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Abstract
We show that the topological Kitaev spin liquid on the honeycomb lattice is extremely fragile against the second-neighbor Kitaev coupling $K_2$, which has recently been shown to be the dominant perturbation away from the nearest-neighbor model in iridate Na$_2$IrO$_3$, and may also play a role in $\alpha$-RuCl$_3$ and Li$_2$IrO$_3$. This coupling naturally explains the zigzag ordering (without introducing unrealistically large longer-range Heisenberg exchange terms) and the special entanglement between real and spin space observed recently in Na$_2$IrO$_3$. Moreover, the minimal $K_1$-$K_2$ model that we present here holds the unique property that the classical and quantum phase diagrams and their respective order-by-disorder mechanisms are qualitatively different due to the fundamentally different symmetries of the classical and quantum counterparts.
Highlights
The search for novel quantum states of matter arising from the interplay of strong electronic correlations, spinorbit coupling (SOC), and crystal field splitting has recently gained strong impetus in the context of 4d and 5d transition metal oxides [1]
We show that the topological Kitaev spin liquid on the honeycomb lattice is extremely fragile against the second-neighbor Kitaev coupling K2, which has recently been shown to be the dominant perturbation away from the nearest-neighbor model in iridate Na2IrO3, and may play a role in α-RuCl3 and Li2IrO3
The layered iridates of the A2IrO3 (A 1⁄4 Na, Li) family [2,3,4,5,6,7] have been at the center of this search because of the prediction [8,9] that the dominant interactions in these magnets constitute the celebrated Kitaev model on the honeycomb lattice, one of the few exactly solvable models hosting gapped and gapless quantum spin liquids (QSLs) [10]
Summary
The search for novel quantum states of matter arising from the interplay of strong electronic correlations, spinorbit coupling (SOC), and crystal field splitting has recently gained strong impetus in the context of 4d and 5d transition metal oxides [1]. Recent calculations by Sizyuk et al [20] based on the ab initio densityfunctional data of Foyevtsova et al [21] have shown that, for Na2IrO3, the next-nearest-neighbor (NNN) exchange paths must give rise to an anisotropic, Kitaev-like coupling K2, which turns out to be AFM This coupling is the largest interaction after K1. A very striking aspect of the zigzag phases (shared by all magnetic phases) of the K1 − K2 model is that they are stabilized only for quantum spins and not for classical spins, despite having a strong classical character These phases are Ising-like (with spins pointing along one of the three cubic axes), they are protected by a large excitation gap in the interacting 1=S spin-wave spectrum, and the spin lengths are extremely close to their classical value of 1=2. This aspect has important ramifications for the phase diagram at zero and finite temperatures T
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