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Electronic states and quadrupole orders in the Pr 1-2-20 systems PrT2Al20(T=Ti, V) are investigated on the basis of the first-principles calculations.The effective 196 orbital model is derived to reproduce the first-principleselectronic structures of LaT2Al20 (T=Ti, V) without contribution from the Pr 4felectrons which are considered to be well localized and is employed tocalculate the Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions betweenquadrupole and octupole moments of the Pr ions. Within the random phaseapproximation for the RKKY Hamiltonian, the most divergent susceptibility isfound to be the quadrupole one for the wave vector Q = (0,0,0) in the case ofPrTi2Al20 while that for Q = (pi/a,0,pi/a) in the case of PrV2Al20 asconsistent with experimental observations in the both cases which exhibit theferro-quadrupole (FQ) and the antiferro-quadrupole (AFQ) orders, respectively.We also discuss the ordered states using the mean-field approximation and findthat, in the case of PrTi2Al20, the 1st-order phase transition to the O20 FQorder with a tiny discontinuity takes place as predicted by the Landau theory.In the case of PrV2Al20, the system exhibits two distinct O22 AFQ orders, AFQ-Iand AFQ-II, and shows subsequent two phase transitions, the 2nd-order one fromnormal to AFQ-I and the 1st-order one from AFQ-I to AFQ-II, that may beresponsible for the double transitions observed by specific heat measurements.

First-principles Study of the RKKY Interaction and the Quadrupole Order in the Pr 1-2-20 systems PrT2Al20 (T=Ti, V)