Average an effective cluster of spin-1/2

[BO PENG]

Dear HeXu,

I hope that you are doing well!

We would like to compute the magnetic interactions between two cluster of atoms. Each cluster is overall spin-1/2, and for each cluster, the magnetic moment is delocalised over three atoms with approximately equal magnitudes. How do we obtain the effective interactions between clusters from the atomic exchange energies output by TB2J?

We are current directly summing over all nine J interactions between each pair of 3-atom clusters to get the effective interaction between the two clusters, and then multiply by four to account for the spin-1/2 on each cluster. The magnons of the full atomic model is faithfully represented by the effective exchange interactions. Should we add additional corrections for the actual magnetisation values on each atom, or is this already included in the TB2J output?

Thank you in advance!

Best wishes,

Bo

[Xu He]

Dear Bo, 

If the intra-cluster exchange is indeed >> the inter-cluster exchange (mimicing the Hund's coupling within one atom), this can be a good approximation. 

A good test is to plot the magnon band structure with the 6 sites, and with the two effective clusters, to see if they matches. 

If not, I think a way to do it is in the spirit of the downfolding procedure. That is given a 6x6 matrix with two 3x3 blocks and the inter-cluster blocks, construct a 2x2 matrix which matches the lowest energy spectrum.  We can discuss if this is needed. 

Best wishes, 

HeXu