  Cuprates, ferropnictides and ferrochalcogenides are three classes of
unconventional high-temperature superconductors, who share similar phase
diagrams in which superconductivity develops after a magnetic order is
suppressed, suggesting a strong interplay between superconductivity and
magnetism, although the exact picture of this interplay remains elusive. Here
we show that there is a direct bridge connecting antiferromagnetic exchange
interactions determined in the parent compounds of these materials to the
superconducting gap functions observed in the corresponding superconducting
materials. High superconducting transition temperature is achieved when the
Fermi surface topology matches the form factor of the pairing symmetry favored
by local magnetic exchange interactions. Our result offers a principle guide to
search for new high temperature superconductors.
