  Progress in layered van der Waals materials has resulted in the discovery of
ferromagnetic and ferroelectric materials down to the monolayer limit.
Recently, evidence of the first purely two-dimensional multiferroic material
was reported in monolayer NiI$_2$. However, probing multiferroicity with
scattering-based and optical bulk techniques is challenging on 2D materials,
and experiments on the atomic scale are needed to fully characterize the
multiferroic order at the monolayer limit. Here, we use scanning tunneling
microscopy (STM) supported by theoretical calculations based on density
functional theory (DFT) to probe and characterize the multiferroic order in
monolayer NiI$_2$. We demonstrate that the type-II multiferroic order displayed
by NiI$_2$, arising from the combination of a magnetic spin spiral order and a
strong spin-orbit coupling, allows probing the multiferroic order in the STM
experiments. Moreover, we directly probe the magnetoelectric coupling of
NiI$_2$ by external electric field manipulation of the multiferroic domains.
Our findings establish a novel point of view to analyse magnetoelectric effects
at the microscopic level, paving the way towards engineering new multiferroic
orders in van der Waals materials and their heterostructures.
