  Negative capacitance in BaTiO$_3$/SrTiO$_3$ superlattices is investigated by
Monte Carlo simulations in an atomistic effective Hamiltonian model, using
fluctuation formulas for responses to the local macroscopic field that
incorporates depolarizing fields. We show epitaxial strain can tune the
negative capacitance of the BaTiO$_3$ ferroelectric layer and the overall
capacitance of the system over a broad temperature range. In addition, we
predict and explain an original switching of the negative capacitance from the
BaTiO$_3$ layer to the SrTiO$_3$ layer at low temperatures for intermediate
strains. Our results indicate how the diffusive character of the multidomain
transition in these superlattices improves their viability for capacitance
applications.
