Ab Initio Spinor Kadanoff-Baym Approach to Nonequilibrium Electron, Phonon and Magnon Dynamics in Itinerant Ferromagnets

Giovanni Marini

arxiv: 2605.31467 · v1 · pith:QELQZR44new · submitted 2026-05-29 · ❄️ cond-mat.mtrl-sci · cond-mat.mes-hall

Ab Initio Spinor Kadanoff-Baym Approach to Nonequilibrium Electron, Phonon and Magnon Dynamics in Itinerant Ferromagnets

Giovanni Marini This is my paper

Pith reviewed 2026-06-28 21:54 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci cond-mat.mes-hall

keywords Kadanoff-Baym equationsspinor formalismultrafast magnetization dynamicsitinerant ferromagnetselectron-phonon-magnon couplingfirst-principles nonequilibrium dynamicsfemtomagnetism

0 comments

The pith

A spinor Kadanoff-Baym framework derives first-principles equations coupling electron, phonon and magnon dynamics in itinerant ferromagnets.

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

The paper develops an ab initio method that extends the Kadanoff-Baym equations to spinor space and incorporates spin-orbit coupling along with spin-dependent self-energies. It derives Markov-approximated scattering integrals and quasiparticle renormalizations that produce a closed set of equations for the coupled dynamics of electrons, phonons and magnons. This setup treats coherent and incoherent magnetic processes within the same many-body perturbation theory framework. A reader would care because the resulting equations can be solved numerically from first principles for periodic systems, removing the need for separate phenomenological models of ultrafast demagnetization.

Core claim

By placing the Kadanoff-Baym equations in spinor space and generalizing the self-energies beyond the charge sector, the work obtains scattering integrals that yield a tractable, closed system of equations for the simultaneous evolution of electron, phonon and magnon populations; these equations are solved from first principles and place coherent and incoherent magnetization dynamics on equal footing.

What carries the argument

Spinor Kadanoff-Baym equations with Markov-approximated, spin-dependent scattering integrals and quasiparticle renormalizations.

If this is right

Coherent precessional motion and incoherent scattering contributions to magnetization change are obtained from the same set of equations.
Ultrafast demagnetization timescales in periodic itinerant ferromagnets become computable without additional model Hamiltonians.
Magnon populations and their coupling to electrons and phonons emerge directly from the electron and phonon self-energies.
The framework extends standard many-body perturbation theory to magnetic degrees of freedom while retaining ab initio parameter-free character.

Where Pith is reading between the lines

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

The equations could be discretized on a real-space or k-space grid to simulate laser-driven switching in thin-film ferromagnets.
Temperature dependence would enter through the initial phonon and magnon distributions, allowing thermal demagnetization studies.
Comparison with time-dependent density-functional theory results for the same material would test consistency between the two first-principles routes.

Load-bearing premise

The Markov approximation together with quasiparticle renormalizations remains valid once self-energies are extended to include spin-dependent interactions.

What would settle it

Numerical solution of the derived equations for nickel under femtosecond laser excitation, followed by direct comparison of the computed magnetization decay curve against time-resolved magneto-optical Kerr effect measurements.

Figures

Figures reproduced from arXiv: 2605.31467 by Giovanni Marini.

**Figure 2.** Figure 2: FIG. 2: Pictorial representation [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3: Diagrammatic representation [PITH_FULL_IMAGE:figures/full_fig_p020_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4: Equations of motion for coupled electrons (light-blue rectangle), magnons (yellow rectangle) and phonons [PITH_FULL_IMAGE:figures/full_fig_p022_4.png] view at source ↗

**Figure 4.** Figure 4: Fig.4. Here, the dynamics of phonon coherences [PITH_FULL_IMAGE:figures/full_fig_p024_4.png] view at source ↗

read the original abstract

This work introduces a theoretical framework based on the Kadanoff-Baym equations in spinor space to study ultrafast magnetization dynamics in itinerant ferromagnetic systems from first principles. By incorporating spin-orbit coupling into the ab initio Hamiltonian and generalizing the self-energies to include terms beyond the charge sector, I derive scattering integrals within the Markov approximation and quasiparticle renormalizations for electrons and phonons in the presence of spin-dependent effective interactions within a many-body perturbation theory approach. I explicitly discuss how magnons emerge in this framework, and derive, through suitable approximations, a close and tractable set of equations for coupled electron,phonon and magnon dynamics that can be solved from first principles. This approach allows to treat coherent and incoherent magnetic dynamics on an equal footing, paving the way for a first principles understanding of ultrafast magnetic dynamics and demagnetization, and opening to a truly predictive theory of femtomagnetism in periodic systems.

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.

Desk Editor's Note private letter to a colleague

The paper extends Kadanoff-Baym to spinor form with magnons but leaves the Markov and quasiparticle approximations untested once spin-dependent self-energies are active.

read the letter

The core contribution is a generalization of the Kadanoff-Baym equations into spinor space that folds in spin-orbit coupling and derives scattering integrals for electrons, phonons, and magnons under the Markov approximation plus quasiparticle renormalizations. It shows how magnons appear naturally in the many-body perturbation theory setup and produces a closed, tractable set of coupled equations meant to be solved from first principles.

