Majorana quantization and half-integer thermal quantum Hall effect in a Kitaev spin liquid

The quantum Hall effect (QHE) in two-dimensional (2D) electron gases, which is one of the most striking phenomena in condensed matter physics, involves the topologically protected dissipationless charge current flow along the edges of the sample. Integer or fractional electrical conductance are measured in units of $e^2/2\pi\hbar$, which is associated with edge currents of electrons or quasiparticles with fractional charges, respectively. Here we discover a novel type of quantization of the Hall effect in an insulating 2D quantum magnet. In $\alpha$-RuCl$_3$ with dominant Kitaev interaction on 2D honeycomb lattice, the application of a parallel magnetic field destroys the long-range magnetic order, leading to a field-induced quantum spin liquid (QSL) ground state with massive entanglement of local spins. In the low-temperature regime of the QSL state, we report that the 2D thermal Hall conductance $\kappa_{xy}^{2D}$ reaches a quantum plateau as a function of applied magnetic field. $\kappa_{xy}^{2D}/T$ attains a quantization value of $(\pi/12)(k_B^2/\hbar)$, which is exactly half of $\kappa_{xy}^{2D}/T$ in the integer QHE. This half-integer thermal Hall conductance observed in a bulk material is a direct signature of topologically protected chiral edge currents of charge neutral Majorana fermions, particles that are their own antiparticles, which possess half degrees of freedom of conventional fermions. These signatures demonstrate the fractionalization of spins into itinerant Majorana fermions and $Z_2$ fluxes predicted in a Kitaev QSL. Above a critical magnetic field, the quantization disappears and $\kappa_{xy}^{2D}/T$ goes to zero rapidly, indicating a topological quantum phase transition between the states with and without chiral Majorana edge modes. Emergent Majorana fermions in a quantum magnet are expected to have a major impact on strongly correlated topological quantum matter.Comment: 7 pages, 8 figures. Submitted versio

Vortex circulation and polarity patterns in closely packed cap arrays

We studied curvature-driven modifications to the magnetostatic coupling of vortex circulation and polarity in soft-magnetic closely packed cap arrays. A phase diagram for the magnetic remanent/transition states at room temperature as a function of diameter and thickness was assembled. For specimens with vortex remanent state (40 nm-thick Permalloy on 330 nm spherical nanoparticles), both vortex circulation and polarity were visualized. Intercap coupling upon vortex nucleation leads to the formation of vortex circulation patterns in closely packed arrays. The remanent circulation pattern can be tailored choosing the direction of the applied magnetic field with respect to the symmetry axis of the hexagonal array. An even and random distribution of vortex polarity indicates the absence of any circulation-polarity coupling

High field level crossing studies on spin dimers in the low dimensional quantum spin system Na2T2(C2O4)(3)(H2O)(2) with T = Ni, Co, Fe, Mn

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Thermodynamic properties of the anisotropic frustrated spin-chain compound linarite PbCuSO4(OH)2

We present a comprehensive macroscopic thermodynamic study of the quasi-one-dimensional (1D) s = 1/2 frustrated spin-chain system linarite. Susceptibility, magnetization, specific heat, magnetocaloric effect, magnetostriction, and thermal-expansion measurements were performed to characterize the magnetic phase diagram. In particular, for magnetic fields along the b axis five different magnetic regions have been detected, some of them exhibiting short-range-order effects. The experimental magnetic entropy and magnetization are compared to a theoretical modeling of these quantities using density matrix renormalization group (DMRG) and transfer matrix renormalization group (TMRG) approaches. Within the framework of a purely 1D isotropic model Hamiltonian, only a qualitative agreement between theory and the experimental data can be achieved. Instead, it is demonstrated that a significant symmetric anisotropic exchange of about 10% is necessary to account for the basic experimental observations, including the three-dimensional (3D) saturation field, and which in turn might stabilize a triatic (three-magnon) multipolar phase. © 2013, American Physical Society