Cryst. Res. Technol. 45, No. 6, 634 – 636 (2010) / DOI 10.1002/crat.201000121

© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Explanations of the optical absorption and ESR spectrum for

tetragonal Ni+ centers in CuAlS2:Ni

+ crystals

Ying Wu1, Li-Juan Wang*

2,3, and Guo-Yue Liu

1

1 School of Physics and Electron, Mianyang Normal University, Mianyang, 621000, P. R. China 2 Dept. of Physics and Electronic Engineering, Neijiang Normal College, Neijiang, 641112, P. R. China 3 School of Electrical Information Engineering, Southwest Nationalities Uni., Chengdu, 610041, P. R. China

Received 26 February 2010, accepted 16 March 2010

Published online 1 April 2010

Key words crystal field, ligand field, optical absorption spectrum, ESR spectrum, CuAlS2:Ni+ crystal.

In this paper, the optical absorption and electron spin resonance (ESR) spectrum of Ni+-doped CuAlS2

crystals have been studied by using a double spin-orbit (SO) coupling approximation model, where the effects

due to the SO coupling of the central metal 3d1 ion and those of ligands are included. From this model, the

formulas of the ESR g factors g//, g⊥ and hyperfine structure constants A//, A⊥ for 3d1 ions in the tetragonal

MX4 clusters are constructed. The optical absorption and ESR parameters for Cu+ sites of CuAlS2 have been

calculated. The results obtained show that Ni+ ions substitute for Cu+ ions sites.

© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

1 Introduction

The optical and electron spin resonance spectroscopy are the important techniques for studying the substituted lattice structure of the transition metal complexes which have at least one unpaired electron on their d orbital [1-6]. Paramagnetic Ni+ ions with 3d9 configurations in crystalline materials have been studied by some workers to obtain information about the structure, electronic and optical properties, etc [7,8]. Among them, CuAlS2 is an important ternary semiconductor, which has the wide band gap and so may be a promising material for blue light-emitting device application [5]. The optical absorption and ESR spectrum of Ni+-doped CuAlS2 have been measured by Kaufmann [8]. The theoretical analysis of optical and ESR spectrum of Ni+-doped CuAlS2 based on single SO coupling have been carried out by Wu et al. [7]. However, the effect of the SO coupling of ligand is not included in their calculations. Considering the same order of magnitude of the SO

coupling coefficients between the ligand S2- ( 0

pζ = 365 cm-1 [9,10]) and the central metal ion Ni+ ( 0

pζ =

605 cm-1 [11]), the two SO coupling approximation should be used here. In the present work, the theoretical formulas of the optical absorption and ESR spectrum have been

established on the basis of the double SO coupling approximation model. The Ni+ ions substituting for Cu+ sites have been calculated by these improved formulas. The calculated results of Cu+ occupied by Ni+ are in good agreement with the experimental data.

2 Calculation method

The [NiS4]7- impurity center in CuAlS2: Ni+ crystal is a tetragonal structure (the point symmetry is either D2d or

Td depending on whether the Ni+ replaces the Cu+ site or the Al3+ site) [12]. The electronic configuration of Ni+

ion is 3d9 and possesses a 2B2g (xy

d ) ground state (replaced Cu+ site) or a 2B1g ( 2 2x y

d−

) ground state

(replaced Al3+ site) in CuAlS2: Ni+ crystal. From the optical spectra and ESR data, the (NiS4)7- tetrahedron in

CuAlS2: Ni+ is compressed along the C4 axis from the crystallographic data [12] and the ground state of the 3d1

ion should be 2B2g ( xyd ). Considering there is the admixture of d orbital of the 3d9 ions and the p orbitals of

ligands via the covalence effects, the LCAO molecular obitals of the [NiS4]7- center can be expressed as

[4,13,14]: ____________________

* Corresponding author: e-mail: wanglijuan20082@163.com

Cryst. Res. Technol. 45, No. 6 (2010) 635

www.crt-journal.org © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

( )t t t t tN d p pσ π

σ πψ = + λ + λ , ( )3

e e e eN d pπ

πψ = + λ

, (1)

where the subscript t or e is the irreducible representation of the D2d group. |dγ> (where γ = t or e) is the central 3dn ion d orbital and |pt

π>, |peπ> and |pt

σ> are the ligand ion p orbitals. Nγ is the covalence factor and λε (where ε =π orσ) is the orbital mixing coefficient. These normalization coefficients can be obtained from the normalization relation

