Kinetic Magnetism in Correlated Systems

• Kinetic magnetism is the emergence of magnetic order from carrier motion, path interference, and non-equilibrium kinetics rather than static exchange interactions.
• In correlated lattice models, doped holes and doublons lower their kinetic energy by selecting specific spin backgrounds, leading to ferromagnetic, antiferromagnetic, or spiral states.
• Experimental platforms like ultracold atoms and moiré materials validate these effects by showcasing particle-hole asymmetry, frustration, and tunable magnetic responses.

Searching arXiv for the cited kinetic-magnetism papers to ground the article in current literature. Kinetic magnetism denotes magnetic order or magnetic response selected by carrier motion, path interference, or nonequilibrium transformation kinetics rather than by static exchange alone. In the narrow usage dominant in strongly correlated lattice models, it refers to magnetism generated because doped holes or doublons lower their kinetic energy in particular spin backgrounds; in broader usage, the same phrase or closely related forms such as “kinetomagnetism” also refer to second-order kinetic exchange in anisotropic ions, current-induced magnetization, and magnetic states governed by kinetic arrest. Taken together, these literatures suggest a common theme: magnetism is controlled by dynamical accessibility and motion, not only by equilibrium spin Hamiltonians (Morera et al., 2022, Iwahara et al., 2015, Chaddah et al., 2010, Cheong et al., 20 Mar 2025).

1. Conceptual scope

In correlated-electron physics, kinetic magnetism is most sharply defined in regimes where the conventional superexchange scale is absent or subdominant. For the Hubbard model,

$$\hat H = -\sum_{\langle i,j\rangle,\sigma} t_{ij}\left(\hat c^\dagger_{i\sigma}\hat c_{j\sigma}+\mathrm{h.c.}\right)+U\sum_i \hat n_{i\uparrow}\hat n_{i\downarrow}-\mu\sum_i \hat n_i,$$

half-filling and large $U/t$ give the familiar superexchange scale

$J=\frac{4t^2}{U},$

but away from half-filling the motion of real carriers can select a preferred spin background. In the strict $U=\infty$ limit, $J\to 0$, so any ordering tendency that survives is purely kinetic in origin (Xu et al., 2022, Sherif et al., 21 Oct 2025).

The term is broader in other subfields. In lanthanide and actinide chemistry it can denote kinetic exchange arising from virtual hopping, including a second-order single-to-double occupied contribution of order $t^2/U$ in strongly anisotropic doublets. In nonequilibrium magnetism it can denote current-induced magnetization. In first-order magnetic transitions it can denote magnetic behavior controlled by kinetic arrest rather than equilibrium phase selection. This diversity is genuine rather than accidental; a cautious synthesis is that “kinetic magnetism” names a family of mechanisms in which motion or transformation rates enter the magnetic problem at leading order (Iwahara et al., 2015, Osumi et al., 2021, Chaddah et al., 2010, 0710.0931).

A common misconception is to equate kinetic magnetism with ferromagnetism alone. The literature does not support that restriction. Depending on dopant type, loop parity, magnetic anisotropy, or external flux, kinetic mechanisms can favor ferromagnetic, antiferromagnetic, singlet-rich, spiral, or phase-separated states (Morera et al., 2022, Sherif et al., 21 Oct 2025, Pereira et al., 18 Jun 2025, Pei et al., 10 Jun 2026).

2. Microscopic origin in correlated lattice models

The canonical microscopic setting is the doped Hubbard or $t$-$J$ model under strong no-double-occupancy constraints. In this regime, the dopant’s closed trajectories permute spins, and the corresponding amplitudes depend on the sign structure of the graph. On bipartite lattices this logic underlies Nagaoka ferromagnetism; on non-bipartite lattices, odd loops can reverse the preference and generate kinetic antiferromagnetism or local singlet formation (Sherif et al., 21 Oct 2025, Pereira et al., 18 Jun 2025).

The triangular lattice is the standard frustrated case. For the infinite-$U$ triangular Hubbard model, the $t$-$U/t$0 Hamiltonian reduces to constrained hopping alone,

$U/t$1

so there is “no magnetic order intrinsically favorable to begin with.” In that setting, finite hole density stabilizes the Haerter–Shastry $U/t$2 antiferromagnet over a substantial doping window, demonstrating that antiferromagnetism itself can be kinetically selected (Sherif et al., 21 Oct 2025).

