Bottom-up design of spin-split and reshaped electronic band structures in antiferromagnets without spin-orbit coupling: Procedure on the basis of augmented multipoles

We propose an efficient microscopic design procedure of electronic band structures having intrinsic spin and momentum dependences in spin-orbit-coupling free antiferromagnets. Our bottom-up design approach to creating desired spin-split and reshaped electronic band structures could result in further findings of practical spin-orbit-coupling free materials exhibiting a giant spin-dependent and/or nonreciprocal transport, magnetoelectric and elastic responses, and so on, as a consequence of such band structures. We establish a systematic guideline to construct symmetric/antisymmetric spin-split and antisymmetrically deformed spin-independent band structures in spin-orbit-coupling free systems by using two polar multipole degrees of freedom, i.e., electric and magnetic toroidal multipoles. The two polar multipoles constitute a complete set and describe arbitrary degrees of freedom in the hopping Hamiltonian, whose onsite and offsite degrees of freedom in a cluster are described as the so-called cluster and bond multipoles, respectively, and another degree of freedom connecting between clusters is expressed as momentum multipoles. By using these multipole descriptions, we elucidate simple microscopic conditions to realize intrinsic band deformations in magnetically ordered states: The symmetric spin splitting is realized in collinear magnets when cluster and bond multipoles contain the same symmetry of multipoles. The antisymmetric spin splitting occurs in noncollinear antiferromagnets when a bond-type magnetic toroidal multipole is present. Furthermore, the antisymmetric band deformation with spin degeneracy is realized in noncoplanar antiferromagnets. We exemplify three lattice systems formed by a triangle unit, triangular, kagome, and breathing kagome structures, to demonstrate the band deformations under the magnetic ordering. On the basis of the proposed procedure, we list up various candidate materials showing intrinsic band deformations in accordance with MAGNDATA, magnetic structures database.