  To understand the coupling factor between Rashba spin-orbital interaction and
ferromagnetic proximity effect, we design a Monte Carlo algorithm to simulate
the spin and charge distributions for the room-temperature Rashba material,
Graphene/Nickel(111) substrate, at finite temperature. We observe that the rate
of exchange fluctuation is a key player to produce giant Rashba spin-orbit
splitting in graphene. More importantly, we monitor the Rashba spin-splitting
phenomenon where the spin-polarized electrons may be escaped from two opposite
edges upon heating. However, the escaped electrons show Gaussian-like
distribution in interior area that is important for spintronic engineers to
optimize the efficiency of spin-state detection. In addition, we investigate if
our Monte Carlo model can explain why room-temperature Rashba effect is
observed in Graphene/Nickel(111) substrate experimentally. All results are
presented in physical units.
