Electric field Induced Dzyaloshinskii-Moriya Interaction in Ferromagnetic Weyl Semimetals

An early stage of non-trivial manifestation of SOI pertains to the issue of a widespread antisymmetric superexchange interaction in form of Dzyaloshinskii-Moriya interaction (DMI) that is an intrinsic property of the material or structure with broken inversion symmetry. From this point of view, it seems promising to search the mechanisms of asymmetrical spin-spin coupling beyond the superexchange interaction. One of such possibilities was shown to be realized in Weyl semimetals (WSM) where indirect spin-spin interaction via Weyl fermions reveals the antisymmetric spin-spin interaction along with conventional Ruderman--Kittel--Kasuya--Yosida (RKKY) interaction. However, the RKKY interaction mediated by the electron scattering between opposite-chirality Weyl nodes does not contribute to DMI. Moreover, the same chirality fermions in inversion-symmetric WSM cannot induce DMI because of compensative effect of different Weyl nodes [1]. In this study we show that chiral anomaly which results in imbalance of Weyl node populations could be a mediator of DMI appearance for remote spin pairs in WSM of high symmetry. In such materials, the non-collinear magnetic B and electric E fields generate DMI with strength proportional to Dzyaloshinskii vector D=d(BE)n, where a unit vector n is directed along the locations r₁ and r₂ of interacted spin pair, and constant d can be estimated in terms of typical WSM material constants as d ~1.3 10^-4 meV cm/ V T for spins separated on several lattice constants. Thus, the moderate electric field 10⁵ V/cm may induce the observable strength D ~1 meV provided B=0.1 T. By order of magnitude this field strength contributes to demagnetizing fields in most ferromagnets that do not need an external source enhancing B. It has also been shown that remote DMI may generate the skyrmions under the locally applied bias in the ferromagnetic slab revealing a different way of WSM spintronic application.

[1] P. Nikoli´c, PRB, 103, 155151 (2021).