Understanding voltage-controlled magnetic anisotropy effect for the manipulation of dipolar-dominated propagating spin waves

Spin waves, known for their ability to propagate without the involvement of moving charges, hold immense promise for on-chip information transfer and processing, offering a path toward post-CMOS computing technologies. This study investigates the potential synergy between propagating Damon-Eshbach spin waves and voltage-controlled magnetization in the pursuit of environmentally sustainable computing solutions. Employing micromagnetic simulations, we assess the feasibility of utilizing spin waves in DE mode in conjunction with localized voltage-induced alterations in surface anisotropy to enable low-energy logic operations. Our findings underscore the critical importance of selecting an optimal excitation frequency and gate width, which significantly influence the efficiency of the phase shift induced in propagating spin waves. Notably, we demonstrate that a realistic phase shift of 2.5$\left[ \pi \ \text{mrad}\right]$ can be achieved at a Co(5nm)/MgO material system via the VCMA effect. Moreover, by tuning the excitation frequency, Co layer thickness, gate width, and the use of a GdO\textsubscript{x} dielectric, we illustrate the potential to enhance the phase shift by a factor of 200 when compared to MgO dielectrics. This research contributes valuable insights towards developing next-generation computing technologies with reduced energy consumption.