Fig. 1: VNA frequency offset measurements of emergent nonlinear spin waves.
From: Emergent coherent modes in nonlinear magnonic waveguides detected at ultrahigh frequency resolution
a Schematics of the frequency offset measurement implemented on a VNA attached to two CPWs on YIG. The RF signal of the microwave source operated at frequency fp is applied to CPW1. The local oscillator operates at the offset frequency fo swept between fo1 and fo2. Mixed signals from the local oscillator and the nonlinear magnons are detected via two Receivers A and B, which detect phase-coherently voltage signals at CPW1 and CPW2, respectively. b Wave-vector dependent group velocity vg at 28, 28.6, and 28.9 mT. No difference is visible at this scale. c Dispersion relation for BVMSWs illustrating the nonadiabatic parametric pumping via forced spin precession at fp and kp. d Fourier analysis of the x-component of the normalized RF magnetic field \({\tilde{h}}_{k}={h}_{k}/{h}_{k}^{\max }\). e Four-magnon scattering processes outside CPW1. The green arrows indicate magnons created by the nonadiabatic pumping process, which have equal wave vectors and frequencies kp/2 and fp/2. At further increased power, they undergo two different processes with time delays that lead to the scattering center outside CPW1 by s. The blue arrows indicate the resultant counter-propagating magnons after the four-magnon scattering. These are detected from both f Receiver A (CPW1) and g Receiver B (CPW2) represented by the blue-colored peaks. Another type of scattering results in two co-propagating magnons, which can only be detected in CPW2 as they propagate in the direction of their parent magnons (red-colored peaks in g). f, g Waterfall plots of scattering parameters SA (signal taken from CPW1) and SB (signal taken from CPW2) measured for different powers. At low powers, a very sharp peak at fp/2 appears, which has a linewidth on the order of tens of kHz, close to our frequency resolution (green colors in f and g). At a power of 1.7 mW, it splits into a pair of symmetric side peaks with a linewidth of sub-MHz. The in-plane magnetic field of 28.6 mT was applied along the x-direction.
