Inelastic neutron scattering provides a powerful probe of the magnetic excitations of quantum magnets. Altermagnets have recently emerged as a new class of magnets with vanishing net magnetization characteristic of antiferromagnets and with a spin-split electronic structure typical of ferromagnets. Here we introduce a minimal Hubbard model with two-sublattice orthorhombic anisotropy as a framework to study altermagnetism. Using unrestricted Hartree-Fock calculations, we find an altermagnetic state for this model that evolves from a metallic state to an insulating state with increasing Hubbard-$U$ Coulomb repulsion. We then examine the inelastic neutron scattering response in these states using random-phase approximation calculations of the dynamic spin susceptibility ${\chi }^{″}(\mathbf{q},\omega )$. We find that the magnetic excitation spectrum depends on its chirality for $\mathbf{q}$ along certain directions in reciprocal space, an observation that may be used in inelastic neutron scattering experiments as a probe of altermagnetism.

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• Magnetic order
• Electron-correlation calculations
• Hubbard model
• Mean field theory
• Neutron scattering
• Random phase approximation