Figure 1
Sketch of the SHO device under investigation and dynamical phase diagram of this device.
(a) Sketch of a bilayer composed of a CoFe ferromagnetic layer and a heavy metal layer (Pt) with a rectangular cross-section. The thick Au electrodes carry the charge current everywhere, except the inter-electrode gap of the width d, where the charge current flows inside the bilayer and excites perpendicular (vertical) spin current going into the CoFe ferromagnetic layer. A rectangular coordinate system for the above described SHO geometry is shown. (b) The angle θM characterizing the equilibrium direction of the static magnetization in the CoFe ferromagnetic layer as a function of the magnitude of the external bias magnetic field B. The vertical line at B = 200 mT separates the regions where it is possible to excite localized and propagating spin-wave modes, respectively. Inset: Cartesian coordinate reference system where the angles θM and θB are shown explicitly. (c) The phase diagram of the SHO excitations on the D vs. I plane. Seven different regions can be distinguished in this phase diagram: uniform states (US), Slonczewski linear modes (SLM), spiral modes (SpM), skyrmions (SKY), and the bistability regions uniform states/skyrmions (US/SKY), Slonczewski linear modes/spiral modes (SLM/SpM) and Slonczewski linear modes/skyrmions (SLM/SKY). The amplitude of the external field is B = 400 mT. The Oersted field is included in the model. DC is the critical value of the i-DMI parameter (see explanations below), Ith is the threshold current, Isky is the current needed to nucleate skyrmions (line between the points ‘A’ and ‘B’); (d) Comparison between the threshold current of the SLM excitation obtained by means of micromagnetic simulations (symbols) and using the analytical formula (3) (solid line).
