This article was updated on the 11th September 2019.
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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.
Recently, a researcher from the Perimeter Institute for Theoretical Physics in Canada, Dr. Solomon Owerre, proposed a new concept: two-dimensional (2D) Dirac magnon nodal-line loops. This is a topological system of one-dimensional closed lines of Dirac magnon nodes, in 2D momentum space, within a quasi-2D quantum magnetic system.
The re-examination of bosonic systems has led to interesting research in the antisymmetric exchange between two neighboring magnetic spins. This research involves topological magnon bands in insulating ordered quantum magnets with inversion symmetry breaking and the allocation of Dzyaloshinskii-Moriya (DM) spin-orbit interactions (SOIs).
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-2D quantum magnetic systems. Current research explores these applications from a theoretical and experimental point of view.
This class of topological magnonic systems is thought to facilitate the next avenue of condensed matter physics, as they show great potential for use in magnon spintronics and magnon thermal devices.
There are many different topological magnonic systems being theorized recently in this emerging field, including 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 information, 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 the 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 believed 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 the 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 that 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 was also evident 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 anticipated to be easily extended for other quasi-2D lattices containing more than two sub-lattices in the unit cell. Searching for their presence physically through inelastic neutron scattering experiments is expected to be particularly interesting.
It is worth noting that research into magnonic analogs within electronic topological semimetals is still a developing field. Lots of theoretical scenarios have been deduced, but the experimental observations are almost non-existent. This has been attributed to the bulk sensitivity of inelastic neutron scattering methods and the lack of observation towards the chiral magnon edge modes.
However, experimentation is possible 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.
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