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We propose a realization of an antisymmetric spin-split band structurethrough magnetic phase transitions without spin-orbit coupling. It enables usto utilize for a variety of magnetic-order-driven cross-correlated andnonreciprocal transport phenomena as similar to those in thespin-orbit-coupling oriented systems. We unveil its general condition as anemergence of a bond-type magnetic toroidal multipole (polar tensor) in thetriangular unit with the noncollinear 120$^{\circ}$-AFM structures. By usingthe concept of augmented multipoles, we systematically analyze the phenomena interms of an effective multipole coupling. Our multipole description isubiquitously applied to any trigonal and hexagonal structures including thetriangular, kagome, and breathing kagome structures, which provides how todesign and engineer materials with a giant antisymmetric spin splitting and itsphysical responses even without the spin-orbit coupling.

Spontaneous Antisymmetric Spin Splitting in Noncollinear Antiferromagnets without Spin-Orbit Coupling