Magnetically ordered yet topologically robust phases emerging in concurrent Kitaev spin liquids

Spin-orbital generalizations of Kitaev model, such as Yao-Lee model, have attracted recent attention due to their enhanced stability of spin liquid phases against perturbations. Motivated by microscopic calculations for the realization of Yao-Lee model showing additional interactions, we study the phase diagram of the Yao-Lee model with added Kitaev and Heisenberg terms. While the plaquette operator is conserved even in the presence of added perturbations, the model becomes no longer exactly solvable. Using perturbation and Majorana mean-field theory, we find magnetic order can arise in the spin sector while the orbital sector remains a liquid for dominant Kitaev interactions, whereas both sectors form liquid phases when Yao-Lee interactions dominate. Additional Heisenberg exchange can enhance or suppress the magnetic order, revealing a rich coexistence of magnetic and topological phases.