Molecular Geometry & Bonding
what the shape decides
Concept

Bipartite — where it appears

A network whose sites split into two sets with every bond joining one set to the other, as in a chain or an even ring. For an antiferromagnet it means no bond is frustrated, and the difference in size between the two sets fixes the ground state's total spin and puts at least that many levels at the centre of a band.

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

A 6×5 patch with one site missing. A 6 by 5 patch of a square structure with one site removed, the two colours of the bipartite structure drawn differently. The disc areas show where the level at zero has its amplitude: entirely on one colour.

A vacancy is not an impurity

An impurity is a site whose energy has been changed, and everything about the level it produces depends on by how much. A vacancy is a site that is not there, and the levels it leaves sit at exactly zero for a reason that cannot be tuned, weakened or moved — the count of them is a difference between two numbers of atoms, and two vacancies do not split however far apart they are put.

solids · Defect Sixteen clusters, and the couplings at which each one's sign changes. The sign of the exponent for every cluster across couplings from 2 to 1000 cm⁻¹, read at a 20–300 K window, with each change of sign marked. No cluster keeps one sign across the range. The clusters with a ground spin change sign twice below 150 cm⁻¹, at couplings that fall as the ground spin rises; the singlets first change sign above 300 cm⁻¹. The spin rule — positive for a singlet ground state, negative otherwise — is right on all sixteen at once only between 20.1 and 47.0 cm⁻¹, and the working point every earlier reading used, 50 cm⁻¹, is just outside it.

The sign rule holds between two poles

The sign of a susceptibility fit's exponent was put down to the parity of the spin count, then to the spin of the ground state, and every cluster tried had the two aligned. A star of four spins is even with a ground spin of one, and its exponent is −6.84. But swept across the coupling, every cluster's sign changes, through poles the ground spin places, and the spin rule is right on all sixteen clusters only between 20.1 and 47.0 cm⁻¹.

applied · Magnetism

Named alongside it

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

ConditioningDefect stateDegeneracyEigenvectorExact diagonalisationExchange couplingLocalisationMagnetic susceptibilityModel limitOne-electron modelsSpin stateSublattice

All concepts