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We present an experimental and theoretical study of the magnetic fielddependence of the mode frequency of thermally excited spin waves in rectangularshaped nanopillars of lateral sizes 60x100, 75x150, and 105x190 nm2, patternedfrom MgO-based magnetic tunnel junctions. The spin wave frequencies weremeasured using spectrally resolved electrical noise measurements. In allspectra, several independent quantized spin wave modes have been observed andcould be identified as eigenexcitations of the free layer and of the syntheticantiferromagnet of the junction. Using a theoretical approach based on thediagonalization of the dynamical matrix of a system of three coupled, spatiallyconfined magnetic layers, we have modeled the spectra for the smallest pillarand have extracted its material parameters. The magnetization and exchangestiffness constant of the CoFeB free layer are thereby found to besubstantially reduced compared to the corresponding thin film values. Moreover,we could infer that the pinning of the magnetization at the lateral boundariesmust be weak. Finally, the interlayer dipolar coupling between the free layerand the synthetic antiferromagnet causes mode anticrossings with gap openingsup to 2 GHz. At low fields and in the larger pillars, there is clear evidencefor strong non-uniformities of the layer magnetizations. In particular, at zerofield the lowest mode is not the fundamental mode, but a mode most likelylocalized near the layer edges.

Quantized spin wave modes in magnetic tunnel junction nanopillars