The dynamics of local magnetic moments induced by itinerant Weyl electrons

Abstract

We derive the effective interactions between local magnetic moments which are mediated by Weyl electrons in magnetic topological semimetals. The resulting spin dynamics is governed by the induced Heisenberg, Kitaev and Dzyaloshinskii-Moriya (DM) interactions with extended range and oscillatory dependence on the distance between the spins. These interactions are realized in multiple competing channels shaped by the multitude of Weyl nodes in the electron spectrum. Microscopic spins need to be spatially modulated with a channel-dependent wavevector in order to take advantage of the interactions. The DM vector is parallel to the displacement between the two interacting spins, and requires the presence of Weyl electron Fermi surfaces. We also derive the Weyl-induced chiral three-spin interaction in the presence of an external magnetic field. This interaction has an extended range as well, and acts upon the spatially modulated spins in various channels. Its tendency is to produce a skyrmion lattice or a chiral spin liquid which exhibits topological Hall effect. Ultimately, the theory developed here addresses magnetic dynamics in relativistic metals even when chiral magnetism is microscopically precluded. We discuss insights into the ordered state of the magnetic Weyl semimetal NdAlSi.

arXiv comment16 pages, 2 figures

References in corpus (64)

• Anyons in an exactly solved model and beyond
• Skyrmion Lattice in a Chiral Magnet
• Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator
• Weyl and Dirac Semimetals in Three Dimensional Solids
• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Weyl Semimetal in a Topological Insulator Multilayer
• Large anomalous Hall effect driven by non-vanishing Berry curvature in non-collinear antiferromagnetic Mn3Ge
• Quantum Hall effects in a Weyl Semi-Metal: possible application in pyrochlore Iridates
• Kitaev quantum spin liquid - concept and materialization
• Observation of the Magnon Hall Effect
• Interface-driven topological Hall effect in SrRuO${}_3$-SrIrO${}_3$ bilayer
• Topological Weyl semimetals in the chiral antiferromagnetic materials Mn3Ge and Mn3Sn
• Scalar spin chirality and quantum Hall effect on a triangular lattice
• Topological and magnetic phases of interacting electrons in the pyrochlore iridates
• Giant Anomalous Hall Effect in the Chiral Antiferromagnet Mn3Ge
• Spin Nernst Effect of Magnons in Collinear Antiferromagnets
• RKKY in half-filled bipartite lattices: graphene as an example
• Effective bilinear-biquadratic model for noncoplanar ordering in itinerant magnets
• Magnon spin Nernst effect in antiferromagnets
• Weyl magnons in breathing pyrochlore antiferromagnets
• Ordering of magnetic impurities and tunable electronic properties of topological insulators
• Thermal Hall conductivity in the frustrated pyrochlore magnet Tb2Ti2O7
• Electronic Orbital Currents and Polarization in Mott Insulators
• Quantized Anomalous Hall Effects in Skyrmion Crystal
• Skyrmion Lattice in Two-Dimensional Chiral Magnet
• The skyrmion lattice phase in three dimensional chiral magnets from Monte Carlo simulations
• Electric-field control of anomalous and topological Hall effects in oxide bilayer thin films
• Fractional topological insulators in three dimensions
• Orbital magnetic field effects in spin liquid with spinon Fermi sea: Possible application to $\kappa$-(ET)${}_2$Cu${}_2$(CN)${}_3$
• Tunable magnon Weyl points in ferromagnetic pyrochlores
• Topological Magnons and Edge States in Antiferromagnetic Skyrmion Crystals
• Topological BF field theory description of topological insulators
• Magnonic topological insulators in antiferromagnets
• Topological spin waves in the atomic-scale magnetic skyrmion crystal
• RKKY interaction of magnetic impurities in Dirac and Weyl semimetals
• Dimensional Crossover Induced Topological Hall Effect in a Magnetic Topological Insulator
• Magnetic texture-induced thermal Hall effects
• Quantum criticality in a metallic spin liquid
• Vortex Crystals with Chiral Stripes in Itinerant Magnets
• Large-$U$ limit of a Hubbard model in a magnetic field: chiral spin interactions and paramagnetism
• Magnetic field induced quantum phases in a tensor network study of Kitaev magnets
• Magnetic field induced intermediate quantum spin-liquid with a spinon Fermi surface
• Ruderman-Kittel-Kasuya-Yosida interaction in Weyl semimetals
• Novel magnetic orderings in the kagome Kondo-lattice model
• Path to stable quantum spin liquids in spin-orbit coupled correlated materials
• Weyl Fermions in antiferromagnetic Mn(3)Sn and Mn(3)Ge
• Skyrmionic spin Seebeck effect via dissipative thermomagnonic torques
• Anisotropic hysteretic Hall-effect and magnetic control of chiral domains in the chiral spin states of Pr${}_2$Ir${}_2$O${}_7$
• Electrodynamic response of type II Weyl semimetals
• RKKY interaction in three-dimensional electron gases with linear spin-orbit coupling
• Self-consistent theory of ferromagnetism on the surface of a topological insulator
• An optical investigation of the strong spin-orbital coupled magnetic semimetal YbMnBi${}_2$
• Spin Helix of Magnetic Impurities in Two-dimensional Helical Metal
• Fractional $S$-duality, Classification of Fractional Topological Insulators and Surface Topological Order
• Spin textures and spin-wave excitations in doped Dirac-Weyl semimetals
• Chiral magnetism: a geometric perspective
• Non-Linear Spin Susceptibility in Topological Insulators
• Quantum field theory of topological spin dynamics
• Indirect exchange interaction between magnetic impurities in the two-dimensional topological insulator based on CdTe/HgTe/CdTe quantum wells
• Theoretical investigation of antiferromagnetic skyrmions in a triangular monolayer
• Helical and skyrmion lattice phases in three-dimensional chiral magnets: Effect of anisotropic interactions
• Topological orders of monopoles and hedgehogs: From electronic and magnetic spin-orbit coupling to quarks
• Incommensurate magnetism mediated by Weyl fermions in NdAlSi
• Large Spontaneous Hall Effects in Chiral Topological Magnets

