We present a theory of spin and orbital physics in the A-site spinel compound FeSc2S4, which experimentally exhibits a broad "spin-orbital liquid" regime. A spin-orbital Hamiltonian is derived from a combination of microscopic consideration and symmetry analysis. We demonstrate a keen competition between spin-orbit interactions, which favor formation of a local "Spin-Orbital Singlet" (SOS), and exchange, which favors magnetic and orbital ordering. Separating the SOS from the ordered state is a quantum critical point (QCP). We argue that FeSc2S4 is close to this QCP on the SOS side. The full phase diagram of the model includes a commensurate-incommensurate transition within the ordered phase. A variety of comparison to and suggestion for experiments are discussed.
Substitutional doping of Cu in diamond: Mott physics with $p$ orbitals
在金刚石中重掺硼（C：B）和硅中重掺硼（Si：B）形成的杂质带中发现超导性，为新的超导材料族的可能性提供了一条途径。基于铜原子在高温超导材料中所起的特殊作用，本文研究了铜原子在金刚石中的替代掺杂效应。在高温超导材料中，铜原子的$d$轨道是产生各种关联诱导相的主要原因。我们广泛的第一性原理计算平均在各种几何形状的基础上密度泛函理论，表明形成的中间带隙，这主要是由于$t_{2g}$和$4p$状态的铜。当杂质浓度大于$\sim 1%, the effect of $ 2 p $ bands of neighboring carbon atoms can be ignored. Based on our detailed analysis, we suggest a two band model for the mid-gap states consisting of a quarter-filled hole like $ t_{2g} $ band, and a half-filled band of $ 4 p $ states. Increasing the concentration of the Cu impurity beyond $ \sim 5%时，完全关闭基质金刚石的光谱间隙。
We study the superconducting gap function of Sr$_2$RuO$_4$. By solving the linearized Eliashberg equation with a correlated pairing vertex extracted from a dynamical mean-field calculation we identify the dominant pairing channels. An analysis of the candidate gap functions in orbital and quasiparticle band basis reveals that an inter-orbital singlet pairing of even parity is in agreement with experimental observations. It reconciles in particular the occurrence of a two-component order parameter with the presence of line-nodes of quasiparticles along the c-axis in the superconducting phase. T…
Singlet-triplet excitations and long range entanglement in the spin-orbital liquid candidate FeSc2S4
自旋轨道液体（SOL）FeSc $_2$ S $_4$的理论模型已经预测其非常接近将自旋轨道液相与长程有序磁相分离的量子临界点。在这里，我们研究磁激发的FeSc $_2$ S $_4$通过时域太赫兹光谱下施加的磁场。在低温下出现的激发，我们归因于从SOL基态的单重态-三重态激发。作为施加的磁场的函数，观察到这种激发的三倍分裂。由于在反转对称的纯自旋系统中，单重态-三重态激发是被禁止的，我们的结果证明了自旋-轨道纠缠单重态基态的非平凡性。使用实验获得的参数，我们比较现有的理论模型，以确定FeSc $_2$ S $_4$的接近量子临界点。在这些模型的上下文中，我们估计的特征长度的单重关联是$ξ/ (\textbf{a}/2) \approx 8.2$（其中$\textbf{a}/2$是最近的邻居晶格常数），建立FeSc $_2$ S $_4$作为一个溶胶与长程纠缠。
Emergent odd-parity multipoles and magnetoelectric effects on a diamond structure: implication to 5$d$ transition metal oxides $A$OsO$_4$ ($A=$ K, Rb, and Cs)
我们报告了我们的理论预测的线性磁电（ME）效应起源于奇宇称多极与自发自旋和轨道有序的金刚石结构。我们推导出一个双轨道模型的$d$电子在$e_g$轨道，包括有效的自旋轨道耦合，这是由于$e_g$和$t_{2g}$轨道之间的混合。我们发现，一旦交错的自旋和轨道顺序自发发生，该模型获得一个净反对称自旋轨道耦合。交错的顺序伴随着奇宇称多极子：磁单极子，四极子和环形偶极子。我们根据自旋和轨道阶的对称性对奇宇称多极子的类型进行了分类。此外，通过使用线性响应理论计算的ME张量，我们表明，交错阶诱导各种线性ME响应。我们详细阐述了所有可能的ME响应，每个交错的顺序，这是有用的，以确定序参数和检测奇奇偶多极子通过测量ME效应。我们还阐明了降低对称性的影响，由一个tetravelet失真，这导致更丰富的ME响应。我们的研究结果的影响进行了讨论，为$5d$过渡金属氧化物，$A$ OsO $_4$（$A=$ K，Rb和Cs），其中的顺序参数没有完全确定。
