Molecular Geometry & Bonding
what the shape decides
Concept

Superexchange — where it appears

The coupling of two spins through the orbitals between them rather than directly. It goes as the square of the hopping divided by the repulsion, which makes it a second-order effect and far larger than any magnetic interaction.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

A coupling that is second order in the hopping. The singlet–triplet splitting of a two-site Hubbard model, and the same quantity multiplied by U. The product settles on −4t² — -4 at U = 64 — which is what makes the coupling a second-order effect rather than a term somebody put in.

What couples two spins

Two magnetic ions a few ångströms apart interact far too strongly to be doing it magnetically — the dipole–dipole energy is about 0.06 wavenumbers and the measured couplings run to hundreds. What couples them is hopping, which the Pauli principle allows for antiparallel spins and forbids for parallel ones, and the exact answer is −4t²/U.

applied · Magnetism The same sample, fitted over four temperature ranges. A pair coupled at -50 cm⁻¹, its susceptibility computed exactly, fitted to a Curie–Weiss law over four ranges. The moment and the Weiss temperature the fit reports both depend on which range was used, and the quality of the fit does not warn about it.

The moment a fit invents

One coupled pair of spins, its susceptibility computed exactly, fitted to a Curie–Weiss law over four temperature ranges. The moments reported are 2.471, 2.535, 2.566 and 3.590 Bohr magnetons, and the Weiss temperatures −51, −78, −78 and −292 K — from one sample, measured perfectly, with three of the four fits agreeing with their own data to better than a part in three hundred.

applied · Magnetism

Named alongside it

The objects these essays reach for when they reach for this one.

Exchange couplingMagnetic momentUnpaired electronsBoltzmannClosed formConventionCoordination complexDouble occupancyElectron correlationHubbard modelLeast-squaresMagnetism

All concepts