  The coexistence and coupling between magnetization and electric polarization
in multiferroic materials provide extra degrees of freedom for creating
next-generation memory devices. A variety of concepts of multiferroic or
magnetoelectric memories have been proposed and explored in the past decade.
Here we propose a new principle to realize a multilevel nonvolatile memory
based on the multiple states of the magnetoelectric coefficient ({\alpha}) of
multiferroics. Because the states of {\alpha} depends on the relative
orientation between magnetization and polarization, one can reach different
levels of {\alpha} by controlling the ratio of up and down ferroelectric
domains with external electric fields. Our experiments in a device made of the
PMN-PT/Terfenol-D multiferroic heterostructure confirm that the states of
{\alpha} can be well controlled between positive and negative by applying
selective electric fields. Consequently, two-level, four-level, and eight-level
nonvolatile memory devices are demonstrated at room temperature. This kind of
multilevel magnetoelectric memory retains all the advantages of ferroelectric
random access memory but overcomes the drawback of destructive reading of
polarization. In contrast, the reading of {\alpha} is nondestructive and highly
efficient in a parallel way, with an independent reading coil shared by all the
memory cells.
