  We present a nuclear magnetic resonance (NMR) and electron spin resonance
(ESR) study of rare-earth titanates derived from the spin-1/2 Mott insulator
YTiO$_3$. Measurements of single-crystalline samples of (Y,Ca,La)TiO$_3$ in a
wide range of isovalent substitution (La) and hole doping (Ca) reveal several
unusual features in the paramagnetic state of these materials. $^{89}$Y NMR
demonstrates a clear discrepancy between the static and dynamic local magnetic
susceptibilities, with deviations from Curie-Weiss behavior far above the Curie
temperature $T_C$. No significant changes are observed close to $T_C$, but a
suppression of fluctuations is detected in the NMR spin-lattice relaxation time
at temperatures of about $3\times T_C$. Additionally, the nuclear spin-spin
relaxation rate shows an unusual peak in dependence on temperature for all
samples. ESR of the unpaired Ti electron shows broad resonance lines at all
temperatures and substitution/doping levels, which we find to be caused by
short electronic spin-lattice relaxation times. We model the relaxation as an
Orbach process that involves a low-lying electronic excited state, which
enables the determination of the excited-state gap from the temperature
dependence of the ESR linewidths. We ascribe the small gap to Jahn-Teller
splitting of the two lower Ti $t_{2g}$ orbitals. The value of the gap closely
follows $T_C$ and is consistent with the temperatures at which deviations from
Curie-Weiss fluctuations are observed in NMR. These results provide insight
into the interplay between orbital and spin degrees of freedom in rare-earth
titanates and indicate that full orbital degeneracy lifting is associated with
ferromagnetic order.
