Microscopic Mechanism for a Higher-Spin Kitaev Model

Abstract

The spin S= 1 2 Kitaev honeycomb model has attracted significant attention, since emerging candidate materials have provided a playground to test non-Abelian anyons. The Kitaev model with higher spins has also been theoretically studied, as it may offer another path to a quantum spin liquid. However, a microscopic route to achieve higher spin Kitaev models in solid state materials has not been rigorously derived. Here we present a theory of the spin S=1 Kitaev interaction in twodimensional edge-shared octahedral systems. Essential ingredients are strong spin-orbit coupling in anions and strong Hund's coupling in transition metal cations. The S=1 Kitaev and ferromagnetic Heisenberg interactions are generated from superexchange paths. Taking into account the antiferromagnetic Heisenberg term from direct-exchange paths, the Kitaev interaction dominates the physics of S=1 system. Using exact diagonalization technique, we show a finite regime of S=1 spin liquid in the presence of the Heisenberg interaction. Candidate materials are proposed, and generalization to higher spins is discussed. * hykee@physics.utoronto.ca

Tensor network wave function of S=1 Kitaev spin liquids

“…We believe that our construction is applicable to the general spin-S Kitaev model and may provide insights into the physics of the possible S = 1 Kitaev materials proposed in Ref. [24] such as the singlelayer NiI 2 or layered A 3 Ni 2 X O 6 (A = Li, Na, X = Bi, Sb).…”

“…On the other hand, the nature may also allow the Kitaev's bond-dependent interactions for higher-spin magnitudes, as recently suggested by electronic structure computations [24]. While the large-spin limit would simply correspond to the classical limit, the ground state of the Kitaev model for relatively small spin magnitudes, especially for S = 1, has not been fully understood as the higher-spin Kitaev models on honeycomb lattice do not have exact solutions.…”

Magnetic anisotropy in ferromagnetic CrI3

“…1(a) and 1(b)] [14], another possible mechanism that can break spin rotational invariance is the off-diagonal term in the Heisenberg-Kitaev (J-K-) Hamiltonian [ Fig. 1(c)] [15][16][17][18][19][20][21][22][23]. For bulk CrI 3 , which orders ferromagnetically below T C = 61 K, the FM order is believed to be a second order phase transition [14].…”

Featureless quantum paramagnet with frustrated criticality and competing spiral magnetism on spin-1 honeycomb lattice magnet

“…The spin-orbital entanglement of the local moments brings rather anistropic interactions between neighboring spins and creates a strong frustration and a disordered Kitaev spin liquid ground state even for a geometrically unfrustrated honeycomb lattice [25]. Recent efforts try to extend spin-1/2 Kitaev materials to high-spin magnets, mainly spin-1 magnets, where the heavy ligand atoms may bring some anisotropic spin interactions through the exchange path [26]. Although exact solutions are not available for high spin Kitaev materials, it is hoped that exotic quantum state may still persist to high spin systems, especially since quantum effect in spin-1 magnets is still strong and magnetic frustration could further enhance it.…”