🔬 mesoscale physics

Out-of-equilibrium spin-valley dynamics of ferromagnets in topological Chern bands

By utilizing circularly polarized light to create and image magnetic domains in twisted MoTe2 bilayers, this study reveals that ferromagnets in topological Chern bands exhibit qualitatively distinct, thermally activated melting dynamics with significantly longer relaxation times compared to metallic domains, highlighting the profound influence of topology and strong correlations on out-of-equilibrium spin-valley evolution.

Original authors: J. James, I. Krastilevskiy, F. Pichler, L. Wang, A. Iafarova, F. Menzel, K. Watanabe, T. Taniguchi, C. Kuhlenkamp, M. Knap, T. Smoleński

Published 2026-08-10

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CC BY 4.0

Original authors: J. James, I. Krastilevskiy, F. Pichler, L. Wang, A. Iafarova, F. Menzel, K. Watanabe, T. Taniguchi, C. Kuhlenkamp, M. Knap, T. Smoleński

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the world of quantum physics as a giant, bustling city where tiny particles like electrons are the citizens. In this city, two very special rules often govern how things behave. The first is topology, which you can think of as the shape of the city's roads. Some roads are loops that can't be untangled, no matter how much you stretch them; this "shape" protects the traffic flow from getting stuck or scattered. The second rule is strong interactions, where the citizens (electrons) are so chatty and pushy that they constantly influence each other, forming complex crowds rather than moving alone.

Now, imagine trying to predict how a sudden traffic jam in this city will clear up. Usually, we think of traffic clearing by cars slowly backing up and shrinking the jam until it disappears. But what if the city's unique road shapes and the citizens' intense chatter changed the rules entirely? What if, instead of shrinking, the jam simply melted away from the inside out? This is the kind of mystery scientists are trying to solve when they look at materials far from their "normal" state. Understanding how these quantum cities behave when they are shaken up is a huge goal for modern physics, because it could help us build faster computers and new types of technology that don't just sit still, but actively do things.

In this study, a team of researchers decided to play with a very special kind of quantum city made from two layers of a material called Twisted MoTe2 (think of it as two sheets of a magical, sticky fabric twisted slightly against each other). They wanted to see what happens when they create a tiny, temporary "traffic jam" of magnetic spins in this material and then watch how it relaxes back to normal. To do this, they used a super-fast, focused pulse of circularly polarized light—like a laser pointer that spins—to flip the magnetic direction of a small patch of the material, creating a "false vacuum" state. This is a bit like forcing a group of people to stand facing the wrong way in a crowd that is all facing the right way.

The researchers then used a second, much weaker light pulse to take a movie of how this "wrong-way" patch healed itself. They found something surprising: the way the patch healed depended entirely on whether the material was acting like a metal or a special "Chern insulator" (a material with those special topological road shapes).

In the metallic version of the material, the magnetic patch behaved like a shrinking bubble. The edges of the patch simply pulled inward, getting smaller and smaller until it vanished. This process was relatively fast, taking only a few microseconds. However, in the Chern insulator version, the patch didn't shrink at all. Instead, it "melted" from the inside out, with tiny spots flipping their direction randomly all over the patch at the same time. This melting process was incredibly slow, taking orders of magnitude longer than the metallic version.

The team suggests that this difference happens because of the material's internal structure. In the metal, the "walls" between the different magnetic directions are wide and smooth, allowing the whole patch to shrink easily. But in the Chern insulator, the topological nature of the material creates very sharp, rigid walls that prevent shrinking. Instead, the only way for the patch to heal is through thermal fluctuations—tiny, random jiggles of heat that slowly flip individual spins one by one.

The researchers also explored what happens when they try to create these magnetic patches using a ring-shaped beam of light (a "doughnut" beam). In the metal, small patches were unstable and would quickly collapse or merge into one giant blob, making it hard to keep them separate. But in the Chern insulator, even tiny, scattered patches remained stable and didn't merge, thanks to the topological protection.

By comparing their real-world experiments with computer simulations, the authors confirmed that the "shrinking" mechanism is the dominant way metals relax, while the "melting" mechanism rules in Chern insulators. They showed that this difference is so strong that the relaxation time in the insulating state can be thousands of times longer than in the metallic state, especially when the magnetic field is just slightly above the point where the material naturally wants to flip.

This work doesn't just tell us about a specific material; it suggests that the shape of the quantum world (topology) and the way particles talk to each other (correlations) fundamentally change how these systems recover from being disturbed. The authors propose that this knowledge could one day help scientists control magnetic states with light much faster and more locally than ever before, opening up new ways to study and manipulate these exotic quantum phases.

Problem and Motivation
Understanding quantum matter far from equilibrium is a central goal of modern physics, particularly at the intersection of many-body correlations, topology, and non-equilibrium dynamics. While strong electromagnetic driving has emerged as a powerful tool for controlling correlated quantum materials, and the combination of topology and interactions has yielded topologically ordered fractional quantum Hall states and their lattice analogues (zero-field fractional Chern insulators, or FCIs), the nature of far-from-equilibrium processes in settings where all three concepts converge remains an outstanding challenge. Twisted MoTe $_2$ (t-MoTe $_2$ ) bilayers offer a promising platform to address this, combining ultrafast optical access with strong Coulomb interactions and nontrivial band topology. Specifically, these systems host gate-tunable ferromagnetic metals intertwined with fractional and integer Chern insulators (FCIs and ICIs), whose spin-valley states can be controlled via circularly polarized light.

