Microscopic origin of the spin-splitting in altermagnets

Abstract: Altermagnets, characterized by spin-split bands without net magnetization, have recently emerged as a promising platform for spintronics. However, their microscopic mechanisms remain elusive, often relying on abstract group theory. In this work, we present an intuitive and pedagogical framework to understand the origin of spin splitting in altermagnets. We identify two essential ingredients: (1) alternating spin-polarized wavefunction localization on sublattices, and (2) broken translational symmetry caused by distortions in non-magnetic ion cages. We discuss a minimal model Hamiltonian based on an atomic exchange-driven spin splitting and anisotropic hopping that captures these effects and reproduces the hallmark features of altermagnetic band structures, including nodal spin degeneracies and large spin splittings. Our model is further validated by ab initio calculations on MnF2. By demystifying the microscopic origins of altermagnetism, our work bridges symmetry analysis and material realizations, shedding light on practical designs of altermagnetic spintronic devices.