Charge order is a common symmetry-broken state in strongly correlated electron systems, found in transition-metal oxides, organic conductors, and low-dimensional quantum materials. Its equilibrium properties are well studied, but nonequilibrium dynamics and control of charge order remain underdeveloped. Unlike magnetic order, for which a mature theory of spin dynamics and magnetization switching methods exists, charge order lacks a microscopic foundation. A recent experiment on electrical switching of charge-order polarity in LuFe2O4 showed a phenomenological analogy to current-induced magnetization switching, but the microscopic connection remained unclear. This work fills that gap by deriving pseudospin dynamics of charge order from a microscopic model.
The starting point is the extended Hubbard model with local (U) and intersite (V) Coulomb repulsion. In the strong charge-ordering regime near half filling, local states reduce to empty |0⟩ and doubly occupied |2⟩ sites. These states form a pseudospin-1/2, where the longitudinal component τz describes the local charge configuration and the transverse components describe quantum transitions between them. Using a Schrieffer-Wolff transformation to second order in hopping, an effective pseudospin Hamiltonian with anisotropic exchange is obtained: an antiferromagnetic Ising coupling Jz stabilizes charge order, while a ferromagnetic transverse coupling J⊥ provides coherent pair transfer. Next, an external electric field is introduced, acting as a staggered longitudinal field on the two pseudospin sublattices. The dynamics is described by Landau-Lifshitz-Gilbert equations with phenomenological Gilbert damping. In the macrospin approximation, collective variables are introduced: the charge-order vector N (difference of sublattice pseudospins) and the conjugate uniform component M (their sum). For strong charge order, M is eliminated, yielding a closed equation of motion for N, analogous to the equation for the Néel vector in an antiferromagnet.
An equation of motion for the charge-order vector N is obtained, containing an inertial term with an effective mass that depends on the electric field, and describing precession and damping. Linearization near equilibrium yields two circular modes with frequencies that can be tuned by the electric field. The critical switching field Ec is determined by the instability condition of transverse fluctuations: at E = Ec, the collective mode frequency vanishes and damping changes sign, leading to exponential growth of fluctuations and reversal of charge-order polarity. For typical parameters (dipole moment p0 ~ eÅ, ZJz ≈ 30 meV, ZJ⊥ ≈ 10 meV), the estimate gives |Ec| ≈ $10^6$ V/cm and collective mode frequency ΩCO/2π ≈ 3.4 THz. These values are comparable to coercive fields of ferroelectrics and frequencies of ferron excitations. Numerical simulation at field E/Ec = 1.2 shows that the longitudinal component Nz oscillates and transitions from +τ0 to −τ0, while the transverse component Nx first grows due to instability, then decays. For nonzero uniform field hz (e.g., due to doping), the trajectory acquires a nutation character, analogous to inertial magnetization dynamics.
This work establishes the pseudospin as a microscopic dynamical degree of freedom for coherent switching and control of charge order. It provides a charge analog of the well-developed theory of spin dynamics in spintronics. Unlike neighboring works that consider sliding of charge-density waves or photoinduced melting of charge order, here a mechanism for coherent rotation of the charge-order vector under an electric field is proposed. This opens a route to electrical control of charge order via pseudospin currents and torques, analogous to spin torques. The results also allow separate determination of exchange parameters Jz and J⊥ from measurements of the collective mode frequency and critical switching field.
The topic can develop toward including spatially inhomogeneous dynamics, gradient terms, and domain walls. Generalization to finite temperatures, coupling to the lattice and phonons, and the role of disorder and defects are possible. It is also interesting to consider quantum fluctuation effects and the possibility of quantum tunneling of the pseudospin. The connection with recent experiments on ultrafast polarity switching in LuFe2O4 and other materials with electronic ferroelectricity may stimulate the search for new systems with controllable charge order.
The results may impact the physics of strongly correlated electrons, ferroelectricity, multiferroics, and spintronics, offering a new way to control charge degrees of freedom. Practically, this could lead to devices for information storage and processing based on charge-order switching.
Immediate next steps include testing predictions in experiments with strong electric fields and time resolution, such as terahertz spectroscopy or ultrafast diffraction. It is also important to investigate the role of domain walls and inhomogeneities in real materials.
This work directly addresses the unresolved problem of microscopic description of nonequilibrium dynamics of charge order in strongly correlated systems. It proposes a concrete mechanism for coherent switching that was previously missing and connects charge order to the well-studied dynamics of antiferromagnets. This fills the gap between static models of charge order and experimental observations of ultrafast switching.
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What the work does
This work derives an effective pseudospin model for charge order from the extended Hubbard model in the strong-interaction regime. The resulting Landau–Lifshitz–Gilbert equations are analogous to antiferromagnetic dynamics, and it is shown that an external electric field acts as a step field, inducing coherent polarity switching once a threshold is exceeded.
Where its strength is
A direct microscopic link between charge order and pseudospin dynamics is established, providing a basis for electrical control in analogy with spin electronics.
Where it could go next
Worth trying
Why this may matter
The proposed pseudospin approach could serve as a general framework for describing the nonequilibrium dynamics of charge orders in various materials and open pathways to charge-based electronic devices.
Nearby works in our archive
The archive is sparse around this work: the closest review is only 0.53, against a usual 0.64. It looks like few have drilled nearby.
The frequency of collective pseudospin excitations of charge order lies in the terahertz range, that is, about a trillion oscillations per second. This is a million times faster than the typical frame rate in movies.