We study how the shape of the spin-wave resonance lines in rf voltage induced FMR can be used to extract the spin-wave density of states and the Gilbert damping within the precessing layer in nanoscale magnetic tunnel junctions that possess perpendicular magnetic anisotropy. We work with a field applied along the easy axis to preserve the cylindrical symmetry of the uniaxial perpendicularly magnetized systems. We first describe the experimental setup to study the susceptibility contributions of the spin waves in the field-frequency space. We then identify experimentally the maximum device size above which the spin waves confined in the free layer can no longer be studied in isolation as the linewidths of their discrete responses make them overlap into a continuous density of states. The rf voltage induced signal is the sum of two voltages that have comparable magnitudes: a first voltage that originates from the linear transverse susceptibility and rectification by magnetoresistance and a second voltage that arises from the nonlinear longitudinal susceptibility and the resultant time-averaged change of the exact micromagnetic configuration of the precessing layer. The transverse and longitudinal susceptibility signals have different dc bias dependencies such that they can be separated by measuring how the device rectifies the rf voltage at different dc bias voltages. The transverse and longitudinal susceptibility signals have different line shapes; their joint studies in both fixed field-variable frequency, or fixed frequency-variable field configurations can yield the Gilbert damping of the free layer of the device with a degree of confidence that compares well with standard ferromagnetic resonance. Our method is illustrated on FeCoB-based free layers in which the individual spin waves can be sufficiently resolved only for disk diameters below 200 nm. The resonance line shapes on devices with 90-nm diameters are consistent with a Gilbert damping of $0.011$. A single value of the damping factor accounts for the line shape of all the spin waves that can be characterized. This damping of 0.011 exceeds the value of 0.008 measured on the unpatterned films, which indicates that device-level measurements are needed for a correct evaluation of dissipation.

• Received 15 March 2017

DOI:https://doi.org/10.1103/PhysRevB.96.104413