Nonlocal Effects on the Magnetic Penetration Depth in d-wave Superconductors

We show that, under certain conditions, the low temperature behavior of the magnetic penetration depth $\lambda(T)$ of a pure d-wave superconductor is determined by nonlocal electrodynamics and, contrary to the general belief, the deviation $\Delta\lambda(T) = \lambda(T)-\lambda(0)$ is proportional to T^2 and not T. We predict that the $\Delta\lambda(T)\propto T^2$ dependence, due to nonlocality, should be observable experimentally in nominally clean high-T_c superconductors below a crossover temperature $T^* = (\xi_o/\lambda_o)\Delta_o \sim 1 K$. Possible complications due to impurities, surface quality and crystal axes orientation are discussed.