Methodology
The authors investigate the out-of-equilibrium dynamics of ferromagnets in t-MoTe $_2$ bilayers using spatially and time-resolved low-temperature magneto-optical microscopy. The experiments are conducted at a base temperature of $T \approx 1.6$ K in a dry magneto-optical cryostat integrated with a confocal microscope. The study utilizes dual-gated t-MoTe $_2$ devices (twist angles $\sim 3.6^\circ$ and $\sim 4.1^\circ$ ) encapsulated in hexagonal boron-nitride (hBN).

The core experimental approach involves a pump-probe scheme using synchronized, cross-circularly polarized light pulses resonant with the attractive polaron (AP) transition:

Domain Creation: A short, strong $\sigma^-$ -polarized pump pulse creates a local magnetic domain (a "false-vacuum" state) with magnetization opposite to the equilibrium background (the "true-vacuum"). The size of this domain is controlled by the pump beam diameter.
Relaxation Monitoring: A weaker, $\sigma^+$ -polarized probe pulse monitors the subsequent spin-valley relaxation of the domain. The probe power is kept low ( $\sim 4$ pW) to ensure non-destructive readout.
Spatial Mapping: To distinguish relaxation mechanisms, the authors perform experiments with both diffraction-limited and expanded pump beams, allowing them to probe domains of varying initial diameters ( $D_0$ ) relative to the fixed probe spot ( $D_{meas} \approx 0.9$ $\mu$ m).
Theoretical Modeling: The dynamics are modeled using a stochastic differential equation (Model-A dynamics) for a non-conserved order parameter. The free energy includes a potential term derived from a microscopic mean-field model and a gradient term characterized by spin stiffness ( $\kappa^2$ ).

Key Contributions and Results
The study demonstrates that the out-of-equilibrium dynamics of ferromagnets in Chern bands are governed by qualitatively different mechanisms depending on whether the system is in a metallic or Chern insulating state (near integer or fractional filling factors).

Distinct Relaxation Timescales:
- Chern Insulators (ICI/FCI): Near integer ( $\nu \approx -1$ ) and fractional ( $\nu \approx -2/3, -3/5$ ) filling factors, the spin relaxation time ( $\tau_{relax}$ ) is orders of magnitude longer than in metallic states, particularly at magnetic fields slightly above the coercive field ( $B/B_c \sim 1$ ).
- Ferromagnetic Metals: In metallic phases (e.g., $\nu \approx -0.8$ ), relaxation is significantly faster.
- Field Dependence: As the magnetic field increases ( $B/B_c \gtrsim 2-3$ ), the energy barrier ( $\Delta_{vac}$ ) separating the false and true vacuum states decreases, accelerating relaxation in all phases until the dynamics become similar and nearly filling-factor independent.
Qualitatively Different Decay Mechanisms:
- Metallic Domains (Shrinking): In ferromagnetic metals, domains collapse primarily by shrinking from their perimeter. This is evidenced by a prominent initial plateau in the spin polarization decay ( $\langle S_z \rangle(t)$ ) when the initial domain size ( $D_0$ ) exceeds the probe spot size. The duration of this plateau scales with the initial domain size. Theoretical analysis attributes this to smooth, broad domain walls with high spin stiffness, which facilitate efficient domain edge propagation.
- Chern Insulator Domains (Melting): In Chern insulators, domains decay via thermal activation (melting) rather than shrinking. The decay is spatially homogeneous, and the relaxation profile is nearly independent of the initial domain size (no initial plateau). This is attributed to very sharp domain walls, a consequence of topologically protected edge modes and negative effective spin stiffness in the ICI phase, which suppress domain shrinking.
Stability of Small Domains at Zero Field:
- Theoretical simulations and experimental "domain writing" using doughnut-shaped beams reveal that small magnetic domains are inherently unstable in ferromagnetic metals at $B=0$ . Small "bubbles" of reversed spin collapse and aggregate into a single large domain only above a critical excitation power threshold.
- In contrast, in Chern insulators, small domains remain stable and do not coalesce, resulting in a smooth, continuous increase in domain area with excitation power.

Significance
The findings demonstrate that the emergence of correlated topological insulators fundamentally modifies the dynamics of electrons in Chern bands. The study highlights the critical role of topology and many-body correlations in shaping the far-from-equilibrium properties of quantum matter, specifically by altering the structure of domain walls and the resulting relaxation pathways.

The work establishes that optical control can drive ferromagnets in t-MoTe $_2$ out of thermal equilibrium, providing a method to dynamically access phase diagrams of far-from-equilibrium ferromagnets in the quantum Hall regime without the need to rapidly change external magnetic fields. The authors suggest this approach could offer new opportunities for the dynamical control of ferromagnets and, in the longer term, provide routes to study transport in the presence of dynamical edge modes or access collective excitations of topologically ordered phases.

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