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Exchange stiffness in ultrathin perpendicularly-magnetized CoFeB layers determined using spin wave spectroscopy

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.