Nonlinear Superconducting Magnetoelectric Effect

Supercurrent flow can induce a nonvanishing spin magnetization in noncentrosymmetric superconductors with spin-orbit interaction. Often known as the non-dissipative magnetoelectric effect, these are most commonly found at linear order in supercurrent flow. Here, we propose that a {\it nonlinear} superconducting magnetoelectric (NSM) effect can naturally manifest in magnet/superconductor heterostructures. In such platforms, NSM manifests as the spin polarization generated as a second-order response to a driving supercurrent. Strikingly, we find NSM survives centrosymmetry and is the leading order magnetic response in a variety of magnetic materials that include both collinear magnets [e.g., $d$-wave planar altermagnet thin film/superconductor (ALM/SC)] as well as noncollinear magnets (e.g., Kagome/SC systems). This renders NSM a powerful electric and non-dissipative means of controlling magnetization in magnet/superconductor heterostructures, a promising platform for superconducting spintronics.