Frustrated magnets are materials in which localized magnetic moments, or spins, interact through competing exchange interactions that cannot be simultaneously satisfied, giving rise to a large degeneracy of the system ground state. Under certain conditions, this can lead to the formation of fluid-like states of matter, so-called spin liquids, in which the constituent spins are highly correlated but still fluctuate strongly down to a temperature of absolute zero. The fluctuations of the spins in a spin liquid can be classical or quantum and show remarkable collective phenomena such as emergent gauge fields and fractional particle excitations. This exotic behaviour is now being uncovered in the laboratory, providing insight into the properties of spin liquids and challenges to the theoretical description of these materials.

Spin liquids in frustrated magnets

http://sces.phys.utk.edu/mostcited/mc1_1114.pdf

Colossal Magnetoresistant Materials: The Key Role of Phase Separation

The 1937 theoretical discovery of Majorana fermions-whose defining property is that they are their own anti-particles-has since impacted diverse problems ranging from neutrino physics and dark matter searches to the fractional quantum Hall effect and superconductivity. Despite this long history the unambiguous observation of Majorana fermions nevertheless remains an outstanding goal. This review paper highlights recent advances in the condensed matter search for Majorana that have led many in the field to believe that this quest may soon bear fruit. We begin by introducing in some detail exotic 'topological' one- and two-dimensional superconductors that support Majorana fermions at their boundaries and at vortices. We then turn to one of the key insights that arose during the past few years; namely, that it is possible to 'engineer' such exotic superconductors in the laboratory by forming appropriate heterostructures with ordinary s-wave superconductors. Numerous proposals of this type are discussed, based on diverse materials such as topological insulators, conventional semiconductors, ferromagnetic metals and many others. The all-important question of how one experimentally detects Majorana fermions in these setups is then addressed. We focus on three classes of measurements that provide smoking-gun Majorana signatures: tunneling, Josephson effects and interferometry. Finally, we discuss the most remarkable properties of condensed matter Majorana fermions-the non-Abelian exchange statistics that they generate and their associated potential for quantum computation.

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New directions in the pursuit of Majorana fermions in solid state systems.

Recent technical advances in the atomic-scale synthesis of oxide heterostructures have provided a fertile new ground for creating novel states at their interfaces. Different symmetry constraints can be used to design structures exhibiting phenomena not found in the bulk constituents. A characteristic feature is the reconstruction of the charge, spin and orbital states at interfaces on the nanometre scale. Examples such as interface superconductivity, magneto-electric coupling, and the quantum Hall effect in oxide heterostructures are representative of the scientific and technological opportunities in this rapidly emerging field.

/pdf/emergent-phenomena-at-oxide-interfaces-29wwyhjrec.pdf

Emergent phenomena at oxide interfaces

An electron in a solid, that is, bound to or nearly localized on the specific atomic site, has three attributes: charge, spin, and orbital. The orbital represents the shape of the electron cloud in solid. In transition-metal oxides with anisotropic-shaped d-orbital electrons, the Coulomb interaction between the electrons (strong electron correlation effect) is of importance for understanding their metal-insulator transitions and properties such as high-temperature superconductivity and colossal magnetoresistance. The orbital degree of freedom occasionally plays an important role in these phenomena, and its correlation and/or order-disorder transition causes a variety of phenomena through strong coupling with charge, spin, and lattice dynamics. An overview is given here on this "orbital physics," which will be a key concept for the science and technology of correlated electrons.

http://science.sciencemag.org/content/sci/288/5465/462.full.pdf

Orbital Physics in Transition-Metal Oxides

We study the magnetic interactions in Mott-Hubbard systems with partially filled t_{2g} levels and with strong spin-orbit coupling. The latter entangles the spin and orbital spaces, and leads to a rich variety of the low energy Hamiltonians that extrapolate from the Heisenberg to a quantum compass model depending on the lattice geometry. This gives way to "engineer" in such Mott insulators an exactly solvable spin model by Kitaev relevant for quantum computation. We, finally, explain "weak" ferromagnetism, with an anomalously large ferromagnetic moment, in Sr2IrO4.

Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models

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 Neel 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.

Kitaev-Heisenberg Model on a Honeycomb Lattice: Possible Exotic Phases in Iridium Oxides A 2 IrO 3

The Kitaev model is an exactly solvable S = 1/2 spin model on a 2D honeycomb lattice, in which the spins fractionalize into Majorana fermions and form a topological quantum spin liquid (QSL) in the ground state. Several complex iridium oxides, as well as α-RuCl3, are magnetic insulators with a honeycomb structure, and it was noticed that they accommodate essential ingredients of the Kitaev model owing to the interplay of electron correlation and spin–orbit coupling. This has led to a race to realize the Kitaev QSL and detect signatures of Majorana fermions. We summarize the theoretical background of the Kitaev QSL ground state and its realization using spin–orbital entangled Jeff = 1/2 moments. We provide an overview of candidate materials and their electronic and magnetic properties, including Na2IrO3, α-Li2IrO3, β-Li2IrO3, γ-Li2IrO3, α-RuCl3 and H3LiIr2O6. Finally, we discuss experiments showing that H3LiIr2O6 and α-RuCl3 in an applied magnetic field exhibit signatures of the QSL state and that α-RuCl3 has unusual magnetic excitations and thermal transport properties consistent with spin fractionalization. The Kitaev quantum spin liquid is an exotic phase of matter exhibiting long-range entanglement and emergent Majorana fermions. This Review summarizes the concept and recent progress in realizing Kitaev model physics in transition metal compounds.

Concept and realization of Kitaev quantum spin liquids

Orbital reconstructions and covalent bonding must be considered as important factors in the rational design of oxide heterostructures with engineered physical properties. We have investigated the interface between high-temperature superconducting (Y,Ca)Ba(2)Cu3O7 and metallic La(0.67)Ca(0.33)MnO3 by resonant x-ray spectroscopy. A charge of about -0.2 electron is transferred from Mn to Cu ions across the interface and induces a major reconstruction of the orbital occupation and orbital symmetry in the interfacial CuO2 layers. In particular, the Cu d(3z(2)-r(2)) orbital, which is fully occupied and electronically inactive in the bulk, is partially occupied at the interface. Supported by exact-diagonalization calculations, these data indicate the formation of a strong chemical bond between Cu and Mn atoms across the interface. Orbital reconstructions and associated covalent bonding are thus important factors in determining the physical properties of oxide heterostructures.

https://science.sciencemag.org/content/sci/318/5853/1114.full.pdf

Orbital Reconstruction and Covalent Bonding at an Oxide Interface

We explore the phase diagram of spin-orbit Mott insulators on a honeycomb lattice, within the Kitaev-Heisenberg model extended to its full parameter space. Zigzag-type magnetic order is found to occupy a large part of the phase diagram of the model, and its physical origin is explained as due to interorbital t(2g)-e(g) hopping. The magnetic susceptibility, spin wave spectra, and zigzag order parameter are calculated and compared to the experimental data, obtaining thereby the spin coupling constants in Na(2)IrO(3) and Li(2)IrO(3).

Giniyat Khaliullin

Papers

Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models

Kitaev-Heisenberg Model on a Honeycomb Lattice: Possible Exotic Phases in Iridium Oxides A 2 IrO 3

Concept and realization of Kitaev quantum spin liquids

Orbital Reconstruction and Covalent Bonding at an Oxide Interface

Zigzag magnetic order in the iridium oxide Na2IrO3.