Land\'e $g$-factors of electrons and holes strongly confined in CsPbI$_3$ perovskite nanocrystals in glass

The Land\'e $g$-factor of charge carriers is a key parameter in spin physics controlling spin polarization and spin dynamics. In turn, it delivers information of the electronic band structure in vicinity of the band gap and its modification in nanocrystals provided by strong carrier confinement. The coherent spin dynamics of electrons and holes are investigated in CsPbI$_3$ perovskite nanocrystals with sizes varied from 4 to 16 nm by means of time-resolved Faraday ellipticity at the temperature of 6 K. The Land\'e $g$-factors of the charge carriers are evaluated through the Larmor spin precession in magnetic fields up to 430 mT across the spectral range from 1.69 to 2.25 eV, provided by variation of the nanocrystal size. The spectral dependence of the electron $g$-factor follows the model predictions when accounting for the mixing of the electronic bands with increasing confinement resulting from a decrease of the nanocrystal size. The spectral dependence of the hole $g$-factor, changing from $-0.19$ to $+1.69$, is considerably stronger than expected from the model. We analyze several mechanisms and conclude that none of them can be responsible for this difference. The renormalizations of the electron and hole $g$-factors roughly compensate each other, providing spectral independence for the bright exciton $g$-factor with a value of about $+2.2$.