The crystal-field splitting third moment in determination of the crystal-field Hamiltonian parametrization. The cubic symmetry case

Documentation of conformity of the crystal field (CF) splitting third moment sigma(3) found by two independent methods proves the usefulness and adequacy of the third moment approach in the CF Hamiltonian (H-CF) parametrization. The first method is based on the experimental CF splitting diagrams of free-ion electron states vertical bar J >, whereas the second, numerical one, employs the (H-CF(3))(J) matrix trace. Unquestionable consistency between the CF splitting moments sigma(2) and sigma(3), the CF parameters, as well as the multipolar characteristics of the initial free-ion electron states have been shown. The usefulness of the CF splitting third moment and its adequacy have been tested by example of CF splitting diagrams for seven free-ion states of the trivalent lanthanide ions: Pr3+, Nd3+, Dy3+, Ho3+, Er3+, Tm3+ in the octahedral Cs(2)NaLnCl(6) host. The CF splitting third order moment, as an odd-order one, being characterized by positive or negative resultant sign and by tangled interdependence on the CF parameters is an important source of complementary information about the H-CF parametrization. (C) 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim