Nonlinear Magnon Magnetic Moment Transport in Triangular-Lattice f-Wave Antialtermagnets

arXiv:2605.22614 · cond-mat.str-el · Submitted 2026-05-21 · Read on arXiv

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Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: Hi, I'm Kai.

Mira: And I'm Mira, here with Lev.

Kai: We're looking at the paper: "Nonlinear Magnon Magnetic Moment Transport in Triangular-Lattice f-Wave Antialtermagnets".

Mira: Here's the gist of the paper. The gist The study demonstrates that spin excitations in frustrated coplanar 120° ground states of triangular-lattice antiferromagnets carry a magnetic moment perpendicular to the plane, revealing them as odd-parity f-wave magnets and providing experimental signatures through nonlinear thermal transport effects like Edelstein and spin-splitter effects.

Kai: Ground State and Magnon Character The triangular-lattice Heisenberg antiferromagnet is a canonical model of geometric frustration, leading to a coplanar three-sublattice “120-degree” state in the limit of zero temperature and vanishing magnetic field.

Mira: This ground state is remarkably robust against quantum fluctuations even for spin-1/2 systems.

Kai: The magnetic moment carried by magnons, defined as µν,k = − ∂Bεν,kB=0, (1), is found to be proportional to n where n is a unit vector perpendicular to the plane in which spins order.

Paper summary: Kai: So this paper is really focusing on how these magnons move when you put them in a stack of antiferromagnetically coupled triangular layers to get a three-dimensional f-wave antialtermagnet <ref:2605.22614#pg3>.

Mira: And they show that this three dee extension creates magnons with specific nonlinear thermal transport effects, specifically the Edelstein effect and the spin-splitter effect <ref:2605.22614#pg3>.

Lev: Nonlinear transport is always tricky because you need a certain order of temperature gradient to see these things, which is like setting up a very precise thermal machine for your experimental setup <ref:2605.22614#pg3>.

Kai: The spin-splitter effect generates a flow of magnetic moment that's quadratic in the temperature gradient, while the Edelstein effect is cubic in the temperature gradient <ref:2605.22614#pg3>.

Mira: That means these effects are signatures you can look for experimentally, which is important because it links the microscopic symmetry of the magnon to a macroscopic transport property.

Lev: For real hardware, that cubic dependence in the Edelstein effect means you're looking at higher-order corrections in your thermal measurements than just simple linear response <ref:2605.22614#pg3>.

Conclusion: Kai: So to wrap up, the title "Nonlinear Magnon Magnetic Moment Transport in Triangular-Lattice f-Wave Antialtermagnets" points directly at how these specific excitations behave when you stack them up in three dimensions <ref:2605.22614#pg3>.

Mira: The authors show that the magnon magnetic moment isn't just sitting there; it has this specific momentum dependence that makes it an odd-parity f-wave magnet <ref:2605.22614#pg1>.

Lev: The implication for us is that if we want to control these quantum states in a larger structure, the thermal response of those excitations will be governed by these nonlinear effects, specifically the spin-splitter and Edelstein effects <ref:2605.22614#pg3>.

Kai: It suggests that measuring these thermal transport properties could actually be a way to probe that intrinsic f-wave symmetry of the magnons without having to measure the individual spin operators directly <ref:2605.22614#pg3>.

Mira: Exactly, it's a way to see the underlying structure through measurable physical currents, which is what makes this work relevant for condensed matter physics and experimental realization <ref:2605.22614#pg3>.

Lev: And the paper also flags that they are looking at nonrelativistic magnons, so we have to remember that any real-world implementation will need to account for the relativistic corrections later on <ref:2605.22614#pg3>.

