Negative Refraction in Ferromagnet-Superconductor Superlattices

Negative refraction, which reverses many fundamental aspects of classical optics, can be obtained in systems with negative magnetic permeability and negative dielectric permittivity. This Letter documents an experimental realization of negative refraction at millimeter waves, finite magnetic fields, and cryogenic temperatures utilizing a multilayer stack of ferromagnetic and superconducting thin films. In the present case the superconducting ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_7$ layers provide negative permittivity while negative permeability is achieved via ferromagnetic $(\mathrm{La}:\mathrm{Sr}){\mathrm{MnO}}_3$ layers for frequencies and magnetic fields close to the ferromagnetic resonance. In these superlattices the refractive index can be switched between positive and negative regions using external magnetic field as tuning parameter.

Figure 1

Upper panel: magnetic susceptibility of the $\mathrm{LSMO}/\mathrm{YBCO}$ superlattice measured in the field-cooling (FC) and zero-field-cooling regime (ZFC). The inset shows schematically the composition of the sample. Lower panel: right scale: resistivity of the superlattices at a frequency of 90 GHz. Left scale: superconducting penetration depth. Dashed lines indicate the transition temperatures between different phases, SC: superconducting; M: metallic; FM: ferromagnetic; and PM: paramagnetic.

Figure 2

Magnetic field dependence of the transmittance (upper panel) and the phase shift (lower panel) of the $\mathrm{LSMO}/\mathrm{YBCO}$ superlattices at $\nu =90\mathrm{GHz}$ and for different temperatures. Symbols: experiment, lines: fits to the Lorentz-like form of the ferromagnetic resonance close to 3.1 T. The inset shows the geometry of the experiment.

Figure 3

Magnetic permeability of $\mathrm{LSMO}/\mathrm{YBCO}$ superlattices at $T=10\mathrm{K}$ as function of magnetic field (a) and replotted in the complex plane (c). The complex refractive index as field dependence (b) and in the complex plane (d). The shaded area corresponds to the region with negative real part of refractive index. The results for $T=200\mathrm{K}$ are given for comparison. In all frames the symbols correspond to experimental data; lines represent the Lorentz model for the FMR line.