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We propose an efficient microscopic design procedure of electronic bandstructures having intrinsic spin and momentum dependences inspin-orbit-coupling free antiferromagnets. Our bottom-up design approach tocreating desired spin-split and reshaped band structures could result infurther findings of practical spin-orbit-coupling free materials exhibiting agiant spin-dependent and/or nonreciprocal transport, magneto-electric andelastic responses as a consequence of such band structures. We establish asystematic guideline to construct symmetric/antisymmetric spin-split andantisymmetrically deformed spin-independent band structures inspin-orbit-coupling free systems by using two polar multipole degrees offreedom, electric and magnetic toroidal multipoles. The two polar multipolesdescribe arbitrary degrees of freedom in the hopping Hamiltonian, whose onsiteand offsite degrees of freedom in a cluster are described as the cluster andbond multipoles, respectively, and another degree of freedom connecting betweenclusters is expressed as momentum multipoles. By using these multipoledescriptions, we elucidate simple microscopic conditions to realize intrinsicband deformations in magnetically ordered states: The symmetric spin splittingis realized in collinear magnets when cluster and bond multipoles contain thesame symmetry of multipoles. The antisymmetric spin splitting occurs innoncollinear antiferromagnets when a bond-type magnetic toroidal multipole ispresent. Furthermore, the antisymmetric band deformation with spin degeneracyis realized in noncoplanar antiferromagnets. We exemplify three lattice systemsin order to demonstrate the band deformations under the magnetic ordering. Onthe basis of the proposed procedure, we list up various candidate materialsshowing intrinsic band deformations in accordance with MAGNDATA, magneticstructures database.

physical review. b./physical review. b

Bottom-up design of spin-split and reshaped electronic band structures  in spin-orbit-coupling free antiferromagnets: Procedure on the basis of  augmented multipoles