Abstract
A micromagnetic model of thin films with columnar microstructure in the form of a matrix with reduced magnetic properties and embedded columns with high aspect ratio is presented. Such microstructure is typical for some films based on rare-earth and 3d transition metal alloys, in particular for La-Co films, that were chosen as an object for our modelling. Described structural features promote an effective perpendicular magnetic anisotropy that for thick enough films leads to formation of the stripe domain pattern. Our work addresses to the problem of finding equilibrium characteristics of stripe domains for the case of infinite columnar films. Herein it is shown how width of stripe domains, remanent magnetization and energies depend on number of replicas of periodic boundary conditions and the size of modelling volume. Equilibrium values of listed quantities can be found by extrapolating obtained dependencies.
Highlights
A long history of studying thin magnetic films yielded a great variety of magnetic patterns such as vortices, periodic stripes, disordered labyrinth domains, etc. having domain walls of different types and a diversity of topological defects.1 The importance of thin films for applications in spintronics and magnetic storage of information specifies a necessity of deep understanding how microstructural features and micromagnetic properties of films as well as external conditions determine their domain structure and how it can be tuned
It appears above a critical film thickness Dcr and it is usually induced by the magnetic anisotropy with out-of-plane easy magnetization axis that joins the competition between short-range exchange and long-range magnetostatic interactions
One of the earliest theoretical description of strong stripe domains in uniform films was done by Kittel3 assuming the square magnetization profile. This approximation is valid only when the film thickness D is much larger than domain width W and the last one is much larger than the width of domain walls δ (δ ≪ W ≪ D)
Summary
A long history of studying thin magnetic films yielded a great variety of magnetic patterns such as vortices, periodic stripes, disordered labyrinth domains, etc. having domain walls of different types and a diversity of topological defects. The importance of thin films for applications in spintronics and magnetic storage of information specifies a necessity of deep understanding how microstructural features and micromagnetic properties of films as well as external conditions determine their domain structure and how it can be tuned. The stripe domain pattern is characterized by periodic out-ofplane magnetization oscillations.2 It appears above a critical film thickness Dcr and it is usually induced by the magnetic anisotropy with out-of-plane easy magnetization axis that joins the competition between short-range exchange and long-range magnetostatic interactions. Lets us focus on amorphous thin films of alloys of rare-earth (R) and 3d transition metals (TM) In such films both perpendicular magnetic anisotropy and stripe domain pattern are observed frequently. Depending on the type of R ion and sputtering conditions, different mechanisms can prevail Another possibility for anisotropy formation is related to a columnar microstructure of R-TM films, which was revealed in Refs. For that the effects of modelling volume size and periodic boundary conditions were analyzed systematically for the case of a film with realistic micromagnetic parameters taken for La-Co alloy
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