Disorder, Low-Energy Excitations, and Topology in the Kitaev Spin Liquid.

The Kitaev model is a fascinating example of an exactly solvable model displaying a spin-liquid ground state in two dimensions. However, deviations from the original Kitaev model are expected to appear in real materials. In this Letter, we investigate the fate of Kitaev's spin liquid in the presence of disorder-bond defects or vacancies-for an extended version of the model. Considering static flux backgrounds, we observe a power-law divergence in the low-energy limit of the density of states with a nonuniversal exponent. We link this power-law distribution of energy scales to weakly coupled droplets inside the bulk, in an uncanny similarity to the Griffiths phase often present in the vicinity of disordered quantum phase transitions. If time-reversal symmetry is broken, we find that power-law singularities are tied to the destruction of the topological phase of the Kitaev model in the presence of bond disorder alone. However, there is a transition from this topologically trivial phase with power-law singularities to a topologically nontrivial one for weak to moderate site dilution. Therefore, diluted Kitaev materials are potential candidates to host Kitaev's chiral spin-liquid phase.

Cluster-Glass Phase in Pyrochlore XY Antiferromagnets with Quenched Disorder.

We study the impact of quenched disorder (random exchange couplings or site dilution) on easy-plane pyrochlore antiferromagnets. In the clean system, order by disorder selects a magnetically ordered state from a classically degenerate manifold. In the presence of randomness, however, different orders can be chosen locally depending on details of the disorder configuration. Using a combination of analytical considerations and classical Monte Carlo simulations, we argue that any long-range-ordered magnetic state is destroyed beyond a critical level of randomness where the system breaks into magnetic domains due to random exchange anisotropies, becoming, therefore, a glass of spin clusters, in accordance with the available experimental data. These random anisotropies originate from off-diagonal exchange couplings in the microscopic Hamiltonian, establishing their relevance to other magnets with strong spin-orbit coupling.

Honeycomb-Lattice Heisenberg-Kitaev Model in a Magnetic Field: Spin Canting, Metamagnetism, and Vortex Crystals.

The Heisenberg-Kitaev model is a paradigmatic model to describe the magnetism in honeycomb-lattice Mott insulators with strong spin-orbit coupling, such as A_{2}IrO_{3} (A=Na, Li) and α-RuCl_{3}. Here, we study in detail the physics of the Heisenberg-Kitaev model in an external magnetic field. Using a combination of Monte Carlo simulations and spin-wave theory, we map out the classical phase diagram for different directions of the magnetic field. Broken SU(2) spin symmetry renders the magnetization process rather complex, with sequences of phases and metamagnetic transitions. In particular, we find various large-unit-cell and multi-Q phases including a vortex-crystal phase for a field in the [111] direction. We also discuss quantum corrections in the high-field phase.

Non-Fermi-Liquid Behavior in Metallic Quasicrystals with Local Magnetic Moments.

Motivated by the intrinsic non-Fermi-liquid behavior observed in the heavy-fermion quasicrystal Au51Al34Yb15, we study the low-temperature behavior of dilute magnetic impurities placed in metallic quasicrystals. We find that a large fraction of the magnetic moments are not quenched down to very low temperatures T, leading to a power-law distribution of Kondo temperatures P(T(K))∼T(K)(α-1), with a nonuniversal exponent α, in a remarkable similarity to the Kondo-disorder scenario found in disordered heavy-fermion metals. For α<1, the resulting singular P(T(K)) induces non-Fermi-liquid behavior with diverging thermodynamic responses as T→0.

Singular field response and singular screening of vacancies in antiferromagnets.

For isolated vacancies in ordered local-moment antiferromagnets we show that the magnetic-field linear-response limit is generically singular: The magnetic moment associated with a vacancy in zero field is different from that in a finite field h in the limit h→0(+). The origin is a universal and singular screening cloud, which moreover leads to perfect screening as h→0(+) for magnets which display spin-flop bulk states in the weak-field limit.

Disorder, cluster spin glass, and hourglass spectra in striped magnetic insulators.

Hourglass-shaped magnetic excitation spectra have been detected in a variety of doped transition-metal oxides with stripelike charge order. Compared to the predictions of spin-wave theory for perfect stripes, these spectra display a different intensity distribution and anomalous broadening. Here we show, based on a comprehensive modeling for La5/3Sr1/3CoO4, how quenched disorder in the charge sector causes frustration, and consequently cluster-glass behavior at low temperatures, in the spin sector. This spin-glass physics, which is insensitive to the detailed nature of the charge disorder, but sensitive to the relative strength of the magnetic interstripe coupling, ultimately determines the distribution of magnetic spectral weight: The excitation spectrum, calculated using spin waves in finite disordered systems, is found to match in detail the observed hour-glass spectrum.