Theoretical Calculations of Strain-Induced Splittings and/or Shifts of and Levels for

Abstract

Under various uniaxial stresses, both strains with low symmetry and isotropic strains of crystals take place. The former gives the strain-induced low-symmetry crystal fields and accordingly splittings of levels; the latter gives the isotropic parts of strain-induced crystal fields and accordingly shifts of levels. By using the wavefunctions obtained from the diagonalization of the complete energy matrix in a regular octahedral field, the relevant matrix elements and accordingly strain-induced splittings and/or shifts of and for have been calculated. Their physical origins have been thoroughly analyzed and revealed. It is the admixtures of basic wavefunctions resulted from the spin-orbit interaction and/or Coulomb interaction and/or Kramers degeneracy that make strain-induced splittings of levels nonzero. In contrast with this, strain-induced shifts come mainly from the zero-order approximate wavefunctions. It is found that there are nonvanishing matrix elements of operators and between wavefunctions with positive and those with negative , which have important effects on strain-induced splittings of levels. The shifts of under both hydrostatic pressure and uniaxial pressure have been uniformly calculated. The important results of and have been evaluated.