Interlayer Exchange Coupling: A General Scheme Turning Chiral Magnets into Magnetic Multilayers Carrying Atomic-Scale Skyrmions

We report on a general principle using interlayer exchange coupling to extend the regime of chiral magnetic films in which stable or metastable magnetic Skyrmions can appear at a zero magnetic field. We verify this concept on the basis of a first-principles model for a Mn monolayer on a W(001) substrate, a prototype chiral magnet for which the atomic-scale magnetic texture is determined by the frustration of exchange interactions, impossible to unwind by laboratory magnetic fields. By means of ab initio calculations for the $\mathrm{Mn}/{\mathrm{W}}_m/{\mathrm{Co}}_n/\mathrm{Pt}/\mathrm{W}(001)$ multilayer system we show that for certain thicknesses $m$ of the W spacer and $n$ of the Co reference layer, the effective field of the reference layer fully substitutes the required magnetic field for Skyrmion formation.

Figure 1

Schematic representation of (a) the single magnetic layer system with Skyrmions stabilized by a magnetic field, $B_{\text{app}}$, applied normally to the film and (b) an equivalent multilayer system with $B_{\text{app}}$ replaced by the IEC between the top free and underlying reference magnetic layers with a fixed out-of-plane magnetization. (c) Energy density (top panel) and average out-of-plane magnetization (bottom panel) for a SS, hexagonal SkL, and saturated FM state as functions of $B_{\text{app}}$ (bottom axis) as well as the corresponding $J_{\mathrm{IEC}}$ (top axis) calculated for Mn/W(001) at zero temperature. The solid green line corresponds to the equilibrium magnetization; the dashed lines correspond to metastable states. The inset shows the dependence of the equilibrium period length $P$ of the SS and the hexagonal SkL, and the size of the isolated Skyrmion (iSk) as a function of $B_{\text{app}}$ and $J_{\mathrm{IEC}}$. (d) Magnetic phase diagram for $\mathrm{Mn}/\mathrm{W}(001)$. The SkL is energetically most favorable in the range between $B_{\mathrm{tr}1}$ and $B_{\mathrm{tr}2}$ (red area). The range of existence for the iSk (shaded gray area) is bounded by an elliptical instability field $B_{\mathrm{iSkE}}$ and a collapse field $B_{\mathrm{iSkC}}$ and intersects with the range of the equilibrium SkL. The temperature stability of the iSks is restricted by the critical temperature $T_c^{*}$, above which the iSks appear in the Skyrmion soup state (yellow area) where Skyrmions with a short lifetime exhibit spontaneous annihilation and nucleation. In the inset, $\mathrm{\Delta }{E}_{\mathrm{SkF}}$ and $\mathrm{\Delta }{E}_{\mathrm{FSk}}$ define the energy barriers for the transition from the iSk state to the FM state and the reverse one, respectively. For details see Ref. [24].

Figure 2

(a) Strength of the IEC between Mn and Co and (b) the MCA of the Co monolayer with respect to the thickness $m$ of the W spacer, corresponding to the calculation for $\mathrm{Mn}/{\mathrm{W}}_m/{\mathrm{Co}}_n/\mathrm{W}(001)$ with $n=1$. For $\mathrm{Mn}/{\mathrm{W}}_7/{\mathrm{Co}}_4/\mathrm{Pt}/\mathrm{W}(001)$, panels (c) and (d) represent the energy of a flat homogeneous SS for the reference Co (squares) and the free Mn (circles) layers, respectively, calculated without SOC with respect to the inverse SS period length ${\lambda }^{-1}$ along the $⟨110⟩$ direction. The dashed (green) line is the fit to the Heisenberg model to calculate the exchange parameters. The solid (red) line is a fit to the Heisenberg model for the pristine $\mathrm{Mn}/\mathrm{W}(001)$ system, used for the calculation presented in Fig. 1.