We propose a realization of an antisymmetric spin-split band structure through magnetic phase transitions without spin-orbit coupling. It enables us to utilize it for a variety of magnetic-order-driven cross-correlated and nonreciprocal transport phenomena as similar to those in spin-orbit-coupling oriented systems. We unveil its general condition as an emergence of a bond-type magnetic toroidal multipole (polar tensor) in a triangular unit with noncollinear 120âˆ antiferromagnetic structures. By using the concept of augmented multipoles, we systematically analyze the phenomena in terms of an effective multipole coupling. Our multipole description is ubiquitously applied to any trigonal and hexagonal structures including triangular, kagome, and breathing kagome structures, and provides a way to design and engineer materials with a giant antisymmetric spin splitting and its physical responses even without spin-orbit coupling.