Complex paramagnetic susceptibility in titanium-doped sapphire at microwave frequencies

Precise determinations below 200 K have been made of the complex susceptibility of Ti3+ and Ti4+-doped-sapphire crystal resonators using the whispering gallery mode method at microwave frequencies. The observed Ti3+ contribution to the frequency-temperature dependence of sapphire was interpreted as arising from the Van Vleck temperature-independent paramagnetic susceptibility. A small anisotropic dielectric contribution resulting from TiO2 clusters also was observed in the Ti4+-doped crystal. In both crystal resonators, the compensation point in the frequency-temperature dependence was found to be dependent on the magnetic energy filling factor in the sapphire and the Ti3+ concentration. An exponential increase in the g-factor was observed as the temperature was reduced below 10 K. A mechanism to explain this effect is proposed. Below 50 K, an Orbach double-resonant-phonon process was dominant, 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 determined.