Large anisotropic exchange in 5d and 4d oxides and halides open the door to new types of magnetic ground states and excitations, inconceivable a decade ago. A prominent case is the Kitaev spin liquid, host of remarkable properties such as protection of quantum information and the emergence of Majorana fermions. Here we discuss the promise for spin-liquid behavior in the 4d5 honeycomb halide α-RuCl3. From advanced electronic-structure calculations, we find that the Kitaev interaction is ferromagnetic, as in 5d5 iridium honeycomb oxides, and indeed defines the largest superexchange energy scale. A ferromagnetic Kitaev coupling is also supported by a detailed analysis of the field-dependent magnetization. Using exact diagonalization and density-matrix renormalization group techniques for extended Kitaev-Heisenberg spin Hamiltonians, we find indications for a transition from zigzag order to a gapped spin liquid when applying magnetic field. Our results offer a unified picture on recent magnetic and spectroscopic measurements on this material and open new perspectives on the prospect of realizing quantum spin liquids in d5 halides and oxides in general.

Temperature-pressure phase diagram of the Kitaev hyperhoneycomb iridate β-Li_{2}IrO_{3} is explored using magnetization, thermal expansion, magnetostriction, and muon spin rotation measurements, as well as single-crystal x-ray diffraction under pressure and ab initio calculations. The Néel temperature of β-Li_{2}IrO_{3} increases with the slope of 0.9  K/GPa upon initial compression, but the reduction in the polarization field H_{c} reflects a growing instability of the incommensurate order. At 1.4 GPa, the ordered state breaks down upon a first-order transition, giving way to a new ground state marked by the coexistence of dynamically correlated and frozen spins. This partial freezing in the absence of any conspicuous structural defects may indicate the classical nature of the resulting pressure-induced spin liquid, an observation paralleled to the increase in the nearest-neighbor off-diagonal exchange Γ under pressure.

Magnetization and high-resolution x-ray diffraction measurements of the Kitaev-Heisenberg material α-RuCl 3 reveal a pressure-induced crystallographic and magnetic phase transition at a hydrostatic pressure of p ∼ 0.2 GPa. This structural transition into a triclinic phase is characterized by a very strong dimerization of the Ru-Ru bonds, accompanied by a collapse of the magnetic susceptibility. Ab initio quantum-chemistry calculations disclose a pressure-induced enhancement of the direct 4d-4d bonding on particular Ru-Ru links, causing a sharp increase of the antiferromagnetic exchange interactions. These combined experimental and computational data show that the Kitaev spin-liquid phase in α-RuCl 3 strongly competes with the crystallization of spin singlets into a valence bond solid. DOI: 10.1103/PhysRevB.97.241108 The Kitaev model on a honeycomb lattice has grown into a hot topic in the last decade due to its exact solubility and its quantum spin-liquid ground state, which would be relevant for, e.g., quantum computing [1,2]. It implies a bonddependent compass-type coupling K and strong intrinsic spin frustration [3]. A crucial ingredient for realizing the Kitaev model in real materials is a strong spin-orbit coupling together with a honeycomb structure. Recently, Kitaev interactions were identified in α-RuCl 3 , from its unusual magnetic excitation spectrum [4,5], its strong magnetic anisotropy [6], and electronic-structure calculations [7,8], which render this material an ideal platform for exploring Kitaev magnetism experimentally.α-RuCl 3 is a j eff = 1/2 Mott insulator with a twodimensional (2D) layered structure of edge-sharing RuCl 6 octahedra forming a honeycomb lattice. At ambient pressure, * g.bastien@ifw-dresden.de Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.the honeycomb layers are arranged in a monoclinic (C2/m) structure at room temperature with one of the three nearestneighbor (NN) Ru-Ru bonds slightly shorter than the other two [9]. A structural phase transition was reported at T S 60 K under cooling and T S 166 K upon warming, but the low-temperature crystal structure is still under debate and could be either rhombohedral (R3) [10,11] or monoclinic (C2/m) [12,13]. The onset of long-range magnetic order at T N 7 K [9] in α-RuCl 3 implies that other magnetic interactions have to be considered in addition to the Kitaev interaction K: a NN Heisenberg J , an off-diagonal coupling , as well as next-NN interactions J 2 and J 3 [7,8,14,15]. While electronic-structure calculations indicate that K is ferromagnetic in α-RuCl 3 and indeed defines the largest exchange energy scale [7,8,14,15], the debate on the minimal effective spin model and precise magnitude of the different couplings is not fully settled yet. By applying a magnetic field in the basal plane, the magnetic zigzag ground sta...

