1. INTRODUCTION

Over the last few years, cavity magnonics has increasingly demonstrated significant advantages in fundamental and applied research [1–4], and it is anticipated to be a vital part of hybrid quantum systems [5] and quantum network nodes [6]. The most common physical realization of a cavity magnonic system is a microwave cavity and ferromagnetic material, such as a yttrium iron garnet (YIG) sphere, which has drawn extensive research and experienced amazing performance in recent decades. So far, insights from experimental and theoretical research based on cavity magnonics have revealed a number of phenomena, including magnon dark modes [7], magnon-induced transparency (MIT) [8], entanglement as a resource of quantum technologies including quantum computing [9,10], quantum teleportation [11], and quantum metrology [12,13], non-Hermitian physics [14–16], and nonclassical states [17–19]. Recently, researchers examined the parity-time (PT)-symmetric magnon laser as well as investigated the threshold along with controllability features [20]. Furthermore, through varying the intensity for the applied magnetic field, the frequency for a magnon laser can be continuously modified in a frequency range of approximately 1–10 GHz, liable to the achievable frequency of the Kittel magnon mode permitted in the ferrimagnet YIG sphere within the experimental reach of current technology [20]. In the context of one of the most recent schemes, the dynamical development of the cavity optomagnonic system within the time domain and the comb structure in its frequency domain, specifically, nonperturbation features, are described in detail [21].

Hybrid quantum systems include microwave photon interaction with magnons via magnetic dipole interaction in cavity magnonic systems [19,22,23], radiation pressure interactions in optomechanical systems [24,25], magnetostrictive interactions in cavity magnomechanical systems [26], and other systems involving parametric amplifiers [27,28]. These nonlinear interactions are weak and challenging to detect in certain systems, but they can become strong enough to be the dominant factor in others. The cross-Kerr effect, for example, is one of the complex nonlinear interactions between fields and waves that can occur in superconducting circuits [29,30], natural ions [31], and atoms [32,33]. The cross-Kerr effect is a nonlinear change in the frequency of a resonator as a function of the number of excitations in another mode that engages the resonator. Another nonlinear effect arising from magnetocrystalline anisotropy in a YIG sample is self-Kerr nonlinearity [19,22], which is typically weak [34] but can be amplified by driving the corresponding spin–wave modes with a drive field. Thus, having an understanding of these nonlinear interactions is not only of fundamental significance, but also useful in a number of different applications. For example, the cross-Kerr effect can be used to construct quantum logic gates [35,36], perform quantum non-demolition measurements [37,38], and generate entangled photons [39]. Recently, a three-mode cavity magnonics system was used to investigate nonreciprocal microwave transmission using both the combined mechanisms of phase modulation and the magnon Kerr nonlinear phenomenon [40].

Motivated by new advancements in hybrid magnomechanical systems, we construct a cavity magnonics system composed of a ferromagnetic material that supports both Kittle and magnetostatic (MS) modes. The goal is to investigate the consequences of nonlinear cross- and self-Kerr interaction on the MIT phenomenon caused by destructive interference of optical fields inside the cavity, where the magnon Kerr effect is caused by magnetocrystalline anisotropy in the YIG sphere. We observe a single-MIT window due to cavity field interaction with the Kittle mode, which then splits into two windows when the Kittle mode interacts with the MS mode, which incorporates another degree of freedom. We explore the self-Kerr effect of both spin modes, specifically, Kittle and MS modes, and notice that the self-Kerr effect of the Kittle mode is responsible for the asymmetric behavior of the absorption profile, whereas the self-Kerr effect of the MS mode splits the single-MIT window into two. Furthermore, the slow and fast light effects are examined in the vicinity of two MIT windows for various control parameter values, namely, the cavity–Kittle mode and cross-Kerr coupling parameter. We report both slow and fast light effects in a single setup, which is an advantage of the proposed scheme over previous work that demonstrated only slow [41–43] or fast [44] light propagation.

The paper is arranged as follows. In Section 2, we present a theoretical model of a general cavity magnonic system consisting a YIG sphere and introduce the effective Hamiltonian for the proposed system. To investigate the dynamics of the system, quantum Langevin equations (QLEs) are derived and then used to deduce a mathematical formula for the outgoing probe field obtained by employing the standard input–output method. In Section 3, numerical results are provided to illustrate the realization and control of single-to-double MIT window profiles, investigate the impact of cross- and self-Kerr effects on the MIT phenomenon, and demonstrate a mechanism for switching from slow to fast light. Finally, we end our work with conclusions in Section 4.

