Nonsymmorphic magnetic Weyl semimetal materials such as ReAlX (Re=rare earth, X=Si/Ge) provide a unique opportunity to explore the correlated phenomena between Weyl fermions and nontrivial magnetic configurations. To be specific, we study a lattice model in which the magnetic configuration is determined by the competition among ferromagnetic (FM) interaction, the Dzyaloshinsky-Moriya interaction, and the Kondo coupling $K_0$ to the Weyl fermion. Both quantum and finite-temperature phase transitions between FM and correlated nesting helical configurations are found. Different from the uncorrelated helimagnet that decouples from the Weyl fermions, this correlated helimagnet induces a magnetic Brillouin zone with a $K_0$-dependent nesting in the band structure of the conduction electrons instead of the monopole-like Weyl cone. By measuring the current induced by the chiral magnetic effect on the conduction electron with nesting Weyl nodes, one can distinguish the correlated nesting helical order from the ferromagnetism because the chiral magnetic effect is considerably suppressed in the former case. These properties we find here may explain the experimental observations in ReAlX.
Comment: 6 pages, 4 figures; more references added