Electrical manipulation of magnetization in magnetic heterostructures with perpendicular anisotropy

•Field-free switching of perpendicular magnetization induced by spin-orbit torque in the metallic magnetic heterostructures.•Manipulation of exchange bias by spin-orbit torque.•Spin-orbit torque switching of magnetization in the perovskite oxides.•Magnetoelectric control of perpendicular magnetization mediated by piezostrain in multiferroic heterostructures.