Propagation of an orbiton in the antiferromagnets: theory and experimental verification

In this short review, which is based on the works published between 2011 and 2016, we discuss the problem of the propagation of a collective orbital excitation (orbiton) created in the Mott insulating and antiferromagnetic ground state. On the theoretical side, the problem is solved by mapping a Kugel-Khomskii spin-orbital model describing an orbiton moving in an antiferromagnet onto an effective t-J model with a 'single hole' moving in an antiferromagnet. The most important consequence of the existence of the above mapping is the fractionalisation of the electron's spin and orbital degree of freedom in the 1D antiferromagnets---a spin-orbital separation phenomenon that is similar to the spin-charge separation in 1D but corresponds to an exotic regime where spinons are faster than holons. Besides a detailed explanation and benchmarking of the mapping, in this review we also discuss its application to several relatively realistic spin-orbital models, that are able to describe the experimentally observed orbital excitation spectra of copper and iridium oxides.