Spin waves involved in three-magnon splitting in synthetic antiferromagnets

Abstract

An important nonlinear effect in magnonics is the 3-magnon splitting where a high frequency magnon splits into two magnons of lower frequencies. Here, we study the 3-magnon splitting in spin wave conduits made from synthetic antiferromagnets. By combining inductive excitation, inductive detection, Brillouin Light Scattering imaging of the spin waves and analytical modeling based on conservation laws, we elucidate the nature of the spin waves involved in this process. We show in particular that low order optical spin waves propagating along the conduit can split in doublets of non-degenerate acoustic spin waves that have a standing wave character in the confined direction and unsymmetrical wavevectors in the direction of the spin wave conduit. Generally, several splitting channels run in parallel. The rules governing the three-magnon splitting and its interplay with the mode confinement have consequences for the applications in non-linear microwave signal processing based on spin waves.

Figures (5)

• Figure 1: Overview of the methods. (a): VNA-FMR measurement of the frequencies of the uniform acoustic and optical modes on an unpatterned SAF. The green arrow sketches the field required to get $\omega_\textrm{op}=2 \omega_\textrm{ac}$ at $\vec{k}=\vec{0}$. (b) Set-up and image of a sample with a stripe of width $w_\textrm{stripe}=20~\mu$m. The microwave losses $S_{21}(\omega)$ between the planes $\Pi_{1}$ and $\Pi_{2}$ were accounted for. (c, d): Illustration of the three-magnon scattering (3MS) processes in SAFs: the stimulus of frequency $f_\textrm{stimulus}$ excites a spin wave from the optical branch with either $k_x^\textrm{opt} <0$ (panel c) or $k_x^\textrm{opt} >0$ (panel d), which splits into two spin waves of the acoustic branch, with frequencies close to $f/2$. (e) Typical signature of this process as recorded with a spectrum analyzer at the lowest power where 3MS is observed. The black peaks are the harmonics of the blue ones.
• Figure 2: Experimental results: (a) Frequencies $\omega_\textrm{ac,1}$ and $\omega_\textrm{ac,2}$ of the doublets of acoustic spin waves versus pump frequency for $\mu_0 h_x^\textrm{peak}=2.7$ mT. The modes are colored two-by-two to achieve $\omega_\textrm{ac,1}+\omega_\textrm{ac,2}=\omega_\textrm{pump}$. A line is at $f_\textrm{pump}/2$ was superimposed for readability purposes. Inset: power spectral densities from which the frequencies are extracted (comparable interval of frequencies). (b) doublet-resolved 3MS thresholds forming the Arnold tongues.
• Figure 3: Influence of stripe width on the frequencies of the acoustic doublets generated by 3MS for a pump at $2\times5.8$ GHz and a dc field of 33 mT. The peaks are colored by pairs according to energy conservation. (a) for a stripe width of 20 $\mu$m where 7 doublets are perceived, including a degenerate one. (b) for a stripe with of 3 $\mu$m where 2 doublets are perceived.
• Figure 4: Imaging of the modes involved in 3MS for $f_\textrm{stimulus}=10.5$ GHz, a field of 27 mT, a stripe width $\approx 2~\mu$m and an antenna (superimposed dotted lines) of width $\approx 1~\mu$m. (a): Optical image of the device. (b): $\mu$BLS spectra near $f_\textrm{stimulus}/2$ for powers $P_\textrm{source}=0$, 2.5, 5, 7.5 and 10 dBm. (c): $\mu$BLS image of the response at the applied frequency. (d, e): Responses at 5.1 and 5.4 GHz corresponding to $|\delta|=150~\textrm{MHz}$. (f, g): Responses at 5.7 and 4.8 GHz ($|\delta|=450~\textrm{MHz}$). Images (c-g) have a logarithmic color scale and are for $P_\textrm{source}=5~\textrm{dBm}$. Right sketches in (d-g): speculated wave profile in the transverse direction.
• Figure 5: Predicted 3MS channels in the conservation model for a 3 $\mu$m-wide stripe. The color code is that of the experiment of Fig. 2. The arrows denote the degenerate splittings. (a) Frequencies of the acoustic magnons resulting from splitting either $\lvert\longleftarrow\rangle_\textrm{opt}$ [blue and purple, scenario of Fig. 1(c)] or $\lvert\rightarrow\rangle_\textrm{opt}$ [black, green and wine, scenario of Fig. 1(d)] optical magnons. A line at half of the pump frequency was superimposed for readability. The lines are bold when the SWs should be measurable by the antenna. (b) Sketches of the transverse profiles of the split magnons. (c) Longitudinal (i.e. propagative) component of the wavevectors $\vec{k}_\textrm{ac}.\vec{e}_x$ of the split magnons.