2. MODEL AND EQUATION OF MOTION

We consider the cavity magnonic system illustrated in Fig. 1, where a small YIG sphere is coupled to a rectangular microwave cavity via the magnetic field of the cavity mode [4,45,46]. The principal reason is that YIGs have relatively high spin densities (${\sim}4.22 \times {10^{27}}\;{{\rm m}^{- 3}}$) and low damping rates (${\sim}1\;{\rm MHz}$), which are necessary for generating strong coupling [47,48] between the microwave cavity photon mode and the YIG’s magnon mode. In the YIG sphere, substantial magnons are usually generated by applying a drive field. The magnons in a small YIG sphere are strongly but dispersively coupled to microwave photons in a cavity. When significant magnons are produced by pumping the YIG sphere, the Kerr effect causes a shift in the cavity’s central frequency, resulting in more noticeable shifts of the magnon modes, including the Kittel mode [49], which has homogeneous magnetization, and MS modes [50,51], which have inhomogeneous magnetization. The two modes are both supported by the collective spin motion and coupled with cavity modes via magnetic dipole interaction. Also, spin moments contribute to the spin uniform precession mode (Kittle mode), which results in a significant dipole moment. As a result, the couplings between the Kittel mode and other electromagnetic fields are usually strong. However, fewer spin moments contribute to the dipole of the MS mode, so the coupling between the MS mode and cavity mode is weak in cavity magnonics [52].

 

Fig. 1. (a) Sketch of a cavity magnonics system consisting of a YIG sphere mounted on a copper cavity and placed in a bias magnetic field polarized along the $z$ direction. Here, ${\omega _d}$ is the driving field frequency. The Kittle and magnetostatic (MS) modes are the two spin–wave modes of the YIG sphere. (b) Schematic diagram showing the coupling of cavity mode with Kittle and MS modes, where ${{g}_{\textit{ab}}}$, ${{g}_{\textit{ac}}}$, ${{g}_{\textit{bc}}}$ are coupling parameters. ${{\cal X}_b}$ and ${{\cal X}_c}$ are the Kittle and MS modes’ self-Kerr coefficients, while ${\kappa _a}$, ${\gamma _b}$, ${\gamma _c}$ represent the dissipation rates associated with cavity, Kittle, and MS modes, respectively.

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After using the dipole and rotating wave approximations, the effective Hamiltonian of the proposed cavity magnonic system can be written as

To investigate the dynamics of the proposed system, we deploy the Heisenberg–Langevin approach [54] to derive the following system of operator coupled differential equations, the well-known QLEs:

To solve the differential equation system Eq. (7), we make use of the following ansatz [56,57]:

Next, to study the characteristic spectra of the probe field, we deploy the standard input–output relation for the cavity field ${{\cal E}_{{\rm out}}} = {{\cal E}_{{\rm in}}} - 2{\kappa _a}a$ [54,58]; the amplitude of the outfield can be written as

After presenting the theoretical model of the proposed cavity magnonic system, including its dynamical equations of motion, and a linearized reduced version of these equations (linearized QLEs), we move next to a presentation of our key findings corroborated by various discussions of the system.

3. RESULTS AND DISCUSSION

In this section, we present the main findings obtained by our model of the proposed cavity magnonic system composed of a YIG sphere placed inside the microcavity. To perform the numerical calculations, we have opted for a choice of relevant empirical parameters based on recent experimental works [14,53]. All parameters are normalized with respect to $\omega = 2\pi \times 18.6$ MHz. The remaining parameters are ${\kappa _a} = 0.78\omega$, ${\gamma _b} = 0.13\omega$, ${\gamma _c} = 0.25\omega$, ${\Delta _a} = 0.53\omega$, $\Delta _b^\prime = - 0.07\omega$, $\Delta _c^\prime = - 0.27\omega$, ${G_{\textit{ab}}} = 2.15\omega$, ${G_{\textit{bc}}} = 0.53\omega$, ${{\cal X}_b} = 0.07\omega$, and ${{\cal X}_c} = 0.16\omega$. In what follows, we provide results pertinent to observation of MIT and the associated dynamics of group delay obtained by properly adjusting the values of the relevant experimentally accessible control parameters.

