  Electric-field control of magnetism without electric currents potentially
revolutionizes spintronics towards ultralow power. Here by using mechanically
coupled phase field simulations, we computationally demonstrate the application
of the strain-mediated magnetoelectric effect for the electric-field control of
magnetic states in heterostructure. In the model heterostructure constituted of
the soft nanomagnet Co and the piezoelectric substrate PMN-PT, both the
volatility of magnetic states and the magnetization switching dynamics excited
by the electric field are explored. It is found that an electric field can
drive the single-domain nanomagnet into an equilibrium vortex state. The
nanomagnet remains in the vortex state even after removing the electric field
or applying a reverse electric field, i.e. the vortex state is extremely stable
and nonvolatile. Only by utilizing the precessional magnetization dynamics, the
180$^\circ$ magnetization switching is possible in small-sized nanomagnets
which are free of the stable vortex state. Electric-field pulses can realize
the deterministic 180$^\circ$ switching if the electric-field magnitude, pulse
width, and ramp time are carefully designed. The minimum switching time is
found to be less than 10 ns. These results provide useful information for the
design of low-power, reliable, and fast electric-field-controlled spintronics.
