Ruderman-Kittel-Kasuya-Yosida interaction in Weyl semimetals

Abstract

We theoretically demonstrate the Ruderman-Kittel-Kasuya-Yosida interaction between magnetic impurities that is mediated by the Weyl fermions embedded inside a three-dimensional Weyl semimetal (WSM). The WSM is characterized by a pair of Weyl points separated in the momentum space. Using the Green's function method and a two-band model, we show that four terms contribute to the magnetic impurity interaction in the WSM phase: the Heisenberg, Dzyaloshinsky-Moriya, spin-frustrated and Ising terms. Except the last term which is vanishingly small in the plane perpendicular to the line connecting two Weyl points, all the other interaction terms are finite. Furthermore, the magnetic spins of the Dzyaloshinsky-Moriya and spin-frustrated terms lie in the plane perpendicular to the line connecting two Weyl points, but in this plane, the magnetic spins of the Ising term have no components. For each contribution, an analytical expression is obtained, falling off with a spatial dependence as $R^{-5}$ at Weyl points and showing beating behavior that depends on the direction between two magnetic impurities.

6 pages, 4 figures

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• Hybridization and anisotropy in the exchange interaction in 3D Dirac semimetals
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• Rashba Sandwiches with Topological Superconducting Phases
• Three-Dimensional Fractional Topological Insulators in Coupled Rashba Layers
• Fermi-arc metals
• Long-range interaction of magnetic moments in a coupled system of S/F/S Josephson junctions with anomalous ground-state phase shift
• Yu-Shiba-Rusinov States and Ordering of Magnetic Impurities Near the Boundary of a Superconducting Nanowire
• Diluted magnetic Dirac-Weyl materials: Susceptibility and ferromagnetism in three-dimensional chiral gapless semimetals
• RKKY coupling in Weyl semimetal thin films
• Tilt-induced anomalous thermal transport in normal/superconducting borophane junctions
• Antibonding Ground state of Adatom Molecules in Bulk Dirac Semimetals
• Incommensurate magnetism mediated by Weyl fermions in NdAlSi
• Strain-induced modulation of exchange interaction in monolayer zigzag nanoribbons of B${}_2$S
• Selective generation and amplification of RKKY interactions by P-N interface
• Anisotropic RKKY interactions mediated by $j=3/2$ quasiparticles in half-Heusler topological semimetal
• An Origin of Dzyaloshinskii-Moriya Interaction at Graphene-Ferromagnet Interfaces Due to the Intralayer RKKY/BR Interaction
• Tuning the electronic structure and magnetic coupling in armchair B${}_2$S nanoribbons using strain and staggered sublattice potential
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• Weyl-mediated Ruderman-Kittel-Kasuya-Yosida interaction revisited: imaginary-time formalism and finite temperature effects
• Electronic properties of the parabolic Dirac system
• RKKY interaction of magnetic impurities in node-line semimetals
• RKKY interaction in a spin-split superconductor
• Diversified Ruderman-Kittel-Kasuya-Yosida Interactions in a Nonsymmorphic Crystal
• Atomic frustrated impurity states in Weyl metals
• Antiferromagnetism and spin density waves in 3D Dirac semimetals
• RKKY interaction in graphene at finite temperature
• Zitterbewegung-mediated RKKY coupling in topological insulator thin films
• Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in Weyl semimetals with tilted energy dispersion
• Tuning topological surface magnetism by bulk alloying
• Dynamic generation of spin spirals of moiré trapped carriers via exciton mediated spin interactions
• RKKY interaction in helical higher-order topological insulators
• Impurities in 3D quadratic band-touching Luttinger semimetals : Friedel and RKKY oscillations
• Correlated helimagnetic configuration in a nonsymmorphic magnetic nodal semimetal
• Fluctuation-driven, topology-stabilized order in a correlated nodal semimetal
• Self-consistent solution for the magnetic exchange interaction mediated by a superconductor