GoodenoughKanamoriAnderson

Goodenough-Kanamori-Anderson rules are qualitative guidelines used to predict the sign and strength of magnetic exchange interactions between magnetic ions in insulating oxides and related compounds. They emerged from the work of John B. Goodenough, Jun Kanamori, and Philip W. Anderson in the 1950s and 1960s on superexchange and covalent bonding in transition-metal oxides, and are often referred to as the GKA rules.

The core idea is that magnetic coupling between two cations is mediated by a nonmagnetic ligand, typically oxygen. Electrons can virtually hop from one metal d orbital to the ligand p orbital and then to the neighboring metal d orbital. The Pauli principle and Hund’s coupling on the ligand govern whether this virtual hopping lowers energy more for parallel or antiparallel spins, thereby setting the sign of the exchange interaction.

Angle and orbital-occupancy considerations are central. For near-180-degree metal–oxygen–metal bonds, the rules commonly predict antiferromagnetic coupling for many partially filled shells, due to favorable virtual hopping of identical orbitals. For near-90-degree bonds, ferromagnetic exchange is often favored, arising from different overlap patterns and Hund’s coupling on the ligand. The exact outcome depends on d-orbital occupancy (such as t2g versus eg), the degree of covalency, and the specific ligand environment.

Applications and limitations: The GKA rules provide a practical framework for interpreting magnetic order in transition-metal oxides, perovskites, cuprates, and manganites. They are qualitative and do not replace quantitative approaches, which are needed to account for charge-transfer effects, orbital ordering, and competing interactions using ab initio or many-body methods.