A method for the selective synthesis of sulfide clusterfullerenes Dy2S@C2n is developed. Addition of methane to the reactive atmosphere reduces the formation of empty fullerenes in the arc-discharge synthesis, whereas the use of Dy2S3 as a source of metal and sulfur affords sulfide clusterfullerenes as the main fullerene products along with smaller amounts of carbide clusterfullerenes. Two isomers of Dy2S@C82 with Cs(6) and C3v(8) cage symmetry, Dy2S@C72-Cs(10528), and a carbide clusterfullerene Dy2C2@C82-Cs(6) were isolated. The molecular structure of both Dy2S@C82 isomers was elucidated by single-crystal X-ray diffraction. SQUID magnetometry demonstrates that all of these clusterfullerenes exhibit hysteresis of magnetization, with Dy2S@C82-C3v(8) being the strongest single molecule magnet in the series. DC- and AC-susceptibility measurements were used to determine magnetization relaxation times in the temperature range from 1.6 K to 70 K. Unprecedented magnetization relaxation dynamics with three consequent Orbach processes and energy barriers of 10.5, 48, and 1232 K are determined for Dy2S@C82-C3v(8). Dy2S@C82-Cs(6) exhibits faster relaxation of magnetization with two barriers of 15.2 and 523 K. Ab initio calculations were used to interpret experimental data and compare the Dy-sulfide clusterfullerenes to other Dy-clusterfullerenes. The smallest and largest barriers are ascribed to the exchange/dipolar barrier and relaxation via crystal-field states, respectively, whereas an intermediate energy barrier of 48 K in Dy2S@C82-C3v(8) is assigned to the local phonon mode, corresponding to the librational motion of the Dy2S cluster inside the carbon cage.

The electronic ground state in many iridate materials is described by a complex wave-function in which spin and orbital angular momenta are entangled due to relativistic spin-orbit coupling (SOC) [1,2]. Such a localized electronic state carries an effective total angular momentum of J ef f = 1/2 [3,4]. In materials with an edge-sharing octahedral crystal structure, such as the honeycomb iridates Li2IrO3 and Na2IrO3, these J ef f = 1/2 moments are expected to be coupled through a special bonddependent magnetic interaction [5][6][7], which is a necessary condition for the realization of a Kitaev quantum spin liquid [8]. However, this relativistic electron picture is challenged by an alternate description, in which itinerant electrons are confined to a benzene-like hexagon, keeping the system insulating despite the delocalized nature of the electrons [9,10]. In this quasi-molecular orbital (QMO) picture, the honeycomb iridates are an unlikely choice for a Kitaev spin liquid. Here we show that the honeycomb iridate Li2IrO3 is best described by a J ef f = 1/2 state at ambient pressure, but crosses over into a QMO state under the application of small (∼0.1 GPa) hydrostatic pressure. This result illustrates that the physics of iridates is extremely rich due to a delicate balance between electronic bandwidth, spin-orbit coupling, crystal field, and electron correlation. arXiv:1803.04056v1 [cond-mat.str-el]

Due to the combination of a substantial spin-orbit coupling and correlation effects, iridium oxides hold a prominent place in the search for novel quantum states of matter, including, e.g., Kitaev spin liquids and topological Weyl states. We establish the promise of the very recently synthesized hyper-honeycomb iridate β-Li2IrO3 in this regard. A detailed theoretical analysis reveals the presence of large ferromagnetic first-neighbor Kitaev interactions, while a second-neighbor antiferromagnetic Heisenberg exchange drives the ground state from ferro to zigzag order via a three-dimensional Kitaev spin liquid and an incommensurate phase. Experiment puts the system in the latter regime but the Kitaev spin liquid is very close and reachable by a slight modification of the ratio between the second- and first-neighbor couplings, for instance via strain.

The marked interplay between the crystalline, electronic, and magnetic structure of atomically thin magnets has been regarded as the key feature for designing next-generation magneto-optoelectronic devices. In this respect, a detailed understanding of the microscopic interactions underlying the magnetic response of these crystals is of primary importance. Here, we combine model Hamiltonians with multireference configuration interaction wavefunctions to accurately determine the strength of the spin couplings in the prototypical single-layer magnet CrI3. Our calculations identify the (ferromagnetic) Heisenberg exchange interaction J = −1.44 meV as the dominant term, being the inter-site magnetic anisotropies substantially weaker. We also find that single-layer CrI3 features an out-of-plane easy axis ensuing from a single-ion anisotropy A = −0.10 meV, and predict g-tensor in-plane components g x x = g y y = 1.90 and out-of-plane component g zz  = 1.92. In addition, we assess the performance of a dozen widely used density functionals against our accurate correlated wavefunctions calculations and available experimental data, thereby establishing reference results for future first-principles investigations. Overall, our findings offer a firm theoretical ground to recent experimental observations.

A range of honeycomb-lattice compounds has been proposed and investigated in the search for a topological Kitaev spin liquid. However, sizable Heisenberg interactions and additional symmetryallowed exchange anisotropies in the magnetic Hamiltonian of these potential Kitaev materials push them away from the pure Kitaev spin-liquid state. Particularly the Kitaev-to-Heisenberg coupling ratio is essential in this respect. With the help of advanced quantum-chemistry methods, we explore how the magnetic coupling ratios depend on pressure in several honeycomb compounds (Na2IrO3, β-Li2IrO3, and α-RuCl3). We find that the Heisenberg and Kitaev terms are affected differently by uniform pressure or strain: the Kitaev component increases more rapidly than the Heisenberg counterpart. This provides a scenario where applying pressure or strain can stabilize a spin liquid in such materials.