Light-wave control of correlated materials using quantum magnetism during time-periodic modulation of coherent transport

The advent of intense phase-coherent mid-infrared (MIR), terahertz (THz), and attosecond laser pulses with well-characterized temporal profiles opened a promising direction for achieving coherent control of quantum materials during sub-oscillation-cycle timescales. During a single cycle of coherence oscillations, quasi-stationary states (e.g., Floquet) have not yet been reached and relaxation is reduced. In quantum materials, emergent phenomena arise from strong couplings between electronic, spin, and lattice degrees of freedom. Adiabatic tuning of such microscopic interactions using static perturbations (high pressure, magnetic or electric fields) is established but affects multiple properties simultaneously, reducing quantum control selectivity. Ultra-short laser fields provide nonequilibrium routes to manipulate structural and electronic properties. Nonlinear ultrafast processes initiated by coherent photoexcitation can dynamically steer quantum materials to nonequilibrium states not accessible via quasi-equilibrium pathways. Unlike high-frequency photoexcitation where hot-carrier relaxation masks quantum dynamics, multicycle driving by intense THz/MIR fields can achieve nonadiabatic quantum tuning via electron acceleration and control of the many-electron wavefunction phase. Coherent electronic transport can drive systems into metastable or pre-thermalized phases and control phase transitions. In the absence of direct light-spin coupling, magnetic properties are generally indirectly influenced by the electric field, yet experiments reveal femtosecond and attosecond coherent magnetism and ultrafast spin-orbit torque dynamics, indicating that magnetic properties can be manipulated during time-periodic field oscillations. Given available multicycle pulses, understanding driven electron-spin dynamics during non-dissipative sub-cycle timescales is needed. Here, the authors investigate theoretically whether light-wave-periodic modulation of electronic hopping between atomic sites with noncollinear local spins can coherently control magnetic states and phase transitions prior to quasi-stationary-state establishment. Emphasis is placed on quantum fluctuations of a responsive background of local spins strongly interacting with itinerant spins, particularly strong electron-magnon couplings during light-driven coherent hopping. Using Hubbard operators to describe quasiparticles in the strong on-site exchange limit and deriving quantum kinetic equations for the density matrix, they compute the nonadiabatic time evolution during a few oscillation cycles. A generalized mean-field approximation truncates the hierarchy, constraining motion to the lowest Hubbard band. Calculated light-driven spin/charge local populations and intersite coherences yield the total energy versus lattice displacement Q, revealing: (i) development of a more homogeneous spatial electronic distribution via light-driven transport assisted by quantum canting of an AFM background; (ii) transient magnetization developing in sync with coherent transport due to modulation of the AFM-ordered core-spin background; and (iii) a light-induced shift of the total energy minimum toward undistorted lattice (Q=0) during few cycles. This suggests experimental coherent control by tailoring the laser temporal profile to drive desired intersite coherences (currents).

The paper situates its work within the context of ultrafast control of quantum materials using phase-coherent MIR/THz/attosecond fields, citing observations of sub-cycle control and lightwave-driven dynamics (e.g., high-harmonic generation, Rabi flopping, and Dirac currents). It notes that static tuning (pressure, fields) lacks selectivity, while ultrafast coherent photoexcitation can access nonequilibrium states and drive phase transitions. Prior experiments reported femtosecond and attosecond magnetism and coherent spin-orbit torque effects, implying indirect electric-field control of magnetism at ultrafast timescales. Theoretical and experimental works on nonadiabatic quantum tuning, metastable phase control, and light-induced superconductivity/topology transitions underscore the potential of multicycle THz/MIR fields to control correlated electron, lattice, and spin dynamics. However, the universal microscopic mechanism for simultaneous control of charge and spin fluctuations during sub-cycle evolution remained unclear, motivating the present study focused on strong electron-magnon coupling and time-periodic modulation of hopping.

