Special alternating links of minimal unlinking number

For any link in the 3-sphere, there is a natural lower bound for the unlinking number in terms of the classical signature. We prove that if this lower bound is sharp for a special alternating link $L$, then the unlinking number of $L$ is necessarily realized by crossing changes in any alternating diagram for $L$. As an application, we compute new values of the unknotting numbers for some special alternating knots with crossing number 11 and 12.