Investigations of crystal-field energy levels and microscopic spin-Hamiltonian parameters of Mn⁴⁺ ions in pyrochlore hosts Y₂Ti₂O₇ and Y₂Sn₂O₇

We investigate the crystal-field energy levels and the microscopic origin of spin-Hamiltonian parameters (SHPs), i.e. g-factors and zero-field splitting parameter D, for the ground state ⁴ A _2g(⁴ F) of Mn⁴⁺ impurity ions at trigonal sites in host pyrochlores, Y₂Ti₂O₇ and Y₂Sn₂O₇. The total Hamiltonian includes the electrostatic and crystal-field (CF) Hamiltonians, and the magnetic interactions, i.e. spin-orbit, spin-spin, spin-other-orbit, and orbit-orbit couplings. The calculations are performed under the complete diagonalization method and microscopic spin-Hamiltonian (CDM/MSH) program. The calculated CF levels agree reasonably well with the observed energy levels for Mn⁴⁺ ions in these compounds. The SHPs are evaluated with the CDM/MSH wave functions as well as by a perturbation loop theory method (PLTM). The g-factors of Mn⁴⁺ in Y₂Ti₂O₇ and Y₂Sn₂O₇ using PLTM are close to those evaluated by CDM, while the PLTM value of D shows appreciable difference with the CDM value. This evidences that the g-factors depend predominately on the lower states, while the higher energy states significantly affect the D value. The contributions of spin-spin, spin-other-orbit, and orbit-orbit couplings to the CF energy levels and the SHPs are discussed. (paper)