Quasicrystalline chiral soliton lattices in a Fibonacci helimagnet

We investigate the ground state magnetic configurations of a Fibonacci chain of classical spins with nearest-neighbor ferromagnetic and monoaxial Dzyaloshinskii-Moriya exchange interactions. Our analysis reveals a diverse array of magnetic textures induced by an external magnetic field perpendicular to the Dzyaloshinskii-Moriya vector. These textures exhibit a spectrum ranging from a quasifully polarized noncollinear state under high magnetic fields, capable of maintaining metastable chiral soliton topological defects, to a variety of quasicrystalline chiral soliton lattices below a critical field ${H}_{c}$. For a range of magnetic fields below ${H}_{c}$, the ground state spin textures result from the interplay between an effective quasiperiodic potential influencing the solitons and their repulsive interactions. At lower magnetic fields, the system experiences a commensurate-incommensurate transition, signified by the appearance of discommensurations in the quasicrystalline soliton lattice. In the absence of an external magnetic field, the ground state assumes a helical configuration with a quasiperiodic pitch angle.