The Huang-Rhys factor S(a_1g) for transition-metal impurities: a microscopic insight

Abstract

AbsIracL A micmsmpic model for evaluating the Huang-Rhys factor S(at8) associated with the symmetric mode of a transition-metal impurity M in insulators is p r o p e l . It is applied Io the first excited states of C?+, Vz+, Mnz+ and Cuz+. If lODq is proportional to R-" (R is the metal-ligand distance) it is shown that S(a1,) is proportional to n' as well as lo [w(al8)]-'. Theoretical calculated values of the exponent n indicate that it varies slightly along the ligand series F-+ C1--+ Br-giving rise to an i n c r r m in S(alg). This expiains why the Stokes shift of systems involving M B ~N unib can be similar or higher than the corresponding shifb of MFN complexes The calculated values of S(alg) are reasonably cl-Io available experimental estimations and support the fact that the wntibution of the at, mode to the Stokes shift is between 50 and 70% for CrX2-(X 5 halides) wmplexes while it is smaller than 40% for the wrrerponding systems involving Mn2+.The dependence of S(a1,) on R is alw analysed, leading to an increase in S(a1,) upon increasing R. This lrend which has been directly verified for Vz+ in chlorides can also explain the increase in the Stokes shift observed experimentally when R is increased.

Optical and vibrational properties of MnF64−complexes in cubic fluoroperovskites: insight through embedding calculations using Kohn–Sham equations with constrained electron density

“…The results for V a and V e constants gathered in table 7 are quite similar to those previously derived by means of both MS-Xα and Extended Hückel methods [23,26,13]. They lead to S a values smaller than unity and thus support the existence of weak progressions involving the a 1g mode for both KMgF 3 :Mn 2+ and KZnF 3 :Mn 2+ systems [8].…”

“…Bearing in mind the results of table 6, a reduction of ∼2 pm in the R 0 value would imply an increase ofhω a close to 30 cm −1 . 4 distortions, respectively [26,23]. For instance, under a Q θ ∼ 3z 2 − r 2 distortion of the octahedron there is a splitting, e , between the x 2 -y 2 and 3z 2 -r 2 levels of the e g orbital as well as a splitting, t , between the x y and the (x z, yz) levels of the t 2g shell.…”

Studies of the tetragonal distortion due to Jahn–Teller effect for the Cu2+ centres in trigonal ZnMF6·6H2O (M = Si, Ti, Zr) crystals from the calculations of spin‐Hamiltonian parameters

“…From the relation Dq ∝ R 0 −n (where n ≈ 5 ± 1.5 [33,34]) and the distances R 0 in Table 1 Table 1. The ratio 2 0 4 0 ( )/ ( ) A R A R is in the range of 8-12 obtained by studying the optical and EPR spectra for 3d n clusters in crystals [29,30,[35][36][37].…”

Investigation on the Spin Hamiltonian Parameters and the Local Structures for Cu2+ Centers in Sodium Phosphate and Heavy Metal Fluoride Glasses

“…However, for the studied Cu 2+ doped in ZLBN glasses, the cubic field parameter Dq (≈ 1052 cm −1 ) [12] was significantly lower than that of the typical Cu-F bonds [12] Dq (≈ 4500 -5500 cm −1 ). Further, from the empirical relationship Dq ∼ R −5 [30,31], the larger impurityligand distance R in the studied ZLBN glasses would be possibly account for the smaller Dq. Therefore, the relatively larger ρ for ZLBN : Cu 2+ than that for SP : Cu 2+ is in agreement with the weaker chemical bonding and lower elastic constant of the impurity-ligand bond due to the longer distance R and lower valence state of the ligand ion in the former.…”