Alternating spin splitting of electronic and magnon bands in two-dimensional altermagnetic materials

Unconventional antiferromagnetism dubbed as altermagnetism was first discovered in rutile structured magnets,which is featured by spin splitting even without the spin-orbital coupling effect.This interesting phenomenon has been discovered in more altermagnetic materials.In this work,we explore two-dimensional altermagnetic materials by studying two series of two-dimensional magnets,including MF4 with M covering all 3d and 4d transition metal elements,as well as TS2 with T=V,Cr,Mn,Fe.Through the magnetic symmetry operation of RuF4 and MnS2,it is verified that breaking the time inversion is a necessary condition for spin splitting.Based on symmetry analysis and first-principles calculations,we find that the electronic bands and magnon dispersion experience alternating spin splitting along the same path.This work paves the way for exploring altermagnetism in two-dimensional materials.