THE HUANG-RHYS FACTOR S(A1G) FOR TRANSITION-METAL IMPURITIES - A MICROSCOPIC INSIGHT

A microscopic model for evaluating the Huang-Rhys factor S(a1g) associated with the symmetric mode of a transition-metal impurity M in insulators is proposed. It is applied to the first excited states of Cr3+, V2+, Mn2+ and Cu2+. If 10Dq is proportional to R(-n)) (R is the metal-ligand distance) it is shown that S(a1g) is proportional to n2 as well as to [omega(a1g)]-3. Theoretical calculated values of the exponent n indicate that it varies slightly along the ligand series F- --> Cl- --> Br- giving rise to an increase in S(a1g). This explains why the Stokes shift of systems involving MBr(N) units can be similar or higher than the corresponding shifts of MF(N) complexes. The calculated values of S(a1g) are reasonably close to available experimental estimations and support the fact that the contribution of the a1g mode to the Stokes shift is between 50 and 70% for CrX6(3-) (X = halides) complexes while it is smaller than 40% for the corresponding systems involving Mn2+. The dependence of S(a1g) on R is also analysed, leading to an increase in S(a1g) upon increasing R. This trend which has been directly verified for V2+ in chlorides can also explain the increase in the Stokes shift observed experimentally when R is increased.