A. Effect of Coupling Strengths on Transmission of Output Probe Field

Here, we examine the absorption and transmission of an outgoing probe field. The properties of the outgoing probe field are obtained by calculating Eqs. (11) and (12), where the real component shows how much probe light is absorbed in a cavity at resonance and how much is transmitted, which leads to the MIT phenomenon. Also, imaginary components represent the probe field’s dispersion. Figure 2 displays the absorption ${u_p}$ and dispersion ${v_p}$ profiles of the outgoing probe field displayed as functions of normalized optical detuning ${\Delta _p}/\omega$, where the absorption and dispersion profiles are represented by red solid and blue dashed curves, respectively. These results have been obtained under different choices of the cavity–Kittle mode coupling strength ${G_{\textit{ab}}}$ and magnon–magnon mode coupling strength ${G_{\textit{bc}}}$ parameters (cross-Kerr coefficient).

 

Fig. 2. Absorption ${u_p}$ and dispersion ${v_p}$ of the probe field displayed versus normalized optical detuning ${\Delta _p}/\omega$: (a) ${G_{\textit{ab}}} = {G_{\textit{bc}}} = 0$, (b) ${G_{\textit{ab}}} = 2.1\omega$, ${G_{\textit{bc}}} = 0$, (c) ${G_{\textit{ab}}} = 0$, ${G_{\textit{bc}}} = 0.5\omega$, and (d) ${G_{\textit{ab}}} = 2.1\omega$, ${G_{\textit{bc}}} = 0.5\omega$. The remaining parameters are the same as in Section 3.

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First, we consider the scenario where both coupling strengths are zero, i.e., ${G_{\textit{ab}}} = {G_{\textit{bc}}} = 0$, as illustrated in Fig. 2(a). In this instance, the probe field and cavity modes become resonant at a certain frequency, and there is an absorption peak for the spectrum. Indeed, from a basic physical viewpoint, when there is no interaction between the cavity mode and any magnon mode, there is no quantum interference between fields, and hence the applied probe field is resonant with cavity modes, which leads to resonance absorption. This is in accordance with a previous study of an optomechanical system with an empty cavity [59].

In the second scenario, i.e., for ${G_{\textit{ab}}} = 2.1\omega$ and ${G_{\textit{bc}}} = 0$, the cavity mode is coupled with only the Kittle mode, while the latter is no longer coupled with the MS mode. In such case, we observe a single-MIT window within the two absorption profiles; see Fig. 2(b). The MIT window between the two absorption profiles is formed as a result of destructive interference between the interacting fields, with a transparency width that can be enhanced by increasing the amplitude of ${G_{\textit{ab}}}$. Next, we analyze a different scenario in which the cavity–Kittle mode coupling strength is set equal to zero $({G_{\textit{ab}}} = 0)$, but the cross-Kerr coefficient is maintained at the nonzero value ${G_{\textit{bc}}} = 0.5\omega$. Again, as in the previous case of Fig. 2(a), we observe a single absorption peak while the MIT window is found to have vanished; see Fig. 2(c). This is expected since in the absence of a cavity field, interference phenomena cannot take place, and hence MIT windows are not forthcoming. Furthermore, as shown in Fig. 2(d), for nonzero values of both coupling strengths, namely, ${G_{\textit{ab}}} = 2.1\omega$ and ${G_{\textit{bc}}} = 0.5\omega$, we report a double-MIT window and a sharp absorption peak profile. In other words, the MIT single window depicted in Fig. 2(b) is split into a double-window profile by exploiting the extra degree of freedom added to the system. Moreover, the corresponding dispersion profile is illustrated by the blue dashed curves in Figs. 2(a)–2(d). It illustrates how within a regime dominated by quantum interference, the coupling strength changes the dispersive behavior from anomalous to normal. Next, we investigate how the coupling strength of the cavity–Kittle mode impacts the profiles of the MIT windows. Prior results showed that the coupling constant ${G_{\textit{ab}}}$ induces a single-MIT window in the absence of a cross-Kerr coefficient [see Fig. 2(b)], which then splits into a two-window profile if the cross-Kerr coefficient is also considered; see Fig. 2(d).

