Mechanisms responsible for microwave properties in high performance dielectric materials

Microwave properties of low-loss commercial dielectric materials are optimized by adding transition-metal dopants or alloying agents (i.e. Ni, Co, Mn) to tune the temperature coefficient of resonant frequency (τf) to zero. This occurs as a result of the temperature dependence of dielectric constant offsetting the thermal expansion. At cryogenic temperatures, the microwave loss in these dielectric materials is dominated by electron paramagnetic resonance (EPR) loss, which results from the spin-excitations of d-shell electron spins in exchange-coupled clusters. We show that the origin of the observed magnetically-induced shifts in the dielectric resonator frequency originates from the same mechanism, as described by the Kramers-Kronig relations. The temperature coefficient of resonator frequency, τf, is related to three material parameters according to the equation, τf = - (½ τε + ½ τµ + αL), where τε, τµ, and αL are the temperature coefficient of dielectric constant, magnetic permeability, and lattice constant, respectively. Each of these parameters for dielectric materials of interest are measured experimentally. These results, in combination with density functional simulations, developed a much improved understanding of the fundamental mechanisms responsible for τf. The same experimental methods have been used to characterize in-situ the physical nature and concentration of performance-degrading point defects in the dielectrics of superconducting planar microwave resonators.