Interplay of internal and external coupling phases in cavity magnonics: from level repulsion to attraction

Abstract

We experimentally validate a unified input--output model that incorporates internal and external coupling phases in a room-temperature cavity magnonic system. By explicitly accounting for phase effects, the model provides full control of interference-induced antiresonances and enables a clear interpretation of the transition from level repulsion to level attraction. Nonreciprocal transmission -- originating from internal phases -- is accurately reproduced under specific coupling conditions. Quantitative agreement between experiments and simulations is obtained across all coupling regimes, demonstrating a practical route toward phase-controlled cavity--magnon devices.

Figures (6)

• Figure 1: (a) Transmission of the dielectric-loaded cavity: Measurement in solid black line; and input-output model (between 3.3 to 15.7 GHz, with fit region indicated by dashed grey lines) with fitted external and intrinsic dissipation rates values in dashed red line. The measurement was conducted without a YIG sphere inside the cavity. (b) Frequency domain simulation of the transmission of the dielectric-loaded cavity with a dielectric width of 566 $\mu$m. The magnitude is depicted in blue, and the phase in red. The modes presenting the same $\Phi_{21}$ jump as the antiresonance at 11.46 GHz are illustrated in purple areas, while the modes presenting an opposite-phase as the antiresonance are illustrated in green areas. The dotted vertical red line indicates the measured antiresonance frequency. (c)-(f) depict the RF magnetic fields of the first four modes and the different YIG positions. Black arrows at the probe locations indicate the orientation of the RF field.
• Figure 2: Left panel -- repulsive coupling regime: (a) Measured transmission magnitude $S_{21}$, with the inset displaying the corresponding $S_{21}$ calculated using Eq. \ref{['Spara']} and the parameters summarized in Tab. \ref{['tab:coupling_res']}. The inset between (a) and (b) illustrates the position of the YIG sphere in the cavity. (b) and (c) show the measured and calculated isolation (ISO) parameters, defined as the difference between $S_{21}$ and $S_{12}$, respectively. The inset in (c) shows the internal coupling of each modes : TM$_{\bm{010}}$, TM$_{\bm{210}}$, TM$_{\bm{110}}$ and TM$_{\bm{310}}$. Right panel -- attractive coupling regime: (d)–(f) display the same measurements and calculations for Pos. 3, where the coupling becomes attractive.
• Figure 3: Coupling-regime transition. (a) $S_{21}$ and (b) ISO as a function of frequency and the YIG-sphere position, scanned from $-3.6$ to $-11.4$ mm ($0$ mm corresponding to the cavity center). The calculation is performed using our model for a fixed magnetic field of $0.4$ T (YIG resonance magnetic field). (c) Evolution of the coupling strengths $g_{u0}$ for the cavity modes. The yellow region between $-8.33$ and $-5.08$ mm corresponds to the response of an attractive regime of the system, denoted by [A], while the remaining region exhibits repulsive behavior [R]. The insets in (a) and (b) show $S_{21}$ and ISO for the YIG position located at $-11.4$, $-6.75$, and $-3.6$ mm. Note that the central inset in (b) shows the ISO variation with a scale from $-0.5$ to $0.5$ dB to enhance the contrast around the critical position.
• Figure 4: (a) Transmission of the dielectric-loaded cavity at different dielectric widths: FD simulation in solid black lines; input-output model with fitted $\gamma_{i0}$ values in dashed red lines; and input-output model with the mean over dielectric widths of the fitted $\gamma_{i0}$ values in dotted green line. (b)-(e) show the mode frequencies in blue and the fitted $\gamma_{i0}/2\pi$ values in orange versus the dielectric width for the first four modes. The mean values of $\gamma_{i0}/2\pi$ over the dielectric widths are represented by the dotted orange lines for each mode.
• Figure 5: Transmission spectra at the 6 YIG sphere positions, showing the magnitude for the input-output model in the first column, the measurements in the second column, and the phase of the measurements in the third column. The antiresonance polariton frequencies from the input-output transmission spectra are indicated by dotted black lines in the third column.