Spin nematics meet spin liquids: Exotic quantum phases in the spin-1 bilinear-biquadratic model with Kitaev interactions

Spin liquid crystals are magnetic analogs of crystals, possessing properties both liquids and solids, a typical example which spin nematics. nematics share many features with liquids, the interplay between them is promising, but little explored, route to uncovering new phases matter. Here, we address this question in context spin-1 magnet on honeycomb lattice, by considering model biquadratic interactions, favoring spin-nematic states, Kitaev-like supporting liquids. Accompanying these, where dipole quadrupole moments compete, find plethora exotic phases, including multiple-$q$ states nonzero scalar chirality, quasi-one-dimensional coplanar phase, twisted conical noncoplanar order state gives way chiral at finite temperature. The implication these results for experiment discussed.