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If, during the preparation, an external magnetic field is applied uponcooling we say it has been field cooled. A novel mechanism for insulator-metaltransition and superconductivity in field-cooled spin-$1/2$ antiferromagnets onbcc lattice is discussed. Applying a magnetic field along the sublattice Bmagnetization, we change the magnetic and transport properties of the material.There is a critical value $H_{cr1}$. When the magnetic field is below thecritical one $H<H_{cr1}$ the prepared material is a spin$-1/2$antiferromagnetic insulator. When $H>H_{cr1}$ the sublattice A electrons aredelocalized and the material is metal. There is a second critical value$H_{cr2}>H_{cr1}$. When $H=H_{cr2}$, it is shown that the Zeeman splitting ofthe sublattice A electrons is zero and they do not contribute to themagnetization of the system. At this quantum partial order point (QPOP) thesublattice B transversal spin fluctuations (magnons) interact with sublattice Aelectrons inducing spin anti-parallel \emph{p}-wave superconductivity whichcoexists with magnetism. At zero temperature the magnetic moment of sublatticeB electrons is maximal. Below the N\'{e}el temperature $(T_N)$ the gap isapproximately constant with a small increase when the system approaches $T_N$.It abruptly falls down to zero at temperatures above $T_N$.

Magnon-induced superconductivity in field-cooled spin-1/2 antiferromagnets