Hybrid magnon -- Nambu-Goldstone excitations in topological superconductor/ferromagnetic insulator thin-film heterostructures

Abstract

We address a previously unexplored type of dynamical proximity effect that occurs in s-wave topological superconductor/ferromagnetic insulator (TS/FI) heterostructures. It is predicted that magnons in the FI and the Nambu-Goldstone (NG) collective superconducting phase mode in the TS are coupled, forming composite magnon-NG excitations. The mechanism of this coupling is associated with the complete spin-momentum locking of electrons in the helical surface state of the TS. The strength of the magnon-NG coupling is strongly anisotropic with respect to the mutual orientation of the magnon wave vector and the equilibrium magnetization of the FI. This effect provides a mechanism for the interconversion of spin signals and the spinless signals carried by collective superconducting excitations, thereby giving new impetus to the development of superconducting spintronics.

Figures (4)

• Figure 1: Schematic of the TS/FI system under consideration. A thin film of a ferromagnetic insulator (FI) is placed on top of a topological superconductor (TS). The two layers interact via the interfacial exchange coupling characterized by the coupling constant $J_{ex}$. The equilibrium magnetization of the FI $\bm m_0 = \hat{x}$ and a magnon excitation $\delta \bm m$ of the FI induce in the TS an equilibrium effective exchange field $\bm h_x$ and a magnon-induced dynamic contribution $\delta \bm h_y$, respectively. The dynamic exchange field $\delta \bm h_y$ triggers a time-dependent response of the superconducting order parameter in the TS, resulting in a hybridized magnon–Nambu–Goldstone (NG) excitation. Inset (upper left): normal-state energy dispersion and Fermi surface of the helical surface state of the TS.
• Figure 2: Dispersion relations of excitations in uncoupled TS and FI layers. The intrinsic decay rate of the NG mode $\kappa_p$ is indicated by the color scale along the corresponding line. The intrinsic decay rate of the magnon $\kappa_m = \alpha \omega$ is not shown for clarity. The Higgs mode is also depicted, however, due to strong overdamping, it manifests as a broad peak in the spectral density rather than a sharp dispersion line. All data correspond to temperature $T=0.1 T_c$, with Dynes broadening parameter $\Gamma \approx 0.018 \Delta_0$. Panels: (a) superconducting plasma frequency $\hbar \omega_p = 4.35 \Delta$, (b) $\hbar \omega_p = 43.5 \Delta$. See main text for details.
• Figure 3: Hybridization between NG and magnon modes. Left column: $\hbar\omega_p = 4.35 \Delta$; right column - $\hbar\omega_p = 43.5 \Delta$. Top row: excitations propagating along the $x$-axis; bottom row: along the $y$-axis. The exchange field is set to $h_0 \approx 1.17 \Delta$; all other parameters are identical to those used in Fig. \ref{['all_modes']}. Insets in panels (a) and (b) display zoomed-out views of the dispersion relations at larger $k_x$ and $\omega$, highlighting the high-frequency behavior of the hybridized modes.
• Figure 4: Damping and dispersion of hybridized magnon–NG modes. Top row: damping $\kappa_{up}$ of the upper magnon-NG excitation branch $\omega_{up}$. Middle row: magnon-NG dispersion. Bottom row: damping $\kappa_{dn}$ of the lower magnon-NG excitation branch $\omega_{dn}$.The left column corresponds to $\hbar\omega_p = 4.35 \Delta$; the right column to $\hbar\omega_p = 43.5 \Delta$. The cyan dotted line indicates the intrinsic magnon damping $\kappa_m = \alpha \omega$ assuming a Gilbert damping constant $\alpha = 10^{-4}$. The black dashed line denoted the intrinsic NG mode damping $\kappa_p$.