  We investigate magnetic properties and strong coupling corrections in the BCS
(Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover regime
of an ultracold Fermi gas. Within the framework of an extended $T$-matrix
theory, we calculate the spin susceptibility $\chi$ above the superfluid phase
transition temperature $T_{\rm c}$. In the crossover region, the formation of
preformed Cooper pairs is shown to cause a non-monotonic temperature dependence
of $\chi$, which is similar to the so-called spin-gap phenomenon observed in
the under-doped regime of high-$T_{c}$ cuprates. From this behavior of $\chi$,
we determine the spin-gap temperature as the temperature at which $\chi$ takes
a maximum value, in the BCS-BEC crossover region. Since the spin susceptibility
is sensitive to the formation of singlet Cooper pairs, our results would be
useful in considering the temperature region where pairing fluctuations are
important in the BCS-BEC crossover regime of an ultracold Fermi gas.
