Cavity based sensing of antiferromagnetic canting and nonzero-momentum spin waves in a van der Waals cavity-magnon-polariton system

TL;DR

This work demonstrates field-tunable cavity-magnon coupling in a CrCl$_3$ van der Waals antiferromagnet coupled to a NbN CPW cavity, revealing nonmonotonic coupling for acoustic and optical AFMR modes and a spin-flop–driven dispersive enhancement near the spin-flop field. By deriving a two-sublattice AFM Hamiltonian and employing input-output theory, the authors fit the field-dependent mode dispersions and extract the coupling strengths $g_{c\alpha}(H)$ and $g_{c\beta}(H)$, while showing that standing spin waves with $k\neq 0$ largely decouple from the cavity. The coexistence of resonant AFMR-cavity interactions with non-interacting SSW channels suggests a route to low-loss information transfer in hybrid devices and illustrates how magnetic phase transitions shape magnon-photon coupling in a layered, van der Waals AFM. These results provide fundamental insight into spin dynamics under field reorientation and lay groundwork for tunable quantum magnonics using two-sublattice antiferromagnets like CrCl$_3$.

Abstract

Cavity-magnon-polaritons are hybrid excitations from the interaction between cavity photons and magnons, the quanta of collective spin oscillations. Along with the tunability of the magnon-photon coupling strength, fast information transfer and conversion speed are desired in hybrid devices. This can be achieved utilizing the propagating nature of spin waves with non-zero momentum for their ultra-fast time dynamics and reduced ohmic dissipation. Antiferromagnets are particularly interesting as hosts for magnons since stray-field interactions are minimized, and they support multiple modes with distinctive magnetic-field behavior across the phase diagram. CrCl3 is a van der Waals antiferromagnet having a strong easy-plane anisotropy and a weak in-plane easy-axis anisotropy. Despite some magnetic resonance studies, the impact of magnetic reorientation of spins in CrCl3 on cavity-magnon-polariton interaction strength as a function of magnetic field remains largely unexplored. In this study, we investigate the coupling between magnons in CrCl3 and photons in a coplanar waveguide resonator as a function of magnetic field. In particular, we find that the magnon-photon coupling strength varies nonmonotonically and distinctly with the magnetic field for both acoustic and optical magnons, enabling tuning of the coupling strength with an external magnetic field as a knob. We find the signature of spin-flop transition in two harmonics of the cavity due to a stronger dispersive coupling between optical magnons and cavity photons at lower fields. Additionally, we find standing modes formed by spin waves with nonzero momentum associated with the two hybrid magnons when the external field is applied at an angle with the crystal plane. These modes do not undergo substantial coupling with the cavity mode unlike the antiferromagnetic modes and can be used as low-loss propagation channels in hybrid devices.

Figures (8)

• Figure 1: (a) Schematic showing CrCl$_3$ crystal placed on a single-port NbN CPW resonator for measuring magnon-photon coupling in reflected signal. (b) Schematic showing van der Waals stacking of atomic layers in CrCl$_3$ along with out-of-plane hard axis and in-plane easy axis. The spacing between the first two layer have been exaggerated to show the oppositely oriented spins in adjacent layers due to inter-planar antiferromagnetic exchange. Standing spin wave (SSW) modes formed across the thickness of the crystal are schematically shown in green lines. (c) Schematic showing the spin-flop transition governing the transformation of adjacent sublattice moments from antiferromagnetic to canted orientation, and the transition at higher field from canted to a collinear ferromagnet-like alignment.
• Figure 2: (a) Field derivative of transmission spectra of CrCl$_3$ on a transmission line as a function of frequency and in-plane magnetic field applied in an orientation shown in the inset (color-bar shows $\frac{d}{dB} |S_{21}|^{2}$ ranging from -40 to +30 dB/T). The acoustic (linear) and the optical (quadratic) AFMR modes are visible. The insets show a timelapse sketch of the orientation and the resultant moment of the two sublattice moments for the corresponding modes (indicated by dashed lines). (b) Field derivative of reflection spectra of CrCl$_3$ on a CPW resonator as a function of frequency and magnetic field (colorbar shows $\frac{d}{dB} |S_{11}|^{2}$ ranging from -40 to +30 dB/T) for a similar field orientation, shown in the inset. Two avoided crossings for coupling of the lower harmonic of the cavity with the acoustic and optical AFMR modes are visible around 5 GHz, and one avoided crossing for coupling of the upper harmonic of the cavity with the FMR mode is visible around 10 GHz following the transition of CrCl$_3$ into collinear FM-like state. (c) The regions marked by a blue and a green dashed rectangle in (b) have been enlarged to show the opposite-ward bend of the lower and the upper cavity mode around 40 mT (colorbar ranges from -100 to +100 dB/T here).
• Figure 3: (a) Magnetic field dependence of frequencies of the optical and the acoustic AFMR modes as calculated using the TSL AF model. (b) Magnetic field dependence of the magnon-photon coupling strengths of the optical and the acoustic AFMR modes with the cavity mode calculated using the TSL AF model and using fit parameters from the fit to the mode dispersion. (c) Reflection coefficient of the full cavity antiferromagnet system calculated from the input-output theory using the field dependencies of the frequency and coupling strength as shown in (a) and (b) (colorbar ranges from -25 to 0 dB) (inset: fit to the mode dispersion using the TSL AF model described in the text).
• Figure 4: (a) Variation of the field derivative of the reflection coefficient $\frac{d}{dB} \abs{S_{11}}^{2} (f)$ with magnetic field for the CrCl$_{3}$ on the CPW resonator when the magnetic field is applied at an angle of 55$\degree$ with the device plane (colorbar ranges from -85 to +65 dB/T). (b) and (c) Zoomed plots showing the field dispersion near the positions of the upper and the lower hybrid AFMR modes formed due to hybridization of the optical and the acoustic magnons (colorbars range from -30 to +25 dB/T). These plots show the multiplicity of SSW modes which does not couple with the cavity mode. The gray dashed lines correspond to the field dispersions of the two hybrid antiferromagnetic modes for a sample with a CrCl$_{3}$ placed on a CPW transmission line and magnetic field applied at a similar 55$\degree$ angle.
• Figure S1: Reflection coefficient, $|S_{11}|^{2}$, expressed in dB, of the full cavity antiferromagnet system calculated from the input-output theory using only the field dependent frequency dispersion as shown in Fig. 3 (a) of the main text and with coupling strengths $g_{\alpha}=0.37$ GHz and $g_{\beta}=0.57$ GHz (the colorbars range from -25 to 0 dB).