitations carry dipole moments. The calculated edge signal reached $_2$2 (Lopez et al., 29 Jun 2026).

Flexoelectric coupling adds another layer of dispersion engineering. In CuInP$_2$3S$_2$4, “flexoferrons” were introduced for polarization fluctuations strongly modified by static and dynamic flexocoupling. Analytical LGD results showed strongly anisotropic, electric-field-dependent dispersion, and the acoustic flexophonon and flexoferron frequency was predicted to tend to zero at nonzero wavevector under increasing applied field, suggesting the appearance of a spatially modulated incommensurate polar phase (Morozovska et al., 23 Jul 2025).

5. Nonlinear, hybrid, and higher-order ferronic phenomena

Ferrons now appear in several nonlinear and hybrid settings. In superconductor/ferroelectric/superconductor trilayers, the $_2$5-polarized ferron branch couples to the confined Swihart photon through the electric-dipole interaction

$_2$6

Diagonalization yields upper and lower ferron–polaritons with an ultrastrong-coupling anticrossing and a THz-scale spectral gap; the $_2$7- and $_2$8-polarized ferrons remain dark in that geometry (Nursagatov et al., 5 Feb 2026).

The concept has also been extended beyond purely electric character. “Multiferrons” were introduced for elliptically excited degenerate $_2$9 modes in LiNbO$70\,\mathrm{K}\le T\le100\,\mathrm{K}$0, which carry both a net in-plane polarization and an out-of-plane magnetization through dynamical multiferroicity. In that construction,

$70\,\mathrm{K}\le T\le100\,\mathrm{K}$1

and the excitations additionally carry electric and magnetic quadrupole and octupole moments termed “multipolons” (Pols et al., 17 Oct 2025).

A different nonlinear regime was demonstrated theoretically in NbOI$70\,\mathrm{K}\le T\le100\,\mathrm{K}$2, where a 3.1 THz ferron mode $70\,\mathrm{K}\le T\le100\,\mathrm{K}$3 coherently upconverts into a 7.0 THz optical phonon $70\,\mathrm{K}\le T\le100\,\mathrm{K}$4. The minimal anharmonic potential was written as

$70\,\mathrm{K}\le T\le100\,\mathrm{K}$5

and two-dimensional THz spectroscopy was predicted to show an off-diagonal peak at $70\,\mathrm{K}\le T\le100\,\mathrm{K}$6, $70\,\mathrm{K}\le T\le100\,\mathrm{K}$7. The same work tied the phase and hysteresis of the upconverted signal to in situ switching of the ferroelectric order parameter (Subedi et al., 19 Mar 2026).

Ferrons have also been proposed as a platform for THz frequency combs. In a ferroelectric thin film, nonlinear polarization-wave dynamics driven by a focused THz field generate sidebands at

$70\,\mathrm{K}\le T\le100\,\mathrm{K}$8

and the efficiency of the comb is exactly proportional to the static electric polarization carried by the ferron modes,

$70\,\mathrm{K}\le T\le100\,\mathrm{K}$9

This directly links a measurable nonlinear output to an intrinsic ferron property (Ye et al., 30 Mar 2026).

Ferron currents can also act on ferroelectric textures. For a domain wall in a uniaxial ferroelectric, the linearized problem maps onto a Schrödinger equation with a Pöschl–Teller potential, implying reflectionless transmission of linear ferrons and no net force. Intrinsic nonlinearities, however, generate second-harmonic scattering and a negative radiation pressure that pulls the domain wall toward the source (Yang et al., 11 Mar 2026).

6. Experimental status and applications

Direct experimental observation of coherent ferrons was reported in the van der Waals ferroelectric NbOI$\rho\propto T$0. Ultrafast optical pumping launched collective oscillations of ferroelectric dipoles, identified through intense and narrow-band THz emission, and coherent ferron propagation was observed along the polar direction at hypersonic velocities exceeding $\rho\propto T$1. The emission was a second-order nonlinear process that required ferroelectric order, as confirmed by comparison with ferroelectric WO$\rho\propto T$2Br$\rho\propto T$3 and non-ferroelectric TaOBr$\rho\propto T$4 (Choe et al., 28 May 2025).

A later NbOX$\rho\propto T$5 study pushed this toward device-level ferronics. In layered NbOX$\rho\propto T$6 ($\rho\propto T$7), multiple ferron modes generated intense narrowband THz emission with quality factors up to 228 and radiation efficiencies up to five orders of magnitude greater than state-of-the-art semiconductor emitters. Resonant excitation of a high-$\rho\propto T$8 ferron mode achieved efficiencies two orders of magnitude higher than intense lithium niobate THz sources, and the ferron oscillations exhibited direct, non-volatile electric-field control through phase reversal and hysteresis (Zhang et al., 7 Sep 2025).

This experimental turn is notable because the 2023 perspective still described ferronics as a field with scarce direct transport measurements and emphasized the need for systematic spectroscopy, direct detection of polarization currents, and device-scale demonstrations (Bauer et al., 2023). The newer literature now adds coherent generation, transport, nonlinear conversion, room-temperature THz emission, and electric-field programmability (Choe et al., 28 May 2025, Zhang et al., 7 Sep 2025).

The application space described across these works includes thermal management, polarization caloritronics, ferronic information processing, quantum interconnects, THz spectroscopy, and hybrid superconducting or photonic platforms (Bauer et al., 2023, Nursagatov et al., 5 Feb 2026, Choe et al., 28 May 2025, Zhang et al., 7 Sep 2025). A plausible implication is that ferrons are becoming a unifying language for electrically active collective modes in ferroelectrics, while the older magnetic-polaron usage remains active in specific correlated-electron contexts.