Relevance of the Heisenberg-Kitaev model for the honeycomb lattice iridates A_2IrO_3

Combining thermodynamic measurements with theoretical density functional and thermodynamic calculations we demonstrate that the honeycomb lattice iridates A2IrO3 (A = Na, Li) are magnetically ordered Mott insulators where the magnetism of the effective spin-orbital S = 1/2 moments can be captured by a Heisenberg-Kitaev (HK) model with Heisenberg interactions beyond nearest-neighbor exchange. Experimentally, we observe an increase of the Curie-Weiss temperature from \theta = -125 K for Na2IrO3 to \theta = -33 K for Li2IrO3, while the antiferromagnetic ordering temperature remains roughly the same T_N = 15 K for both materials. Using finite-temperature functional renormalization group calculations we show that this evolution of \theta, T_N, the frustration parameter f = \theta/T_N, and the zig-zag magnetic ordering structure suggested for both materials by density functional theory can be captured within this extended HK model. Combining our experimental and theoretical results, we estimate that Na2IrO3 is deep in the magnetically ordered regime of the HK model (\alpha \approx 0.25), while Li2IrO3 appears to be close to a spin-liquid regime (0.6 < \alpha < 0.7).Comment: Version accepted for publication in PRL. Additional DFT and thermodynamic calculations have been included. 6 pages of supplementary material include

Ground-state properties of the spin-1/2 antiferromagnetic Heisenberg model on the triangular lattice: A variational study based on entangled-plaquette states

We study, on the basis of the general entangled-plaquette variational ansatz, the ground-state properties of the spin-1/2 antiferromagnetic Heisenberg model on the triangular lattice. Our numerical estimates are in good agreement with available exact results and comparable, for large system sizes, to those computed via the best alternative numerical approaches, or by means of variational schemes based on specific (i.e., incorporating problem dependent terms) trial wave functions. The extrapolation to the thermodynamic limit of our results for lattices comprising up to N=324 spins yields an upper bound of the ground-state energy per site (in units of the exchange coupling) of $-0.5458(2)$ [$-0.4074(1)$ for the XX model], while the estimated infinite-lattice order parameter is $0.3178(5)$ (i.e., approximately 64% of the classical value).Comment: 8 pages, 3 tables, 2 figure

Breathing chromium spinels a showcase for a variety of pyrochlore Heisenberg Hamiltonians

We address the long standing problem of the microscopic origin of the richly diverse phenomena in the chromium breathing pyrochlore material family. Combining electronic structure and renormalization group techniques we resolve the magnetic interactions and analyze their reciprocal space susceptibility. We show that the physics of these materials is principally governed by long range Heisenberg Hamiltonian interactions, a hitherto unappreciated fact. Our calculations uncover that in these isostructural compounds, the choice of chalcogen triggers a proximity of the materials to classical spin liquids featuring degenerate manifolds of wave vectors of different dimensions A Coulomb phase with three dimensional degeneracy for LiInCr4O8 and LiGaCr4O8, a spiral spin liquid with two dimensional degeneracy for CuInCr4Se8 and one dimensional line degeneracies characteristic of the face centered cubic antiferromagnet for LiInCr4S8, LiGaCr4S8, and CuInCr4S8. The surprisingly complex array of prototypical pyrochlore behaviors we discovered in chromium spinels may inspire studies of transition paths between different semi classical spin liquids by doping or pressur

Pinwheel valence bond crystal ground state of the spin 1 2 Heisenberg antiferromagnet on the shuriken lattice

We investigate the nature of the ground state of the spin 1 2 Heisenberg antiferromagnet on the shuriken lattice by complementary state of the art numerical techniques, such as variational Monte Carlo VMC with versatile Gutzwiller projected Jastrow wave functions, unconstrained multivariable variational Monte Carlo mVMC , and pseudofermion pseudo Majorana functional renormalization group PFFRG PMFRG methods. We establish the presence of a quantum paramagnetic ground state and investigate its nature, by classifying symmetric and chiral quantum spin liquids, and inspecting their instabilities towards competing valence bond crystal VBC orders. Our VMC analysis reveals that a VBC with a pinwheel structure emerges as the lowest energy variational ground state, and it is obtained as an instability of the U 1 Dirac spin liquid. Analogous conclusions are drawn from mVMC calculations employing accurate BCS pairing states supplemented by symmetry projectors, which confirm the presence of pinwheel VBC order by a thorough analysis of dimer dimer correlation functions. Our work highlights the nontrivial role of quantum fluctuations via the Gutzwiller projector in resolving the subtle interplay between competing order

Evidence for a three dimensional quantum spin liquid in PbCuTe2O6

The quantum spin liquid is a highly entangled magnetic state characterized by the absence of static magnetism in its ground state. Instead, the spins fluctuate in a highly correlated way down to the lowest temperatures. Quantum spin liquids are very rare and are confined to a few specific cases where the interactions between the magnetic ions cannot be simultaneously satisfied known as frustration . Lattices with magnetic ions in triangular or tetrahedral arrangements, which interact via isotropic antiferromagnetic interactions, can generate such a frustration. Three dimensional isotropic spin liquids have mostly been sought in materials where the magnetic ions form pyrochlore or hyperkagome lattices. Here we present a three dimensional lattice called the hyper hyperkagome that enables spin liquid behaviour and manifests in the compound PbCuTe2O6. Using a combination of experiment and theory, we show that this system exhibits signs of being a quantum spin liquid with no detectable static magnetism together with the presence of diffuse continua in the magnetic spectrum suggestive of fractional spinon excitation

Intertwined nematic orders in a frustrated ferromagnet

We investigate the quantum phases of the frustrated spin 12J1 amp; 8722;J2 amp; 8722;J3 Heisenberg model on the square lattice with ferromagnetic J1 and antiferromagnetic J2 and J3 interactions. Using the pseudofermion functional renormalization group technique, we find an intermediate paramagnetic phase located between classically ordered ferromagnetic, stripy antiferromagnetic, and incommensurate spiral phases. We observe that quantum fluctuations lead to significant shifts of the spiral pitch angles compared to the classical limit. By computing the response of the system with respect to various spin rotation and lattice symmetry breaking perturbations, we identify a complex interplay between different nematic spin states in the paramagnetic phase. While retaining time reversal invariance, these phases either break spin rotation symmetry, lattice rotation symmetry, or a combination of both. We therefore propose the J1 amp; 8722;J2 amp; 8722;J3 Heisenberg model on the square lattice as a paradigmatic example where different intimately connected types of nematic orders emerge in the same mode

Quantum paramagnetism and helimagnetic orders in the Heisenberg model on the body centered cubic lattice

We investigate the spin S 1 2 Heisenberg model on the body centered cubic lattice in the presence of ferromagnetic and antiferromagnetic nearest neighbor J1, second neighbor J2, and third neighbor J3 exchange interactions. The classical ground state phase diagram obtained by a Luttinger Tisza analysis is shown to host six different noncollinear helimagnetic orders in addition to ferromagnetic, N el, stripe, and planar antiferromagnetic orders. Employing the pseudofermion functional renormalization group PFFRG method for quantum spins S 1 2 we find an extended nonmagnetic region, and significant shifts to the classical phase boundaries and helimagnetic pitch vectors caused by quantum fluctuations, while no new long range dipolar magnetic orders are stabilized. The nonmagnetic phase is found to disappear for S 1. We calculate the magnetic ordering temperatures from PFFRG and quantum Monte Carlo methods, and make comparisons to available dat