Indirect magnetic interaction mediated by Fermi arc and boundary reflection near Weyl semimetal surface

Abstract

We theoretically investigate the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between magnetic impurities distributed in the vicinity of the surface of a Weyl semimetal. Contrary to previous studies, we further take into account the influence of interplay of the Fermi arc and bulk states, and interface refection. It is shown that the RKKY pattern is significantly mediated by the Fermi-arc surface state along with the interface reflection. The Fermi-arc surface state mediates the RKKY interaction by interfering with the bulk states. The resulting interference contribution in the short-range impurity distance R is comparable in magnitude to the bulk-band contribution and even dominates the latter near the surface. It either enhances or weakens the bulk contribution, depending on the relative orientation of impurities and Fermi energy. More importantly, for the long-range impurity distance the interference term dominates in that it can prolong the decay rate from the original bulk R −5 -law to R −2 (R −3 ) for finite (zero) Fermi energy. The interface reflection not only enhances the magnitude of the RKKY interaction and changes its anisotropy from the original XXZ to XYZ or Ising spin model, but also generates extra twisted RKKY terms parallel to the line connecting Weyl nodes, lacked in the scenario without the interface effect. They originate from the interaction between the impurity and the mirror image of the other impurity. We further analyze in detail the spatial anisotropy of the decay rate and beating pattern. These findings provide a deeper insight into surface magnetic interaction mediated by Weyl fermions.anomaly [25,[30][31][32], negative magnetoresistance [33][34][35], and untraditional superconductivity [36,37]. Another remarkable topological property of WSMs is the existence of topologically protected surface states. The surface states in k-space form Fermi arc, connecting the Weyl nodes projected to the surface Brillouin zone. Different from the gapless surface state of topological insulators, which inhabits within the bulk band gap and is depart from the bulk sates, the Fermi-arc surface states in WSMs are directly connected to the bulk states. Consequently, the surface properties of WSMs are contributed by both the bulk and surface states. To detect the Fermi arc, many literatures have focused on specific impurity scattering, such as quasiparticle interference (or Friedel oscillations) [38][39][40][41] and Kondo effect [42,43], and other interesting transport properties. However, the magnetic properties with respect to Fermi-arc states receive no attention.Introduction of magnetic impurities to Dirac materials opens up the possibility for their application potential in spintronics. Among magnetic impurities, the effective magnetic interaction mediated by the electrons of host material, namely the Ruderman-Kittel-Kasuya-Yoshida (RKKY) interaction [44], is crucial for magnetic ordering of the impurities. The nature of the RKKY interaction is determined by the dispersion and magnetic texture in h...

RKKY interaction on the surface of three-dimensional Dirac semimetals

“…[45] and for ferromagnetic noncentrosymmetric Weyl semimetal in Ref. [44]. This correction vanishes in the case of topological insulator provided µ → 0, while it dominates the RKKY interaction in the case of a Weyl semimetal.…”

“…In the case of the ferromagnetic Weyl semimetal the unidirectional surface states contribute to RKKY only by interfering with the bulk states [44]. The spectrum of the Fermi arc is protected from the gap opening, provided /v plotted as a function of the chemical potential µ.…”

“…While finalizing this work, we have become aware of a paper addressing the problem of RKKY interaction on the surface of a ferromagnetic noncentrosymmetric Weyl semimetal with two Weyl cones in the band structure [44]. In that model, purely Fermi arc surface states do not contribute to the RKKY interaction.…”

Signatures of interfacial topological chiral modes via RKKY exchange interaction in Dirac and Weyl systems

“…In recent times, a few proposals have been put forwarded to extract the contributions of the Fermi arcs which appear across the interface between the WSM and vacuum via RKKY exchange interaction [48,76]. The contributions of the bulk states are inevitably present in those studies when the impurities are located at two opposite surfaces.…”

An Origin of Dzyaloshinskii-Moriya Interaction at Graphene-Ferromagnet Interfaces Due to the Intralayer RKKY/BR Interaction

“…The exchange interaction between the local magnetic mo-ments, S 1 and S 2 , induced by proximity effect of a ferromagnet with the itinerant electron spins σ can be given by [49,51,52]…”