  CeSiI has been recently isolated in the ultrathin limit, establishing CeSiI
as the first intrinsic two-dimensional van der Waals heavy-fermion material up
to 85 K. We show that, due to the strong Ce spin-orbit coupling, the local
moments develop a multipolar real-space magnetic texture, leading to local
pseudospins with a nearly vanishing net moment. To elucidate its Kondo-screened
regime, we extract from first principles the parameters of the Kondo lattice
model describing this material. We develop a fractional pseudofermion
methodology in combination with ab initio calculations to reveal the nature of
the Kondo-screened heavy fermion state in CeSiI. Using this formalism, we
analyze the competing magnetic interactions leading to a heavy-fermion order as
a function of the magnetic exchange between the localized f-electrons and the
strength of the Kondo coupling. Our results show that the magnetic exchange
interactions promote an unconventional momentum-dependent heavy-fermion Kondo
screened phase, establishing the nature of the heavy-fermion behavior of
ultrathin CeSiI observed experimentally.
