Skyrmion-(Anti)Vortex Coupling in a Chiral Magnet-Superconductor Heterostructure

We report experimental coupling of chiral magnetism and superconductivity in $[\mathrm{IrFeCoPt}]/\mathrm{Nb}$ heterostructures. The stray field of skyrmions with radius $\approx 50\mathrm{nm}$ is sufficient to nucleate antivortices in a 25 nm Nb film, with unique signatures in the magnetization, critical current, and flux dynamics, corroborated via simulations. We also detect a thermally tunable Rashba-Edelstein exchange coupling in the isolated skyrmion phase. This realization of a strongly interacting skyrmion-(anti)vortex system opens a path toward controllable topological hybrid materials, unattainable to date.

Figure 1

(a) Schematic of a Néel skyrmion creating an antivortex with flux $-{\mathrm{\Phi }}_0\equiv -h/2e$ antiparallel to the external magnetic field $H$. Antivortex currents $j_s$ flow at radii up to $\lambda$; Rashba-Edelstein currents $j_{\mathrm{ex}}$ are maximal at $r_{\mathrm{sk}}$, where the local out-of-plane magnetic moment $m_z=0$. The superconducting order parameter $|\mathrm{\Psi }|$ is suppressed over a length $\xi$ in the vortex core. (b) Sample compositions: numbers (e.g., Ir1, Pt2) indicate layer thicknesses in nm and there are 10 stacked repeats of the [${\mathrm{Ir}}_1{\mathrm{Fe}}_{0.5}{\mathrm{Co}}_{0.5}{\mathrm{Pt}}_1$] unit. (c) Magnetization $M(H)$ and topological Hall resistivity ${\rho }^{\mathrm{TH}}(H)$ at temperature $T=5\mathrm{K}$ for a $[{\mathrm{Ir}}_1{\mathrm{Fe}}_{0.5}{\mathrm{Co}}_{0.5}{\mathrm{Pt}}_1{]}^{10}$ film. Arrows indicate field sweep directions; green/red dashed lines indicate skyrmion nucleation/annihilation fields $H_{\mathrm{nuc}}/H_{\mathrm{ann}}$, respectively, and the saturation magnetization $M_s=1.45{\mathrm{MAm}}^{-1}$. (d)–(i) MFM images at $T=5.5\mathrm{K}$ in a bare $[{\mathrm{Ir}}_1{\mathrm{Fe}}_{0.5}{\mathrm{Co}}_{0.5}{\mathrm{Pt}}_1{]}^{10}$ film during a $H=0.25\mathrm{T}\to -0.4\mathrm{T}$ sweep. Scale bars are 500 nm; color bars indicate the MFM probe resonance shift $\mathrm{\Delta }f$ in Hz, proportional to $m_z$. (j)–(l) STS images of a 25 nm Nb film ($S$-type structure) in (j) $H=0\mathrm{mT}$, (k) 30 mT, and (l) 60 mT at $T=0.4\mathrm{K}$. Scale bars are 100 nm; the color bar shows the normalized zero-bias conductance (see the Supplemental Material, Sec. IV [28]) which rises inside the vortex cores.

Figure 2

Magnetization loops at 2 K, 10 K for (a) a MS sample ($T_c=5.75\mathrm{K}$) and (b) a MIS sample ($T_c=6.25\mathrm{K}$). Black arrows indicate field sweep directions. (c) Evolution of the superconducting magnetization $M_{\text{super}}(H)$ through $H_{\mathrm{nuc}}$, extracted by subtracting $m(H,T=10\mathrm{K})$ from $m(H,T<T_c)$. Data from a reference 25 nm Nb film are labeled $S$. Green arrows and dashed lines highlight the change in $M_{\text{super}}(H)$ below $H_{\mathrm{nuc}}$. For complete $T$-dependent $M_{\text{super}}(H)$ loops, see the Supplemental Material, Sec. V [28]. (d) Calculated supercurrent profile above two Néel skyrmions at $H=125\mathrm{mT}$. Blue arrows indicate antivortex currents induced above skyrmion cores; red arrows depict vortex currents outside skyrmion domains. Vortex-antivortex annihilation is prevented by supercurrents screening the skyrmion stray field (gray arrows), maximal at the skyrmion domain wall. (e),(f) Supercurrent-induced field $h$ simulated at $H=25$, 125 mT, where vortices/antivortices are visible as red/blue dots and solid lines show the contours of magnetic domain walls. Scale bars are 250 nm; simulations from $150\to -200\mathrm{mT}$ are shown in the Supplemental Material, Sec. VI C [28]. (g) Field-dependent simulated antivortex density $N_{\mathrm{AVx}}$ for MS and MIS heterostructures. (h) Scaled magnetization $M_{\text{scaled}}=a{M}_{\text{super}}+b$ in MS samples (squares, diamonds) and a MIS sample (asterisks) for $2\mathrm{K}<T<5\mathrm{K}$. The inset shows a similar scaling for $N_{\mathrm{AVx}}(H)$.

Figure 3

(a) Field-dependent critical currents $J_c(H)$ in MS, MIS heterostructures and a 25 nm Nb film ($S$), extracted from $V(I)$ curves at $T=2\mathrm{K}$ (see the Supplemental Material, Sec. VII [28]). The arrow shows the field sweep direction. $H_{\mathrm{nuc}}$, $H_{\mathrm{ann}}$ from Fig. 1 are highlighted by green and red dashed lines. (b) Thermal evolution of the magnetic relaxation $\mathrm{\Delta }{M}_{\text{super}}(H)$ in MS and MIS heterostructures. $\mathrm{\Delta }{M}_{\text{super}}(H)$ is the change in $M_{\text{super}}$ in a 60 s period after changing the field. (c) Antivortex-facilitated vortex tunneling through chiral domains. The Lorentz force $F_L$ from the applied current $J_{\mathrm{ext}}$ acts in opposite directions for vortices/antivortices. Consequently, vortex-antivortex pairs mutually annihilate on one side of the skyrmion/stripe, before spontaneously reemerging on the opposite side.

Figure 4

(a) $M_{\text{super}}(H)$ comparison between MS and MIS samples for a downward field sweep through $H_{\mathrm{nuc}}$ at $T=2\mathrm{K}$. Dashed lines are linear fits in the $0.17\text{T}<H<0.22\text{T}$ range; arrows indicate the response field $H_{\mathrm{Sc}}$ [defined by a 1% deviation from linearity in $M_{\text{super}}(H)$]. (b) Comparison of normalized $J_c(H)$ in MS and MIS samples during a field sweep at $T=2\mathrm{K}$. Arrows indicate $J_c(H)$ rising above the background (defined by an $S$ film) at $H_{\mathrm{Sc}}$. (c) Thermal evolution of $H_{\mathrm{Sc}}$ probed by magnetization (squares, diamonds, asterisks) and transport (circle, cross); see the Supplemental Material, Sec. VIII [28] for source data and details. Dashed/dotted lines highlight the trends displayed by MS/MIS bilayers.