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

TL;DR

This paper studies how tilting in the energy dispersion of Weyl semimetals affects the RKKY magnetic interaction, revealing a slower decay and anisotropic behavior that could influence long-range magnetic ordering.

Contribution

It provides an analytical and numerical analysis of RKKY interaction in tilted Weyl semimetals, highlighting the impact of tilt on decay rate and anisotropy of the coupling.

Findings

RKKY coupling decays as 1/R at large distances in tilted WSMs.

Tilt causes quadratic variation of RKKY with tilt parameter at small tilt.

RKKY interaction becomes anisotropic and oscillates between ferromagnetic and antiferromagnetic.

Abstract

Ruderman-Kittel-Kasuya-Yosida (RKKY) is an essential long range magnetic interaction between magnetic impurities or magnetic layered structures, the magnitude of which oscillates with the distance ($\mathrm{R}$) between them. We have 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 electron is locked with the pseudo-spin. Two important features are revealed, firstly, at the small tilt limit, we show that the RKKY coupling varies quadratically with the tilt parameter and strikingly, at large separation distance $\mathrm{R}$, the coupling decays as $1/\mathrm{R}$ compared to the conventional of $1/\mathrm{R}^{3}$ dependence exhibited by WSMs with non-tilted dispersion. The slower decay by two orders i.e. ($1/\mathrm{R}$ as opposed to $1/\mathrm{R}^{3}$) of the RKKY coupling is significant for maintaining long range RKKY coupling. Secondly, the RKKY coupling exhibits an anisotropy with respect to the angle between the tilt direction ($\mathbf{w}$) and the separation direction $\mathbf{R}$ unlike the case of non-tilted WSMs which exhibit isotropic RKKY coupling. Consequently, the RKKY coupling in tilted WSMs alternately favours 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.