  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.
