Fractionalized excitations are of considerable interest in recent condensed-matter physics. Fractionalization of the spin degrees of freedom into localized and itinerant Majorana fermions are predicted for the Kitaev spin liquid, an exactly solvable model with bond-dependent interactions on a two-dimensional honeycomb lattice. As function of temperature, theory predicts a characteristic two-peak structure of the heat capacity as fingerprint of these excitations. Here we report on detailed heat-capacity experiments as function of temperature and magnetic field in high-quality single crystals of α-RuCl 3 and undertook considerable efforts to determine the exact phonon background. We measured single-crystalline RhCl 3 as non-magnetic reference and performed ab-initio calculations of the phonon density of states for both compounds. These ab-initio calculations document that the intrinsic phonon contribution to the heat capacity cannot be obtained by a simple rescaling of the nonmagnetic reference using differences in the atomic masses. Sizable renormalization is required even for non-magnetic RhCl 3 with its minute difference from the title compound. In α-RuCl 3 in zero magnetic field, excess heat capacity exists at temperatures well above the onset of magnetic order. In external magnetic fields far beyond quantum criticality, when long-range magnetic order is fully suppressed, the excess heat capacity exhibits the characteristic two-peak structure. In zero field, the lower peak just appears at temperatures around the onset of magnetic order and seems to be connected with canonical spin degrees of freedom. At higher fields, beyond the critical field, this peak is shifted to 10 K. The high-temperature peak located around 50 K is hardly influenced by external magnetic fields, carries the predicted amount of entropy, R/2 ln2, and may resemble remnants of Kitaev physics.

We perform a systematic first-principles study of phosphorene in the presence of typical monovalent (hydrogen and fluorine) and divalent (oxygen) impurities. The results of our modeling suggest a decomposition of phosphorene into weakly bonded one-dimensional (1D) chains upon single- and double-side hydrogenation and fluorination. In spite of a sizable quasiparticle band gap (2.29 eV), fully hydrogenated phosphorene was found to be dynamically unstable. In contrast, complete fluorination of phosphorene gives rise to a stable structure, which is an indirect gap semiconductor with a band gap of 2.27 eV. We also show that fluorination of phosphorene from the gas phase is significantly more likely than hydrogenation due to the relatively low energy barrier for the dissociative adsorption of F2 (0.19 eV) compared to H2 (2.54 eV). At low concentrations, monovalent impurities tend to form regular atomic rows of phosphorene, though such patterns do not seem to be easily achievable due to high migration barriers (1.09 and 2.81 eV for H2 and F2, respectively). Oxidation of phosphorene is shown to be a qualitatively different process. Particularly, we observe instability of phosphorene upon oxidation, leading to the formation of disordered amorphous-like structures at high concentrations of impurities.

Cubic crystal structure and regular octahedral environment of Ir 4+ render antifluorite-type K2IrCl6 a model fcc antiferromagnet with a combination of Heisenberg and Kitaev exchange interactions. High-resolution synchrotron powder diffraction confirms cubic symmetry down to at least 20 K, with a low-energy rotary mode gradually suppressed upon cooling. Using thermodynamic and transport measurements, we estimate the activation energy of ∆ 0.7 eV for charge transport, the antiferromagnetic Curie-Weiss temperature of θCW −43 K, and the extrapolated saturation field of Hs 87 T. All these parameters are well reproduced ab initio using U eff = 2.2 eV as the effective Coulomb repulsion parameter. The antiferromagnetic Kitaev exchange term of K 5 K is about one half of the Heisenberg term J 13 K. While this combination removes a large part of the classical ground-state degeneracy, the selection of the unique magnetic ground state additionally requires a weak second-neighbor exchange coupling J2 0.2 K. Our results suggest that K2IrCl6 may offer the best possible cubic conditions for Ir 4+ and demonstrates the interplay of geometrical and exchange frustration in a high-symmetry setting.arXiv:1903.01660v2 [cond-mat.str-el]