Weyl-mediated Ruderman-Kittel-Kasuya-Yosida interaction revisited: imaginary-time formalism and finite temperature effects

Abstract

Noncentrosymmetric magnetic Weyl semimetals provide a platform for investigating the interplay among magnetism, inversion symmetry breaking, and topologically nontrivial Weyl fermions. The Weyl-mediated Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction may be related to the magnetic orders observed in rare-earth magnetic Weyl semimetals. Previous studies of RKKY interaction between magnetic impurities in Weyl semimetals found Heisenberg, Ising-like, and Dzyaloshinskii-Moriya (DM) types of interactions. However, different range functions are obtained in the literature. In this work, we calculate the Weyl-mediated RKKY interaction by using the divergence-free imaginary-time formalism and obtain exact analytical results at finite temperature. The discrepancies among zero temperature range functions in the literature are resolved. At nonzero temperature, the interaction strength decays exponentially in the long distance limit. But in the short distance limit, the DM interaction shows a thermal enhancement, an effect persists up to higher temperature for shorter distance. This provides a mechanism stabilizing the helical order observed in rare-earth magnetic Weyl semimetals.

updated version, 12 pages, 4 figures, and 2 tables

References in corpus (17)

• Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase
• RKKY in half-filled bipartite lattices: graphene as an example
• Topological Magnetic Phase in the Candidate Weyl Semimetal CeAlGe
• Observation of Weyl fermions in a magnetic non-centrosymmetric crystal
• Transition from Intrinsic to Extrinsic Anomalous Hall Effect in the Ferromagnetic Weyl Semimetal PrAlGe${}_{1-x}$Si${}_x$
• RKKY interaction in three-dimensional electron gases with linear spin-orbit coupling
• Topological spiral magnetism in the Weyl semimetal SmAlSi
• The dynamics of local magnetic moments induced by itinerant Weyl electrons
• Stripe Helical Magnetism and Two Regimes of Anomalous Hall Effect in NdAlGe
• GdAlSi: An antiferromagnetic topological Weyl semimetal with non-relativistic spin splitting
• RKKY interaction of magnetic impurities in multi-Weyl semimetals
• Optical signatures of type-II Weyl fermions in the noncentrosymmetric semimetals $R$AlSi ($R$=La, Ce, Pr, Nd, Sm)
• Nernst effect of high-mobility Weyl electrons in NdAlSi enhanced by a Fermi surface nesting instability
• Anomalous Hall effect with plateaus observed in a magnetic Weyl semimetal NdAlGe at low temperatures
• The type-I antiferromagnetic Weyl semimetal InMnTi${}_2$
• Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in Weyl semimetals with tilted energy dispersion
• Correlated helimagnetic configuration in a nonsymmorphic magnetic nodal semimetal

Cited by in corpus (1)

• Correlated helimagnetic configuration in a nonsymmorphic magnetic nodal semimetal