Abstract
Knowledge of the spin-wave dispersion relation is a prerequisite for the explanation of many magnonic phenomena as well as for the practical design of magnonic devices. Spin-wave dispersion measurement by established optical techniques such as Brillouin light scattering or the magneto-optical Kerr effect at ultralow temperatures is often forbiddingly complicated. By contrast, microwave spectroscopy can be used at all temperatures but it usually lacks spatial and wave-number resolution. Here we develop a variable-gap-propagating-spin-wave-spectroscopy (VGPSWS) method for the deduction of the dispersion relation of spin waves in a wide frequency and wave-number range. The method is based on the phase-resolved analysis of the spin-wave transmission between two antennas with variable spacing, in conjunction with theoretical data treatment. We validate the method for in-plane magnetized $\mathrm{Co}$-$\mathrm{Fe}$-$\mathrm{B}$ and yttrium iron garnet thin films in $\mathbf{k}\ensuremath{\perp}\mathbf{B}$ and $\mathbf{k}\ensuremath{\parallel}\mathbf{B}$ geometries by deducing the full set of material and spin-wave parameters, including spin-wave dispersion, hybridization of the fundamental mode with the higher-order perpendicular standing spin-wave modes, and surface spin pinning. The compatibility of microwaves with low temperatures makes this approach attractive for cryogenic magnonics at the nanoscale.
Highlights
The properties of magnetic materials are of great interest due to several application concepts regarding, for example, memories, sensors, microwave devices, or logic devices [1]
In thin films, only the fundamental mode is observed when the experimentally accessible frequency range is limited to a few gigahertz
We show that spin-wave dispersion measurement using a vector network analyzer (VNA) is possible with a high level of detail determined by the VNA frequency step
Summary
The properties of magnetic materials are of great interest due to several application concepts regarding, for example, memories, sensors, microwave devices, or logic devices [1]. The data are measured at a power output of 0-dBm for a 30-nm-thick Co-Fe-B film over the 1.8-μm gap in the k ⊥ B geometry (magnetostatic surface waves) and with 500-nm-wide striplines used as excitation and detection antennas. This geometry is known to be nonreciprocal with an exponential distribution of the dynamic magnetization along the layer’s thickness due to the surface localization of the mode [28,29].
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