This is a reasonable incremental step for people already working in nonequilibrium Green's functions for magnetic systems. Treating coherent and incoherent channels on the same footing is a sensible goal for ultrafast demagnetization studies, and the abstract indicates the author has worked through the formal steps to include magnon degrees of freedom.

The main limitation is that the central approximations are not checked in the spin sector. The Markov truncation and pole-shift renormalizations are standard when self-energies are charge-like, but adding spin-flip and magnon channels changes the memory kernels and timescales. Nothing in the presented material demonstrates that those approximations remain controlled or that the resulting equations stay accurate once the self-energy acquires spin structure. Without at least a model calculation or timescale estimate, the claim of a predictive first-principles theory rests on an unverified assumption.

This is for theorists already comfortable with Kadanoff-Baym methods who want to see one route to coupled e-ph-magnon dynamics. A reader looking for validated numerics or direct comparison to experiment will find little here. It is worth sending to referees who know the Green's function literature, because the topic is relevant and the formal extension is laid out clearly enough to be critiqued in detail.

Referee Report

1 major / 0 minor

Summary. The paper introduces a theoretical framework based on the Kadanoff-Baym equations formulated in spinor space to study ultrafast magnetization dynamics in itinerant ferromagnetic systems from first principles. It incorporates spin-orbit coupling into the ab initio Hamiltonian, generalizes self-energies beyond the charge sector, derives scattering integrals under the Markov approximation with quasiparticle renormalizations for electrons and phonons, discusses the emergence of magnons, and obtains a tractable set of coupled equations for electron, phonon, and magnon dynamics that can be solved ab initio. The central claim is that this treats coherent and incoherent magnetic dynamics on an equal footing.

Significance. If the central approximations remain controlled, the framework would provide a first-principles route to predictive modeling of femtomagnetism and demagnetization in periodic systems by placing coherent and incoherent channels on the same footing within many-body perturbation theory.

major comments (1)

[Derivation of tractable set of equations for coupled electron, phonon and magnon dynamics] The derivation of the coupled e-ph-magnon equations relies on the Markov approximation plus quasiparticle renormalizations after extending self-energies to spin-dependent interactions (including SOC and magnon channels). No explicit test or error estimate is supplied showing that the memory-kernel truncation and pole-shift renormalization remain valid once spin-flip and magnon scattering channels are active; this assumption is load-bearing for the claim that coherent and incoherent dynamics are treated on equal footing from first principles.

Simulated Author's Rebuttal

1 responses · 1 unresolved

We thank the referee for the careful reading of our manuscript and the constructive feedback. We address the single major comment below.

read point-by-point responses

Referee: [Derivation of tractable set of equations for coupled electron, phonon and magnon dynamics] The derivation of the coupled e-ph-magnon equations relies on the Markov approximation plus quasiparticle renormalizations after extending self-energies to spin-dependent interactions (including SOC and magnon channels). No explicit test or error estimate is supplied showing that the memory-kernel truncation and pole-shift renormalization remain valid once spin-flip and magnon scattering channels are active; this assumption is load-bearing for the claim that coherent and incoherent dynamics are treated on equal footing from first principles.

Authors: We agree that the manuscript, being a formal derivation within many-body perturbation theory, does not supply explicit numerical tests or quantitative error estimates for the Markov approximation and quasiparticle pole-shift renormalization once spin-flip and magnon channels are included. The Markov truncation and renormalization steps are applied uniformly to the spinor self-energies after the extension to SOC and magnon-mediated interactions, following the same logic used in the charge sector. To strengthen the presentation, we will add a dedicated subsection that discusses the expected validity regime of these approximations, based on timescale separation arguments and comparisons with existing literature on spin-dependent scattering in ferromagnets. This addition will explicitly address the conditions under which coherent and incoherent channels remain on equal footing. revision: yes

standing simulated objections not resolved

A quantitative numerical benchmark or error estimate for the Markov and quasiparticle approximations in the presence of active magnon scattering would require a full ab initio implementation and simulation of the derived equations, which lies outside the scope of the present theoretical framework paper.

Circularity Check

0 steps flagged

No circularity: derivation applies standard MBPT approximations to extended spinor Hamiltonian

full rationale

The provided abstract and framework description show a derivation that starts from the Kadanoff-Baym equations in spinor space, incorporates SOC into the ab initio Hamiltonian, generalizes self-energies beyond the charge sector, and then applies the Markov approximation plus quasiparticle renormalizations to obtain scattering integrals and coupled e-ph-magnon equations. These steps follow the conventional structure of nonequilibrium many-body perturbation theory without any quoted reduction of a claimed prediction back to a fitted parameter, self-definition, or load-bearing self-citation. The central claim that coherent and incoherent dynamics are treated on equal footing is presented as a consequence of the extended equations under the stated approximations, not as a tautology. No evidence of the enumerated circularity patterns appears in the given text.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Abstract-only; limited visibility into parameters or axioms. Relies on standard domain assumptions of many-body theory plus the Markov approximation.

