Self-induced Floquet states via three-wave processes in synthetic antiferromagnets

Abstract

We present a mechanism for self-induced Floquet states involving acoustic and optical modes in synthetic antiferromagnets. By driving optical modes off-resonantly with radiofrequency fields in the canted antiferromagnetic state, limit cycles arising from the predator-prey dynamics of the acoustic and optical mode populations can appear. The cyclic growth and decay of these mode populations induce a time-periodic modulation of the canted state, which subsequently generates Floquet states. These states appear as a rich frequency comb in the power spectrum of magnetization oscillations.

Figures (13)

• Figure 1: (a) Dependence of the eigenmode frequencies on the applied static field, $H_x$, with the sketch of the equilibrium magnetizations of the SAF shown in the top insetl. The 3MS arrow indicates the matching condition, i.e., where $\omega_\mathrm{op} = 2\omega_\mathrm{ac}$. (b) Threshold pumping field for 3MS, $h_{\mathrm{rf},c}$, as a function of frequency detuning between the pumping frequency $f_\mathrm{rf}$ and $f_\mathrm{op}$ at $H_x = H_\mathrm{3MS}$. The top inset illustrates the field configuration.
• Figure 2: Population dynamics of the (a) optical and (b) acoustic mode for different rf field amplitudes, $h_\mathrm{rf}$, under the matching condition $\omega_\mathrm{rf}=\omega_\mathrm{op}$.
• Figure 3: Population dynamics and correlation with the mean state at $H_x= H_\mathrm{3MS}$ and a detuned stimulus frequency $\omega_\mathrm{rf}=12.68~\mathrm{GHz} < \omega_\mathrm{op}$ for an rf field of 2 kA/m. The initial state is the energy minimum. (a): Population $n_\mathrm{op}(t)$ of optical modes. (b) Period-averaged mean state $\langle m_x(t) \rangle$. (c) Acoustic population $n_\mathrm{ac}(t)$. (d) Correlation between the optical population and the period-averaged mean state.
• Figure 4: Self-induced Floquet modes. The field $H_x = 55~\mathrm{kA/m} > H_\mathrm{3MS}$ is larger than the matching condition. A non-resonant stimulus is applied with $\omega_\mathrm{rf} = 12.68\mathrm{~GHz} < \omega_\mathrm{op} < 2\omega_\mathrm{ac}$ is applied, with a peak amplitude $h_\mathrm{rf}=2.2$ kA/m (2.8 mT). (a) Time dependence of the acoustic and optical mode populations. (b) Population phase plot showing limit cycle. (c) Power spectral density of the mode population, $S_n$, exhibiting a characteristic frequency at 672 MHz. (d) Time dependence of $x$-component of the magnetization of the first layer $m_{x1}(t)$ within the limit cycle. (e) Power spectral density of $m_{x1}$, $S_m$, showing the frequency combs around $\omega_\mathrm{rf}/2$ and its harmonics.
• Figure S1: Population dynamics for an rf field $H_x^\textrm{rf}=1~\textrm{kA/m}$ and perfectly matching conditions when starting from the thermal seed and resonantly pumping the optical mode. (a) Time-resolved population population of the optical mode. (b) Idem for the acoustic mode. Inset: population-population plot. (c) Sum of the two populations (blue) and total energy of the system (green).