- Model Hamiltonian: H(t) = H_local + H_hop(t). H_local includes strong on-site Hund’s ferromagnetic exchange between itinerant spin s (1/2) and localized core spin S at each site, Zeeman coupling to a weak external magnetic field used to break symmetry, and local lattice-dependent energies. H_hop(t) describes coherent intersite hopping, including transient modulation by the light-wave electric field via the Peierls substitution (expanded to linear order in vector potential for few-cycle dynamics) and/or phonon coherence. - Local basis and strong-correlation treatment: Employ composite-fermion quasiparticles created by Hubbard operators to describe transitions between multielectron/multiatom local configurations that diagonalize H_local. Basis includes N_e-electron core-spin eigenstates |im⟩ (m = S,...,−S) and N_e+1 configurations |i a M⟩ that are eigenstates of total spin J = S + s with J = S + 1/2 retained (lower Hubbard band); upper Hubbard band (J = S − 1/2) neglected. Local configuration labels a encompass orbital/multiatom character and Jahn-Teller (JT) split states dependent on local lattice displacement Q_i. - Spin framework: Work in local coordinate systems with z-axis aligned to quasi-equilibrium spin canting angles θ_i (AFM reference θ_i = 0, π). Quantum spin fluctuations are included by allowing populations of all M ≤ S − 1/2 and m ≤ S − 1 configurations during transport due to off-diagonal exchange (electron-magnon coupling). Strong-coupling limit J_H → ∞ assumed; quantum canting originates from off-diagonal terms and intersite coupling. - Driving fields and time scales: Time-periodic modulation of hopping V(t) over few cycles (~100 fs pulse) by MIR/THz electric fields E(t) = E_0 sin(ω_p t), characterized by Rabi energy d_R(t) = e a E(t) (a lattice constant). Consider T2 ~ 10–20 fs (dephasing of intersite coherences) and T1 ~ 200–500 fs (population lifetimes), with t_p ~ 100 fs pulse durations; T1 exceeds an oscillation cycle to suppress dissipation during steering. - Density matrix formalism: Real-space density matrix on a lattice includes on-site populations and coherences ρ_i for |im⟩ and |iaM⟩, and intersite coherences P_ij^{βα}(M) between configurations at different sites. Quantum kinetic equations of motion for populations and coherences are derived (Supplementary Note 1), ensuring exact charge and spin conservation. Electronic current follows from continuity via intersite coherences. - Lattice and unit cell: Use a three-dimensional CE-type AFM charge/orbital-ordered unit cell (relevant to Pr0.7Ca0.3MnO3 experiments), with zig-zag FM chains in AFM-coupled planes; alternating bridge (Q_B ≠ 0) and corner (Q_C = 0) sites. Numerical convergence obtained on a 4×4×4 lattice with two local configurations per site. - Energy landscape computation: Using the time-dependent nonthermal density matrix ρ(Q_B, t) (populations and coherences), compute total energy E(Q_B, t) = ⟨H_local⟩ + ⟨H_hop(t)⟩ + k Q_B^2 (elastic energy characterized by k), to assess light-induced changes in energy minima as a function of Q_B and time. - Adiabatic benchmark: As reference, solve for adiabatic ramp of hopping V_αβ(t) from 0 to static t_αβ over time T to obtain stationary states and equilibrium spin canting distributions.

- Light-wave-driven quantum transport and spin canting: Few-cycle time-periodic modulation of hopping V(t) drives coherent intersite charge transfer accompanied by quantum spin canting of the AFM core-spin background via strong electron-magnon coupling. This enables hopping between AFM sites that is classically forbidden (S → ∞, J_H → ∞), populating M < S + 1/2 and m < S configurations. - Transient magnetization in sync with transport: Due to spatially nonuniform light-driven core-spin modulation S_z(t) at bridge (Q_B ≠ 0) and corner (Q_C = 0) sites, a net femtosecond magnetization emerges during the pulse. The difference in S_z(t) dynamics between site types grows with increased Rabi energy d_R and appropriate ω_p relative to intersite energy gaps. - Nonthermal populations and coherences: Time evolution under multicycle driving produces a nonthermal density matrix ρ(Q_B, t) with delayed development of different spin-state populations (observable time delays in Fig. 1h), indicative of non-instantaneous spin dynamics during oscillation cycles and Rabi-like back-and-forth coherent motion. - Oscillation signatures: Coherent itinerant spin and charge populations display oscillations at approximately 2ω_p, characteristic of second-order (and higher) nonlinear processes under strong multicycle fields; such signatures are averaged out at high optical frequencies but persist for MIR/THz drives. - Charge homogenization: With increasing d_R, the initial charge imbalance between bridge and corner sites diminishes, leading to a more homogeneous charge distribution throughout the lattice during the pulse. - Field-thresholded energy-landscape switching: Computed total energy E(Q_B, t) as a function of Q_B shows field-dependent evolution: (i) below threshold (e.g., d_R ≈ 50 meV), the global minimum remains at finite Q_B > 0 (insulating), with phonon softening and non-parabolic E(Q_B); (ii) intermediate fields (d_R ≈ 100 meV) further soften and reshape E(Q_B); (iii) above threshold (d_R ≈ 400 meV), a new global minimum emerges near Q_B ≈ 0 during the pulse, corresponding to a metallic phase (per band calculations) not realized in equilibrium. Multiple transient local minima indicate a nonequilibrium phase transition pathway. - Time scales and parameters: Simulations use pulse duration t_p ~ 100 fs; dephasing T2 ~ 10–20 fs; population lifetimes T1 ~ 200–500 fs (measured ~500 fs in an insulating AFM manganite); CE-AFM 4×4×4 lattice. Rabi energies explored include ~50, 100, and 400 meV, with threshold behavior when d_R approaches the intersite energy barrier controlled by Q_B. - Adiabatic vs nonadiabatic contrast: Under adiabatic ramping of V(t), stationary populations are reached without significant shifts in equilibrium Q_s or large spin distortions; under nonadiabatic few-cycle driving, pronounced quantum spin fluctuations, transient magnetization, charge homogenization, and energy-minimum shift to Q_B ~ 0 arise.

