A RULE FOR COUNTING NEIGHBORS IN RARE-EARTH TRANSITION-METAL COMPOUNDS

In (R, T) compounds (R: rare earth; T: 3d transition metal) such as R2T17, R2T14B, and so on, the exchange interaction between a rare-earth spin (operator) S(R) and the neighbouring 3d spins can be written as -2J(RT)Z(RT)S(R).<S(T)>, where <S(T)> is a site average of the expectation value of the transition metal spins in the molecular field approximation. Z(RT) is the number of nearest T neighbours of an R-atom. A more precise definition is given in the main text. Analogously, Z(TR), the average number of nearest R neighbours of a T atom can be defined. We stress that a consistent definition must lead to the relation Z(RT)N(R) = Z(TR)N(T) for a stoichiometric compound containing N(R) rare-earth atoms and N(T) transition metal atoms per formula unit. Appropriate definitions are discussed for more intricate cases, in particular for off-stoichiometric compounds.