The ultrastrong photon-to-magnon coupling is reached with an on-chip hybrid system using superconducting phenomena.

The interplay between superconductivity and magnetism is one of the oldest enigmas in physics. Usually, the strong exchange field of ferromagnet suppresses singlet superconductivity via the paramagnetic effect. In EuFe₂(As_0.79P_0.21)₂, a material that becomes not only superconducting at 24.2 K but also ferromagnetic below 19 K, the coexistence of the two antagonistic phenomena becomes possible because of the unusually weak exchange field produced by the Eu subsystem. We demonstrate experimentally and theoretically that when the ferromagnetism adds to superconductivity, the Meissner state becomes spontaneously inhomogeneous, characterized by a nanometer-scale striped domain structure. At yet lower temperature and without any externally applied magnetic field, the system locally generates quantum vortex-antivortex pairs and undergoes a phase transition into a domain vortex-antivortex state characterized by much larger domains and peculiar Turing-like patterns. We develop a quantitative theory of this phenomenon and put forth a new way to realize superconducting superlattices and control the vortex motion in ferromagnetic superconductors by tuning magnetic domains—unprecedented opportunity to consider for advanced superconducting hybrids.

In this work, ultrastrong photon-to-magnon coupling is demonstrated for on-chip multilayered superconductor-ferromagnet-insulator hybrid thin-film structures reaching a coupling strength above 6 GHz, coupling ratio about 0.6, single-spin coupling strength about 350 Hz, and cooperativity about ${10}^4$. Strong characteristics of coupling are achieved owing to a radical suppression of the photon phase velocity in an electromagnetic resonator. With achieved coupling, the spectrum reveals the inapplicability of the Dicke quantum model, and evidences a contribution of the diamagnetic $A^2$ interaction term in the Hamiltonian of the system, which satisfies the Thomas-Reiche-Kuhn sum rule. The contribution of the $A^2$ term denotes the validity of the Hopfield quantum model and manifests observation of a different hybrid polariton quasiparticle, namely the plasmon-magnon polariton.

In this work, magnetization dynamics is studied in superconductor-ferromagnet-superconductor three-layered films in a wide frequency, field, and temperature ranges using the broad-band ferromagnetic resonance measurement technique. It is shown that in the presence of both superconducting layers and of superconducting proximity at both superconductor-ferromagnet interfaces a massive shift of the ferromagnetic resonance to higher frequencies emerges. The phenomenon is robust and essentially long-range: it has been observed for a set of samples with the thickness of ferromagnetic layer in the range from tens up to hundreds of nanometers. The resonance frequency shift is characterized by proximity-induced magnetic anisotropies: by the positive in-plane uniaxial anisotropy and by the drop of magnetization. The shift and the corresponding uniaxial anisotropy grow with the thickness of the ferromagnetic layer. For instance, the anisotropy reaches 0.27 T in experiment for a sample with a 350-nm-thick ferromagnetic layer, and about 0.4 T in predictions, which makes it a ferromagnetic film structure with the highest anisotropy and the highest natural resonance frequency ever reported. Various scenarios for the superconductivity-induced magnetic anisotropy are discussed. As a result, the origin of the phenomenon remains unclear. Application of the proximity-induced anisotropies in superconducting magnonics is proposed as a way for manipulations with a spin-wave spectrum.

We consider adiabatic superconducting cells operating as an artificial neuron and synapse of a multilayer perceptron (MLP). Their compact circuits contain just one and two Josephson junctions, respectively. While the signal is represented as magnetic flux, the proposed cells are inherently nonlinear and close-to-linear magnetic flux transformers. The neuron is capable of providing the one-shot calculation of sigmoid and hyperbolic tangent activation functions most commonly used in MLP. The synapse features both positive and negative signal transfer coefficients in the range $\sim (-0.5,0.5)$ . We briefly discuss implementation issues and further steps toward the multilayer adiabatic superconducting artificial neural network, which promises to be a compact and the most energy-efficient implementation of MLP.

Vortices in quantum condensates exist owing to a macroscopic phase coherence. Here we show, both experimentally and theoretically, that a quantum vortex with a well-defined core can exist in a rather thick normal metal, proximized with a superconductor. Using scanning tunneling spectroscopy we reveal a proximity vortex lattice at the surface of 50 nm—thick Cu-layer deposited on Nb. We demonstrate that these vortices have regular round cores in the centers of which the proximity minigap vanishes. The cores are found to be significantly larger than the Abrikosov vortex cores in Nb, which is related to the effective coherence length in the proximity region. We develop a theoretical approach that provides a fully self-consistent picture of the evolution of the vortex with the distance from Cu/Nb interface, the interface impedance, applied magnetic field, and temperature. Our work opens a way for the accurate tuning of the superconducting properties of quantum hybrids.