  Multiferroic materials provide robust and efficient routes for the control of
magnetism by electric fields, which has been diligently sought after for a long
time. The two-dimensional (2D) vdW multiferroics is a more exciting endeavour.
To date, the nonvolatile manipulation of magnetism through ferroelectric
polarization still remains challenging in a 2D vdW heterostructure
multiferroic. Here, we report a van der Waals (vdW) heterostructure
multiferroic comprising atomically thin layered antiferromagnet (AFM) CrI3 and
ferroelectric (FE) {\alpha}-In2Se3. We demonstrate anomalously layer-selective
nonreciprocal and nonvolatile electric-field control of magnetization by the
ferroelectric polarization. The nonreciprocal electric control originates from
an intriguing antisymmetric enhancement of interlayer ferromagnetic coupling in
the opposite ferroelectric polarization configurations of {\alpha}-In2Se3,
which favor to selectively switch the spins in the second layer. Our work
provides numerous possibilities for creating diverse heterostructure
multiferroics at the limit of few atomic layers for multi-stage magnetic
memories and brain inspired in-memory computing.
