**Quantum magnetic systems are materials that exhibit topological properties, usually attributed to electronic systems. In a recent JPCM letter, Solomon Owerre provides new theoretical insights into the Magnon Hall Effect. Read on to find out more from Solomon himself:**

In quantum ferromagnetic insulators, topological magnon bands and the associated magnon – Hall Effect are induced by the Dzyaloshinskii–Moriya interaction (DMI) or spin orbit coupling (SOC). These properties are present even at zero magnetic field and, are usually attributed to time-reversal symmetry breaking by the DMI or SOC. Since the inception of topological magnon insulators, it has become well established that DMI is the primary source of topological magnon effects in quantum magnets. This is supported by the experimental realization of the magnon Hall effect in kagome and pyrochlore ferromagnets Cu(1-3, bdc) and Lu_{2}V2O_{7} respectively. Recently, thermal Hall conductivity of spin excitations has been reported in geometrically frustrated Kagome volborthite Cu_{3}V_{2}O_{7}(OH)_{2}.2H_{2}O with no evidence of DMI. This material shows a finite Hall conductivity only at nonzero magnetic field. Although Kagome volborthite is known to exhibit magnetic ordering in the presence of a magnetic field (possibly with a q=0 propagation wavevector), the absence of Hall conductivity at zero field suggests that there is another source of topological effects in magnetic systems apart from the DMI.

In our recent letter we address this problem from a theoretical perspective. We consider the frustrated star lattice which is a variant of the Kagome lattice, but the former possesses six sites in the unit cell as opposed to three in the latter. The star lattice antiferromagnet is also realized experimentally in Polymeric Iron (III) Acetate with both spin frustration and long-range magnetic ordering. It should be noted that DMI is naturally present on both lattices because the midpoint of the bonds connecting two sites is not an inversion center. There is a possibility of q=0 magnetic ordering in the star lattice due to geometric frustration. However, the magnon bands of the q=0 magnetic ordering are not topological even at finite DMI: it can be regarded as a two-dimensional magnonic Dirac semimetal. This means that the Berry curvature vanishes and thermal Hall conductivity is zero. Interestingly, a magnetic field applied perpendicular to the star plane can induce a non-coplanar spin texture exhibiting a finite spin scalar chirality defined as the solid angle subtended by three neighboring spins. The presence of spin scalar chirality is the basis of chiral spin liquid physics and it has a topological origin without the need of DMI or magnetic ordering. These observations give the possibility of topological effects in insulating frustrated magnets without the need of DMI or magnetic ordering as observed theoretically in our letter.

**About the author**

This work was conducted at Perimeter Institute for Theoretical Physics. Solomon Owerre is a postdoctoral researcher at this institute, and he is involved in developing condensed matter physics across Africa.

This work is licensed under a Creative Commons Attribution 3.0 Unported License

Categories: JPhys+