Tunable negative permeability in a three-dimensional superconducting metamaterial

We report on highly tunable radio frequency (rf) characteristics of a low-loss and compact three dimensional (3D) metamaterial made of superconducting thin film spiral resonators. The rf transmission spectrum of a single element of the metamaterial shows a fundamental resonance peak at $\sim$24.95 MHz that shifts to a 25$\%$ smaller frequency and becomes degenerate when a 3D array of such elements is created. The metamaterial shows an $\emph{in-situ}$ tunable narrow frequency band in which the real part of the effective permeability is negative over a wide range of temperature, which reverts to gradually near-zero and positive values as the superconducting critical temperature is approached. This metamaterial can be used for increasing power transfer efficiency and tunability of electrically small rf-antennas.