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The exchange stiffness of magnetic materials is one of the essentialparameters governing magnetic texture and its dynamics in magnetic devices. Theeffect of single-element doping on exchange stiffness has been investigated forseveral doping elements for permalloy (NiFe alloy), a soft magnetic materialwhose soft magnetic properties can be controlled by doping. However, the impactof more practical multi-element doping on the exchange stiffness of permalloyis unknown. This study investigates the typical magnetic properties, includingexchange stiffness, of permalloy systematically co-doped with Mo and Cu usingbroadband ferromagnetic resonance spectroscopy. We find that the exchangestiffness, which decreases with increasing doping levels, is proportional to apower of magnetization, which also decreases with increasing doping levels. Themagnetization, $M_{\rm s}$, dependence of the exchange stiffness constant, $A$,of all the investigated samples, irrespective of the doping levels of eachelement, lies on a single curve expressed as $A\propto M_{\rm s}^n$ withexponent $n$ close to 2. This empirical power-law relationship provides aguideline for predicting unknown exchange stiffness in non-magneticelement-doped permalloy systems.

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