Two-step Mott transition in Ni(S,Se)_{2}: μSR studies and charge-spin percolation model

A pyrite system NiS_{2−x}Se_{x} exhibits a bandwidth controlled Mott transition via (S,Se) substitutions in a two-step process: the antiferromagnetic insulator (AFI) to antiferromagnetic metal (AFM) transition at x∼0.45 followed by the AFM to paramagnetic metal (PMM) transition at x∼1.0. Among a few other Mott systems which exhibit similar two-step transitions, Ni(S,Se)_{2} is of particular interest because a large intermediate AFM region in the phase diagram would provide unique opportunities to study the interplay between the spin and charge order. Muon spin relaxation (μSR) measurements on NiS_{2−x}Se_{x} have been carried out on seven different Se concentrations from x=0 to 1.0. The results on quantum evolution demonstrate significantly random spin correlations in the AFM region associated with a rapid reduction of the average local static Ni moment size with increasing x, yet without signatures of macroscopic phase separation as confirmed by nearly full volume fraction participating in the static muon relaxation process up to x∼ 0.9 at low temperatures. The observed time spectra in the AFM region indicate Lorentzian distribution of static internal field expected for a spatially dilute spin structure. No signature of dynamic critical behavior was observed in thermal phase transitions. The previous neutron scattering studies found sharp magnetic Bragg peaks with a slower reduction of the average ordered moment size in the AFM region. By comparing and combining the muon and neutron results, here we propose a picture where the spin order is maintained by the percolation of “nonmetallic” localized and dangling Ni moments surrounded by S, while the charge transition from AFI to AFM is caused by the percolation of the conducting paths generated by the Ni-Se-Ni bonds. This model of interpenetrating charge and spin percolation captures the behavior of experimental results on (a) Se concentration for the insulator to metal transition, (b) Se concentration for the AFM to PMM transition, (c) variation of Hall effect in the AFM region due to conducting Ni charges on the backbone of the percolating charge network, (d) evolution of the neutron Bragg intensity, (e) evolution of the muon static local fields, and (f) spatial variation of the local conductance observed by STM.