The prolonged decay of RKKY interactions by interplay of relativistic and non-relativistic electrons in semi-Dirac semimetals

TL;DR

This paper explores how the interplay of relativistic and non-relativistic electrons in semi-Dirac semimetals prolongs the decay of RKKY interactions, enhancing magnetic coupling detection and control in spintronics applications.

Contribution

It introduces a theoretical analysis of anisotropic dispersion effects on RKKY interactions and proposes a general decay formula for semi-Dirac semimetals, advancing understanding beyond isotropic Dirac systems.

Findings

RKKY decay is significantly prolonged in semi-Dirac semimetals.

The Dzyaloshinskii-Moriya interaction is notably enhanced around the relativistic direction.

A new general formula for RKKY decay rate in anisotropic systems is proposed.

Abstract

The Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction has been extensively explored in isotropic Dirac systems with linear dispersion, which typically follows an exponent decaying rate with the impurity distance $R$, i.e., $J\propto 1/R^d$ ($1/R^{2d-1}$) in $d$-dimensional systems at finite (zero) Fermi energy. This fast decay makes it rather difficult to be detected and limits its application in spintronics. Here, we theoretically investigate the influence of anisotropic dispersion on the RKKY interaction, and find that the introduction of non-relativistic dispersion in semi-Dirac semimetals (S-DSMs) can significantly prolong the decay of the RKKY interaction and can remarkably enhance the Dzyaloshinskii-Moriya interaction around the relativistic direction. The underlying physics is attributed to the highly increased density of states in the linear-momentum direction as a result of the interplay of relativistic and non-relativistic electrons. Furthermore, we propose a general formula to determine the decaying rate of the RKKY interaction, extending the typical formula for isotropic DSMs. Our results suggest that the S-DSM materials are a powerful platform to detect and control the magnetic exchange interaction, superior to extensively adopted isotropic Dirac systems.