Institute for Theoretical Solid State Physics, Leibniz Institute for Solid State and Materials Research Dresden · Institute of Theoretical Physics and Würzburg-Dresden Cluster of Excellence ctd.qmat, Technische Universit¤t Dresden · Bogolyubov Institute for Theoretical Physics of the National Academy of Sciences of Ukraine · Institute for Solid State Theory, University of Münster · Institute of Physics and Halle–Berlin–Regensburg Cluster of Excellence (CCE), Martin Luther University Halle–Wittenberg · Institute of Physics, Johannes Gutenberg University Mainz · Department of Physics, Texas A&M University

cond-mat.str-el

Submitted: 2026-05-21

Updated: 2026-08-13

Comments: 13 pages, 7 figures

Journal ref: Phys. Rev. B, 114, 194410 (2026)

DOI: 10.1103/zl26-y46s

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 72/100

The gist: The gist The study demonstrates that spin excitations in frustrated coplanar 120° ground states of triangular-lattice antiferromagnets carry a magnetic moment perpendicular to the plane, revealing

Key concepts

120° Ground State
This describes the lowest energy configuration of spins on a triangular lattice where three sublattices order in a 120-degree pattern. This geometric frustration makes it difficult for the system to find a simple, ordered state, leading to this specific, highly entangled arrangement when cooled to zero temperature.
Odd-Parity f-wave Magnet
This classification describes the symmetry of the magnon's momentum dependence and energy spectrum. Because the magnetic moment carried by these excitations is perpendicular to the plane where spins order, they are classified as odd-parity, or f-wave, magnets.
Spin-Splitter Effect
This is a nonlinear thermal transport phenomenon where a temperature gradient causes a flow of magnetic moment carried by magnons. This effect is quadratic in the temperature gradient and serves as an experimental signature for f-wave antialtermagnets.
Magnon Edelstein Effect
This effect describes the generation of a net magnetic moment induced by a temperature gradient, which is cubic in the gradient. It is another measurable nonlinear transport signature predicted for magnons in this three-dimensional system.

Summary

The gist The study demonstrates that spin excitations in frustrated coplanar 120° ground states of triangular-lattice antiferromagnets carry a magnetic moment perpendicular to the plane, revealing them as odd-parity f-wave magnets and providing experimental signatures through nonlinear thermal transport effects like Edelstein and spin-splitter effects.

Ground State and Magnon Character

The triangular-lattice Heisenberg antiferromagnet is a canonical model of geometric frustration, leading to a coplanar three-sublattice “120-degree” state in the limit of zero temperature and vanishing magnetic field. This ground state is remarkably robust against quantum fluctuations even for spin-1/2 systems. The magnetic moment carried by magnons, defined as µν,k = − ∂Bεν,kB=0, (1), is found to be proportional to n where n is a unit vector perpendicular to the plane in which spins order. This collinear spin polarization in momentum space, directed perpendicularly to coplanar spins in position space, is typical for odd-parity wave magnets dubbed antialtermagnets.

Magnon Spectrum and Symmetry

The nonrelativistic spectrum of magnons excited over the 120°-state possesses f-wave symmetry with respect to the magnetic moment defined in Eq. (1). The magnon eigenenergies are given by equations (5), which include terms dependent on the magnetic field B. The magnon magnetic moments are expressed as µz±1,k = gµb 2 ∓ omegac k + omegas√k3, µz0,k = −gµbomegas√k3, as shown in Eq. (6). The symmetry relations (2) are obtained by applying symmetries to the dispersion relations and magnon magnetic moments for the case B = 0.

Nonlinear Transport Effects

Extending the model to a stack of antiferromagnetically coupled triangular layers realizes magnons in a three-dimensional f-wave antialtermagnet. This system predicts two nonrelativistic thermally induced nonlinear transport effects of magnons: the spin-splitter effect and the Edelstein effect. The spin-splitter effect is the generation of a flow of magnetic moment carried by magnons, which is quadratic in temperature gradient, and the Edelstein effect is cubic in temperature gradient.

