  The effects of magnetic vortices and nonmagnetic impurities on the low energy
quasiparticle excitations and the spin-lattice relaxation rate are examined in
the iron-based superconductors for the $s_{\pm}$-, $s$- and d-wave pairing
symmetries, respectively. The main effect of the vortices is to enhance the
quasiparticle excitations and the spin-lattice relaxation rate for all
symmetries, and leads to a $T^{3}$ dependence of the relaxation rate followed
by a nearly $T$-linearity at lower temperatures. This enhancement can only be
seen for the $s_{\pm}$- and d-wave symmetries in the presence of nonmagnetic
impurities. These results suggest that the $s_{\pm}$-wave and d-wave pairing
states behave similarly in response to the magnetic field and nonmagnetic
impurities, therefore it may be impossible to distinguish them on the basis of
the measurements of spin-lattice relaxation rates when a magnetic field and/or
impurity scatterings are present.
