Phase-factor-controlled surface spirals in the magnetic conical phase: The role of in-plane directionality

In chiral magnets, the magnetic textures surrounding domain walls exhibit a rich variety of structures, offering insights into fundamental physics and potential applications in spintronic devices. Conical spirals and related structures possess intrinsic in-plane directionalities governed by the phase factor ${\ensuremath{\phi}}_{0}$, which are often obscured in long spirals, owing to cylindrical symmetry, but become prominent in short spirals or thin films. Using micromagnetic simulations, we systematically studied magnetic textures at ferromagnetic conical interfaces (FCIs), including one-dimensional (1D) and two-dimensional (2D) FCIs with various shapes. Surface spirals (SSs) emerge adjacent to these FCIs, closely linked to the cone's in-plane reorientation. In 1D FCIs, reorientation controls the presence, shape, and topological charge of the SS, with a discontinuity point observed where spirals with opposite charges form on opposite sides. In 2D FCIs, eyebrowlike SSs are evident. The reorientation angle between top and bottom SSs is controlled by the film thickness, similar to stacked spirals reported previously. We further demonstrate that SSs form at the facets of skyrmion clusters within the conical phase, as confirmed by both simulations and Lorentz transmission electron microscopy in thin ${\mathrm{Co}}_{8}{\mathrm{Zn}}_{10}{\mathrm{Mn}}_{2}$ films. The experiments specifically reveal two distinct formation pathways: thermally activated cogrowth and field-driven transformation from residual helices. These findings establish ${\ensuremath{\phi}}_{0}$ as a fundamental control parameter for magnetic states, enabling promising spintronic functionalities, such as multistate memory through SS polymorphism and energy-efficient neuromorphic computing via controlled topological transitions.