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His research with Malvin Ruderman helped explain conduction-electron-mediated exchange. Berkeley collects recollections of his research and teaching: physics.berkeley.edu/node/808.

An interaction between a nucleus's magnetic or electric multipole moments and its electronic surroundings. Magnetic contact and dipolar terms can couple nuclear spin to electron spin or orbital magnetic moments. The resulting small energy shifts contribute to hyperfine structure; the contact term can also mediate conduction-electron-mediated exchange between nuclear moments in a metal.

With Charles Kittel, he calculated conduction-electron-mediated exchange between nuclear magnetic moments. His later research included neutron stars. Columbia's account of his career also recalls his enthusiasm for order-of-magnitude teaching.^[ref]

Exchange interactions arise from quantum electronic motion, Coulomb interactions and fermionic antisymmetry. A localized-spin description can be written $H={\sum }_{i<j}{J}_{ij}{\mathbf{S}}_i\cdot {\mathbf{S}}_j$. In this explicit plus-sign convention $J<0$ favors parallel spins and $J>0$ favors antiparallel spins; many texts put a minus sign into the Hamiltonian and reverse that convention.

Direct exchange involves overlapping orbitals and their Coulomb exchange matrix elements. The Pauli exclusion principle correlates spin symmetry with spatial symmetry, changing the electronic energy. Orbital occupation and competing kinetic processes determine which spin state is favored; the preference is not universally ferromagnetic.

Superexchange couples moments through virtual hopping, often via a nonmagnetic ligand. For two half-filled orbitals in the simple repulsive one-band model, the antiferromagnetic coupling is $J\simeq 4|t{|}^2/U$: virtual double occupation lowers the antiparallel-spin state more effectively. Orbital geometry and intermediate-state interactions can change the sign in other configurations. Real charge transport can remain insulating while this magnetic coupling acts.

Double exchange instead uses actual carrier motion between mixed-valence sites. Local Hund's coupling ties the mobile electron's spin to a core moment. Parallel neighboring cores allow a larger effective hopping amplitude and a lower carrier kinetic energy, favoring ferromagnetism. The original model explicitly connected conduction and magnetic order in manganese perovskites.^[ref]

Conduction-electron-mediated exchange couples localized moments through a metal's electronic spin response. Its strength and sign depend on separation and the Fermi surface; in a simple three-dimensional asymptotic model the range factor oscillates as $\cos (2k_{F}r)/r^3$. The original nuclear-moment calculation was motivated by resonance-line broadening in silver.^[ref] In an itinerant metal, an alternative description compares the kinetic-energy cost of unequal spin populations with the exchange-energy gain; the Stoner criterion expresses when spontaneous polarization is favorable.

The resulting order also depends on the lattice and competing couplings. In ferromagnetism, moments align to give a nonzero moment within a domain. In antiferromagnetism, opposing sublattices cancel their moments. In ferrimagnetism, oppositely ordered sublattices have unequal moments and leave a net one. A bulk zero magnetization alone cannot distinguish antiferromagnetic order from a disordered state or canceling magnetic domains.

The manganese monoxide neutron diffraction experiment makes that distinction experimentally. A monochromatic neutron beam scatters from powdered material, and a counter records angular intensity. Comparing the same compound at room temperature and $80\mathrm{K}$ reveals additional low-temperature magnetic reflections, indexed by a larger magnetic unit cell, while nuclear reflections persist. That spatial periodicity is evidence of alternating order even though the net moment cancels.^[ref]