Figure 3 depicts the absorption and dispersion profiles of the outgoing probe field plotted as a function of optical detuning for various values of cavity–Kittle mode coupling strength. For ${G_{\textit{ab}}} = 2.08\omega$, we observe a double-MIT profile whose two windows are separated by a high absorption peak realized with $\delta \lt \omega$; see Fig. 3(a). Moreover, by increasing the magnitude of the cavity–Kittle mode coupling strength one can further reduce the amplitude of the middle absorption peak without affecting the magnitudes of the other two absorption symmetric peaks; see the example given in Figs. 3(b)–3(d). This suggests that increasing the cavity–Kittle mode interaction strength reduces the magnitude of the absorption peak, with the ability to reach a threshold after which any further increase in this control parameter may transform double-MIT windows into a single window. Since we have previously demonstrated that in the presence of a cross-Kerr coefficient, a double-MIT window profile can be obtained, it follows that under the condition ${G_{\textit{ab}}} \gg {G_{\textit{bc}}}$, the effect of the cross-Kerr coefficient is suppressed, and hence we may obtain a single-MIT window profile. (Note that the dispersion profile in the figure is represented in each panel by a blue dashed line with a small kink-like peak at $\delta \approx 0$, which is not visible due to scaling.)

 

Fig. 3. Absorption ${u_p}$ and dispersion ${v_p}$ of the probe field versus normalized optical detuning ${\Delta _p}/\omega$: (a) ${G_{\textit{ab}}} = 2.08\omega$, (b) ${G_{\textit{ab}}} = 2.10\omega$, (c) ${G_{\textit{ab}}} = 2.12\omega$, and (d) ${G_{\textit{ab}}} = 2.14\omega$. The remaining parameters are as in Fig. 2.

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Furthermore, we analyze the effect of the cross-Kerr coefficient on the outgoing probe field. Figure 4 displays the absorption ${u_p}$ and dispersion ${v_p}$ spectra of the probe field computed as a function of the optical detuning parameter ${\Delta _p}/\omega$. In this case, we obtained results for various cross-Kerr coefficient ${G_{\textit{bc}}}$ values under constant cavity–Kittle mode coupling strength ${G_{\textit{ab}}} = 2.15\omega$. Recall that in the earlier results, we already demonstrated that in the absence of a cross-Kerr coefficient, a single-MIT window [see Fig. 2(b)] can be observed, which then splits into double-MIT windows for a nonzero value of the cross-Kerr coefficient, as shown in Fig. 2(d). Here, we provide additional analysis of the process for changes in the probe field properties caused by increasing the cross-Kerr coefficient value. The results obtained by our model show that as the value of the cross-Kerr coefficient ${G_{\textit{bc}}}$ is increased, the double-MIT profile windows and the absorption profile peaks become more visible and sharply distinguishable; see Fig. 4. Thus, we highlight the potential of utilizing proper values for cross-Kerr coefficients to achieve the double-MIT profile phenomenon as noted above. In addition, the corresponding results of the dispersion profile of the outgoing probe field are shown in each panel of Fig. 4.

 

Fig. 4. Absorption ${u_p}$ and dispersion ${v_p}$ of the probe field versus normalized optical detuning ${\Delta _p}/\omega$: (a) ${G_{\textit{bc}}} = 0.45\omega$, (b) ${G_{\textit{bc}}} = 0.48\omega$, (c) ${G_{\textit{bc}}} = 0.51\omega$, and (d) ${G_{\textit{bc}}} = 0.54\omega$. The remaining parameters are as in Fig. 2.

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To recap the results of this subsection, the absorption and dispersion spectra of the probe field were illustrated, and the single-to-double MIT windows and absorption profiles were found to be realizable by proper tuning of relevant control parameters, specifically, the cavity–Kittle modes and cross-Kerr coefficients. We observed that for a large value of the cavity–Kittle mode coupling constant, the cross-Kerr effects are suppressed, and the double-MIT window profile is switched to a single-MIT window profile, after which the effect of self-Kerr coefficients on the MIT windows and absorption peaks were investigated.

B. Effect of Self-Kerr Coefficients on Magnon-Induced Transparency

In this subsection, we investigate the impact of the self-Kerr coefficient on the MIT and absorption phenomena. Figure 5 depicts the absorption profile ${u_p}$ of the outgoing probe field plotted as a function of normalized optical detuning ${\Delta _p}/\omega$ for different values of the self-Kerr coefficient of Kittle mode ${{\cal X}_b} = {\Delta _p}/\omega$ (red solid curve), ${{\cal X}_b} = 0.08\omega$ (blue dotted curve), and ${{\cal X}_b} = 0.16\omega$ (green dashed curve), while the self-Kerr coefficient of the MS mode remains fixed, i.e., ${{\cal X}_c} = 0.16\omega$. For ${{\cal X}_b} = 0$, we observe the profile of double-MIT windows separated by high absorption peaks. The absorption peaks show asymmetric behavior. A further increase in the self-Kerr coefficient of the Kittle mode can reduce the amplitude of the absorption peaks that separate the double-MIT windows while also causing an enhancement of the asymmetric behavior of the other two absorption peaks. The inset in Fig. 5 displays the enhanced estimation of the absorption profile of the probe field against the various values of the self-Kerr coefficient of the Kittle mode. Therefore, in this case the self-Kerr coefficient of the Kittle mode can influence only the asymmetric behavior of the absorption profile of the outgoing probe field with no impact on the amplitude of the MIT windows.

