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首页> 外文期刊>Physical review >Spin-orbit coupling in octamers in the spinel sulfide CuIr_2S_4: Competition between spin-singlet and quadrupolar states and its relevance to remnant paramagnetism
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Spin-orbit coupling in octamers in the spinel sulfide CuIr_2S_4: Competition between spin-singlet and quadrupolar states and its relevance to remnant paramagnetism

机译：尖晶石硫化物CuIr_2S_4中八聚体的自旋轨道耦合：自旋单态与四极态之间的竞争及其与剩余顺磁性的关系

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We theoretically investigate magnetic properties in the low-temperature phase with the formation of eight-site clusters, octamers, in the spinel compound CuIr_2S_4. The octamer state was considered to be a spin-singlet state induced by a Peierls instability through the strong anisotropy of d orbitals, the so-called orbital Peierls state. We reexamine this picture by taking into account the spin-orbit coupling, which was ignored in the previous study. We derive a low-energy effective model between j_(eff) = 1/2 quasispins on Ir~(4+) cations in an octamer from the multiorbital Hubbard model with the strong spin-orbit coupling by performing the perturbation expansion from the strong correlation limit. The effective Hamiltonian is in the form of the Kitaev-Heisenberg model but with an additional interaction, a symmetric off-diagonal exchange interaction originating from the perturbation process including both d-d and d-p-d hoppings. Analyzing the effective Hamiltonian on two sites and the octamer by the exact diagonalization, we find that there is competition between a spin-singlet state and a quadrupolar state. The former singlet state is a conventional one, adiabatically connected to the orbital Peierls state. On the other hand, the latter quadrupolar state is stabilized by the additional interaction, which consists of a linear combination of different total spin momenta along the spin quantization axis. In the competing region, the model exhibits paramagnetic behavior with a renormalized small effective moment at low temperature. This peculiar remnant paramagnetism is not obtained in the Kitaev-Heisenberg model without the additional interaction. Our results renew the picture of the octamer state and provide a scenario for the intrinsic paramagnetic behavior recently observed in a muon spin rotation experiment [K. M. Kojima et al., Phys. Rev. Lett. 112, 087203 (2014)].
机译：我们从理论上研究了在尖晶石化合物CuIr_2S_4中形成八位簇八聚体的低温相的磁性。八面体状态被认为是由Peierls不稳定性通过d轨道的强各向异性（所谓的轨道Peierls状态）引起的自旋单态。我们通过考虑自旋轨道耦合来重新检查这张图，在先前的研究中忽略了这一点。通过强自旋轨道耦合的扰动展开，我们从强轨道自旋耦合的多轨道哈伯德模型中，推导了八聚体上Ir〜（4+）阳离子上的Ir〜（4+）上j_（eff）= 1/2 quaspins之间的低能效模型。限制。有效的哈密顿量为Kitaev-Heisenberg模型的形式，但具有附加的相互作用，即源自d-d和d-p-d跳跃的扰动过程的对称非对角交换相互作用。通过精确的对角化分析两个位置上的有效哈密顿量和八面体，我们发现自旋-单重态和四极态之间存在竞争。前一个单重态是常规状态，绝热连接到轨道Peierls状态。另一方面，后者的四极状态通过附加相互作用而得以稳定，该附加相互作用由沿着自旋量化轴的不同总自旋动量的线性组合组成。在竞争区域，该模型表现出顺磁行为，并且在低温下具有重新归一化的小有效矩。没有额外的相互作用，在Kitaev-Heisenberg模型中无法获得这种特殊的残余顺磁性。我们的结果更新了八面体状态的图片，并为最近在μ子自旋旋转实验中观察到的固有顺磁行为提供了一种方案[K.小岛M.牧师112，087203（2014）]。

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