The ability to observe topological insulators and semimetals in an electronic system has generated great interest within the field of condensed matter physics. Such interest has also led to the re-examination of the band structures within bosonic systems. Now, a Researcher from the Perimeter Institute for Theoretical Physics in Canada has proposed a new idea of 2D Dirac magnon nodal-line loops- which is a topological system of one-dimensional closed lines of Dirac magnon nodes, in two-dimensional (2D) momentum space, within a quasi-2D quantum magnetic system.
The re-examination of bosonic systems has led to an interesting research area involving topological magnon bands in insulating ordered quantum magnets with inversion symmetry breaking, and the allocation of Dzyaloshinskii-Moriya (DM) spin-orbit interactions (SOIs) i.e the antisymmetric exchange between two neighboring magnetic spins.
An application area related to this re-examination that is also gathering a lot of attention is in the study of topological magnetic spin excitations in quasi-two-dimensional (2D) quantum magnetic systems. Current research explores these applications from a theoretical and experimental point of view.
This class of topological magnonic systems are thought to facilitate the next avenue of condensed matter physics, as they show a great potential for use in magnon spintronics and magnon thermal devices.
In this emerging field, there are many different topological magnonic systems being theorized recently and include Weyl magnon points in 3D pyrochlore antiferromagnets and ferromagnets and Dirac points in quasi-2D quantum magnetic systems.
Dr Owerre has now proposed a new, unstudied, topological arrangement of Dirac magnon nodal loops, or 2D closed lines of Dirac magnon nodes in 2D momentum space. These are stipulated to be in quasi-2D quantum magnets, namely those which are a direct analog of 2D electronic Dirac nodal-line semimetals in composite lattices.
For those new to condensed matter physics, magnons are charge-neutral bosonic quasiparticles, with no Lorentz force, conduction bands or valence bands. A Dirac node is where the valence and conduction bands within a semimetal touch at points, or in lines, generally at the Dirac points within the lattice. The appearance of a line of Dirac nodes in momentum space, can also lead to formation of a Dirac loop where the energy vanishes linearly with the perpendicular components of momentum.
Because of their potential for these applications, Dr Owerre performed his study around a theoretical honeycomb bilayer ferromagnet, which is realized in hexagonal chromium compounds CrX3 (X= Br, Cl or I) possessing a honeycomb lattice with small interlayer interactions and couplings. It is also thought that other layered quasi-2D quantum systems could be used.
Dr Owerre used linear spin wave theory to produce a linearized Holstein-Primakoff (HP) spin-boson mapping method, using polarized spins and aligned magnetic fields. Invariant under inversion symmetry was used to interchange the sub-lattices using a Z2 invariance. The calculations also involved the substitution of the spin-boson transformations, the Fourier transformation of the quadratic bosonic Hamiltonians and diagonalization of the Hamiltonians.
The Dirac magnon-nodal loops occurred when two magnon bands overlapped in momentum space, when the interlayer coupling was not equal to 0. This is a different mechanism to Dirac magnon points where two magnon bands touch at discrete points, at high symmetry points, of the Brillouin zone (BZ).
The overlapping of magnon bands led to formation of 1D closed lines of Dirac magnon nodes, where the 2D Dirac magnon nodal line-loops were topologically protected by the invariance of the parity eigenvalue arising from the inversion and time-reversal symmetry. It was also found the topology is robust against weak Dzyaloshinskii-Moriya interactions (unlike other approaches) and possessed chiral magnon edge modes.
The research also showed that within a realistic scenario, the interlayer coupling was smaller than the intralayer coupling, and the Dirac magnon nodal loops centered at the corners of the Brillouin Zone. It also materialized that the Dzyaloshinskii-Moriya spin-orbit interactions could be allowed in the lattice due to the inversion symmetry breaking the bonds of the second-nearest neighboring sites.
The idea of 1D closed lines of Dirac magnon nodes is thought to be easily extended for other quasi-2D lattices containing more than two sub-lattices in the unit cell. It is thought to be of particular interest to search for their presence physically through inelastic neutron scattering experiments.
It is worth noting that the field of magnonic analogs within electronic topological semimetals is still a developing field, where lots of theoretical scenarios have been deduced, but the experimental observations are almost non-existent. This has been attributed to bulk sensitivity of inelastic neutron scattering methods and the lack of observation towards the chiral magnon edge modes.
It does, however, have the possibility to be realized experimentally in quantum magnetic systems, as the bulk topological magnon bands have been realized in kagomé lattice ferromagnets. So, the next logical step for the fields is to employ edge sensitive methods, alongside other techniques such as light and electron scattering methods, in an effort to further propel the field of topological magnonics.
“Dirac Magnon Nodal Loops in Quasi-2D Quantum Magnets”- Owerre S. A., Scientific Reports, 2017, DOI:10.1038/s41598-017-07276-8