  The exchange energy of an arbitrary collinear-spin many-body system in an
external magnetic field is a functional of the spin-resolved charge and current
densities, $E_x[n_{\uparrow},n_{\downarrow},j_{\uparrow},j_{\downarrow}]$.
Within the framework of density-functional theory (DFT), we show that the
dependence of this functional on the four densities can be fully reconstructed
from either of two extreme limits: a fully polarized system or a completely
unpolarized system. Reconstruction from the limit of an unpolarized system
yields a generalization of the Oliver-Perdew spin scaling relations from
spin-DFT to current-DFT. Reconstruction from the limit of a fully polarized
system is used to derive the high-field form of the local-spin-density
approximation to current-DFT and to magnetic-field DFT.
