  We theoretically investigate magnetic properties of a unitary Fermi gas in a
harmonic trap. Including strong pairing fluctuations within the framework of an
extended $T$-matrix approximation (ETMA), as well as effects of a trap
potential within the local density approximation (LDA), we calculate the local
spin susceptibility $\chi(T,r)$ above the superfluid phase transition
temperature $T_{\rm c}$. We show that the formation of preformed singlet Cooper
pairs anomalously suppresses $\chi(T,r)$ in the trap center near $T_{\rm c}$.
We also point out that, in the unitarity limit, the spin-gap temperature in a
uniform Fermi gas can be evaluated from the observation of the spatial
variation of $\chi(T,r)$. Since a real ultracold Fermi gas is always in a trap
potential, our results would be useful for the study of how this spatial
inhomogeneity affects thermodynamic properties of an ultracold Fermi gas in the
BCS-BEC crossover region.
