Ab-initio calculation of exchange interactions in YMnO3

The density functional based calculations of the electronic structure of YMnO3 are performed for selected spin configurations and from the differences of the total energies the exchange integrals are determined. To improve the description of strongly correlated 3d electrons of Mn the LDA+U method is employed. The strongest exchange interaction is found between the nearest neighbor Mn spins, the interaction between the next nearest neighbors being more than order of magnitude weaker.
Exchange integrals are inversely proportional to the parameter U, pointing to the dominance of the superexchange interaction. Due to the triangular arrangement of the nearest Mn the magnetism is geometrically frustrated so that biquadratic or/and anisotropic exchange may be important. The calculation of noncollinear spin structures indicates the presence of the biquadratic exchange interaction.