Quantum spin liquid is a disordered magnetic state with fractional spin excitations. Its clearest example is found in an exactly solved Kitaev honeycomb model where a spin flip fractionalizes into two types of anyons, quasiparticles that are neither fermions nor bosons: a pair of gauge fluxes and a Majorana fermion. Here we demonstrate this kind of fractionalization in the Kitaev paramagnetic state of the honeycomb magnet α-RuCl3. The spin-excitation gap measured by nuclear magnetic resonance consists of the predicted Majorana fermion contribution following the cube of the applied magnetic field, and a finite zero-field contribution matching the predicted size of the gauge-flux gap. The observed fractionalization into gapped anyons survives in a broad range of temperatures and magnetic fields despite inevitable non-Kitaev interactions between the spins, which are predicted to drive the system towards a gapless ground state. The gapped character of both anyons is crucial for their potential application in topological quantum computing.

We present a study of the static magnetic properties and spin dynamics in Cobalt valence tautomers (VT), molecules where a low-spin (LS) to high-spin (HS) crossover driven by an intramolecular electron transfer can be controlled by the temperature, by the external pressure or by light irradiation. In the investigated complex, a LS-Co(III) ion bound to a dinegative organic ligand can be reversibly converted into the HS-Co(II) bound to a mononegative one. By combining magnetization measurements with Nuclear Magnetic Resonance (NMR) and Muon Spin Relaxation (µSR), we have investigated the static magnetic properties and the spin dynamics as a function of the temperature. Moreover, the effect of the external pressure as well as of the infrared light irradiation have been explored through magnetometry and NMR measurements to determine the spin dynamics of the HS state. The photoinduced HS state, which can have a lifetime of several hours below 30 K, is characterized by spin dynamics in the MHz range, which persist at least down to 10 K. The application of an external pressure causes a progressive increase of the LS-HS crossover, which reaches room temperature for pressures around 10 kbar.

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