An effective low-energy Hamiltonian of itinerant electrons for iridium oxide Na2IrO3 is derived by an ab initio downfolding scheme. The model is then reduced to an effective spin model on a honeycomb lattice by the strong coupling expansion. Here we show that the ab initio model contains spin-spin anisotropic exchange terms in addition to the extensively studied Kitaev and Heisenberg exchange interactions, and allows us to describe the experimentally observed zigzag magnetic order, interpreted as the state stabilized by the antiferromagnetic coupling of the ferromagnetic chains. We clarify possible routes to realize quantum spin liquids from existing Na2IrO3.
An effective low-energy Hamiltonian of itinerant electrons for iridium oxide Na2IrO3 is derived by an ab initio downfolding scheme. The model is then reduced to an effective spin model on a honeycomb lattice by the strong coupling expansion. Here we show that the ab initio model contains spin-spin anisotropic exchange terms in addition to the extensively studied Kitaev and Heisenberg exchange interactions, and allows us to describe the experimentally observed zigzag magnetic order, interpreted as the state stabilized by the antiferromagnetic coupling of the ferromagnetic chains. We clarify possible routes to realize quantum spin liquids from existing Na2IrO3.
Using quantum chemistry calculations we shed fresh light on the electronic structure and magnetic properties of RuCl3, a proposed realization of the honeycomb Kitaev spin model. It is found that the nearest-neighbor Kitaev exchange K is weaker than in 5d5 Ir oxides but still larger than other effective spin couplings. The electronic-structure computations also indicate a ferromagnetic K in the halide, which is supported by a detailed analysis of the field-dependent magnetization. From exact-diagonalization calculations for extended Kitaev-Heisenberg Hamiltonians we additionally find that a transition from zigzag order to a spin-liquid ground state can be induced in RuCl3 with external magnetic field.
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.
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.
Iridium oxides with a honeycomb lattice have been identified as platforms for the much anticipated Kitaev topological spin liquid: the spin-orbit entangled states of Ir(4+) in principle generate precisely the required type of anisotropic exchange. However, other magnetic couplings can drive the system away from the spin-liquid phase. With this in mind, here we disentangle the different magnetic interactions in Li2IrO3, a honeycomb iridate with two crystallographically inequivalent sets of adjacent Ir sites. Our ab initio many-body calculations show that, while both Heisenberg and Kitaev nearest-neighbour couplings are present, on one set of Ir-Ir bonds the former dominates, resulting in the formation of spin-triplet dimers. The triplet dimers frame a strongly frustrated triangular lattice and by exact cluster diagonalization we show that they remain protected in a wide region of the phase diagram.
In the recent years, interest in TM oxides with 5d valence electrons has grown immensely due to the realization of novel spin-orbit coupled ground states. In these compounds, e.g., iridates and osmates, the intriguing situation arises where the spin-orbit and electron-electron interactions meet on the same energy scale. This has created a new window of interest in these compounds since the interplay of crystal field effects, local multiplet physics, spin-orbit couplings, and intersite hopping can offer novel types of correlated ground states and excitations. In 5d5 iridates, a spin-orbit entangled j = 1/2 Mott insulating state has been realized recently. A remarkable feature of such a ground state is that it gives rise to anisotropic magnetic interactions. The 2D honeycomb-lattice 213 iridium oxides, A2IrO3 (A=Li,Na), have been put forward to host highly anisotropic bond-dependent spin-spin interactions that resemble the Kitaev spin model, which supports various types of topological phases relevant in quantum computing. The 2D square-lattice 214 iridates Sr2IrO4 and Ba2IrO4 are, on the other hand, appealing because of their perceived structural and magnetic simi- larity to La2CuO4, the mother compound of the cuprate high-Tc superconductors. This has promoted the latter iridium oxide compounds as novel platforms for the search of high-Tc superconductivity. To put such considerations on a firm footing, it is essential to quantify the different coupling strengths and energy scales, as they for instance appear in effective Hamiltonian descriptions of these correlated systems. Moreover, it is important to correctly describe their effects. In this thesis, the electronic structure and magnetic properties of 5d5 (mainly 214 and 213) iridates are studied using wave-function-based quantum chemistry methods. These methods are fully ab initio and are capable of accurately treating the electron-electron interactions without using any ad hoc parameters. The spin-orbit entangled j = 1/2 ground state in 214, 213 and other lower symmetry Sr3CuIrO6 and Na4Ir3O8 iridates is first analyzed in detail, by studying the local electronic structure of the 5d5 Ir4+ ion. We establish that the longer-range crystal anisotropy, i.e., low-symmetry fields related to ionic sites beyond the nearest neighbor oxygen cage, strongly influence the energies of Ir d levels. The ground state in all the compounds studied is j = 1/2 like with admixture from j ≃ 3/2 states ranging from 1 – 15 %. Further, the average j ≃ 1/2 → j ≃ 3/2 excitation energy we find is around 0.6 eV. The NN magnetic exchange interactions we computed for 214 iridates are predominantly isotropic Heisenberg-like with J ~ 60 meV, 3 – 4 times smaller than found in isostructural copper oxides. However, the anisotropic interactions are an order of magnitude larger than those in cuprates. Our estimates are in excellent agreement with those extracted from experiments, e.g., resonant inelastic x-ray scattering measurements. For the 213 honeycomb-lattice Na2IrO3 our calculations show that the relevant spin Hamiltonian contains further anisotropic terms beyond the Kitaev-Heisenberg model. Nevertheless, we predict that the largest energy scale is the Kitaev interaction, 10 to 20 meV, while the Heisenberg superexchange and off-diagonal symmetric anisotropic couplings are significantly weaker. In the sister compound Li2IrO3, we find that the structural inequivalence between the two types of Ir-Ir links has a striking influence on the effective spin Hamiltonian, leading in particular to two very different NN superexchange pathways, one weakly AF (~ 1 meV) and another strongly FM (−19 meV). The latter gives rise to rigid spin-1 triplets on a triangular lattice.
We derive and study a spin one-half Hamiltonian on a honeycomb lattice describing the exchange interactions between Ir4+ ions in a family of layered iridates A2IrO3 (A=Li,Na). Depending on the microscopic parameters, the Hamiltonian interpolates between the Heisenberg and exactly solvable Kitaev models. Exact diagonalization and a complementary spin-wave analysis reveal the presence of an extended spin-liquid phase near the Kitaev limit and a conventional Néel state close to the Heisenberg limit. The two phases are separated by an unusual stripy antiferromagnetic state, which is the exact ground state of the model at the midpoint between two limits.