  We study the (de)localization phenomena of one-component lattice fermions in
spin backgrounds. The O(3) classical spin variables on sites fluctuate
thermally through the ordinary nearest-neighbor coupling. Their complex
two-component (CP$^1$-Schwinger boson) representation forms a composite U(1)
gauge field on bond, which acts on fermions as a fluctuating hopping amplitude
in a gauge invariant manner. For the case of antiferromagnetic (AF) spin
coupling, the model has close relationship with the $t$-$J$ model of
strongly-correlated electron systems. We measure the unfolded level spacing
distribution of fermion energy eigenvalues and the participation ratio of
energy eigenstates. The results for AF spin couplings suggest a possibility
that, in two dimensions, all the energy eigenstates are localized. In three
dimensions, we find that there exists a mobility edge, and estimate the
critical temperature $T_{\ss LD}(\delta)$ of the localization-delocalization
transition at the fermion concentration $\delta$.
