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

We propose a realization of an antisymmetric spin-split band structure through magnetic phase transitions without spin-orbit coupling. It enables us to utilize for a variety of magnetic-order-driven cross-correlated and nonreciprocal transport phenomena as similar to those in the spin-orbit-coupling oriented systems. We unveil its general condition as an emergence of a bond-type magnetic toroidal multipole (polar tensor) in the triangular unit with the noncollinear 120$^{\circ}$-AFM 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 the triangular, kagome, and breathing kagome structures, which provides how to design and engineer materials with a giant antisymmetric spin splitting and its physical responses even without the spin-orbit coupling.