From hybrid magnon topology in ferromagnets to magnons and thermal Hall effects in altermagnets

Topological magnons promise dissipationless spin transport and thermal‑Hall phenomena. Magnon topology requires magnetic non-Bravais lattices, such as the honeycomb [1-2] or kagome lattice [3], resulting in multiple magnon branches. In Ref. [4], we circumvent this requirement by hybridizing a single-magnon state with a two-magnon bound state in a square-lattice ferromagnet. We generate a topologically nontrivial magnon edge state, even though the requirement of the non-Bravais lattice is not given. This hybrid of a single-magnon and a two-magnon bound state carries heat and contributes to the magnon anomalous thermal Hall effect.

Magnons in insulating altermagnets also contribute to this effect. In contrast to antiferromagnets, we show in Ref. [5] that the time-reversal symmetry breaking of altermagnets allows a spontaneous crystal thermal Hall effect, as well as a spin Nernst effect, without the application of a magnetic field.

Magnons in altermagnets are generally also influenced by spin-orbit coupling. The relativistic spin-orbit coupling is able to change the dispersion relation of the magnons, and this raises the question of whether this change could diminish or even suppress the altermagnetic splitting of the magnons. In Ref. [6], we investigate this change of the dispersion in the two temperature-dependent magnetic phases of the iron oxide hematite (alpha-Fe₂O₃). In both the easy-axis phase below, and the weak ferromagnetic phase above the Morin transition we find that the effects of spin-orbit coupling are concentrated at the Brillouin zone center and do not destroy the altermagnetic splitting of the magnons.

References

[1] S. A. Owerre, J. Phys.: Condens. Matter 28, 386001 (2016)

[2] S. K. Kim et al., Phys. Rev. Lett. 117, 227201 (2016)

[3] A. Mook et al., Phys. Rev. B 89, 134409 (2014)

[4] A. Mook, R. Hoyer al., Phys. Rev. B 107, 064429 (2023) (Editors’ suggestion)

[5] R. Hoyer et al., Phys. Rev. B 111, L020412 (2025)

[6] R. Hoyer et al., Phys. Rev. B 112, 064425 (2025) (Editors’ suggestion)