Complex paramagnetic susceptibility in titanium-doped sapphire at microwave frequencies

Precise determinations below 200 K have been made of the complex susceptibi lity of Ti3+ and Ti4+-doped-sapphire crystal resonators using the whisperin g gallery mode method at microwave frequencies. The observed Ti3+ contribut ion to the frequency-temperature dependence of sapphire was interpreted as arising from the Van Vleck temperature-independent paramagnetic susceptibil ity. A small anisotropic dielectric contribution resulting from TiO2 cluste rs also was observed in the Ti4+-doped crystal. In both crystal resonators, the compensation point in the frequency-temperature dependence was found t o be dependent on the magnetic energy filling factor in the sapphire and th e Ti3+ concentration. An exponential increase in the g-factor was observed as the temperature was reduced below 10 K. A mechanism to explain this effe ct is proposed. Below 50 K, an Orbach double-resonant-phonon process was do minant, with characteristic energies equivalent to temperatures of 54 +/- 1 K and 27 +/- 1 K. Above 70 K it is suggested that Raman scattering was the major loss mechanism. The paramagnetic susceptibility of the doped crystal and the relaxation rate of the Orbach loss process were uniquely determine d.