Johannes Reuther

Relevance of the Heisenberg-Kitaev model for the honeycomb lattice iridates A2IrO3.

Combining thermodynamic measurements with theoretical calculations we demonstrate that the 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 interactions beyond nearest-neighbor exchange. Experimentally, we observe an increase of the Curie-Weiss temperature from θ≈-125  K for Na2IrO3 to θ≈-33  K for Li2IrO3, while the ordering temperature remains roughly the same T(N)≈15  K. Using functional renormalization group calculations we show that this evolution of θ and T(N) as well as the low temperature zigzag magnetic order can be captured within this extended HK model. We estimate that Na2IrO3 is deep in a magnetically ordered regime, while Li2IrO3 appears to be close to a spin-liquid regime.

Finite-temperature phase diagram of the Heisenberg-Kitaev model

We discuss the finite-temperature phase diagram of the Heisenberg-Kitaev model on the hexagonal lattice, which has been suggested to describe the spin-orbital exchange of the effective spin-1/2 momenta in the Mott insulating Iridate Na2IrO3. At zero-temperature this model exhibits magnetically ordered states well beyond the isotropic Heisenberg limit as well as an extended gapless spin liquid phase around the highly anisotropic Kitaev limit. Using a pseudofermion functional renormalization group (RG) approach, we extract both the Curie-Weiss scale and the critical ordering scale (for the magnetically ordered states) from the RG flow of the magnetic susceptibility. The Curie-Weiss scale switches sign -- indicating a transition of the dominant exchange from antiferromagnetic to ferromagnetic -- deep in the magnetically ordered regime. For the latter we find no significant frustration, i.e. a substantial suppression of the ordering scale with regard to the Curie-Weiss scale. We discuss our results in light of recent experimental susceptibility measurements for Na2IrO3.

Physical realization of a quantum spin liquid based on a complex frustration mechanism

A detailed and systematic study of Ca10Cr7O28 reveals all the hallmarks of spin-liquid behaviour, in spite of the compound’s unusually complex structure.

Spiral order in the honeycomb iridate Li2IrO3

The honeycomb iridates A_2IrO_3 (A = Na, Li) constitute promising candidate materials to realize the Heisenberg-Kitaev model (HKM) in nature, hosting unconventional magnetic as well as spin-liquid phases. Recent experiments suggest, however, that Li_2IrO_3 exhibits a magnetically ordered state of incommensurate spiral type which has not been identified in the HKM. We show that these findings can be understood in the context of an extended Heisenberg-Kitaev scenario satisfying all tentative experimental evidence: (i) the maximum of the magnetic susceptibility is located inside the first Brillouin zone, (ii) the Curie-Weiss temperature is negative relating to dominant antiferromagnetic fluctuations, and (iii) significant second-neighbor spin exchange is involved.

Magnetic order and paramagnetic phases in the quantumJ1-J2-J3honeycomb model

Recent work shows that a quantum spin liquid can arise in realistic fermionic models on a honeycomb lattice. We study the quantum spin-1/2 Heisenberg honeycomb model, considering couplings J1, J2, and J3 up to third nearest neighbors. We use an unbiased pseudofermion functional renormalization group method to compute the magnetic susceptibility and determine the ordered and disordered states of the model. Aside from antiferromagnetic, collinear, and spiral order domains, we find a large paramagnetic region at intermediate J2 coupling. For larger J2 within this domain, we find a strong tendency to staggered dimer ordering, while the remaining paramagnetic regime for low J2 shows only weak plaquet and staggered dimer response. We suggest this regime to be a promising region to look for quantum spin liquid states when charge fluctuations would be included.

Rashba spin-orbit coupling in the Kane-Mele-Hubbard model

Spin-orbit (SO) coupling is the crucial parameter to drive topological-insulating phases in electronic band models. In particular, the generic emergence of SO coupling involves the Rashba term which fully breaks the SU(2) spin symmetry. As soon as interactions are taken into account, however, many theoretical studies have to content themselves with the analysis of a simplified U(1)-conserving SO term without Rashba coupling. We intend to fill this gap by studying the Kane-Mele-Hubbard (KMH) model in the presence of Rashba SO coupling and present the first systematic analysis of the effect of Rashba SO coupling in a correlated two-dimensional topological insulator. We apply the variational cluster approach (VCA) to determine the interacting phase diagram by computing local density of states, magnetization, single particle spectral function, and edge states. Preceded by a detailed VCA analysis of the KMH model in the presence of U(1)-conserving SO coupling, we find that the additional Rashba SO coupling drives new electronic phases such as a metallic regime and a weak topological-semiconductor phase which persist in the presence of interactions.

Quantum phases of the planar antiferromagneticJ1−J2−J3Heisenberg model

We present results of a complementary analysis of the frustrated planar J_1-J_2-J_3 spin-1/2 quantum-antiferromagnet. Using dynamical functional renormalization group, high-order coupled cluster calculations, and series expansion based on the flow equation method, we have calculated generalized momentum resolved susceptibilities, the ground state energy, the magnetic order parameter, and the elementary excitation gap. From these we determine a quantum phase diagram which shows a large window of a quantum paramagnetic phase situated between the Neel, spiral and collinear states, which are present already in the classical J_1-J_2-J_3 antiferromagnet. Our findings are consistent with substantial plaquette correlations in the quantum paramagnetic phase. The extent of the quantum paramagnetic region is found to be in satisfying agreement between the three different approaches we have employed.

Magnetic ordering phenomena of interacting quantum spin Hall models

The two-dimensional Hubbard model defined for topological band structures exhibiting a quantum spin Hall effect poses fundamental challenges in terms of phenomenological characterization and microscopic classification. In the limit of infinite coupling U at half filling, the spin model Hamiltonians resulting from a strong coupling expansion show various forms of magnetic ordering phenomena depending on the underlying spin-orbit coupling terms. We investigate the infinite U limit of the Kane-Mele Hubbard model with z-axis intrinsic spin-orbit coupling as well as its generalization to a generically multi-directional spin orbit term which has been claimed to account for the physical scenario in monolayer Na2IrO3. We find that the axial spin symmetry which is kept in the former but broken in the latter has a fundamental impact on the magnetic phase diagram as we vary the spin orbit coupling strength. While the Kane-Mele spin model shows a continuous evolution from conventional honeycomb Neel to XY antiferromagnetism which avoids the frustration imposed by the increased spin-orbit coupling, the multi-directional spin-orbit term induces a commensurate to incommensurate transition at intermediate coupling strength, and yields a complex spiral state with a 72 site unit cell in the limit of infinite spin-orbit coupling. From our findings, we conjecture that in the case of broken axial spin symmetry there is a large propensity for an additional phase at sufficiently large spin-orbit coupling and intermediate U.

Numerical treatment of spin systems with unrestricted spin length S : A functional renormalization group study

We develop a generalized pseudo-fermion functional renormalization group (PFFRG) approach that can be applied to arbitrary Heisenberg models with spins ranging from the quantum case

Functional renormalization group for three-dimensional quantum magnetism

S=1/2