Quantum fluctuations in two-dimensional altermagnets

The magnetic properties of two-dimensional altermagnets can be obtained from a square lattice Heisenberg model with antiferromagetic nearest neighbor interaction and two types of next-nearest neighbor interactions arranged in a checkerboard pattern. Using nonlinear spin-wave theory we calculate for this model the corrections to the renormalized magnon spectrum and the staggered magnetization to first order in the inverse spin quantum number $1/S$. We also show that to order $1/S^2$ the ground state energy is not sensitive to the component of the interaction which is responsible for altermagnetism. At the $Γ$-point the $1/S$-correction to the magnon dispersion vanishes so that quantum fluctuations do not induce a gap in the magnon spectrum of altermagnets, as expected by Goldstone’s theorem. We extract the leading $1/S$-corrections to the spin-wave velocity and the effective mass characterizing the curvature of the magnon dispersion in altermagnets.

💡 Research Summary

The paper investigates quantum fluctuations in two‑dimensional altermagnets by studying a square‑lattice Heisenberg model that incorporates antiferromagnetic nearest‑neighbor exchange J and two inequivalent next‑nearest‑neighbor exchanges D and E arranged in a checkerboard pattern. When D = E the model reduces to the well‑known J₁‑J₂ antiferromagnet; the case D ≠ E introduces the altermagnetic component, quantified by J′₂ = (D − E)/2. The authors perform a nonlinear spin‑wave expansion around the classical Néel state, using the Holstein‑Primakoff representation and a systematic 1/S expansion (S is the spin quantum number).

The Hamiltonian is separated into a classical part H⁽⁰⁾, a quadratic part H₂, and a quartic part H₄. After Fourier transformation and a Bogoliubov rotation, the quadratic sector yields two magnon branches
ω₍±₎(k) = 4JS εₖ ∓ 4J′₂S sin(kₓa) sin(k_ya),
where εₖ = √