Micromagnetics of conical-helix textures in thin films with different kinds of Dzyaloshinskii-Moriya interactions

Abstract Chiral spin textures in ferromagnetic materials with Dzyaloshinskii-Moriya interactions (DMIs) have attracted significant interest in recent years owing to their potential applications in nanodevices. This work focuses on describing stable conical-helix configurations hosted in ultrathin films with DMI and perpendicular anisotropy. These states are studied for different kinds of DMIs, including symmetry classes $${\mathcal{T}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>T</mml:mi> </mml:math> , $${{\mathcal{C}}}_{nv}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mi>C</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>n</mml:mi> <mml:mi>v</mml:mi> </mml:mrow> </mml:msub> </mml:math> , isotropic and anisotropic $${{\mathcal{D}}}_{2d}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mi>D</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>d</mml:mi> </mml:mrow> </mml:msub> </mml:math> , $${{\mathcal{D}}}_{n}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mi>D</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>n</mml:mi> </mml:mrow> </mml:msub> </mml:math> , $${{\mathcal{C}}}_{n}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mi>C</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>n</mml:mi> </mml:mrow> </mml:msub> </mml:math> , and $${{\mathcal{S}}}_{4}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mi>S</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>4</mml:mn> </mml:mrow> </mml:msub> </mml:math> . A parameterised analytical model of these configurations is proposed, enabling the determination of optimal parameters characterising the magnetic texture, such as the pitch vector or nucleation field. To substantiate the results, micromagnetic simulations are developed for comparison with the theoretical solutions. Numerical solutions are optimised by implementing finite-difference codes that use next-nearest neighbours and explicit Robin boundary conditions stemming from symmetric exchange and DMI. It is shown that these numerical enhancements decrease anisotropic effects in helical solutions. This study establishes a method to analyse conical-helix textures in thin-film systems with any DMI, which can be simulated with higher precision using the open-access codes developed here.