  We measure the frequencies of spin waves in nm-thick perpendicularly
magnetized FeCoB systems, and model the frequencies to deduce the exchange
stiffness of this material in the ultrathin limit. For this, we embody the
layers in magnetic tunnel junctions patterned into circular nanopillars of
diameters ranging from 100 to 300 nm and we use magneto-resistance to determine
which rf-current frequencies are efficient in populating the spin wave modes.
Micromagnetic calculations indicate that the ultrathin nature of the layer and
the large wave vectors used ensure that the spin wave frequencies are
predominantly determined by the exchange stiffness, such that the number of
modes in a given frequency window can be used to estimate the exchange. For 1
nm layers the experimental data are consistent with an exchange stiffness A= 20
pJ/m, which is slightly lower that its bulk counterpart. The thickness
dependence of the exchange stiffness has strong implications for the numerous
situations that involve ultrathin films hosting strong magnetization gradients,
and the micromagnetic description thereof.
