Magnon-phonon coupling of synthetic antiferromagnets in a surface acoustic wave cavity resonator

Technical Summary: Magnon-Phonon Coupling in Synthetic Antiferromagnets within a SAW Cavity Resonator

Problem Statement
The interaction between phonons and magnons is a critical area of study for advancing quantum technologies and understanding coupling mechanisms. While strong magnon-phonon coupling requires matching the resonance frequencies of surface acoustic waves (SAWs) and magnons, a significant challenge exists in ferromagnetic thin films. Typically, the magnon resonance frequency in such films is in the multi-GHz range, whereas SAWs are often excited at lower frequencies (around 1 GHz). To achieve frequency matching, researchers have historically used materials with low magnetization, such as Nickel (Ni). However, even in Ni, the required magnetic fields to align these frequencies are often small, leading to multi-domain formation that impedes the coherent excitation of magnons. Furthermore, the quality factor of SAW cavity resonators tends to degrade at higher frequencies. Consequently, there is a need for a system that allows for the study of magnon-phonon coupling in materials with large saturation magnetization while maintaining coherent excitation conditions.

Methodology
The authors investigated magnon-phonon coupling using a synthetic antiferromagnet (SAF) composed of a CoFeB/Ru/CoFeB trilayer, comparing it against a CoFeB single-layer reference film. The experimental setup involved a SAW cavity resonator fabricated on a piezoelectric Y+128°-cut LiNbO3 substrate. The device featured interdigital transducers (IDTs) and Bragg reflectors made of Ti/Au to confine SAWs, creating a cavity with a quality factor exceeding $10^3$ at room temperature.

The SAF structure consisted of Ta(3)/Ru(3)/CoFeB(5)/Ru(0.53)/CoFeB(5)/Ru(3) (thicknesses in nm), while the reference sample was a 10 nm thick CoFeB single layer. The researchers employed a vector network analyzer (VNA) to measure the scattering matrix ($S_{ij}$) of the device. By applying an in-plane external magnetic field ($H_{ext}$) at various angles ($\phi_H$), they modulated the magnetization direction and the magnon resonance frequency. The transmission spectra ($|S_{21}|^2$) were analyzed to observe changes in amplitude, resonance frequency, and spectral linewidth ($\kappa_a$) as the magnon frequency approached the SAW cavity resonance frequency (approximately 1.8 GHz).

Key Contributions and Results

1. SAF as a Superior Platform: The study demonstrates that the SAF structure significantly lowers the acoustic magnon resonance frequency compared to a single ferromagnetic layer. This shift allows the magnon and SAW resonance frequencies to coincide at a sufficiently large external magnetic field ($\mu_0 H_{res} \approx 16.7$ mT), a condition where multi-domain formation is suppressed, enabling coherent magnon excitation. In contrast, the CoFeB single-layer film showed negligible changes in the SAW spectrum under similar conditions, as its resonance field is near zero, leading to incoherent excitation due to domain formation.
2. Spectral Linewidth Modulation: When the acoustic magnons in the SAF were excited near resonance, the researchers observed distinct modifications in the SAW cavity transmission spectrum. Specifically, at the resonance field, the transmission amplitude ($A_a$) decreased, the resonance frequency ($\omega_a$) shifted, and the spectral linewidth ($\kappa_a$) broadened significantly. These changes were minimal in the single-layer reference sample.
3. Quantitative Coupling Strength: By analyzing the difference in the spectral linewidth between the resonant and off-resonant conditions, and utilizing a macrospin-like model based on the Landau-Lifshitz-Gilbert (LLG) equation and elastic wave equations, the authors quantified the coupling.
   • The magnon-phonon coupling constant ($g$) was estimated to be $\sim 15.6$ MHz at a SAW resonance frequency of 1.8 GHz.
   • The corresponding magnomechanical cooperativity ($C$) was calculated to be $\sim 0.66$.
4. Angular Dependence: The cooperativity $C$ exhibited a strong dependence on the magnetic field angle ($\phi_H$), reaching a maximum at $60^\circ$ and $120^\circ$. The authors attribute this to the presence of uniaxial magnetic anisotropy (likely shape anisotropy) in the CoFeB layers, which influences the relative angle between magnetization and the strain field. Numerical calculations assuming uniaxial anisotropy aligned well with these experimental observations.

Significance
The paper claims that synthetic antiferromagnets provide an ideal platform for studying magnon-phonon coupling in SAW cavity resonators. By overcoming the limitations of single-layer ferromagnetic films—specifically the issue of multi-domain formation at low magnetic fields—the SAF structure enables the exploration of materials with large saturation magnetization and potentially low magnetic damping. The successful quantitative reproduction of experimental results using macrospin models and the extraction of a coupling constant comparable to or exceeding previous reports in Ni films suggest that SAFs are a viable and effective medium for on-chip cavity magnomechanics. This work establishes a foundation for developing quantum technologies that rely on strong magnon-phonon interactions without the constraints of low-magnetization materials.