 

Fig. 5. Absorption ${u_p}$ profile of the probe field versus normalized optical detuning ${\Delta _p}/\omega$ for: ${{\cal X}_b} = 0$ (red solid curve), ${{\cal X}_b} = 0.08\omega$ (blue dotted curve), and ${{\cal X}_b} = 0.16\omega$ (green dashed curve). The inset shows a broader view of the absorption profile of the outgoing probe field. The additional parameters are the same as in Fig. 2.

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Next, we investigate how changing the self-Kerr coefficient of the MS mode can modify the MIT and absorption peak profiles. Figure 6 depicts the absorption profile ${u_p}$ of the outgoing probe field plotted as a function of normalized optical detuning ${\Delta _p}/\omega$ for different values of the self-Kerr coefficient of the MS mode. The results are shown for ${{\cal X}_c} = 0$ (red solid curve), ${{\cal X}_c} = 0.14\omega$ (blue dotted curve), and ${{\cal X}_c} = 0.16\omega$ (green dashed curve), whereas the self-Kerr coefficient of the Kittle mode is kept fixed at ${{\cal X}_b} = 0.07\omega$. The results illustrate that the absorption profile of the outgoing probe field displays a wider single-MIT window in the absence of self-Kerr coefficients of MS modes, i.e., ${{\cal X}_c} = 0$. However, by increasing the value of ${{\cal X}_c}$, each single-MIT profile windows split into a double window. Further increase in this control parameter may result in a more enhanced visibility of the double-MIT window profile, a behavior illustrated in the inset of Fig. 6. Thus, the self-Kerr coefficient of the MS mode provides a new degree of freedom capable of splitting single-MIT window profiles into double-window profiles.

 

Fig. 6. Absorption ${u_p}$ profile of the probe field versus normalized optical detuning ${\Delta _p}/\omega$ for: ${{\cal X}_c} = 0$ (red solid curve), ${{\cal X}_c} = 0.14\omega$ (blue dotted curve), and ${{\cal X}_c} = 0.16\omega$ (green dashed curve). The inset depicts a broader view of the absorption profile of the probe field. The remaining parameters are as in Fig. 2.

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To summarize, in this subsection, we examined the impact of the self-Kerr coefficients of both spin modes on the MIT and absorption spectra, where it was demonstrated that the self-Kerr coefficient of the Kittle mode is capable of modifying the asymmetric behavior of the absorption profile, whereas the self-Kerr coefficient of the MS mode is responsible for splitting the single-MIT into two distinct windows. Thus, investigating the impact of self-Kerr coefficients of Kittle and MS modes on MIT window profiles is significant for the correct interpretation of interference phenomena in cavity magnonics. In the following subsection, we explore the propagation of the group delay of the outgoing probe field, which exhibits slow and fast light phenomena.

 

Fig. 7. Group delay ${\tau _{g}}$ versus normalized optical detuning ${\Delta _p}/\omega$ for: (a) ${G_{{ab}}} = 1.88\omega$ (red solid curve), ${G_{{ ab}}} = 2.04\omega$ (blue dotted curve), and ${G_{{ ab}}} = 2.15\omega$ (green dashed curve); (b) ${G_{{ bc}}} = 0.43\omega$ (red solid curve), ${G_{{ bc}}} = 0.48\omega$ (blue dotted curve), and ${G_{{bc}}} = 0.53\omega$ (green dashed curve), where ${G_{{ ab}}}$ and ${G_{{bc}}}$ are coupling constants corresponding to cavity–Kittle modes and magnon–magnon modes, respectively. The region ${\tau _{g}} \lt 0$ enclosed by a circle signifies the fast light regime, whereas the two pointed peaks represent the slow light scenario. The remaining parameters are the same as in Fig. 2.

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C. Dynamics of Slow and Fast Light

The phenomena of slow and fast light have been observed in atomic vapors and solid-state materials using a number of techniques. Controlling the group velocity of light pulses to cause very slow or very fast propagation is one prominent application of these approaches [60,61]. For instance, processes of electromagnetically induced transparency (EIT) in atomic vapors or Bose–Einstein condensate were employed in slow light studies [62,63]. Hau et al. presented an experimental demonstration of EIT in an ultracold sodium atom gas, where optical pulses move at a speed 20 million times slower than the speed of light in a vacuum. Aside from slow light, fast light was reported in atomic cesium gas and a silicon microphotonic device [64]. Afterwards, Safavi-Naeini et al. demonstrated the ability of designed photon–phonon interactions to control the velocity of light while also exhibiting EIT and programmable optical delays in a nanoscale optomechanical crystal [65]. Therefore, it is of natural interest to investigate whether there is a viable physical configuration capable of switching from slow to fast light or vice versa. In the following, we present a cavity magnonics system wherein we investigate the propagation of group delay and address switching from slow to fast light within a single configuration.

The results for slow and fast light were obtained by using the mathematical expression for group delay: Eq. (14). Figure 7 illustrates the propagation of group delay ${\tau _{g}}$ plotted as a function of normalized optical detuning ${\Delta _p}/\omega$ for different values of: (a) ${G_{{ab}}} = \{1.88\omega , 2.04\omega , 2.15\omega \}$ and (b) ${G_{{bc}}} = \{0.43\omega , 0.48\omega , 0.53\omega \}$, where ${G_{{ab}}}$ and ${G_{{bc}}}$ denote the cavity–Kittle mode coupling strength and cross-Kerr coefficient, respectively. Here, we demonstrate the results of the group delay in the region where the double-MIT window profiles exist. As can be seen from Figs. 3 and 4, both MIT window dips occur on the left of the optical detuning, i.e., ${\Delta _p}/\omega \lt 0$, because we employ off-detuning values of the effective detuning values of Kittle and MS modes, i.e., $\Delta _b^\prime = - 0.07\omega$, $\Delta _c^\prime = - 0.27\omega$. Initially, we present the results of group delay versus optical detuning for various values of the cavity–Kittle mode coupling constant ${G_{{ ab}}}$; see Fig. 7. The results also show that increasing the cavity–Kittle mode coupling constant reduces the amplitude of the dip at ${\Delta _{ p}} \approx 2.6\omega$. Because the group delay value at this point is negative, this corresponds to fast light. These findings are in line with the results given in Fig. 3, where the cavity–Kittle mode coupling constant lowers the absorption profile of the probe field and has an effect on the amplitude of MIT windows. Physically, the group delay is negative, indicating slow light during the MIT windows caused by destructive interference of fields and vice versa. To further investigate the impact of the cross-Kerr effect on the propagation of group delay, Fig. 7(b) shows the propagation of group delay versus optical detuning for different values of cross-Kerr coefficients ${G_{{ bc}}}$. The results are shown in the range of optical detuning where the two MIT windows exist, as demonstrated in Fig. 4. The group delay has two distinct peaks that represent slow light dynamics; however, the dip enclosed by a dashed circle represents fast light dynamics [because we noticed in previous results (see Fig. 4) that increasing the value of the cross-Kerr coefficient changes the absorption profile of the probe field], hence illustrating the slow and fast light effects in the two MIT windows profiles. Therefore, the proposed scheme suggests a mechanism for switching from slow to fast light in a single configuration.

4. CONCLUSIONS

We investigated various optomechanical nonlinear effects involving cross- and self-Kerr interactions in a cavity magnonics system composed of a microcavity and a ferromagnetic material (YIG sphere) that exhibits both Kittle and MS modes. Based on our analytical and numerical results, we observed MIT and magnon-induced absorption caused by quantum interference of optical fields inside a cavity. The impact of coupling parameters such as cavity–Kittle modes and magnon–magnon modes (cross-Kerr effect) is investigated. In addition, we explained how to properly adjust these parameters to achieve single-to-double MIT windows. Furthermore, it was established that the self-Kerr effect of both Kittle and MS modes can alter the MIT and absorption phenomena, with the self-Kerr effect of Kittle mode causing asymmetric absorption behavior and the self-Kerr effect of MS mode splitting the single-MIT window into two distinct windows. The propagation of group delay was investigated in the vicinity of MIT windows. It was observed that increasing the cross-Kerr effect can help maintain slow light for a longer period of time. Our theoretical model could provide a new platform for studying nonlinear effects in cavity magnonics, which have applications in quantum memory [66], quantum entanglement [17], and quantum information processing.