Accurate model of the stripe domain phase of perpendicularly magnetized multilayers

Abstract

We develop an accurate analytical model for the stray field energy of parallel stripe domains in multilayer films with perpendicular magnetic anisotropy, taking into account the effects of finite domain wall width and variable domain wall angle. By minimizing the total energy we predict the domain width, the domain wall width, and the domain wall angle for given material parameters. We show how the domain wall width depends on the film thickness and the domain size. We explore the domain wall angle as a function of Dzyaloshinskii-Moriya interaction (DMI) and derive a threshold value D thr beyond which the system is in a Néel state. We find that thicker films require larger values of DMI to stabilize the Néel state. Finally, we test the effective medium theory, which allows treating multilayers as effective single layer films and provide criteria for the applicability of the model in the presence of both surface and volume stray fields. Our results are supported by micromagnetic simulations, which indicate that the predictions are still precise even if the system is in a labyrinthine domain state. Using our model, otherwise inaccessible magnetic parameters, such as the DMI constant or the exchange constant, can now be obtained straight-forwardly from static measurements of the stripe domain width in such films.

Unraveling the role of dipolar versus Dzyaloshinskii-Moriya interactions in stabilizing compact magnetic skyrmions

“…It is a direct consequence of the competition between long-range dipolar interaction, which favors a Bloch rotation, and interfacial DMI, which favors a Néel rotation. Note that a similar threshold is observed in the case of straight domain walls [35,53]:…”

Individual skyrmion manipulation by local magnetic field gradients

“…where A is the exchange stiffness and K e f f is the effective perpendicular anisotropy constant. Accordingly, domain formation becomes more favourable in the presence of a finite DMI and measurements of the domain width can then be used to directly quantify D 16,30 . In particular, following the approach implemented by Woo et al 16 , we extracted D from the equilibrium domain width of the demagnetised state, where up and down domains have the same average size.…”

Walker Breakdown with a Twist: Dynamics of Multilayer Domain Walls and Skyrmions Driven by Spin-Orbit Torque

“…For typical material parameters, this velocity is of the order of tens of m/s, corresponding to the velocity range in recent experiments [21,[45][46][47][48]. The breakdown originates from the interplay of SOT, DMI, and magnetostatic interactions [42], thanks to which DWs in some layers can be driven toward a Bloch configuration amenable to precession (because of the surface-volume stray field interactions [42]) while others maintain a Néel (or tran-sient [49]) character. This, in turn, allows the dampinglike SOT, which acts as an effective field ∝ sin(ψ), to continue to drive the magnetostatically-coupled composite structure even though the Bloch layers are not directly susceptible to the driving torque.…”