Towards the realization of quantum spin-orbital liquids in 4d and 5d transition metal compounds

Alexei Kitaev proposed in 2006 his simple but elegant spin model on a honeycomb lattice that is exactly solvable and has a quantum spin liquid (QSL) ground state, in which the S=1/2 spins fractionalize into two kinds of Majorana fermions [1]. A few years later, the concept of a J_eff=1/2 spin-orbital Mott insulator [2] was experimentally established in the layered perovskite Sr₂IrO₄ with 5d⁵ Ir⁴⁺, where the large spin-orbit coupling of the order of a half eV, larger than the crystal field splitting within the t_2g manifold, gives rise to an almost isolated half-filled J_eff=1/2 band and enhances the effect of electron correlations. The discovery of the J_eff=1/2 spin-orbital Mott state gave a hint to George Jackeli and Giniyat Khaliullin [3] to propose an experimental realization of the Kitaev model in materials using the J_eff = 1/2 pseudo-spin with internal spin and orbital degrees of freedom. The theoretical design of Kitaev materials by Jackeli and Khaliullin triggered an extensive search for the Kitaev QSL state and the Majorana fermions hidden behind it in a family of Ir⁴⁺, Ru³⁺ and more recently Co²⁺ [4] honeycomb compounds, where the d⁵ (d⁷) transition metal ions octahedrally coordinated with anions form an edge-shared honeycomb network [5]. In this talk, I would like to discuss the rapid progress and the future prospect in the materialization of the Kitaev QSL, as well as the hunt for Majorana fermions through the detection of unusual thermal transport in the Kitaev candidate materials, light and shadow, and the extension of materials search to other types of exotic spin-orbital entangled states [6].