Complex spin configurations in hybrid magnetic multilayer structures due to mutual spin imprinting

Hybrid Co/Pd-Permalloy multilayer structures exhibit multiple domain phases resulting from mutual spin imprinting, dependent on the precise layer composition and thickness. While such hybrid structures can support either a pure Landau closure-domain pattern or a perpendicular exchange-spring magnetization structure, numerical analysis also revealed an anomalous mixed Landau-maze domain state. Mutual imprinting of the spin configuration between the layers was strongest for the latter multidomain state, which we propose is a consequence of exchange energy dissipation over the two lateral dimensions. An analytical derivation of domain phase boundaries was consistent with the micromagnetic simulations and gave important insight into their origin.

Figure 1

(a) Schematic of the $\mathrm{N}{\mathrm{i}}_{80}\mathrm{F}{\mathrm{e}}_{20}/\mathrm{Co}/\mathrm{Pd}$ structure. Micromagnetic calculations of the individual layers show (b) Landau pattern formation in Permalloy and (c) Co/Pd adopts out-of-plane spin structure $(t_{\mathrm{Py}}=30\mathrm{nm},M_{\mathrm{Co}/\mathrm{Pd}}=400\mathrm{kA}{\mathrm{m}}^{-1}$, and $K_{\mathrm{Co}/\mathrm{Pd}}=150\mathrm{kJ}{\mathrm{m}}^{-3}$, arrows indicate the magnetization vector).

Figure 2

(a) Domain phase diagram for $t_{\mathrm{Py}}=30\mathrm{nm}$ structure show how Co/Pd material properties affect the remanent out-of-plane domain state in the Co/Pd layer $\left(z=-9.6\mathrm{nm}\right)$. Grayscale shading has been colorized to indicate the designated phase according to the color scheme shown in the legend. The lines plot the 1D predictions of the upper and lower domain phase boundaries, given in Eqs. (3)) and (5)), respectively. (b) Effect of Co/Pd material properties on the magnetic domain phase, $t_{\mathrm{Py}}=10$, 20, and 50 nm.

Figure 3

Polar spin angle θ at various $K_{\mathrm{Co}/\mathrm{Pd}}$ along a line intersecting the vortex core (a) top surface of the Py layer and (b) bottom surface of the Co/Pd layer. Vortex core at $x=400\mathrm{nm}$. Oscillations in θ are due to the profile intersecting different maze domains. (c) Variation of θ through the structure thickness. Bold line: 1D model prediction [Eqs. (6))–(8)] with $K_{\mathrm{Co}/\mathrm{Pd}}=400\mathrm{kJ}{\mathrm{m}}^{-3}$. $t_{\mathrm{Py}}=30\mathrm{nm}$ and $M_{\mathrm{Co}/\mathrm{Pd}}=400\mathrm{kA}{\mathrm{m}}^{-1}$ in all cases.