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arxiv: 2606.30732 · v1 · pith:ZSHURTSYnew · submitted 2026-06-29 · ❄️ cond-mat.str-el

Magnetic Bloch Oscillations in Odd-Wave Magnets and the Nonlinear Edelstein Effect

Jonas Habel , Johannes Knolle This is my paper

Pith reviewed 2026-07-01 01:57 UTC · model grok-4.3

classification ❄️ cond-mat.str-el
keywords magnetic Bloch oscillationsodd-wave magnetsEdelstein effectnonlinear responseTHz spectroscopyspin-charge couplingnon-equilibrium dynamics
0
0 comments X

The pith

Magnetization in odd-wave magnets undergoes Bloch oscillations before reaching the steady-state Edelstein value.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that odd-wave magnets display oscillations in magnetization when an electric field is applied, before the system settles into the constant Edelstein magnetization. These magnetic Bloch oscillations arise in minimal models of p-wave magnets in one and two dimensions and are analyzed with both analytical and numerical methods. The steady-state Edelstein response itself turns out to be nonlinear in the strength of the driving field. The oscillations constitute a transient, non-equilibrium signature of spin-charge coupling that can be observed through higher-harmonic signals in THz lightwave spectroscopy.

Core claim

The magnetization of odd-wave magnets can undergo Bloch oscillations before relaxing to the steady-state Edelstein value. This is demonstrated analytically and numerically in a minimal one-dimensional model of a p-wave magnet and generalized to two dimensions. The Edelstein magnetization is generically nonlinear in the applied electric field. Magnetic Bloch oscillations provide a genuine non-equilibrium signature of spin-charge coupling and can be detected in materials through higher-harmonic generation in THz sub-cycle lightwave spectroscopy.

What carries the argument

Magnetic Bloch oscillations driven by the combination of electric-field acceleration of electrons and the odd-parity spin texture of the magnet, which produces transient oscillations in magnetization before scattering destroys coherence.

If this is right

  • The Edelstein magnetization is nonlinear in the applied electric field.
  • Oscillatory magnetization precedes relaxation whenever coherence time is long enough relative to the Bloch period.
  • Higher-harmonic generation in THz spectroscopy serves as an experimental signature of the oscillations.
  • The effect persists when the one-dimensional model is extended to two dimensions.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Transient oscillatory regimes could appear in other magnets with strong spin-momentum locking whenever scattering is weak on the Bloch timescale.
  • Time-resolved probes may reveal non-equilibrium spin dynamics that steady-state measurements would miss.
  • The nonlinearity of the Edelstein response implies that linear-response assumptions break down at moderate field strengths in these systems.

Load-bearing premise

The minimal one-dimensional model of a p-wave magnet and its two-dimensional generalization capture the essential physics of odd-wave magnets and the coherence conditions required for magnetic Bloch oscillations.

What would settle it

Time-resolved measurement of magnetization in a candidate odd-wave magnet under a sudden electric field that shows no oscillatory component before the DC Edelstein value is reached, or THz spectra lacking higher harmonics attributable to these oscillations.

Figures

Figures reproduced from arXiv: 2606.30732 by Johannes Knolle, Jonas Habel.

Figure 1
Figure 1. Figure 1: (a) Sketch of the minimal 1D model proposed in [20]. Electrons can hop to neighboring lattice sites with spin [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (a) Fourier transform of the magnetization vs. frequency [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: (a) Sketch of the 2D square lattice generalization of the minimal 1D model, analogous to Ref. [20]. Electrons can [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Fourier spectra of the magnetization for [PITH_FULL_IMAGE:figures/full_fig_p015_4.png] view at source ↗
read the original abstract

Bloch oscillations (BOs) are a quantum phenomenon in which electrons subjected to an electric field in a periodic potential exhibit an oscillating current without a net drift. In real conductors, scattering reduces the coherence required for BOs driving the system toward a steady state with a DC current. While previous studies have focused on charge transport, charge carriers also possess spin, raising the question of whether BOs can emerge in magnetic observables. Here, we show that the magnetization of odd-wave magnets can undergo BOs before relaxing to the steady-state Edelstein value, a phenomenon we term $\textit{magnetic}$ BOs. Using analytical and numerical methods, we demonstrate this effect in a minimal one-dimensional model of a p-wave magnet and generalize it to two dimensions. Our analysis further reveals that the Edelstein magnetization is generically nonlinear in the applied electric field. Finally, we argue that magnetic BOs can be detected in materials through higher-harmonic generation in THz sub-cycle lightwave spectroscopy. Magnetic BOs provide a genuine non-equilibrium signature of spin-charge coupling in unconventional magnets.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper claims that the magnetization of odd-wave magnets undergoes transient magnetic Bloch oscillations (BOs) under an applied electric field before relaxing to the steady-state nonlinear Edelstein magnetization. This is demonstrated analytically and numerically in a minimal 1D p-wave magnet model, generalized to 2D, with the effect proposed as detectable via higher-harmonic generation in THz sub-cycle lightwave spectroscopy, providing a non-equilibrium signature of spin-charge coupling.

