SYMMETRY ANALYSIS IN NEUTRON-DIFFRACTION STUDIES OF MAGNETIC-STRUCTURES .4. THEORETICAL GROUP-ANALYSIS OF EXCHANGE HAMILTONIAN

By analyzing the exchange Hamiltonian, we develop the technique of determining the magnetic structures liable to occur in a crystal. The technique rests on Bertaut's idea that the exchange matrix eigenfunction corresponds to some magnetic structure. A technically simple and efficient method of diagonalizing the exchange matrix is worked out using the devices of space group representation theory. A method is presented to find the magnetic structures with equal exchange energy (exchange multiplets). The occurrence of exchange multiplets results from the additional invariance of the exchange Hamiltonian under rotation of all the spins. The degeneracy within the exchange multiplet may be the reason why some magnetic structures arise not according to one irreducible representation of the space group. The theory is illustrated with reference to an example of the magnetic structure of spinels. © 1979.