Kinetic Ferromagnetism and Topological Magnons of the Hole-Doped Kitaev Spin Liquid

We study the effect of hole doping on the Kitaev spin liquid (KSL) and find that for ferromagnetic (FM) Kitaev exchange $K$ the system is very susceptible to the formation of a FM spin polarization. Through density matrix renormalization group (DMRG) simulations on finite systems, we uncover that the introduction of a single hole with a hopping strength of just $t\sim 0.28K$ is enough to disrupt fractionalization and polarize the spins in the [001] direction due to an order-by-disorder mechanism. Taking into account a material relevant FM anisotropic spin exchange $\Gamma$ drives the polarization towards the [111] direction via a reorientation transition into a topological FM state with chiral magnon excitations. We develop a parton mean-field theory incorporating fermionic holons and bosonic spinons/magnons, which accounts for the doping induced FM phases and topological magnon excitations. We discuss experimental signatures and implications for Kitaev candidate materials.