Coupling of microwave photons to optical and acoustic magnon modes in the layered antiferromagnetic insulator ${\mathrm{CrCl}}_3$

We study a magnon-photon coupling system consisting of a layered antiferromagnetic insulator ${\mathrm{CrCl}}_3$ and a planar superconducting cavity. By changing the position of the ${\mathrm{CrCl}}_3$ crystal on the cavity, we separately demonstrate the cavity mode coupled with an acoustic mode and an optical mode when the magnetic moments are in a spin-flop transition. Based on the coupled Landau-Lifshitz-Gilbert equations and Kirchhoff's equation, we predict that both the net magnetization and the Néel vector contribute to the coupling between the optical mode and cavity mode, and only the net magnetization participates in the coupling of the acoustic mode and cavity mode. This paper highlights the vital role played by the Néel vector as the key parameter of an antiferromagnet in magnon-photon coupling, which offers insight into designing antiferromagnet spintronic devices.

Figure 1

(a) X-ray diffraction pattern from the plane of a ${\mathrm{CrCl}}_3$ crystal. The platelike ${\mathrm{CrCl}}_3$ single crystals grown by chemical vapor transport are shown in the inset. (b) Crystal structure of ${\mathrm{CrCl}}_3$. (c) Magnetic structure of ${\mathrm{CrCl}}_3$ at zero magnetic field while below the Néel temperature.

Figure 2

(a) A schematic diagram for the experimental setup. The amplified portion shows the structure of the superconducting cavity. (b) The transmission spectra $|S_{21}|$ of the typical cavity mode without the sample. (c) The resonance frequency shifts with the external magnetic fields. The microwave magnetic field distributions of (d) $|h_x|$, (e) $|h_y|$, and (f) $|h_z|$ on the surface of a superconducting cavity.

Figure 3

Schematic diagrams of the magnetization procession for the (a) acoustic mode and (b) optical mode with the rectangular sample respectively placed on the side and on the top of the cavity. The transmission spectra mappings in the experiment for the (c) acoustic mode and (d) optical mode coupling with the cavity mode in the spin-flop transition. The corresponding theoretical results of the coupled systems for the (e) acoustic-cavity modes and (f) optical-cavity modes are calculated by Eq. (5).

Figure 4

Transmission spectra $|S_{21}|$ of (a) acoustic-cavity mode coupling and (b) optical-cavity mode coupling, respectively. Extracted (c) peak positions and (e) linewidth from the transmissions of the acoustic mode and cavity mode coupling system in (a). (d) Dispersion and (f) normalized linewidth of the optical-cavity modes. The solid lines in (c)–(f) correspond to the calculated results by Eq. (4).

Figure 5

Schematic diagrams used to separately measure the (a) acoustic mode and (b) optical mode, respectively. The transmission spectra mappings for the (c) acoustic mode and (d) optical mode.