Spin Dynamics and Dirac Nodes in a Kagome Lattice

Abstract

Herein, the spin dynamics for various magnetic configurations arranged on a Kagome lattice is investigated. Using a Holstein–Primakoff expansion of the isotropic Heisenberg Hamiltonian with multiple exchange parameters, the development and evolution of magnetic Dirac nodes with both anisotropy and magnetic field are examined. From the classical energies, the phase diagrams for the ferromagnetic (FM), antiferrimagnetic (AfM), and the 120° phases are shown as functions of J1, J2, J3, and anisotropy. Furthermore, the production of bosonic Dirac and Weyl nodes in the spin‐wave spectra is shown. Through frustration of the magnetic geometry, a connection to the asymmetric properties of the Kagome lattice and the various antiferromagnetic configurations is discerned. Most interesting is the 120° phase, which does not have Dirac nodes when considering only J1 due to the formation of an analogous antiferromagnetic honeycomb lattice, but gains Dirac symmetry with next‐nearest neighbor interactions. Additionally, the presence of flat modes that are characteristic of cluster excitations is shown. Further study of external frustrations from a magnetic field and anisotropy reveals a tunability of the exchange interactions and nodal points.

Topological Magnons: A Review

“…The Dirac points are protected here by effective time reversal and inversion symmetries and are therefore gapped out by arbitrarily weak symmetry-breaking perturbations. It is possible to devise realistic models for several different lattices and magnetic structures where Dirac points appear in magnon spectra − in other words where the protecting symmetries are present at least at the linear spin wave level (52,53,54,55,56). This includes the generalization of Dirac crossings to three dimensions where they are four-fold degenerate (57).…”

Dynamic Quantum Matter

“…This approach is illustrated by applying it to multiple systems ranging from a generalized www.advancedsciencenews.com www.ann-phys.org harmonic oscillator to a spin-half particle in a magnetic field, which is the proto-typical example of a fermionic system. D. Boyko et al, in their original article, [5] examines the spin dynamics of Dirac bosons in the Kagome lattice. Using a spin-spin exchange Hamiltonian, they determine the conditions needed for various spin configurations with multiple nearest-neighbor interactions to modify Dirac nodes.…”

Effects of exchange distortions in the magnetic Kagome lattice

“…These types of cluster modes are not unheard of as they have been observed in structures like the pyrochlore lattice [16]. Furthermore, Boyko et al also revealed that, to first order, the 120 • phase mimics the antiferromagnetic (AFM) honeycomb lattice due to the net in and out spin configurations [40]. However, unlike the AFM honeycomb lattice, the Kagome lattice can break this degeneracy with second-and third-order interactions.…”

“…Previously, Boyko et al examined the spin-wave dynamics of the Kagome lattice for three different magnetic configurations [out-of-plane ferromagnetic (FM), out-of-plane antiferrimagnetic (AfM), and 120 • phase] and various isotropic nearest, next-nearest, and nextnext-nearest neighbor interactions [40]. In this work, it was shown that, to first order, the FM phase produced three modes, wherein two modes were dispersive, longrange order modes, and one was a non-dispersive, clusterlike flat band.…”

“…When considering the collinear Heisenberg model, exchange competition can produce frustration in the system and require an axial anisotropy to stabilize due to underlying non-collinear states [6,12,40]. Frustrated states can also come from the interactions between orbitals that typically result in FM or AFM orders but may become complicated by the competition between interactions as well as any induced crystal-field anisotropies.…”