Approaching soft X-ray wavelengths in nanomagnet-based microwave technology

Abstract

Seven decades after the discovery of collective spin excitations in microwave-irradiated ferromagnets, there has been a rebirth of magnonics. However, magnetic nanodevices will enable smart GHz-to-THz devices at low power consumption only, if such spin waves (magnons) are generated and manipulated on the sub-100 nm scale. Here we show how magnons with a wavelength of a few 10 nm are exploited by combining the functionality of insulating yttrium iron garnet and nanodisks from different ferromagnets. We demonstrate magnonic devices at wavelengths of 88 nm written/read by conventional coplanar waveguides. Our microwave-to-magnon transducers are reconfigurable and thereby provide additional functionalities. The results pave the way for a multi-functional GHz technology with unprecedented miniaturization exploiting nanoscale wavelengths that are otherwise relevant for soft X-rays. Nanomagnonics integrated with broadband microwave circuitry offer applications that are wide ranging, from nanoscale microwave components to nonlinear data processing, image reconstruction and wave-based logic.

Figure 1. Resonantly driven nanodisks for injection and detection of large-amplitude spin waves in thin YIG.

(a) Sketch of the experiment. Large-magnetization ferromagnetic nanodisk arrays (green) were positioned between CPWs (yellow) and insulating YIG (violet). The magnetization M of YIG is parallel to the CPWs. (b) Sketched microwave-to-magnon transduction: the resonant spin-precessional motion in disks (large arrows) is exploited to excite short-wavelength spin waves (small arrows highlighted by the oval) in YIG. Depending on the frequency, different wave vectors k₁+nG (n=1, 2, 3, …) are induced. denotes a reciprocal lattice vector perpendicular to the CPW. Spin waves propagate to the detector CPW indicated by the horizontal arrow. (c) Colour-coded transmission signal S₁₂ monitoring spin-wave propagation between CPW1 to CPW2. Green and orange arrows guide the eyes and highlight two branches that cross near the centre of the graph. Green (orange) arrows indicate the resonant excitation of the permalloy nanodisks (YIG at large wave vector k_SW). (d) Transmission spectrum S₁₂ at −69 mT (broken line in c) displaying propagation of spin waves through YIG with enlarged amplitude when permalloy nanodisks resonate together with YIG. Blue arrows indicate non-resonant spin-wave excitation. (e) Enlarged oscillating transmission signal (imagninary (IMG) part) around 7.6 GHz attributed to k_SW=k₁+6G=48 rad μm⁻¹=4.8 × 10⁵ rad cm⁻¹. The corresponding wavelength amounts to 131±3 nm.

Figure 2. Reconfigurable microwave-to-magnon transducer exciting exchange-dominated spin waves.

(a) Colour-coded absorption spectra S₁₁ measured on the permalloy (Py)/YIG hybrid sample in reflection configuration. The field is varied from −100 to +100 mT. The blue arrows highlight excitation of YIG at k₁. The green arrows highlight the FMR branch of Py nanodisks that show hysteretic behaviour. White arrows indicate spin-wave modes attributed to channelling effects due to the static stray field of the dots. (b) Colour-coded spectra S₁₂ monitoring three sets of spin waves propagating through YIG (orange arrows). The parameter regime agrees with the white square in a. (c) Line spectrum S₁₂ (imagninary (IMG) part) taken at −30 mT when nanodisks were saturated. Here, three resonantly enhanced modes are seen. (d) Line spectrum S₁₂ taken at +30 mT when the nanodisks were in the unsaturated state. (e) Relative amplitudes of transmitted spin waves as a function of the wave vector k (experiment, symbols; expected values following ref. , red lines). Black, full (open) squares indicate modes k₁–k₄ (grating coupler modes without crossing of the nanodisk FMR branch) measured at −10 mT. Filled orange squares depict spin-wave modes in YIG with crossing of the nanodisk FMR branch. Error bars are a measure of the trace noise in S₁₂ (as displayed in d) compared with the signal strength. All signals are normalized to the amplitude of the respective k₁ mode taken as 100%.

Figure 3. Spin waves with induced by resonating CoFeB nanodisks.

(a) Colour-coded absorption spectra S₁₁ measured on a CoFeB/YIG hybrid sample. The field is swept from −100 to +100 mT. Field regions for saturated and unsaturated states are highlighted by vertical lines. (b) Dispersion relation of the YIG thin film calculated for 90 mT (line). The black circles show eigenfrequencies obtained on CoFeB/YIG at the same absolute field. Error bars reflect the uncertainty of the resonance frequency due to noise and are extracted by taking the s.e. from fitting a Lorentz curve to the respective resonant peak in the measured spectra. (c) Transmission signal S₁₂ that we attribute to k_SW=k₁+9G.