A magnetic skyrmion is a topological object consisting of a skyrmion core, an outer domain, and a wall that separates the skyrmion core from the outer domain. The skyrmion size and wall width are two fundamental quantities of a skyrmion that depend sensitively on material parameters such as exchange energy, magnetic anisotropy, Dzyaloshinskii–Moriya interaction, and magnetic field. However, quantitative understanding of the two quantities is still very poor. Here we present a general theory on skyrmion size and wall width. The two formulas we obtained agree almost perfectly with simulations and experiments for a wide range of parameters, including most of the existing materials that support skyrmions.

We show that parity-time ($\mathcal{P}\mathcal{T}$) symmetry can be spontaneously broken in the recently reported energy level attraction of magnons and cavity photons. In the $\mathcal{P}\mathcal{T}$-broken phase, the magnon and photon form a high-fidelity Bell state with maximum entanglement. This entanglement is steady and robust against the perturbation of the environment, which is in contrast to the general wisdom that expects instability of the hybridized state when the symmetry is broken. This anomaly is further understood by the compete of non-Hermitian evolution and particle number conservation of the hybrid system. As a comparison, neither $\mathcal{P}\mathcal{T}$-symmetry breaking nor steady magnon-photon entanglement is observed inside the normal level repulsion case. Our results may open an exciting window to utilize magnon-photon entanglement as a resource for quantum information science.

An optical frequency comb consists of a set of discrete and equally spaced frequencies and has found wide applications in the synthesis over a broad range of spectral frequencies of electromagnetic waves and precise optical frequency metrology. Despite the analogies between magnons and photons in many aspects, the analog of an optical frequency comb in magnonic systems has not been reported. Here, we theoretically study the magnon-skyrmion interaction and find that a magnonic frequency comb (MFC) can be generated above a threshold driving amplitude, where the nonlinear scattering process involving three magnons prevails. The mode spacing of the MFC is equal to the breathing-mode frequency of the skyrmion and is thus tunable by either electric or magnetic means. The theoretical prediction is verified by micromagnetic simulations, and the essential physics can be generalized to a large class of magnetic solitons. Our findings open a new pathway to observe frequency comb structures in magnonic devices that may inspire the study of fundamental nonlinear physics in spintronic platforms in the future.

The new field of spin cavitronics focuses on the interaction between the magnon excitation of a magnetic element and the electromagnetic wave in a microwave cavity. In the strong interaction regime, such an interaction usually gives rise to the level anticrossing for the magnonic and the electromagnetic mode. Recently, the attractive level crossing has been observed, and it is explained by a non-Hermitian model Hamiltonian. However, the mechanism of such attractive coupling is still unclear. We reveal the secret by using a simple model with two harmonic oscillators coupled to a third oscillator with large dissipation. We further identify this dissipative third party as the invisible cavity mode with large leakage in cavity-magnon experiments. This understanding enables one to design dissipative coupling in all sorts of coupled systems.

Magnon-photon coupling inside a cavity has been experimentally realized and has attracted significant attention for its potential docking with quantum information science. Whether this coupling implies the steady entanglement of photons and magnons is crucial for its usage in quantum information but is still an open question. Here we study the entanglement properties among magnons and photons in an antiferromagnet-light system and find that the entanglement between a magnon and a photon is nearly zero, while the magnon-magnon entanglement is very strong and can be even further enhanced through the coupling with the cavity photons. The maximum enhancement occurs when the antiferromagnet is resonant with the light. The essential physics can be well understood within the picture of cavity-induced cooling of the magnon-magnon state near its joint vacuum with stronger entanglement. Our findings can be used to cool magnetic magnons toward their ground state and may also be significant to extend the cavity spintronics to quantum manipulation. Furthermore, the hybrid antiferromagnet-light system provides a natural platform to manipulate the deep strong correlations of continuous modes with a generic stable condition and easy tunability.