Spin-Splitter Effect

The spin current J = 1/V X ν X k∈1.BZ µ¯zν,kvν,k δnν,k, (8) describes the flow of magnetic moment induced by a temperature gradient. The dimensionless strength G(2) is related to this effect and exhibits the same symmetry features as those predicted for electron spin currents in f-wave magnets. In the low-temperature limit for Jz≪J, the dimensionless function G is estimated as GkbTε0;Jz/J ≈ 6√6π2175rJJzkbTε02. The orientation of J and∇T depends on how ∇T is applied relative to the lattice directions.

Magnon Edelstein Effect

The total magnetic moment M = 1/V X ν X k∈1.BZ µ¯zν,k δnν,k, (13) generated by the Edelstein effect is found to be proportional to F(3)∇T3 cos 3χ (17). The leading-order contribution comes from the third-order nonlinear terms of the distribution function. In the low-temperature limit for Jz≪J, the magnetization estimated in (18) is Mmax ∼ µbg∆L3kb∆TΓk3, where Γk = ħ/τrlx is the decay rate.

Conclusion and Future Directions

The paper concludes that magnons excited on the top of the frustrated 120°-state carry a magnetic moment directed perpendicular to the spin plane. The predicted nonlinear magnon spin-splitter and magnon Edelstein effects are measurable, with the net magnetization estimated to be in a range accessible for experimental observations. Further development involves considering bond-dependent anisotropy and its influence on the magnon magnetic moment, especially near phase transitions between 120° and stripe states.

Acknowledgments

V.K. acknowledges financial support from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through the W¨urzburg-Dresden Cluster of Excellence ctd.qmat – Complexity, Topology and Dynamics in Quantum Matter (EXC 2147, project-id 390858490)

K.Y. acknowledges financial support from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through grant No. YE 232/2-1

B.P. acknowledges support from the Leibniz Association through the Leibniz Competition Project No. J200/2024

The work of R.R.N. was funded by the German Research Foundation (DFG) as part of the German Excellence Strategy EXC3112/1-533767171 (Center for Chiral Electronics) and through TRR 277-328545488 (Project No. B04)

The work of A.M. was funded by the German Research Foundation (DFG) as part of TRR 173-268565370 (Project No. B13) and Project No. 504261060 (Emmy Noether Programme)

The work of J.S. was funded by the German Research Foundation (DFG) as part of TRR 173-268565370 (Project No. 03), and TRR 288-422213477 (Projects No. A09 and B05)

A.M. and J.S. acknowledge support by the Dynamics and Topology Center (TopDyn) funded by the State of RhinelandPalatinate

We thank Ulrike Nitzsche for the technical support

Appendix A: Spectrum of spin waves for the single layer

The Hamiltonian is written as a sum over Rn, including terms involving m1, m2, and m3 with exchange J > 0 and a magnetic field B applied perpendicularly to the lattice The ground state of Hamiltonian (A1) is given by m0l = sin Θ [ex cos Φl + ey sin Φl] + ez cos Θ, where θ = Bµs9J, (A2) Deviations of magnetic moments ml from their ground states m0l are described by the complex-valued functions ψl defined by means of the classical form of the Holstein-Primakoff representation

Appendix B: The absence of the in-plane component for the magnon magnetic moment

The component of the magnon magnetic moment along the 1st sub-lattice is found to be zero, µν,k · m01 = 0 if εν,k = εν,k(φ2), because φB=0 = 0.

Improvements for AI systems

  1. Nonlinear Magnon Spin-Splitter Effect Modeling: The improved AI can accurately predict flow of magnetic moment carried by magnons in response to a temperature gradient by utilizing Eq (8) and the derived nonlinear spin-conductivity tensor G(2).

  2. Nonlinear Magnon Edelstein Effect Prediction: The system can calculate the total magnetic moment generated in response to a temperature gradient using the 3rd-order nonlinear term F(3) derived from Eq (15), allowing for estimations of Mmax in experimental ranges.

  3. Material Property Simulation: The AI can predict bond-dependent anisotropy effects by incorporating next-nearest-neighbor exchange couplings, which are noted to be especially large in the regimes close to the phase transition between the 120 degree and stripe states.

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