The local interference mechanism can be seen already on a single triangle. With one hole and two fully polarized spins, the ground-state energy is $U/t$3; with opposite spins, the two paths no longer destructively interfere and the energy becomes $U/t$4. This local comparison is the minimal counter-Nagaoka argument for triangular-lattice kinetic antiferromagnetism (Sherif et al., 21 Oct 2025).

At finite temperature above the superexchange scale, the same logic survives in a different language. On triangular-type lattices with $U/t$5, high-temperature analyses and tensor-network calculations show that hole doping induces effective antiferromagnetic correlations, while electron doping induces Nagaoka-type ferromagnetic correlations. The paper summarizes this by an effective scale

$U/t$6

with $U/t$7 for hole doping and $U/t$8 for electron doping, so the kinetic term can exceed $U/t$9 in magnitude (Morera et al., 2022).

3. Frustration, doping asymmetry, and magnetic polarons

Frustration makes kinetic magnetism strongly particle-hole asymmetric. In an ultracold-atom realization of the anisotropic triangular-lattice Hubbard model at $J=\frac{4t^2}{U},$0, the nearly isotropic triangular limit showed robust antiferromagnetic nearest-neighbor correlations on the hole-doped side, but rapid suppression and eventual sign reversal on the particle-doped side. The nearest-neighbor correlator became ferromagnetic above approximately $J=\frac{4t^2}{U},$1, and at $J=\frac{4t^2}{U},$2 the measured values were

$J=\frac{4t^2}{U},$3

The same work emphasized that what was observed was short-ranged ferromagnetic correlation at finite temperature, not a demonstrated thermodynamic ferromagnetic phase (Xu et al., 2022).

The interpretation is that particle and hole dopants see opposite effective hopping signs on triangular loops. With the sign convention of that experiment, particle dopants prefer a ferromagnetic triplet background because it allows constructive quantum interference around triangular plaquettes, whereas hole dopants prefer an antiferromagnetic singlet background. This is the experimentally most direct modern statement of kinetic magnetism in a doped frustrated Hubbard system (Xu et al., 2022).

A complementary formulation is in terms of magnetic polarons. In the high-temperature spin-incoherent Mott regime, a hole or doublon dresses itself with a preferred local spin cloud. The relevant three-point correlator is

$J=\frac{4t^2}{U},$4

Numerically, hole polarons on triangular lattices carry antiferromagnetic clouds, while doublon polarons carry ferromagnetic ones (Morera et al., 2022).

Above half-filling, DMRG on the triangular Hubbard model found that strong coupling and low doublon doping produce Nagaoka-type ferromagnetic polarons whose attraction leads to phase separation between a fully polarized finite-doping region and the half-filled commensurate spin-density wave. At intermediate $J=\frac{4t^2}{U},$5, the competition between antiferromagnetic superexchange and kinetic magnetism yields an incommensurate SDW instead of immediate ferromagnetism. The strong-coupling estimate

$J=\frac{4t^2}{U},$6

captures the growth of total spin with doublon number in the Nagaoka-polaron regime (Morera et al., 2024).

4. Geometry and topology as control parameters

A central result of recent work is that kinetic magnetism is highly programmable by geometry. For the single-dopant hard-core Hubbard model interpolating from square to triangular connectivity, the hole-doped system shows a crossover from kinetic ferromagnetism to kinetic antiferromagnetism as one diagonal hopping $J=\frac{4t^2}{U},$7 is turned on. The crossover in the nearest-neighbor spin correlator occurs around $J=\frac{4t^2}{U},$8, and the extrapolated $J=\frac{4t^2}{U},$9 value is $U=\infty$0 (Pereira et al., 18 Jun 2025).

On arbitrary graphs, local frustration centers can be embedded deliberately. Exact diagonalization shows that odd-loop motifs bind local singlets while still sharing a delocalized hole, so the effect of frustration is not merely to weaken Nagaoka ferromagnetism but to sculpt the spatial pattern of spin order. In ladders and grids, frustration centers localize magnons more strongly than holes; on random graphs, total spin anticorrelates with odd-loop content and with the frustration index, while bondwise spin alignment tracks the local loop environment (S et al., 10 Jul 2025).

Quantum-dot array studies make this graph dependence quantitative. For finite Hubbard clusters one hole away from half-filling, algebraic connectivity $U=\infty$1 and the sitewise variation of Katz centrality predict the robustness of Nagaoka ferromagnetism. In square arrays,

$U=\infty$2

and geometries with large $U=\infty$3 and low Katz-centrality fluctuation per site exhibit larger $U=\infty$4, even though the local ferromagnetic spin-correlation cloud becomes weaker. A perpendicular magnetic field introduces Peierls phases and a critical flux beyond which Nagaoka ferromagnetism is destroyed; tuning the flux to $U=\infty$5 yields a counter-Nagaoka state with antiferromagnetic correlations (Hernandez-Cepeda et al., 18 Dec 2025).

