In 2006 Alexei Kitaev put forth an exactly solvable model of S=1/2 spins on a honeycomb lattice [1]. The ground state of this model is a quantum spin liquid (QSL) exhibiting Majorana fermion excitations. Subsequently Jackeli and Khaliullin showed how the Kitaev Hamiltonian might actually be realized in the laboratory [2]. This stimulated a great deal of experimental activity, initially on various iridates, and more recently on the honeycomb magnet a-RuCl_{3}, including a rather spectacular claim that a quantized thermal Hall effect is observed [3]. This seminar will briefly introduce the Kitaev model and its relationship to physical materials along with a brief discussion of fractional magnetic excitations. The focus will then turn to the physics seen in a-RuCl_{3}, with an emphasis on our group’s neutron scattering measurements [4-6]. At low temperaturesa-RuCl_{3}orders in an antiferromagnetic zigzag structure. Despite this ordering, inelastic neutron scattering and spectroscopic measurements yield evidence for a fractionalized magnetic excitation spectrum. The magnetic order can be suppressed by a magnetic field of 7.5 Tesla applied appropriately in the honeycomb plane, and this results in a disordered quantum phase that is likely some sort of quantum spin liquid. Measurements of the excitation spectrum as a function of field show features that may be related to a high field topological phase transition.

- Kitaev, A. Anyons in an exactly solved model and beyond.
*Phys*.**321**, 2-111 (2006). - Jackeli, G. & Khaliullin, G. Mott insulators in the strong spin-orbit coupling limit: From Heisenberg to a quantum compass and Kitaev models.
*Rev. Lett*.**102**, 017205 (2009). - Kasahara, Y. et al. Majorana quantization and half-integer thermal quantum Hall effect in a Kitaev spin liquid.
*Nature***559**, 227-231 (2018). - Banerjee, A. et al. Proximate Kitaev quantum spin liquid behaviour in a honeycomb magnet.
*Mater*.**15**, 733-740 (2016). - Banerjee, A. et al. Neutron scattering in the proximate quantum spin liquid α-RuCl3.
*Science***356**, 1055-1059 (2017). - Banerjee, A. et al., Excitations in the field-induced quantum spin liquid state of α-RuCl3.
*npj Quantum Materials***3**, 8 (2018).