Multipolar ordering from dynamical mean field theory with application to CeB6
Magnetic and multipolar ordering in f electron systems takes place at low temperatures of order 1--10 Kelvin. Combinations of first-principles with many-body calculations for such low-energy properties of correlated materials are challenging problems. We address multipolar ordering in f electron systems based on the dynamical mean-field theory (DMFT) combined with density functional theory. We derive the momentum-dependent multipolar susceptibilities and interactions in two ways: by solving the Bethe-Salpeter (BS) equation of the two-particle Green's function and by using a recently developed approximate strong-coupling formula. We apply the formalism to the prototypical example of multipolar ordering in CeB6 using the Hubbard-I solver, and demonstrate that the experimental quadrupole transition is correctly reproduced. The results by the approximate formula show good agreement with those by the BS equation. This first-principles formalism for multipolar ordering based on DMFT has applications which are beyond the reach of the traditional RKKY formula. In particular, more itinerant electron systems including 5f, 4d and 5d electrons can be addressed.