The kagome lattice adds a further layer of frustration. In the single-hole $U=\infty$6 problem, a doped hole near full polarization binds reversed spins into an RVB polaron. For small numbers of reversed spins the polaron is dispersive but extremely heavy; for $U=\infty$7 reversed spins the reported bandwidth drops below $U=\infty$8, consistent with self-trapping. As magnetization is reduced, the local RVB physics evolves toward $U=\infty$9 antiferromagnetic correlations, showing that kinetic magnetism on highly frustrated lattices can interpolate between short-range valence-bond structure and semiclassical order (Pei et al., 10 Jun 2026).

Particle statistics also matter. In the antiferromagnetic bosonic $J\to 0$0-$J\to 0$1 model on the square lattice, DMRG found partially filled stripes at low doping, a partially polarized ferromagnetic regime driven by Nagaoka polarons at intermediate doping, and a fully polarized ferromagnet at larger doping or larger $J\to 0$2. This suggests that some phenomena associated with kinetic ferromagnetism are strengthened when fermionic exchange signs are removed (Harris et al., 2024).

5. Materials platforms and predictive approaches

Ultracold-atom simulators have become a primary platform because they permit single-site measurements of equal-time correlators and tunable frustration. In anisotropic triangular optical lattices loaded with $J\to 0$3Li, the half-filled system evolves from short-range Néel correlations to a short-range $J\to 0$4 spiral as $J\to 0$5 approaches unity, while doping reveals the strong particle-hole asymmetry discussed above. The relevant observable is the connected spin correlator

$J\to 0$6

measured with single-site resolution (Xu et al., 2022).

Moiré materials provide a solid-state counterpart. In MoSe$J\to 0$7/WS$J\to 0$8, optical measurements near the $J\to 0$9 Mott state found that the state at $t^2/U$0 is approximately paramagnetic, while for $t^2/U$1 the magnetic susceptibility increases sharply and the Curie-Weiss constant becomes positive, consistent with ferromagnetic correlations on the electron-doped side. The interpretation uses an extended triangular-lattice $t^2/U$2-$t^2/U$3 model with assisted hopping, in which doublon motion is enhanced relative to hole motion and thereby amplifies kinetic ferromagnetism (Ciorciaro et al., 2023).

First-principles-inspired continuum calculations now reach the same terrain from the opposite direction. Neural-network variational Monte Carlo applied directly to moiré Hamiltonians predicts an itinerant ferromagnetic metal in WSe$t^2/U$4/WS$t^2/U$5 at $t^2/U$6, diagnosed by a partially filled minority-spin Fermi sea and $t^2/U$7, while a twisted $t^2/U$8-valley homobilayer at $t^2/U$9 becomes a Néel antiferromagnetic insulator once localization is strong enough for kinetic superexchange to dominate. The paper explicitly frames both outcomes as consequences of the competition between kinetic energy and Coulomb interaction (Geier et al., 9 Feb 2026).

Interface systems offer another route. In a bilayer $t$0 Hubbard model for a Mott-insulator/band-insulator interface, perturbation theory at large interlayer offset $t$1 yields an effective ferromagnetic coupling in the Mott layer,

$t$2

generated by virtual motion through the high-density metallic layer. DMRG then finds nearly saturated ferromagnetism at high density and Néel order at low density, supporting the claim that kinetic magnetism is enhanced by proximity between localized and itinerant subsystems (Iaconis et al., 2015).

6. Broader terminological extensions

The phrase is also used in exchange theory. For strongly anisotropic doublets with unquenched orbital momentum, a new single-to-double occupied kinetic exchange mechanism appears already in second order, $t$3, and can be as strong as conventional single-to-single occupied superexchange. In non-collinear anisotropic systems this contribution can make the total exchange ferromagnetic, especially for late lanthanides and some $t$4 or $t$5 transition-metal ions. This extends standard Anderson–Goodenough–Kanamori reasoning into the spin-orbit-entangled regime (Iwahara et al., 2015).

In another branch of the literature, “kinetomagnetism” denotes current-induced magnetization. One symmetry-based classification states that the essential prerequisite is broken $t$6 symmetry, and relates odd- and even-order current-induced magnetization to altermagnetic point groups. A related chiral formulation proposes that in a chiral medium any moving object induces magnetization along its direction of motion, unifying diagonal current-induced magnetization, natural optical activity, magnetochiral effects, and chiral phonons under a common symmetry principle (Cheong et al., 20 Mar 2025, Huang, 2024).

