  We describe a spin logic device with controllable magnetization switching of
perpendicularly magnetized ferromagnet / heavy metal structures on a
ferroelectric (1-x)[Pb(Mg1/3Nb2/3)O3]-x[PbTiO3] (PMN-PT) substrate using
current-induced spin-orbit torque. The devices were operated without an
external magnetic field and controlled by voltages as low as 10 V applied
across the PMN-PT substrate, which is much lower compared to previous reports
(500 V). The deterministic switching with smaller voltage was realized from the
virgin state of the PMN-PT. Ferroelectric simulation shows the unsaturated
minor loop exhibits obvious asymmetries in the polarizations. Larger
polarization can be induced from the initial ferroelectric state, while it is
difficult for opposite polarization. The XNOR, AND, NAND and NOT logic
functions were demonstrated by the deterministic magnetization switching from
the interaction between the spin-orbit torque and electric field at the
PMN-PT/Pt interface. The nonvolatile spin logic scheme in this work is simple,
scalable, programmable, which are favorable in the logic-in-memory design with
low energy consumption.
