Magnetic excitations and spin-gap phenomenon in the BCS-BEC crossover regime of an ultracold Fermi gas*

We investigate the uniform spin susceptibility $\chi$ and strong-coupling corrections in the BCS-BEC crossover regime of an ultracold Fermi gas. Within the framework of an extended $T$-matrix theory,\footnote{T.Kashimura, R.Watanabe, and Y.Ohashi, Phys. Rev. A \textbf{86}, 043622 (2012).} we show that $\chi$ exhibits non-monotonic temperature dependence in the normal state, and is suppressed near the superfluid phase transition temperature $T_{\rm c}$. This spin-gap phenomenon is found to be deeply related to the pseudogap phenomenon appearing in the single-particle density of states. To characterize this magnetic phenomenon, we introduce the spin-gap temperature $T_{\rm s}$ as the temperature at which $\chi$ takes a maximum value. Determining $T_{\rm s}$ in the entire BCS-BEC crossover region, we identify the spin-gap regime in the phase diagram of a Fermi gas with respect to the temperature and the strength of a pairing interaction. Since the spin-gap is crucial key phenomenon in high-$T_{\rm c}$ cuprates, our results would be useful for the study of this many-body phenomenon using ultracold Fermi gases, as well as in observing the pseudogap phenomenon through the spin-gap phenomenon.