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The Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction has been extensivelyexplored in isotropic Dirac systems with linear dispersion, which typicallyfollows 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 andlimits its application in spintronics. Here, we theoretically investigate theinfluence of anisotropic dispersion on the RKKY interaction, and find that theintroduction of non-relativistic dispersion in semi-Dirac semimetals (S-DSMs)can significantly prolong the decay of the RKKY interaction and can remarkablyenhance the Dzyaloshinskii-Moriya interaction around the relativisticdirection. The underlying physics is attributed to the highly increased densityof states in the linear-momentum direction as a result of the interplay ofrelativistic and non-relativistic electrons. Furthermore, we propose a generalformula to determine the decaying rate of the RKKY interaction, extending thetypical formula for isotropic DSMs. Our results suggest that the S-DSMmaterials are a powerful platform to detect and control the magnetic exchangeinteraction, superior to extensively adopted isotropic Dirac systems.

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