The findings demonstrate that strong coupling between light-driven coherent electronic transport and local-moment quantum fluctuations provides a mechanism to manipulate magnetic states on sub-cycle timescales without requiring direct light-spin coupling. Quantum spin canting mediated by electron-magnon interactions enables transport across AFM-aligned sites, leading to transient magnetization synchronized with transport dynamics. The nonthermal redistribution of charge and spin across inequivalent lattice sites modifies the total energy landscape during the drive, enabling ultrafast access to metastable or pre-thermalized phases, including a metallic state near Q_B ≈ 0 that is not attained in equilibrium. This mechanism complements and differs from quasi-stationary Floquet approaches by focusing on nonadiabatic evolution before relaxation sets in and from models of ultrafast magnetism based on adiabatic spin/phonon populations or spin-orbit torque alone. The results support prospects for THz/attosecond magneto-electronics and coherent spintronics in correlated materials, where tailored multicycle MIR/THz fields can steer phase transitions and spin textures in sync with quantum transport, potentially enabling light-induced switches affecting both spins and lattice.

The study introduces a generally applicable theoretical framework based on Hubbard-operator quantum kinetics to describe nonequilibrium spin-charge dynamics in correlated materials under few-cycle light-wave driving. It shows that time-periodic modulation of coherent hopping can: (i) promote charge homogenization via quantum transport assisted by quantum spin canting; (ii) induce transient magnetization synchronized with transport; and (iii) reshape the total energy landscape to favor an undistorted (Q ≈ 0) metallic transient state above a field threshold. These results provide a microscopic mechanism for femtosecond/attosecond magnetism driven by electric fields through electron-magnon coupling and suggest routes for coherent control of magnetism and structural phases at faster-than-THz rates. Future research directions include: computing coupled lattice dynamics Q_B(t) self-consistently with the electronic density matrix; incorporating dissipation beyond phenomenological T1/T2; extending to multi-band/upper Hubbard bands; exploring material-specific parameters via ab initio-informed tight-binding; and designing pulse sequences to optimize desired intersite coherences and phase switching.

- Strong-coupling approximation: Upper Hubbard band (J = S − 1/2) is neglected; J_H → ∞ limit used. Spin dynamics on timescales ~ J_H^{-1} are not captured. - Truncation/mean-field treatment: Generalized mean-field approximation constrains dynamics to the lowest Hubbard band and truncates the density-matrix hierarchy. - Lattice treatment: Local lattice displacements Q_i are treated as classical variables; coherent lattice dynamics Q_B(t) are not computed self-consistently. Energy landscape around Q_B ~ 0 is noted to be less accurate due to near-degenerate intersite levels. - Hamiltonian simplifications: Off-diagonal terms in H_local are not included; Peierls coupling is treated to linear order in vector potential; spin canting considered within chosen local axes with a weak external B field to break symmetry. - Finite-size and model system: Simulations use a 4×4×4 lattice and CE-type AFM unit cell parameters; quantitative predictions may vary with system size and material-specific details. - Dissipation and decoherence: Dephasing (T2) and relaxation (T1) are included phenomenologically; full coupling to baths is not explicitly modeled.