Spin waves and high-frequency response in layered superconductors with helical magnetic structure

We evaluate the spin-wave spectrum and dynamic susceptibility in a layered superconductors with helical interlayer magnetic structure. We especially focus on the structure in which the moments rotate 90$^{\circ}$ from layer to layer realized in the iron pnictide RbEuFe$_{4}$As$_{4}$. The spin-wave spectrum in superconductors is strongly renormalized due to the long-range electromagnetic interactions between the oscillating magnetic moments. This leads to strong enhancement of the frequency of the mode coupled with uniform field and this enhancement exists only within a narrow range of the c-axis wave vectors of the order of the inverse London penetration depth. The key feature of materials like RbEuFe$_{4}$As$_{4}$ is that this uniform mode corresponds to the maximum frequency of the spin-wave spectrum with respect to c-axis wave vector. As a consequence, the high-frequency surface resistance acquires a very distinct asymmetric feature spreading between the bare and renormalized frequencies. We also consider excitation of spin waves with Josephson effect in a tunneling contact between helical-magnetic and conventional superconductors and study the interplay between the spin-wave features and geometrical cavity resonances in the current-voltage characteristics.