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

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.

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Cited by in corpus (2)

• Ferrimagnetic Regulation of Weyl Fermions in a Noncentrosymmetric Magnetic Weyl Semimetal
• Weyl-mediated Ruderman-Kittel-Kasuya-Yosida interaction revisited: imaginary-time formalism and finite temperature effects