Theory of Moiré Magnetism in Twisted Bilayer α-RuCl3.

Motivated by the recent developments in moiré superlattices of van der Waals magnets and the desire to control the magnetic interactions of α-RuCl3, here we present a comprehensive theory of the long-range ordered magnetic phases of twisted bilayer α-RuCl3. Using a combination of first-principles calculations and atomistic simulations, we show that the stacking-dependent interlayer exchange gives rise to an array of magnetic phases that can be realized by controlling the twist angle. In particular, we discover a complex hexagonal domain structure in which multiple zigzag orders coexist. This multidomain order minimizes the interlayer energy while enduring the energy cost due to domain wall formation. Further, we show that quantum fluctuations can be enhanced across the phase transitions. Our results indicate that magnetic frustration due to stacking-dependent interlayer exchange in moiré superlattices can be exploited to tune quantum fluctuations and the magnetic ground state of α-RuCl3.

Magnetic anisotropy reversal driven by structural symmetry-breaking in monolayer α-RuCl3.

Layered α-RuCl3 is a promising material to potentially realize the long-sought Kitaev quantum spin liquid with fractionalized excitations. While evidence of this state has been reported under a modest in-plane magnetic field, such behaviour is largely inconsistent with theoretical expectations of spin liquid phases emerging only in out-of-plane fields. These predicted field-induced states have been largely out of reach due to the strong easy-plane anisotropy of bulk crystals, however. We use a combination of tunnelling spectroscopy, magnetotransport, electron diffraction and ab initio calculations to study the layer-dependent magnons, magnetic anisotropy, structure and exchange coupling in atomically thin samples. Due to picoscale distortions, the sign of the average off-diagonal exchange changes in monolayer α-RuCl3, leading to a reversal of spin anisotropy to easy-axis anisotropy, while the Kitaev interaction is concomitantly enhanced. Our work opens the door to the possible exploration of Kitaev physics in the true two-dimensional limit.

Symmetric Kondo Lattice States in Doped Strained Twisted Bilayer Graphene.

We use the topological heavy fermion (THF) model and its Kondo lattice (KL) formulation to study the possibility of a symmetric Kondo (SK) state in twisted bilayer graphene. Via a large-N approximation, we find a SK state in the KL model at fillings ν=0,±1,±2 where a KL model can be constructed. In the SK state, all symmetries are preserved and the local moments are Kondo screened by the conduction electrons. At the mean-field level of the THF model at ν=0,±1,±2,±3 we also find a similar symmetric state that is adiabatically connected to the symmetric Kondo state. We study the stability of the symmetric state by comparing its energy with the ordered (symmetry-breaking) states found in [H. Hu et al., Phys. Rev. Lett. 131, 026502 (2023).PRLTAO0031-900710.1103/PhysRevLett.131.026502, Z.-D. Song and B. A. Bernevig, Phys. Rev. Lett. 129, 047601 (2022).PRLTAO0031-900710.1103/PhysRevLett.129.047601] and find the ordered states to have lower energy at ν=0,±1,±2. However, moving away from integer fillings by doping the light bands, our mean-field calculations find the energy difference between the ordered state and the symmetric state to be reduced, which suggests the loss of ordering and a tendency toward Kondo screening. In order to include many-body effects beyond the mean-field approximation, we also performed dynamical mean-field theory calculations on the THF model in the nonordered phase. The spin susceptibility follows a Curie behavior at ν=0,±1,±2 down to ∼2 K where the onset of screening of the local moment becomes visible. This hints to very low Kondo temperatures at these fillings, in agreement with the outcome of our mean-field calculations. At noninteger filling ν=±0.5,±0.8,±1.2 dynamical mean-field theory shows deviations from a 1/T susceptibility at much higher temperatures, suggesting a more effective screening of local moments with doping. Finally, we study the effect of a C_{3z}-rotational-symmetry-breaking strain via mean-field approaches and find that a symmetric phase (that only breaks C_{3z} symmetry) can be stabilized at sufficiently large strain at ν=0,±1,±2. Our results suggest that a symmetric Kondo phase is strongly suppressed at integer fillings, but could be stabilized either at noninteger fillings or by applying strain.

Ultrasharp Lateral p-n Junctions in Modulation-Doped Graphene.

We demonstrate ultrasharp (≲10 nm) lateral p-n junctions in graphene using electronic transport, scanning tunneling microscopy, and first-principles calculations. The p-n junction lies at the boundary between differentially doped regions of a graphene sheet, where one side is intrinsic and the other is charge-doped by proximity to a flake of α-RuCl3 across a thin insulating barrier. We extract the p-n junction contribution to the device resistance to place bounds on the junction width. We achieve an ultrasharp junction when the boundary between the intrinsic and doped regions is defined by a cleaved crystalline edge of α-RuCl3 located 2 nm from the graphene. Scanning tunneling spectroscopy in heterostructures of graphene, hexagonal boron nitride, and α-RuCl3 shows potential variations on a sub 10 nm length scale. First-principles calculations reveal that the charge-doping of graphene decays sharply over just nanometers from the edge of the α-RuCl3 flake.