The ground-state phases of alternating-bond spin-1 diamond chains are investigated. Each ground state consists of an array of spin clusters separated by singlet dimers owing to an infinite number of local conservation laws. If no singlet dimers are present, the ground state is equivalent to that of a spin chain with infinite length.For strong frustration, we find a series of quantum phase transitions as in the case of alternating-bond mixed diamond chains with spins 1 and 1/2. For intermediate frustration, we find the nonmagnetic Haldane or dimer phases according to whether the bond alternatio…
Valence bond crystal in a pyrochlore antiferromagnet with orbital degeneracy
本文讨论了三重轨道简并$S=1/2$磁性离子的烧绿石晶格的基态。我们推导出一个有效的自旋轨道哈密顿量，并表明轨道自由度可以调制自旋交换，消除无限自旋简并烧绿石结构的特点。由此产生的状态是自旋单重态二聚体的集合，由于它们的相对取向而具有残余简并性。后者被磁弹性相互作用提升，在自旋单态相空间中诱导，迫使四重态畸变。这种理论为在B-尖晶石MgTi $_2$ O $_4$中观察到的螺旋自旋单态模式提供了解释。
The possibility of "orbitally selective Mott transitions" within a multiband Hubbard model, in which one orbital with large on-site electron-electron repulsion $U_1$ is insulating and another orbital, to which it is hybridized, with small $U_{-1}$, is metallic, is a problem of long-standing debate and investigation. In this paper we study an analogous phenomenon, the co-existence of metallic and insulating bands in a system of orbitals with different electron-phonon coupling (EPC). To this end, we examine two variants of the bilayer Holstein model: a uniform bilayer and a "Holstein-Metal inter…
Spin Singlet State in Heptamers Emerging in Spinel Oxide AlV$_2$O$_4$
本文给出了钒尖晶石氧化物AlV $_2$ O $_4$电子态的理论结果。该材料是平均价为V $^{2.5+}$的混合价体系，V阳离子构成受抑烧绿石结构。它显示了在$\sim 700$ K处的结构转变，导致形成七个V位点簇--七聚体。我们研究的七聚体的电子状态，明确考虑轨道自由度以及电子相关性。我们表明，基态的七聚体的现实参数成为自旋单线态，因为强$σ$型键合状态的$t_{2g}$轨道。在实验中的磁化率的温度依赖性是自然理解的，在七聚体中的这种单线态形成。我们的研究结果表明，在AlV $_2$ O $_4$轨道物理是相关的，以稳定的簇型单重态，而不是以前提出的电荷有序态与价跳跃。
Magnetic field dependence of excitations near spin-orbital quantum criticality
尖晶石FeSc $_2$ S $_4$被提出来实现近临界自旋轨道单重态（SOS），其中纠缠的自旋和轨道矩在自旋和轨道阶的边缘上的全局单重态中波动。在这里，我们报告粉末非弹性中子散射测量，观察磁激发的全带宽，我们发现，自旋轨道三体激发的SOS状态可以捕获以及在零和应用磁场高达8.5 T的频谱的关键方面。所观察到的低能量谱权重的移位，以更高的能量时，增加施加的字段自然地解释了纠缠的自旋轨道特性的磁状态，一种行为，这是在强烈的对比，只有自旋单态基态系统，其中自旋间隙减少时，增加施加的字段。
When spin-orbit-entangled $d$-electrons reside on a honeycomb lattice, rich quantum states are anticipated to emerge, as exemplified by the $d^5$ Kitaev materials. Distinct yet equally intriguing physics may be realized with a $d$-electron count other than $d^5$. We found that the layered ruthenate Ag$_3$LiRu$_2$O$_6$ with $d^4$ Ru$^{4+}$ ions at ambient pressure forms a honeycomb lattice of spin-orbit-entangled singlets, which is a playground for frustrated excitonic magnetism. Under pressure, the singlet state does not develop the expected excitonic magnetism but experiences two successive t…
Tomonaga-Luttinger spin liquid in the spin-1/2 inequilateral diamond-chain compound K$_3$Cu$_3$AlO$_2$(SO$_4$)$_4$
K $_3$ Cu $_3$ AlO $_2$（SO $_4$）$_4$是一种高度一维的自旋为1/2的不等边金刚石链反铁磁体。在非弹性中子散射谱中观察到自旋连续谱和自旋单重态二聚体激发，这与理论预测非常一致：二聚体-单体复合结构，其中二聚体由强反铁磁（AFM）耦合引起，单体形成几乎孤立的量子AFM链控制低能激发。此外，μ子自旋旋转/弛豫光谱显示没有长程有序下降到90 mK，这是大约三个数量级低于量子原子力显微镜链的交换相互作用。因此，K $_3$ Cu $_3$ AlO $_2$（SO $_4$）$_4$被认为是在接近基态的低温下表现出Tomonaga-Luttinger自旋液体行为的化合物。
