Ferromagnetic resonance spectroscopy of parametric magnons excited by a four-wave process

Using a magnetic resonance force microscope, we have performed ferromagnetic resonance spectroscopy of the parametric magnons created by a four-wave process. This is achieved by measuring the differential response to a small amplitude modulation superimposed to a large constant excitation power that drives the dynamics of the uniform mode in the saturation regime. By sweeping the applied field, we observe an abrupt readjustment of the total number of magnons each time the excitation coincides with a parametric mode. This gives rise to ultranarrow peaks whose linewidth is lower than $5\times {10}^{-6}$ of the applied field.

Figure 1

(Color online) (a) Schematic of the microstrip cavity (1). The FMR spectrum of a micron-size YIG disk (2) is detected mechanically by magnetic resonance force microscopy (3). On the right is shown $P\left(t\right)$, the waveform of the power injected in the microwave circuit (1). (b) Static deflection of the cantilever as a function of $H_{\mathrm{ext}}$. The trace is the line shape of the uniform mode in the foldover regime. (c) Vibration amplitude of the cantilever measured by a lock-in synchronous with the amplitude modulation. This differential characteristic reveals the parametric excitation spectrum.

Figure 2

(Color online) (a) Differential spectrum as a function of the modulation depth $ϵ$, when $P_{\max }=-17\mathrm{dBm}$ is kept constant. $B$ is the broadening of the isolated parametric peak indicated by the triangle. (b) $B$ as a function of $ϵ$.

Figure 3

(Color online) Differential spectrum as a function of $P_{\max }$. In this set of measurement, $ϵ$ is kept constant at $ϵ=0.1$.

Figure 4

(Color online) (a) Magnon manifold for our perpendicularly magnetized YIG disk. The shaded area represents the trade-off between exchange energy, increasing with $k$, and demagnetizing energy, decreasing with the angle ${\theta }_k$ between $\mathit{k}$ and ${\mathit{M}}_s$ $(0⩽{\theta }_k⩽\pi ∕2)$. The confinement by the finite size of the sample introduces a discretization of the normal modes (dots). The four-wave process couples the uniform mode (red dot with white center) to the parametric modes at ${\theta }_k\approx 0$ (green dots with black centers) (b) Schematic of the distortion of the line shape induced by the four-wave process: the staircase behavior of $(M_s-M_z)∕\left(\gamma \hslash \right)={\sum }_k{N}_k$ reveals the parametric spectrum in the differential characteristics $\partial M_z∕\partial {\omega }_s$.