Topological semimetals induced by magnetic control of the cluster multipoles in pyrochlore iridates

Pyrochlore iridate antiferromagnet is the first material in which Weyl fermions are predicted to exist in condensed matter. However, the accumulated reports show that Weyl semimetal (WSM) phase in the material can be realized in a narrow region in the parameter space, so the smoking-gun evidence for WSM is still missing. As unique transport phenomena under magnetic field, which can appear by Weyl fermions, have been reported, in this work, we theoretically propose that magnetic field is a promising way to realize WSM phase, by expanding the WSM range and creating novel WSM phases through additional band inversions. Here, the central role is played by the quadratic band crossing (QBC) at Γ point with fourfold degeneracy in the paramagnet state. Due to the large degeneracy of QBC and strong spin-orbit coupling, Luttinger q-term or anisotropic Zeeman Effect can be included, as well as usual Zeeman Effect. Moreover, the relative magnitude of two Zeeman terms can be controlled by varying the orientation of four spins in the unit cell, which, in turn, manipulates the topological property of iridium band structure. The intriguing behavior occurs beacuse the unit cell comprises a cluster of four spins in a tetrahedron whose multipole moments can be tuned by the spin orientation.