Topological-insulator work gives a particularly concrete realization of this nonequilibrium meaning. There the kinetic magnetoelectric effect is an orbital analogue of the Edelstein effect: a longitudinal current carried by topological surface states produces a nonequilibrium orbital magnetization. Because the current is confined to surfaces, the response per current can exceed that in ordinary metals by $t$7–$t$8 orders of magnitude, and the effect depends explicitly on the surface termination rather than only on bulk topology (Osumi et al., 2021).

A quite different usage appears in first-order magnetic transitions. “Magnetic glass” describes a low-temperature state produced when a first-order magnetic transformation is interrupted by kinetic arrest, so that the high-temperature magnetic phase survives as a non-ergodic remnant below $t$9. The framework is organized by the relative locations of $J$0, the supercooling limit $J$1, and the arrest temperature $J$2, and diagnosed by hysteresis, phase coexistence, devitrification, and CHUF protocols (Chaddah et al., 2010).

Photomagnetic molecular systems supply another kinetics-governed meaning. In the heptanuclear complex $J$3, photomagnetism is attributed not to large differences in oscillator strengths across spin manifolds but to a long-lived trapped $J$4 charge-transfer state with slow internal conversion. The resulting $J$5 curves after irradiation are governed by population kinetics and thermally activated escape from the trapped high-spin state (0710.0931).

Finally, continuum electronic-structure theory contributes a different but conceptually adjacent viewpoint. For Pauli spinors, the density, spin density, and current density determine or bound positive kinetic-energy densities. In particular,

$J$6

is exact for one spinor and a lower bound for many-electron states. This establishes that noncollinear magnetization texture itself constrains kinetic energy, even outside lattice-model notions of kinetic magnetism (Tellgren, 2018).

7. Diagnostics, misconceptions, and open questions

Across these literatures, kinetic magnetism is diagnosed by observables that track either carrier-conditioned spin structure or nonequilibrium magnetic response. In lattice problems these include local correlators, momentum-space structure factors, hole-spin-spin correlators, quasiparticle residues, and charge structure factors; in moiré materials they include Curie-Weiss analysis and polarization-selective optical probes; in kinetic-arrest systems they include magnetization, resistivity, hysteresis, devitrification, and CHUF protocols (Xu et al., 2022, Morera et al., 2022, Sherif et al., 21 Oct 2025, Ciorciaro et al., 2023, Chaddah et al., 2010).

A recurrent caution is that much of the strongest evidence concerns short-range or finite-size behavior rather than thermodynamic order. The triangular-lattice cold-atom experiment observed local ferromagnetic nearest-neighbor correlations, not long-range ferromagnetism. The finite-density Haerter–Shastry work established a metallic $J$7 antiferromagnetic regime and an intermediate multimer/stripe regime on cylinders, but not a complete two-dimensional phase diagram. The square-to-triangular single-dopant study identified a finite-temperature crossover in local correlations, not a finite-temperature phase transition (Xu et al., 2022, Sherif et al., 21 Oct 2025, Pereira et al., 18 Jun 2025).

Another misconception is that particle-hole asymmetry near half-filling can be read off from the noninteracting band structure alone. The triangular-lattice optical-lattice experiment explicitly argues that the strong asymmetry and the sign reversal of local spin correlations are interaction-driven and reproduced by DQMC, not by a noninteracting treatment. Likewise, the moiré ferromagnetism observed above $J$8 is interpreted as abrupt doping-induced ferromagnetic correlation rather than equilibrium exchange already present in the Mott state (Xu et al., 2022, Ciorciaro et al., 2023).

Several problems remain open. Finite-$J$9 competition between kinetic selection and superexchange is still unresolved in triangular Hubbard systems. Sign problems limit finite-temperature simulations away from half-filling. Cylinder and cluster studies leave the thermodynamic fate of intermediate stripe, multimer, or low-spin graph phases unsettled. In broader usages, the shared term itself remains non-uniform: a plausible implication is that future work will continue to distinguish carrier-motion-driven magnetism, kinetics-controlled magnetic transformations, and current-induced magnetization more sharply, even when all three are legitimately “kinetic” in origin (Xu et al., 2022, Morera et al., 2024, Sherif et al., 21 Oct 2025, Cheong et al., 20 Mar 2025).