Significance. If the minimal model correctly encodes the required spin-momentum locking and coherence conditions, the result would introduce a novel extension of Bloch oscillations to magnetic observables in unconventional magnets and offer a falsifiable prediction for experiment. The analytical/numerical demonstration within the model and the explicit detection proposal are strengths. However, the significance for real materials is limited by the toy-model nature of the 1D Hamiltonian and its 2D extension.

major comments (2)
  1. [minimal one-dimensional model] The central claim that magnetic BOs appear before relaxation to the Edelstein value is load-bearing on the relaxation mechanism having a timescale longer than the BO period set by the electric field and lattice. The 1D model section must explicitly detail the scattering implementation (e.g., how the relaxation term is added to the equations of motion or density matrix) and verify that oscillations survive without extraneous dephasing from interband transitions or disorder.
  2. [two-dimensional generalization] The 2D generalization must show that the odd-parity spin-momentum locking is preserved and that magnetic BOs are not suppressed by additional channels present in higher dimensions. Without this, the claim that the effect is generic to odd-wave magnets rather than an artifact of the 1D toy model remains unestablished.
minor comments (2)
  1. The abstract and introduction could include a brief explicit definition of 'odd-wave magnets' and the precise form of the odd-parity spin-momentum locking to aid readers unfamiliar with the terminology.
  2. Figure captions for the numerical results should state the specific parameter values (field strength, relaxation rate) used to generate the plotted oscillations.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We address each major comment below and will revise the manuscript to provide the requested details and analysis.

read point-by-point responses

  1. Referee: [minimal one-dimensional model] The central claim that magnetic BOs appear before relaxation to the Edelstein value is load-bearing on the relaxation mechanism having a timescale longer than the BO period set by the electric field and lattice. The 1D model section must explicitly detail the scattering implementation (e.g., how the relaxation term is added to the equations of motion or density matrix) and verify that oscillations survive without extraneous dephasing from interband transitions or disorder.

    Authors: We agree that the relaxation mechanism and its timescale relative to the BO period are central to the claim. In the revised manuscript we will expand the 1D model section with an explicit description of the scattering implementation, including the precise form of the relaxation term added to the equations of motion or density matrix. We will also add numerical checks confirming that the oscillations remain visible for relaxation times longer than the BO period and that interband transitions or disorder do not introduce extraneous dephasing within the minimal-model assumptions. revision: yes

  2. Referee: [two-dimensional generalization] The 2D generalization must show that the odd-parity spin-momentum locking is preserved and that magnetic BOs are not suppressed by additional channels present in higher dimensions. Without this, the claim that the effect is generic to odd-wave magnets rather than an artifact of the 1D toy model remains unestablished.

    Authors: We acknowledge the need for a clearer demonstration that the effect is not an artifact of one dimension. The 2D Hamiltonian is constructed to retain the required odd-parity spin-momentum locking. In the revision we will add explicit analysis showing that this locking is preserved and that magnetic BOs survive the additional scattering channels present in 2D, by comparing relevant timescales and confirming that the oscillations are not suppressed under the model conditions. This will strengthen the argument for generality to odd-wave magnets. revision: yes

Circularity Check

0 steps flagged

No significant circularity; claims rest on explicit model calculations

full rationale

The paper defines a minimal 1D p-wave magnet Hamiltonian (and 2D extension), then analytically and numerically computes magnetization dynamics under electric field, showing transient oscillations that relax to a nonlinear Edelstein magnetization. This is a direct forward calculation from the stated model equations; no step reduces a claimed prediction to a fitted input by construction, no uniqueness theorem is imported via self-citation, and no ansatz is smuggled. The abstract and description indicate the result is demonstrated within the chosen model rather than asserted as model-independent, so the derivation chain is self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no identifiable free parameters, axioms, or invented entities; the central claims rest on an unspecified minimal model whose assumptions cannot be audited from the given text.

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discussion (0)

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