Probing ultrafast spin-relaxation and precession dynamics in a cuprate Mott insulator with 7-fs optical pulses

A charge excitation in a two-dimensional Mott insulator is strongly coupled with the surrounding spins, which is observed as magnetic-polaron formations of doped carriers and a magnon sideband in the Mott-gap transition spectrum. However, the dynamics related to the spin sector are difficult to measure. Here, we show that pump-probe reflection spectroscopy with 7-fs laser pulses can detect the optically induced spin dynamics in Nd$_2$CuO$_4$, a cuprate Mott insulator. The bleaching signal at the Mott-gap transition is enhanced at $\sim$18 fs, which corresponds to the spin-relaxation time in magnetic-polaron formations and is characterized by the exchange interaction. More importantly, ultrafast coherent oscillations appear in the time evolutions of the reflectivity changes, and their frequencies (1400-2700 cm$^{-1}$) are equal to the probe energy measured from the Mott-gap transition peak. These oscillations originate from interferences between charge excitations with two magnons and provide direct evidence for charge-spin coupling.