= Solution
<Exchange interaction> arises from Coulomb interaction together with the antisymmetry required for identical electrons. Different spin states require different spatial symmetry and therefore different pair correlations and Coulomb energy; exchange is not the classical magnetic dipole force between spins. For electrons in distinct atomic orbitals, positive direct exchange favors parallel spins, underlying <Hund's rules> and the formation of local moments.
In a solid with localized moments, a common convention is $H=-J\sum_{\langle ij\rangle}\mathbf S_i\cdot\mathbf S_j$. Then $J>0$ favors <ferromagnetism> and $J<0$ favors <antiferromagnetism>. <Superexchange> through a ligand and other virtual hopping processes can produce either effective sign depending on orbital occupancy and geometry; half-filled orbitals often give antiferromagnetic coupling. For itinerant electrons, the <Stoner criterion> describes a competition between exchange energy gain and the kinetic cost of splitting the spin populations.
Experiments distinguish these descriptions through both static and dynamic response. <Magnetic neutron diffraction> locates magnetic Bragg peaks and therefore the ordering wavevector; an antiferromagnet can have such peaks despite zero bulk moment. <Inelastic neutron scattering> measures spin-wave dispersion, from which an exchange scale can be fitted. A Curie-Weiss susceptibility intercept gives complementary information about dominant coupling, but its sign alone does not establish the actual ordered structure.
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