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Asymptotic couplings by reflection are constructed for a class of nonlinear monotone SPDEs (s-tochastic partial differential equations). As applications, gradient estimates as well as exponential convergence are derived for the associated Markov semigroup. The main results are illustrated by stochastic generalized porous media equations, stochastic p-Laplacian equations, and stochastic generalized fast-diffusion equations. We emphasize that the gradient estimate is studied for the first time for these equations.