Fig. 1: Screw-like spin textures of ACMs and asymmetric dispersion of magnons at zero magnetic field.
From: Geometry-induced spin chirality in a non-chiral ferromagnet at zero field
a, Simulated spin texture of a right-handed ACM in the remanent state consisting of a hollow ferromagnetic tube with a surface spiral. The colour wheel represents the magnetization direction which inherits the screw-like topology. b, SEM image of a RH ACM, fabricated by conformal coating of a ferromagnetic nickel layer on a 3D scaffold. c,d, XMCD images measured at the nickel L3 absorption pre-edge for the segment marked with a purple square in b. The extracted spin configurations after application of +250 mT and −250 mT along the central axis of the ACMs are labelled by +0 mT (c) and −0 mT (d), and are sketched in e and f, respectively. g, Dispersion relation of the lowest magnon band on tubes with LH (green curve) and RH (purple) helical textures under a tilting angle of 20° with the longitudinal axis. Insets: spin configurations (purple arrows) and corresponding toroidal moment vectors τ motivating the non-reciprocal propagation of magnons (indicated via differently large wavevectors +k and −k collinear with τ and the z direction).