Pseudoelasticity of SrNi2P2 Micropillar via Double Lattice Collapse and Expansion.

The maximum recoverable strain of most crystalline solids is less than 1% because plastic deformation or fracture usually occurs at a small strain. In this work, we show that a SrNi2P2 micropillar exhibits pseudoelasticity with a large maximum recoverable strain of ∼14% under uniaxial compression via unique reversible structural transformation, double lattice collapse-expansion that is repeatable under cyclic loading. Its high yield strength (∼3.8 ± 0.5 GPa) and large maximum recoverable strain bring out the ultrahigh modulus of resilience (∼146 ± 19 MJ/m3), a few orders of magnitude higher than that of most engineering materials. The double lattice collapse-expansion mechanism shows stress-strain behaviors similar to that of conventional shape-memory alloys, such as hysteresis and thermo-mechanical actuation, even though the structural changes involved are completely different. Our work suggests that the discovery of a new class of high-performance ThCr2Si2-structured materials will open new research opportunities in the field of pseudoelasticity.

Anomalous Quantum Oscillations in a Heterostructure of Graphene on a Proximate Quantum Spin Liquid.

The quasi-two-dimensional Mott insulator α-RuCl_{3} is proximate to the sought-after Kitaev quantum spin liquid (QSL). In a layer of α-RuCl_{3} on graphene, the dominant Kitaev exchange is further enhanced by strain. Recently, quantum oscillation (QO) measurements of such α-RuCl_{3} and graphene heterostructures showed an anomalous temperature dependence beyond the standard Lifshitz-Kosevich (LK) description. Here, we develop a theory of anomalous QO in an effective Kitaev-Kondo lattice model in which the itinerant electrons of the graphene layer interact with the correlated magnetic layer via spin interactions. At low temperatures, a heavy Fermi liquid emerges such that the neutral Majorana fermion excitations of the Kitaev QSL acquire charge by hybridizing with the graphene Dirac band. Using ab initio calculations to determine the parameters of our low-energy model, we provide a microscopic theory of anomalous QOs with a non-LK temperature dependence consistent with our measurements. We show how remnants of fractionalized spin excitations can give rise to characteristic signatures in QO experiments.

Spin Vortex Crystal Order in Organic Triangular Lattice Compound.

Organic salts represent an ideal experimental playground for studying the interplay between magnetic and charge degrees of freedom, which has culminated in the discovery of several spin-liquid candidates such as κ-(ET)_{2}Cu_{2}(CN)_{3} (κ-Cu). Recent theoretical studies indicate the possibility of chiral spin liquids stabilized by ring exchange, but the parent states with chiral magnetic order have not been observed in this material family. In this Letter, we discuss the properties of the recently synthesized κ-(BETS)_{2}Mn[N(CN)_{2}]_{3} (κ-Mn). Based on analysis of specific heat, magnetic torque, and NMR measurements combined with ab initio calculations, we identify a spin-vortex crystal order. These observations definitively confirm the importance of ring exchange in these materials and support the proposed chiral spin-liquid scenario for triangular lattice organics.

Erratum: Lattice Dynamics Coupled to Charge and Spin Degrees of Freedom in the Molecular Dimer-Mott Insulator κ-(BEDT-TTF)_{2}Cu[N(CN)_{2}]Cl [Phys. Rev. Lett. 123, 027601 (2019)].

This corrects the article DOI: 10.1103/PhysRevLett.123.027601.

Evolution from B_{2g} Nematics to B_{1g} Nematics in Heavily Hole-Doped Iron-Based Superconductors.

Recent experiments reported an unusual nematic behavior of heavily hole-doped pnictides AFe_{2}As_{2}, with alkali A=Rb, Cs. In contrast to the B_{2g} nematic order of the parent AeFe_{2}As_{2} compounds (with alkaline earth Ae=Sr, Ba), characterized by unequal nearest-neighbor Fe-Fe bonds, in the hole-doped systems nematic order is observed in the B_{1g} channel, characterized by unequal next-nearest-neighbor Fe-Fe (diagonal Fe-As-Fe) bonds. In this Letter, using density functional theory, we attribute this behavior to the evolution of the magnetic ground state along the series Ae_{1-x}A_{x}Fe_{2}As_{2}, from single stripes for small x to double stripes for large x. Our simulations using the reduced Stoner theory show that fluctuations of Fe moments are essential for the stability of the double-stripe configuration. We propose that the change in the nature of the magnetic ground state is responsible for the change in the symmetry of the vestigial nematic order that it supports.

