Accurate calculation of the transverse anisotropy in perpendicularly magnetized multilayers

TL;DR

This paper introduces a universal analytical method to accurately calculate the transverse anisotropy constant in perpendicular magnetic multilayers using static measurements, improving upon conventional approximations.

Contribution

The authors derive a general analytical expression for the transverse anisotropy constant in multilayers, enabling precise calculations from static characterizations.

Findings

The new model provides a transverse anisotropy value 7 times different from conventional methods.

Application to a common multilayer system demonstrates the model's significance.

Static parameters like layer thickness and saturation magnetization are sufficient for calculations.

Abstract

The transverse anisotropy constant and the related D\"oring mass density are key parameters of the one-dimensional model to describe the motion of magnetic domain walls. So far, no general framework is available to determine these quantities from static characterizations such as magnetometry measurements. Here, we derive a universal analytical expression to calculate the transverse anisotropy constant for the important class of perpendicular magnetic multilayers. All the required input parameters of the model, such as the number of repeats, the thickness of a single magnetic layer, and the layer periodicity, as well as the effective perpendicular anisotropy, the saturation magnetization, and the static domain wall width are accessible by static sample characterizations. We apply our model to a widely used multilayer system and find that the effective transverse anisotropy constant is a factor 7 different from the when using the conventional approximations, showing the importance of using our analysis scheme.