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: in all high temperature superconductors, the Fermi surface topology matches the form factor of the pairing symmetry favored by local magnetic exchange interactions. We suggest that this match offers a principle guide to search for new high temperature superconductors.

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