axioms (2)

domain assumption Markov approximation applies to scattering integrals
Explicitly invoked for deriving scattering integrals and tractable equations.
domain assumption Quasiparticle renormalizations remain valid with spin-dependent self-energies
Used to obtain renormalizations for electrons and phonons.

pith-pipeline@v0.9.1-grok · 5705 in / 1129 out tokens · 29530 ms · 2026-06-28T21:54:14.496373+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

7 extracted references · 1 canonical work pages

[1]

In metals, Kohn-Sham eigenvalues may already represent a good starting point 113

Ground state electron quasiparticle ener- gies are needed for the magnetic equilibrium state. In metals, Kohn-Sham eigenvalues may already represent a good starting point 113. These can be calculated through any (non- collinear) magnetic density-functional theory (DFT) implementation, for example employ- ing Quantum ESPRESSO104,154,155, or within many-bod...
[2]

Phonon frequencies for the magnetic ground state must be calculated, for example employ- ing the linear response algorithm implemented within Quantum ESPRESSO103 or through fi- nite differences methods. 26
[3]

This can be done for example starting from the electron-phonon coupling calculation for the noncollinear magnetic case, as implemented in Quantum ESPRESSO104,154,155

The Wannier interpolation procedure for the electron-phonon coupling157 must be ex- tended to the noncollinear magnetic case. This can be done for example starting from the electron-phonon coupling calculation for the noncollinear magnetic case, as implemented in Quantum ESPRESSO104,154,155
[4]

These can be obtained for example in the Kohn-Sham spin orbital basis at DFT level

Optical dipole matrix elements for the mag- netic noncollinear case are needed, Eq.6. These can be obtained for example in the Kohn-Sham spin orbital basis at DFT level
[5]

Electron-electron interaction matrix elements Win the noncollinear magnetic case for metal- lic systems, through any many body perturba- tion theory code, for example yambo or Berke- ley GW133,156,158
[6]

I note that the magnon frequencies in Fig.4 are in principle time-dependent

Magnon dispersions and their interpolation. I note that the magnon frequencies in Fig.4 are in principle time-dependent. However, I ex- pect the time-dependence to be weak in metal- lic systems because the time dependence is ul- timately related to the time-dependent change in screening. Thus, employing equilibrium (or linear response) magnon frequencies ...
[7]

Ultrafast optical manipulation of magnetic order,

A practical way to calculate the electron- magnon coupling, Eq.71, from first principles. This can be achieved through the knowledge ofWscreened Coulomb matrix elements and magnon wavefunction, which can be obtained through the solution of the BSE (see e.g. Refs.127–132), neglecting the residueR q and renormalizing magnon eigenvectors so that the magnetiz...

work page doi:10.1021/acs.nanolett.7b05118 2010

[1] [1]

In metals, Kohn-Sham eigenvalues may already represent a good starting point 113

Ground state electron quasiparticle ener- gies are needed for the magnetic equilibrium state. In metals, Kohn-Sham eigenvalues may already represent a good starting point 113. These can be calculated through any (non- collinear) magnetic density-functional theory (DFT) implementation, for example employ- ing Quantum ESPRESSO104,154,155, or within many-bod...

[2] [2]

Phonon frequencies for the magnetic ground state must be calculated, for example employ- ing the linear response algorithm implemented within Quantum ESPRESSO103 or through fi- nite differences methods. 26

[3] [3]

This can be done for example starting from the electron-phonon coupling calculation for the noncollinear magnetic case, as implemented in Quantum ESPRESSO104,154,155

The Wannier interpolation procedure for the electron-phonon coupling157 must be ex- tended to the noncollinear magnetic case. This can be done for example starting from the electron-phonon coupling calculation for the noncollinear magnetic case, as implemented in Quantum ESPRESSO104,154,155

[4] [4]

These can be obtained for example in the Kohn-Sham spin orbital basis at DFT level

Optical dipole matrix elements for the mag- netic noncollinear case are needed, Eq.6. These can be obtained for example in the Kohn-Sham spin orbital basis at DFT level

[5] [5]

Electron-electron interaction matrix elements Win the noncollinear magnetic case for metal- lic systems, through any many body perturba- tion theory code, for example yambo or Berke- ley GW133,156,158

[6] [6]

I note that the magnon frequencies in Fig.4 are in principle time-dependent

Magnon dispersions and their interpolation. I note that the magnon frequencies in Fig.4 are in principle time-dependent. However, I ex- pect the time-dependence to be weak in metal- lic systems because the time dependence is ul- timately related to the time-dependent change in screening. Thus, employing equilibrium (or linear response) magnon frequencies ...

[7] [7]

Ultrafast optical manipulation of magnetic order,

A practical way to calculate the electron- magnon coupling, Eq.71, from first principles. This can be achieved through the knowledge ofWscreened Coulomb matrix elements and magnon wavefunction, which can be obtained through the solution of the BSE (see e.g. Refs.127–132), neglecting the residueR q and renormalizing magnon eigenvectors so that the magnetiz...

work page doi:10.1021/acs.nanolett.7b05118 2010