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== Compute Coupling Constants ==
Calculation of multipolar exchange interactions remains a challenging issue in many aspects. Although there were many works based on fitting the model Hamiltonians with experiments, predictions of the coupling constants based on first-principle schemes remain lacking. Currently there are two studies implemented first-principles approach to explore multipolar exchange interactions. An early study was developed in 80's. It is based on a mean field approach that can greatly reduce the complexity of coupling constants induced by RKKY mechanism, so the multipolar exchange Hamiltonian can be described by just a few unknown parameters and can be obtained by fitting with experiment data.<ref>R. Siemann and B. R. Cooper, Phys. Rev. Lett. 44, 1015 (1980)</ref> Later on, a first-principles approach to estimate the unknown parameters was further developed and got good agreements with a few selected compounds, e.g. cerium momnpnictides.<ref>J. M. Wills and B. R. Cooper, Phys. Rev. B 42, 4682 (1990)</ref> Another first-principle approach was also proposed recently.<ref name="multipolar exchange"/> It maps all the coupling constants induced by all static exchange mechanisms to a series of
== References ==
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