We report a high-resolution experimental detection of the resonant behavior of magnetic vortices confined in small disk-shaped ferromagnetic dots. The samples are magnetically soft FeNi disks of diameter 1.1 and 2.2 µm, and thickness 20 and 40 nm patterned via electron beam lithography onto microwave co-planar waveguides. The vortex excitation spectra were probed by a vector network analyzer operating in reflection mode, which records the derivative of the real and the imaginary impedance as a function of frequency. The spectra show well-defined resonance peaks in magnetic fields smaller than the characteristic vortex annihilation field.Resonances at 162 and 272 MHz were detected for 2.2 and 1.1 µm disks with thickness 40 nm, respectively. A resonance peak at 83 MHz was detected for 20-nm thick, 2-µm diameter disks.The resonance frequencies exhibit weak field dependence, and scale as a function of the dot geometrical aspect ratio. The measured frequencies are well described by micromagnetic and analytical calculations that rely only on known properties of the dots (such as the dot diameter, thickness, saturation magnetization, and exchange stiffness constant) without any adjustable parameters. We find that the observed resonance originates from the translational motion of the magnetic vortex core.
Dynamic microwave properties of arrays of circular Ni and Ni81Fe19 dots were studied by X-band ferromagnetic resonance (FMR) technique. All of the dots had the same radius 0.5μm, thickness 50–70nm, and were arranged into rectangular or square array with different interdot separations. In the case of perpendicular magnetization multiple (up to 8) sharp resonance peaks were observed below the main FMR peak, and the relative positions of these peaks were independent of the interdot separations. Quantitative description of the observed multiresonance FMR spectra is given using the dipole-exchange spin wave dispersion equation for a perpendicularly magnetized film where in-plane wave vector is quantized due to the finite dot radius, and the inhomogenetiy of the intradot static demagnetization field in the nonellipsoidal dot is taken into account.
Spin excitations of the magnetic vortex state in ferromagnetic nanodots are measured using Brillouin light scattering. Arrays of permalloy dots with 800-nm diameter and 60-nm thickness were fabricated by means of electron beam lithography and lift-off procedures. Two excitation modes are observed experimentally in the vortex state. One mode, at ϳ12 GHz, decreases slightly in frequency to 11 GHz as an in-plane magnetic field is applied. The lower mode, at ϳ8 GHz, is almost independent of applied field strength. Numerical and analytical calculations of the dynamic magnetization based on the Landau-Lifshitz equation of motion allows us to identify the higher and lower frequency modes as corresponding to dipole-dominated spin excitations localized inside the dot and at the dot edges, respectively.
CMB-S4—the next-generation ground-based cosmic microwave background (CMB) experiment—is set to significantly advance the sensitivity of CMB measurements and enhance our understanding of the origin and evolution of the universe. Among the science cases pursued with CMB-S4, the quest for detecting primordial gravitational waves is a central driver of the experimental design. This work details the development of a forecasting framework that includes a power-spectrum-based semianalytic projection tool, targeted explicitly toward optimizing constraints on the tensor-to-scalar ratio, r, in the presence of Galactic foregrounds and gravitational lensing of the CMB. This framework is unique in its direct use of information from the achieved performance of current Stage 2–3 CMB experiments to robustly forecast the science reach of upcoming CMB-polarization endeavors. The methodology allows for rapid iteration over experimental configurations and offers a flexible way to optimize the design of future experiments, given a desired scientific goal. To form a closed-loop process, we couple this semianalytic tool with map-based validation studies, which allow for the injection of additional complexity and verification of our forecasts with several independent analysis methods. We document multiple rounds of forecasts for CMB-S4 using this process and the resulting establishment of the current reference design of the primordial gravitational-wave component of the Stage-4 experiment, optimized to achieve our science goals of detecting primordial gravitational waves for r > 0.003 at greater than 5σ, or in the absence of a detection, of reaching an upper limit of r < 0.001 at 95% CL.
The evolution of a magnetic “vortex” state in submicron ferromagnetic disks has been studied as functions of disk diameter and thickness. The vortex core displacement in the applied magnetic field was calculated by minimizing the total magnetic energy consisting of the magnetostatic, exchange, and Zeeman energies. A simple analytical expression for the initial magnetic susceptibility is deduced. The initial susceptibility increases with increasing disk diameter and decreasing thickness. The calculations agree well with the experimental data obtained for the 60 nm thick permalloy disk arrays with a variable diameter from 0.2 to 0.8 μm.
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