Kitaev physics beyond 4d5 and 5d5 honeycomb lattices: understanding 3d7-3d7 exchange, strategies for optimizing Kitaev couplings

具有层状蜂窝结构的磁系统是一个活跃的研究课题。著名的Kitaev自旋液体可以在这样的化合物中实现，这是一种显示长程量子纠缠和非常规分数激发的集体物质状态。Kitaev模型的基本特征是，对于三个磁链中的每一个都有不同类型的位间耦合，这三个磁链分别来自蜂窝晶格的一个给定的磁位，KSixSjx，KSiySky和KSizSlz，其中j，k，l是参考（伪）自旋i的最近邻居。正是在这种形式下，也就是Kitaev最初分析的形式，这个模型是完全可解的。作为实现它的潜在平台，5d 5和4d 5蜂窝材料如Na 2 IrO 3和RuCl 3在早期阶段被指出。然而，事实证明，即使在铱酸盐和铼酸盐中K很大，也有额外的残余各向同性海森堡J耦合，这些耦合往往会阻碍量子自旋液体的形成。在寻找替代设置的过程中，最近出现了一些3d 7钴和镍蜂窝化合物。基于有效模型超交换理论的考虑，导致的结论是，原则上可以实现优于5d 5铱酸盐和4d 5铼酸盐中实现的K/J比上级，似乎在最新的实验数据中找到支持。在这个参考框架中，我们想解决的基本电子相互作用机制在3d 7蜂窝系统的主要目前的兴趣定量和系统的方式，使用先进的量子化学电子结构计算。需要澄清的主要方面是（i）Kitaev和Heisenberg相互作用（K/J）之间的比率，并从这里开始，在这些3d 7化合物中稳定的自旋液体基态的前景， (ii)非对角Siα-Sjβ有效交换耦合强度（iii）3d 7 t2 g5 eg 2蜂窝状氧化物中的位间虚拟过程与蜂窝状5d 5/4d 5氧化物/卤化物中的t2 g5-t2 g5超交换之间的相似之处和不同之处，（iv）O笼三角畸变对有效位间相互作用强度和使K/J比最大化的M-O-M键角的影响，（v）M-O 2-M磁路旁边的不太标准的化学环境（即，强共价Pn-O和Te-O键）影响磁性。使用基于波函数的量子化学的多组态和多参考方法将能够在平等的基础上平衡处理竞争电子组态和不同的超交换过程。我们的工作将为这些材料的相关电子结构提供新的见解，并将在过渡金属化合物的Kitaev-Heisenberg磁性背景下提供坚实的参考实验数据。

Magnetic systems with a layered honeycomb structure represent a topic of active research. The celebrated Kitaev spin liquid may be realized in such compounds, a collective state of matter displaying long-range quantum entanglement and unconventional fractionalized excitations. This has been argued to be relevant for applications in topological quantum computing.The essential feature of the Kitaev model is that there is a different type of intersite coupling for each of the three magnetic links originating from a given magnetic site of the honeycomb lattice, KSixSjx, KSiySky, and KSizSlz, where j, k, l are nearest neighbors of the reference (pseudo)spin i. Just in this form, the one initially analyzed by Kitaev, the model is exactly solvable. As potential platforms for materializing it, 5d5 and 4d5 honeycomb materials such as Na2IrO3 and RuCl3 were pointed out at the early stages. It turns out however that, even if K is large in iridates and ruthenates, there are additionally residual isotropic Heisenberg J couplings that tend to obstruct the formation of the quantum spin liquid. In the search for alternative settings, a number of 3d7 cobalt and nickel honeycomb compounds were very recently brought to the fore. Considerations based on effective-model superexchange theory, leading to the conclusion that K/J ratios superior to those realized in 5d5 iridates and 4d5 ruthenates can be in principle achieved, seem to find support in the latest experimental data. In this frame of reference, we would like to address the underlying electronic interaction mechanisms in 3d7 honeycomb systems of major present interest quantitatively and in a systematic manner, using advanced quantum-chemical electronic-structure computations. Principal aspects to be clarified are (i) the ratio between Kitaev and Heisenberg interactions (K/J) and starting from here the prospects for robust spin liquid ground states in these 3d7 compounds, (ii) the strength of off-diagonal Siα-Sjβ effective exchange couplings (so-called Γ's), (iii) what is similar and what is different between intersite virtual processes in 3d7 t2g5eg2 honeycomb oxides and t2g5-t2g5 superexchange in honeycomb 5d5/4d5 oxides/halides, (iv) the effect of O-cage trigonal distortion on the strength of the effective intersite interactions and the M-O-M bond angles that maximize the K/J ratio, (v) how the less standard chemical environment next to the M-O2-M magnetic paths (i.e., strongly covalent Pn-O and Te-O bonds) affects magnetism. The use of multiconfiguration and multireference methods from wavefunction-based quantum chemistry will enable a balanced treatment, on equal footing, of competing electron configurations and of the different superexchange processes. Our work will set the playground for new insights into the correlated electronic structures of these materials and will provide solid reference ab intio data in the context of Kitaev-Heisenberg magnetism in transition-metal compounds.