Effect of Nonlocal Correlations on the Electronic Structure of LiFeAs.

We investigate the role of nonlocal correlations in LiFeAs by exploring an ab initio-derived multiorbital Hubbard model for LiFeAs via the two-particle self-consistent (TPSC) approach. The multiorbital formulation of TPSC approximates the irreducible interaction vertex to be an orbital-dependent constant, which is self-consistently determined from local spin and charge sum rules. Within this approach, we disentangle the contribution of local and nonlocal correlations in LiFeAs and show that in the local approximation one recovers the dynamical mean field theory result. The comparison of our theoretical results to most recent angular-resolved photoemission spectroscopy and de Haas-van Alphen data shows that nonlocal correlations in LiFeAs are decisive to describe the measured spectral function A(k[over →],ω), Fermi surface, and scattering rates. These findings underline the importance of nonlocal correlations and benchmark different theoretical approaches for iron-based superconductors.

Electronic Properties of α-RuCl_{3} in Proximity to Graphene.

In the pursuit of developing routes to enhance magnetic Kitaev interactions in α-RuCl_{3}, as well as probing doping effects, we investigate the electronic properties of α-RuCl_{3} in proximity to graphene. We study α-RuCl_{3}/graphene heterostructures via ab initio density functional theory calculations, Wannier projection, and nonperturbative exact diagonalization methods. We show that α-RuCl_{3} becomes strained when placed on graphene and charge transfer occurs between the two layers, making α-RuCl_{3} (graphene) lightly electron doped (hole doped). This gives rise to an insulator-to-metal transition in α-RuCl_{3} with the Fermi energy located close to the bottom of the upper Hubbard band of the t_{2g} manifold. These results suggest the possibility of realizing metallic and even exotic superconducting states. Moreover, we show that in the strained α-RuCl_{3} monolayer the Kitaev interactions are enhanced by more than 50% compared to the unstrained bulk structure. Finally, we discuss scenarios related to transport experiments in α-RuCl_{3}/graphene heterostructures.

Sawtooth Torque in Anisotropic j_{eff}=1/2 Magnets: Application to α-RuCl_{3}.

The so-called "Kitaev candidate" materials based on 4d^{5} and 5d^{5} metals have recently emerged as magnetic systems displaying strongly anisotropic exchange interactions reminiscent of the Kitaev's honeycomb model. Recently, these materials have been shown to commonly display a distinct sawtooth angular dependence of the magnetic torque over a wide range of magnetic fields. While higher order chiral spin interactions have been considered as a source of this observation, we show here that bilinear anisotropic interactions and/or g anisotropy are each sufficient to explain the observed torque response, which may be distinguished on the basis of high-field measurements. These findings unify the understanding of magnetic torque experiments in a variety of Kitaev candidate materials.

Lattice Dynamics Coupled to Charge and Spin Degrees of Freedom in the Molecular Dimer-Mott Insulator κ-(BEDT-TTF)_{2}Cu[N(CN)_{2}]Cl.

Inelastic neutron scattering measurements on the molecular dimer-Mott insulator κ-(BEDT-TTF)_{2}Cu[N(CN)_{2}]Cl reveal a phonon anomaly in a wide temperature range. Starting from T_{ins}∼50-60 K where the charge gap opens, the low-lying optical phonon modes become overdamped upon cooling towards the antiferromagnetic ordering temperature T_{N}=27 K, where also a ferroelectric ordering at T_{FE}≈T_{N} occurs. Conversely, the phonon damping becomes small again when spins and charges are ordered below T_{N}, while no change of the lattice symmetry is observed across T_{N} in neutron diffraction measurements. We assign the phonon anomalies to structural fluctuations coupled to charge and spin degrees of freedom in the BEDT-TTF molecules.

Role of Hydrogen in the Spin-Orbital-Entangled Quantum Liquid Candidate H_{3}LiIr_{2}O_{6}.

Motivated by recent reports of H_{3}LiIr_{2}O_{6} as a spin-orbital-entangled quantum liquid, we investigate via a combination of density functional theory and nonperturbative exact diagonalization the microscopic nature of its magnetic interactions. We find that while the interlayer O─H─O bond geometry strongly affects the local magnetic couplings, these bonds are likely to remain symmetrical due to large zero-point fluctuations of the H positions. In this case, the estimated magnetic model lies close to the classical tricritical point between ferromagnetic, zigzag, and incommensurate spiral orders, what may contribute to the lack of magnetic ordering. However, we also find that substitution of H by D (deuterium) as well as disorder-induced inhomogeneities destabilizes the O─H or D─O bonds, modifying strongly the local magnetic couplings. These results suggest that the magnetic response in H_{3}LiIr_{2}O_{6} is likely sensitive to both the stoichiometry and the microstructure of the samples and emphasize the importance of a careful treatment of hydrogen for similar systems.

