Exchange stiffness proportional to power of magnetization in permalloy co-doped with Mo and Cu

TL;DR

This study reveals that in permalloy co-doped with Mo and Cu, the exchange stiffness is proportional to a power of magnetization, providing a predictive relationship for magnetic properties in doped systems.

Contribution

It is the first systematic investigation of multi-element doping effects on exchange stiffness in permalloy, establishing a power-law relationship between exchange stiffness and magnetization.

Findings

Exchange stiffness decreases with doping levels.

Exchange stiffness is proportional to magnetization raised to a power close to 2.

The power-law relationship can predict exchange stiffness in doped permalloy.

Abstract

The exchange stiffness of magnetic materials is one of the essential parameters governing magnetic texture and its dynamics in magnetic devices. The effect of single-element doping on exchange stiffness has been investigated for several doping elements for permalloy (NiFe alloy), a soft magnetic material whose soft magnetic properties can be controlled by doping. However, the impact of more practical multi-element doping on the exchange stiffness of permalloy is unknown. This study investigates the typical magnetic properties, including exchange stiffness, of permalloy systematically co-doped with Mo and Cu using broadband ferromagnetic resonance spectroscopy. We find that the exchange stiffness, which decreases with increasing doping levels, is proportional to a power of magnetization, which also decreases with increasing doping levels. The magnetization, $M_{\rm s}$, dependence of the exchange stiffness constant, $A$, of all the investigated samples, irrespective of the doping levels of each element, lies on a single curve expressed as $A\propto M_{\rm s}^n$ with exponent $n$ close to 2. This empirical power-law relationship provides a guideline for predicting unknown exchange stiffness in non-magnetic element-doped permalloy systems.