Creating Weyl nodes and controlling their energy by magnetization rotation

Abstract

As they do not rely on the presence of any crystal symmetry, Weyl nodes are robust topological features of an electronic structure that can occur at any momentum and energy. Acting as sinks and sources of Berry curvature, Weyl nodes have been predicted to strongly affect the transverse electronic response, like in the anomalous Hall or Nernst effects. However, to observe large anomalous effects the Weyl nodes need to be close to or at the Fermi-level, which implies the band structure must be tuned by an external parameter, e.g. chemical doping or pressure. Here we show that in a ferromagnetic metal tuning of the Weyl node energy and momentum can be achieved by rotation of the magnetization. Taking Co 3 Sn 2 S 2 as an example, we use electronic structure calculations based on density-functional theory to show that not only new Weyl fermions can be created by canting the magnetization away from the easy axis, but also that the Weyl nodes can be driven exactly to the Fermi surface. We also show that the dynamics in energy and momentum of the Weyl nodes strongly affect the calculated anomalous Hall and Nernst conductivities.Materials hosting unconventional quasiparticles, such as Weyl semimetals, constitute a framework with potential for novel electronic devices. One of the grounds for such expectation is the possibility of enhancing the response to external fields by taking advantage of the topological properties of the electronic states. For a material to specifically host Weyl fermions the spin degeneracy of the electronic bands has to be removed by breaking either inversion or time-reversal symmetry (Θ). Karplus and Luttinger [1] first noticed that in a Θ-broken system the spin-orbit coupling can introduce in the manifold of Bloch states a left-right asymmetry which in turn, in the presence of an electric field, causes a Hall current at zero magnetic field. This scattering-independent mechanism originates in the so-called anomalous velocity of the wave-packets, which can be written in terms of the Berry curvature of the Bloch states in momentum space. Weyl nodes are monopoles of Berry curvature which implies first, that they can only be created and annihilated in pairs of opposite monopole charge and second, that wave-packets made out of Weyl fermions can have a large anomalous velocity. As this velocity is perpendicular to the electric field, Weyl systems can exhibit enhanced transverse electronic responses, as in the Hall or Nernst effects.This effect has been argued to be at work in different materials in which the anomalous velocity contribution intrinsic to the band-structure is at the heart of enhanced electric and thermoelectric performance both in the regime of linear [2][3][4][5][6][7] as well as in nonlinear response [8,9]. Still, a central problem for optimizing Berry-curvature-based effects is the energy of the Weyl fermions which currently is not a controlled variable from a material design point of view. Indeed, as the only symmetry restriction is to break inversion or Θ, Weyl nodes can occur at any...

Magnetism and anomalous transport in the Weyl semimetal PrAlGe: possible route to axial gauge fields

“…The existence of such nanoscale domain walls in a Weyl semimetal could make PrAlGe a hitherto unique local platform for tunable axial gauge fields of Weyl fermions in a three-dimensional solid. This makes the RAlGe system particularly promising to explore this physics, since the electronic structure, magnetism and nature of Weyl nodes is expected to depend strongly on the magnetic rare earth ion R. 12,44,45 Therefore chemical substitution promises a straightforward route towards an easy low magnetic field control of both Weyl node types and possible axial gauge fields of Weyl fermions, complementing other control methods such as rotation of a uniform magnetisation, 46 photo-induction, 47,48 or external pressure-induction, 49 and thus adding to the catalogue of functional responses that may be useful for applications.…”

Dirac fermions and flat bands in the ideal kagome metal FeSn

“…These promising theoretical proposals have driven and guided recent experimental efforts toward the realization and study of topological kagome metals based on binary and ternary intermetallic compounds [11][12][13][14][15][16][17][18][19][20][21][22] . At variance with other widely studied s or p orbital-based topological systems that are close to the non-interacting limit, the kagome lattice in these intermetallic materials is populated by the low-energy 3d electrons of transition metals (Fig.…”

Magnetic Textures and Dynamics in Magnetic Weyl Semimetals

“…It was suggested by the first-principles calculations that a rotation of the magnetization from the out-of-plane direction to the inplane direction eventually modulates the arrangement of the Weyl nodes, with their complicated trajectories in the Brillouin zone. [169] It was also theoretically confirmed that a simplified twoorbital tight-binding model on kagome lattice with Kane-Meletype spin-orbit interaction well reproduces the Weyl-node structure observed in the first-principles calculations; [170] their agreement implies that the out-of-plane spin component dominantly participates in spin-orbit coupling in Co 3 Sn 2 S 2 , in the vicinity of the Fermi level. As a result, we can roughly expect that the outof-plane component of the magnetization shifts the Weyl nodes and contributes to the pseudo-gauge field, as we have seen in the spin-momentum-locked model Hamiltonian, while the in-plane component couples to the electron spin conventionally as in normal metals.…”