Uncovering the Mechanism of the Impurity-Selective Mott Transition in Paramagnetic V_{2}O_{3}.

While the phase diagrams of the one- and multiorbital Hubbard model have been well studied, the physics of real Mott insulators is often much richer, material dependent, and poorly understood. In the prototype Mott insulator V_{2}O_{3}, chemical pressure was initially believed to explain why the paramagnetic-metal to antiferromagnetic-insulator transition temperature is lowered by Ti doping while Cr doping strengthens correlations, eventually rendering the high-temperature phase paramagnetic insulating. However, this scenario has been recently shown both experimentally and theoretically to be untenable. Based on full structural optimization, we demonstrate via the charge self-consistent combination of density functional theory and dynamical mean-field theory that changes in the V_{2}O_{3} phase diagram are driven by defect-induced local symmetry breakings resulting from dramatically different couplings of Cr and Ti dopants to the host system. This finding emphasizes the high sensitivity of the Mott metal-insulator transition to the local environment and the importance of accurately accounting for the one-electron Hamiltonian, since correlations crucially respond to it.

Probing α-RuCl_{3} Beyond Magnetic Order: Effects of Temperature and Magnetic Field.

Recent studies have brought α-RuCl_{3} to the forefront of experimental searches for materials realizing Kitaev spin-liquid physics. This material exhibits strongly anisotropic exchange interactions afforded by the spin-orbit coupling of the 4d Ru centers. We investigate the dynamical response at finite temperature and magnetic field for a realistic model of the magnetic interactions in α-RuCl_{3}. These regimes are thought to host unconventional paramagnetic states that emerge from the suppression of magnetic order. Using exact diagonalization calculations of the quantum model complemented by semiclassical analysis, we find a very rich evolution of the spin dynamics as the applied field suppresses the zigzag order and stabilizes a quantum paramagnetic state that is adiabatically connected to the fully polarized state at high fields. At finite temperature, we observe large redistributions of spectral weight that can be attributed to the anisotropic frustration of the model. These results are compared to recent experiments and provide a road map for further studies of these regimes.

Evidence for Electronically Driven Ferroelectricity in a Strongly Correlated Dimerized BEDT-TTF Molecular Conductor.

By applying measurements of the dielectric constants and relative length changes to the dimerized molecular conductor κ-(BEDT-TTF)_{2}Hg(SCN)_{2}Cl, we provide evidence for order-disorder type electronic ferroelectricity that is driven by the charge order within the (BEDT-TTF)_{2} dimers and stabilized by a coupling to the anions. According to our density functional theory calculations, this material is characterized by a moderate strength of dimerization. This system thus bridges the gap between strongly dimerized materials, often approximated as dimer-Mott systems at 1/2 filling, and nondimerized or weakly dimerized systems at 1/4 filling, exhibiting a charge order. Our results indicate that intradimer charge degrees of freedom are of particular importance in correlated κ-(BEDT-TTF)_{2}X salts and can create novel states, such as electronically driven multiferroicity or charge-order-induced quasi-one-dimensional spin liquids.

Role of the Open-Shell Character on the Pressure-Induced Conductivity of an Organic Donor-Acceptor Radical Dyad.

Single-component conductors based on neutral organic radicals have received a lot of attention due to the possibility that the unpaired electron can serve as a charge carrier without the need of a previous doping process. Although most of these systems are based on delocalized planar radicals, we present here a nonplanar and spin localized radical based on a tetrathiafulvalene (TTF) moiety, linked to a perchlorotriphenylmethyl (PTM) radical by a conjugated bridge, which exhibits a semiconducting behavior upon application of high pressure. The synthesis, electronic properties, and crystal structure of this neutral radical TTF-Ph-PTM derivative (1) are reported and implications of its crystalline structure on its electrical properties are discussed. On the other hand, the non-radical derivative (2), which is isostructural with the radical 1, shows an insulating behavior at all measured pressures. The different electronic structures of these two isostructural systems have a direct influence on the conducting properties, as demonstrated by band structure DFT calculations.

J Freezing and Hund's Rules in Spin-Orbit-Coupled Multiorbital Hubbard Models.

We investigate the phase diagram of the spin-orbit-coupled three orbital Hubbard model at arbitrary filling by means of dynamical mean-field theory combined with the continuous-time quantum Monte Carlo method. We find that the spin-freezing crossover occurring in the metallic phase of the nonrelativistic multiorbital Hubbard model can be generalized to a J-freezing crossover, with J=L+S, in the spin-orbit-coupled case. In the J-frozen regime the correlated electrons exhibit a nontrivial flavor selectivity and energy dependence. Furthermore, in the regions near n=2 and n=4 the metallic states are qualitatively different from each other, which reflects the atomic Hund's third rule. Finally, we explore the appearance of magnetic order from exciton condensation at n=4 and discuss the relevance of our results for real materials.