' { There is a flaw in the analysis however in that Koidl appears

to have treated the spin-orbit interaction as a perturbation on the energy levels determined by the Jahn-Teller effect, regardless of the strength of the Jahn-Teller interaction. If this is weak then it '

■ **

should be treated as a perturbation on the spin-orbit interaction and

6.7

not vice versa. Fortunately other authors have treated the problem

of the state in ZnS:Mn^^^^ and ZnSe;Mn^^^^ and have agrèed as to

the general description of the two zero-phonon lines arising from' a strong Jahn-Teller coupling to E modes - i.e. the region where Koidl’s calculation is valid.

The discrepancy between the theoretical values obtâned by Koidl and those obtained experimentally for ZnSe:Mn was attributed by him

(92 93)

to the effect of covalency * . This effect arises through the

admixture of ligand (i.e. Se) orbitals, which are p-functions, into the central ion d-functions. There will be symmetry limitations on the possible admixtures, caüsed by the requirement that the total

wavefunctions still transform as bases of the irreducible representations

(in the cases under discussion either or Tg). In this way the

effect of the ligands on the first-order spin-orbit coupling may be written

. “ u h (6.6)

where the summation over y is over the central ion plus the four ligands,

is the one-electron spin-orbit constant of the y-th ion, and Z .(y)

the orbital angular momentum of the i-th electron of the y-th ion,

centred at the origin of the y-th ion. From eq (6.6) it is readily

seen that the first order spin-orbit interaction depends on the spin- orbit constant of the ligands, which as a crude approximation is

dependent on the mass of the ligands, and so the effect should be,greater for selenium ligands than for sulphur ones.

As given in eq (6.6), the effect of the ligands is a first-order

one in the spin-orbit coupling, and according to Koidl^^^\ the first order spin-orbit coupling is fully quenched by the strong Jahn-Teller

Using the same model as Koidl^^^\ Parrot et al^^^^ claim reasonable

Jahn-Teller coupling with an E vibrational mode gives approximately

The model proposed by Koidl cannot however explain the splitting of the '^Tg manifold in ZnSe:Mn, although including the effects of

6.8

• ■

effect. However the effect of covalency in determining the residual

splitting of the states in the '^T^ or manifold would then appear

in second order spin-orbit interactions, although this calculation |

has not been performed.

4 W;

agreement between theory and experiment for the splitting of the T^ state of ZnSe:Mn, without considering the effect of covalency. This is due to a more accurate experimental determination of this splitting

(obtained as 11.5 cm than the value 20 cm used by Kbidl^^^^

for comparison with his theoretical value of *v7.5 cm ^ . A comparison of theoretical and experimental values for the splittings of the

'^T^ and states is given in table (6.1) for both ZnSeiMn and ,

ZnS:Mn. . . . .4

Study of table (6.1) reveals that Koidl’s^^^^ model of strong , .'1

correct values of the splittings for the *^T^ and ^T^ states in ZnS:Mn '4

and also for the ^T^ state in ZnSe:Mn,

'.'i

I

covalency to second order in the spin-orbit interaction would be an vf

interesting calculation. As noted by Fournier et al,^^^^ the ^T.^^ state appears to be more strongly coupled to the lattice than the

^T„ state (see 4.1 and ref, (41)) and so anght be expected to ' /:

experience a stronger. Jahn-Teller effect. This fact, together with the results of uniaxial stress measurements has led to a different

model being proposed for the T^ states in both ZnS:Mn and ZnSe:Mn^^^‘^ ^ \

namely one in which the spin-orbit interaction and Jahn-Teller inter- ’.‘■I

action are of approximately equal magnitude-, so that neither can be

6.9

treated as a perturbation on the other. (This approximation cannot

be obtained from Figs. (6.5) and (6.6) since the calculations leading

to these diagrams are valid only for a strong Jahn-Teller effect.) Due to the difficulty in diagonalising the Hamiltonian with respect

to the spin-orbit and Jahn-Teller effects simultaneously, only spin-

4 .

orbit interactions within the T^ manifold were considered, with no allowance for covalent effects except that the spin-orbit coupling strength was treated as a parameter. The Jahn-Teller coupling strength was also treated as a parameter. The experimental observations (97) for ■ZnSe:Mn were best fitted by taking the spin-orbit coupling parameter

-1 • . “1 (4)

as 750 cm (against" 'v 400 cm for the free Mn ion) and a Jahn-

Tejler coupling strength of 1.2 (measured in units of hw, the coupling -1 (92 99)

mode frequency taken as 75 cm • " \ this being the lowest energy

peak in the phonon density of states). Fig. (6,7) shows the splittings of the ^T^ state in ZnSe:Mn, determined from the data presented in^^^^ as a function of Jahn-Teller coupling strength, for a spin-orbit

“1

constant of 750 cm . The occurrence of only two lines was also

explained in this work (97) on the basis of the relative dipole strengths

of transitions from the level to various states within the "^T^

manifold. These are shoim in Fig. (6.8) as a function of Jahn-Teller

coupling strength for a spin-orbit parameter of 750 cm from which

it can be seen that only two levels, Fg(5/2) and Fg have an appreciable

dipole strength. The Fg(3/2) line is weak, and the strength of the Fy line is identically zero.

6 4

The splitting of the A^ T^ zero phonon line in ZnSe:Mn as

measured here, is however 11.5 cm ^ (3&, 1.42 meV), which would require (from Fig. (6.7)) a Jahn-Teller coupling strength of 1.6. Calculating

I