Schematic illustration of a 10 mT SOT field that is localized at a depth of 2 nm at the two interfaces in the asymmetric Ta/Py/Pt (black line, top panel) and symmetric Ta/Py/Ta (red line, bottom panel) samples with 9 nm Py layer. For the asymmetric (symmetric) sample, the SOT fields localized at the two Py interfaces are parallel (antiparallel) with respect to each other. Black arrows illustrate the z -axis-projected magnetization dynamical components across the Py thickness. One can see that the in-phase precession of the magnetization at the two interfaces supports the even- n modes ( n = 2, black dashed line in the top panel), while the antiphase precession results in the odd- n modes ( n = 3, black dashed line in the bottom panel). All modes are unpinned, as the interface anisotropy is not strong enough anymore to pin the exchange-dominated spin waves.
