Ultra-fast photo-carrier relaxation in Mott insulators with short-range spin correlations

Ultra-fast spectroscopy can reveal the interplay of charges with low energy degrees of freedom, which underlies the rich physics of correlated materials. As a potential glue for superconductivity, spin fluctuations in Mott insulators are of particular interest. A theoretical description of the coupled spin and charge degrees of freedom is challenging, because magnetic order is often only short-lived and short-ranged. In this work we theoretically investigate how the spin-charge interactions influence the relaxation of a two-dimensional Mott-Hubbard insulator after photo-excitation. We use a nonequilibrium variant of the dynamical cluster approximation, which, in contrast to single-site dynamical mean-field theory, captures the effect of short-range correlations. The relaxation time is found to scale with the strength of the nearest-neighbor spin correlations, and can be 10–20 fs in the cuprates. Increasing the temperature or excitation density decreases the spin correlations and thus implies longer relaxation times. This may help to distinguish the effect of spin-fluctuations on the charge relaxation from the influence of other bosonic modes in the solid.