# Topological honeycomb magnon Hall effect: A calculation of thermal Hall conductivity of magnetic spin excitations

## Abstract

Quite recently, the magnon Hall effect of spin excitations has been observed experimentally on the kagome and pyrochlore lattices. The thermal Hall conductivity κ{sup xy} changes sign as a function of magnetic field or temperature on the kagome lattice, and κ{sup xy} changes sign upon reversing the sign of the magnetic field on the pyrochlore lattice. Motivated by these recent exciting experimental observations, we theoretically propose a simple realization of the magnon Hall effect in a two-band model on the honeycomb lattice. The magnon Hall effect of spin excitations arises in the usual way via the breaking of inversion symmetry of the lattice, however, by a next-nearest-neighbour Dzyaloshinsky-Moriya interaction. We find that κ{sup xy} has a fixed sign for all parameter regimes considered. These results are in contrast to the Lieb, kagome, and pyrochlore lattices. We further show that the low-temperature dependence on the magnon Hall conductivity follows a T{sup 2} law, as opposed to the kagome and pyrochlore lattices. These results suggest an experimental procedure to measure thermal Hall conductivity within a class of 2D honeycomb quantum magnets and ultracold atoms trapped in a honeycomb optical lattice.

- Authors:

- African Institute for Mathematical Sciences, 6 Melrose Road, Muizenberg, Cape Town 7945, South Africa and Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo, Ontario N2L 2Y5 (Canada)

- Publication Date:

- OSTI Identifier:
- 22597777

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Applied Physics

- Additional Journal Information:
- Journal Volume: 120; Journal Issue: 4; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-8979

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ATOMS; EXCITATION; HALL EFFECT; MAGNETIC FIELDS; MAGNETS; PYROCHLORE; SPIN; TEMPERATURE DEPENDENCE; TEMPERATURE RANGE 0065-0273 K; TOPOLOGY; TWO-DIMENSIONAL CALCULATIONS

### Citation Formats

```
Owerre, S. A., E-mail: solomon@aims.ac.za.
```*Topological honeycomb magnon Hall effect: A calculation of thermal Hall conductivity of magnetic spin excitations*. United States: N. p., 2016.
Web. doi:10.1063/1.4959815.

```
Owerre, S. A., E-mail: solomon@aims.ac.za.
```*Topological honeycomb magnon Hall effect: A calculation of thermal Hall conductivity of magnetic spin excitations*. United States. https://doi.org/10.1063/1.4959815

```
Owerre, S. A., E-mail: solomon@aims.ac.za. Thu .
"Topological honeycomb magnon Hall effect: A calculation of thermal Hall conductivity of magnetic spin excitations". United States. https://doi.org/10.1063/1.4959815.
```

```
@article{osti_22597777,
```

title = {Topological honeycomb magnon Hall effect: A calculation of thermal Hall conductivity of magnetic spin excitations},

author = {Owerre, S. A., E-mail: solomon@aims.ac.za},

abstractNote = {Quite recently, the magnon Hall effect of spin excitations has been observed experimentally on the kagome and pyrochlore lattices. The thermal Hall conductivity κ{sup xy} changes sign as a function of magnetic field or temperature on the kagome lattice, and κ{sup xy} changes sign upon reversing the sign of the magnetic field on the pyrochlore lattice. Motivated by these recent exciting experimental observations, we theoretically propose a simple realization of the magnon Hall effect in a two-band model on the honeycomb lattice. The magnon Hall effect of spin excitations arises in the usual way via the breaking of inversion symmetry of the lattice, however, by a next-nearest-neighbour Dzyaloshinsky-Moriya interaction. We find that κ{sup xy} has a fixed sign for all parameter regimes considered. These results are in contrast to the Lieb, kagome, and pyrochlore lattices. We further show that the low-temperature dependence on the magnon Hall conductivity follows a T{sup 2} law, as opposed to the kagome and pyrochlore lattices. These results suggest an experimental procedure to measure thermal Hall conductivity within a class of 2D honeycomb quantum magnets and ultracold atoms trapped in a honeycomb optical lattice.},

doi = {10.1063/1.4959815},

url = {https://www.osti.gov/biblio/22597777},
journal = {Journal of Applied Physics},

issn = {0021-8979},

number = 4,

volume = 120,

place = {United States},

year = {2016},

month = {7}

}