Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction in Weyl semimetals with tilted energy dispersion

Abstract

The Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction is an essential long-range magnetic interaction between magnetic impurities or magnetic layered structures, the magnitude of which oscillates with the distance between them. We investigated the RKKY interaction between two magnetic impurities in both time-reversal and inversion symmetry-broken Weyl semimetals (WSMs) where the energy dispersion is tilted in momentum space and the momentum of the conduction electrons is locked with the pseudo-spin. Two important features are revealed: firstly, at the small tilt limit, the RKKY coupling varies quadratically with the tilt parameter and strikingly, at large separation distances , decays as compared to the conventional dependence exhibited by WSMs with non-tilted dispersion. The slower decay by two orders (i.e. as opposed to ) of the RKKY coupling is significant for maintaining a long-range RKKY coupling. Secondly, the RKKY coupling exhibits an anisotropy with respect to the angle between the tilt direction (w) and the separation direction R, unlike the case of non-tilted WSMs, which exhibits isotropic RKKY coupling. Consequently, the RKKY coupling in tilted WSMs alternately favors ferromagnetic and anti-ferromagnetic orders and vice-versa with the change of the angle. Our results are derived analytically and verified by numerical calculations based on realistic parameter values.