Effect of Electric Field on the Exchange-Stiffness Constant in a Co12Fe72 B16 Disk-Shaped Nanomagnet 65 nm in Diameter

The exchange stiffness constant denoted by Aex is one of the fundamental physical quantities from the Heisenberg exchange Hamiltonian for ferromagnetic materials. A recent theoretical prediction shows the possibility that Aex in ferromagnetic metal films can be effectively tuned by the application of an electric field at the surface. In this paper, we demonstrate that the thermally excited spin-wave modes in magnetic tunnel junctions contain modulations upon application of an electric field through a MgO tunneling barrier. Different modulations of different spin-wave eigenmodes provide quantitative information regarding the electric field effects on the exchange stiffness, perpendicular anisotropy energy, and saturation magnetization. An electric field of 1 V/nm modulated Aex by 8.1% at room temperature. The results are significantly higher than those predicted from the Slater-Pauling curve and recent theoretical work.