Cited by in corpus (19)

• Topological spin crystals by itinerant frustration
• Topological spiral magnetism in the Weyl semimetal SmAlSi
• Stabilization mechanisms of magnetic skyrmion crystal and multiple-$Q$ states based on momentum-resolved spin interactions
• Kramers nodal lines and Weyl fermions in SmAlSi
• Stripe Helical Magnetism and Two Regimes of Anomalous Hall Effect in NdAlGe
• Skyrmion crystals in centrosymmetric triangular magnets under hexagonal and trigonal single-ion anisotropy
• Temperature-Dependent and Magnetism-Controlled Fermi Surface Changes in Magnetic Weyl Semimetals
• Fermi-arc metals
• Gravitational anomaly in the ferrimagnetic topological Weyl semimetal NdAlSi
• Universal spin wave damping in magnetic Weyl semimetals
• Antiferro skyrmion crystal phases in a synthetic bilayer antiferromagnet under an in-plane magnetic field
• Weyl-mediated Ruderman-Kittel-Kasuya-Yosida interaction revisited: imaginary-time formalism and finite temperature effects
• Four-Spin Interactions as a Route to Multiple-Q Topological Magnetic Order
• Single crystalline orthorhombic GdAlGe as a rare earth magnetic Dirac nodal-line metal
• Meron-antimeron crystals in noncentrosymmetric itinerant magnets on a triangular lattice
• Incommensurate magnetic order drives singular angular magnetoresistance in a Weyl semimetal
• Axionic Instability of Periodic Weyl-Semimetal Superstructures
• Isotropic Dirac fermion and anomalous oscillator strength of zeroth Landau level transition
• Finite-temperature stability of skyrmion crystals in frustrated magnets: Role of sixfold anisotropy and uniform spin mode in momentum space