In solids, crystal field splitting refers to the lifting of atomic orbital degeneracy by the surrounding ions through the static electric field. Similarly, we show that the degenerated $d$ orbitals, which were derived in the harmonic oscillator approximation, are split into a low-lying $d_{x^2+y^2}$ singlet and a $d_{x^2-y^2/xy}$ doublet by the high-order Taylor polynomials of triangular optical potential. The low-energy effective theory of the orbital Mott insulator at $2/3$ filling is generically described by the Heisenberg-Compass model, where the antiferro-orbital exchange interactions of …
The $A$-site spinel NiRh$_2$O$_4$ is the only known realization of a spin-1 diamond lattice magnet and is predicted to host unconventional magnetic phenomena driven by frustrated nearest and next-nearest neighbor exchange as well as orbital degeneracy. Previous works found no sign of magnetic order but found a gapped dispersive magnetic excitation indicating a possible valence bond magnetic ground state. However, the presence of many competing low energy degrees of freedom and limited empirical microscopic constraints complicates further analysis. Here, we carry out resonant inelastic x-ray sc…
Spin-orbit (SO) Mott insulators are regarded as a new paradigm of magnetic materials, whose properties are largely influenced by SO coupling and featured by highly anisotropic bond-dependent exchange interactions between the spin-orbital entangled Kramers doublets, as typically manifested in $5d$ iridates. Here, we propose that a very similar situation can be realized in cuprates when the Cu$^{2+}$ ions reside in a tetrahedral environment, like in spinel compounds. Using first-principles electronic structure calculations, we construct a realistic model for the diamond lattice of the Cu$^{2+}$ …
We introduce a variational state for one-dimensional two-orbital Hubbard models that intuitively explains the recent computational discovery of pairing in these systems when hole doped. Our Ansatz is an optimized linear superposition of Affleck-Kennedy-Lieb-Tasaki valence bond states, rendering the combination a valence bond liquid dubbed Orbital Resonant Valence Bond. We show that the undoped (one electron/orbital) quantum state of two sites coupled into a global spin singlet is exactly written employing only spin-1/2 singlets linking orbitals at nearest-neighbor sites. Generalizing to longer…
Between Mott and cluster Mott: spin-orbit entangled dimer singlets in Ba$_3$CeRu$_2$O$_9$
University of Cologne（科隆大学）；Stockholm University（斯德哥尔摩大学）；Deutsches Elektronen-Synchrotron DESY（德国电子同步辐射中心）；IFW Dresden（德累斯顿联邦物理研究所）；Technische Universität Dresden（德累斯顿工业大学）
Functional renormalization group approach to the singlet-triplet transition in quantum dots
利用泛函重整化群方法研究了具有两个不同轨道的量子点在Hund耦合作用下的零偏压输运性质。通过调节轨道态的能量分离，量子点可以被驱动通过单重态-三重态跃迁。我们的方法，Karrasch { \em et al}的方法的基础上，我们适用于自旋相关的相互作用，恢复的量子点输运性质的关键特性，很少的数值工作。我们目前的结果在附近的过渡和比较我们的结果与以前的数值重整化群的结果和预测的微扰重整化群的电导。
Superconductivity found in doped NdNiO$_2$ is puzzling as two local symmetries of doped NiO$_2$ layers compete, with presumably far-reaching implications for the involved mechanism: a cuprate-like regime with Zhang-Rice singlets {\cblue is replaced by local triplet states at realistic values of charge-transfer energy, which would suggest a rather different superconductivity scenario from high-$T_c$ cuprates}. We address this competition by investigating Ni$_4$O$_8$ clusters with periodic boundary conditions in the parameter range relevant for the superconducting nickelates. With increasing val…