2 2 1/ 2[1 ( ) ( ) 2 ( ) 2 ( )]t dp dpN S S−

σ π σ π= + λ + λ + λ σ + λ π 2 1/ 2[1 3( ) 6 ( )]e dpN S

−

σ π= + λ + λ π (2)

in which the group overlap integrals

Sdp(σ) = < dt | σt >, Sdp(π) = < dt | πt > = < de | πe > / 3 . (3) According to the crystal- and ligand-field theory, the effects of SO coupling including the central 3dn ion and the ligand can be given as

( ) ( )SO SO d SO pH H H= ζ + ζ ( ) ( )d d p pR l s R l s= ζ ⋅ + ζ ⋅� �

� �

(4)

in which d

ζ and p

ζ are, respectively, the SO coupling parameters of the central metal and ligand ions. l�

and

s

�

are orbital and spin angular momentums, respectively. Thus, for 3d9 ion in tetragonal MX4 cluster, by using the above single electron basis functions and the

perturbation theory [15, 16], the three order perturbation formulas of ESR spectrum g factors g//, g⊥ and hyperfine structure constants A//, A⊥ based on the double SO coupling approximation can be given as

' ' 2' ' '

// 2

1 1 2 2

( / 2)8 4s

s

k gk kg g

E E E E

+ ζζ ζζ= + − − ,

' 2 ' ' ' 2' ' ' 2 ' '

2 2

2 1 2 2 1

/ 2 22 2 2s s

s

g k gk k kg g

E E E E E⊥

ζ − ζζ ζζ ζ − ζζ= + + − − (5)

4 3'

// //7 7A ( ) [( ) ( )]

s sP P g g g g

⊥= κ − + − + − , 2 11'

7 14A ( ) [ ( )]

sP P g g

⊥ ⊥= κ + + − (6)

with 2 0 2 0( / 2)t d t pNζ = ζ + λ ζ , 0 0( )( / 2)t e d t e pN N′ζ = ζ −λ λ ζ , 2 2

2[1 2 ( ) / 2]t t dp g tk N S t= + λ + λ ,

2( )[1 ( ) ( ) / 2]t e t dp g e dp g t ek N N S t S e′ = + λ + λ −λ λ . (7)

The crystal field energy levels E1, E2 and E3 are 2 2

1 2 1( ) ( ) 10E E B E B Dq= − = , 2 2

2 2( ) ( ) 3 5E E B E E Ds Dt= − = − + ,

2 2

3 2 1( ) ( ) 10 4 5E E B E A Dq Ds Dt= − = − − , (8)

where Dq is the cubic crystal field parameter, Ds, Dt are the tetragonal field parameters, which can be calculated from the Newman’s superposition model [17].

4 4

4 03( )sinDq A R= θ , 4 2

2 07( )(3cos 1)]

sD A R= θ− , 4 4 4 2

4 021( )(7sin 35cos 30cos 3)]

tD A R= θ+ θ− θ+ (9)

in which R0 (≈Rh≈2.351 Å [12], Rh is bond length between the metal and ligand in the host crystal) is the

reference distance. ( )2 0A R and ( )4 0

A R are the intrinsic parameters characterized the reference distance R0.

The ratio ( )2 0A R / ( )4 0

A R is in the range 8~12 obtained from 3dn clusters in many crystals [4,18-20] and we

take ( )2 0A R / ( )4 0

A R ≈9 here. The tetragonal bond angle θ (≈55.95°) can be estimated by the crystal structure

data [12]. The hyperfine structure parameters P and P’ are related to the dipole-dipole interaction of the electronic and

nuclear moments of a Ni+ ion.

0tP N P= ,

0t eP N N P′ = , (10)

where hyperfine structure constant P0 (≈102×10-4cm-1) for a free Ni+ ion [8,21]. In eq. 6, κ (≈0.3 [8,21]) is the core polarization constant which is related to the unpaired electron density at the nickel nucleus.

From the reference distance R0 and the Slater-type SCF functions [22,23], we calculate the group overlap integrals Sdp(π) ≈ 0.007198 and Sdp(σ) ≈ 0.026904. Obviously, if the parameters λπ and λσ are known, the parameters Nγ can be calculated by using Eq. (2). We assume λπ and λσ as the adjustable parameters. Thus, in

the above formulas, only λπ, λσ and 4

A are unknown. By fitting the calculated optical absorption spectra and

ESR data to the experimental values, we obtain

λπ≈ –0.6193, λσ≈ 0.7850, 4

A ≈ 560 Å. (11)

The calculated normalization coefficients, the spin-orbit parameters, the orbital reduction factors and the

636 Y. Wu et al.: Absorption and ESR spectrum for tetragonal Ni+ centers in CuAlS2:Ni+ crystals

© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.crt-journal.org

dipolar hyperfine constants for CuAlS2: Ni+ are listed in table 1. The calculated optical absorption spectra, ESR parameters gi and Ai are compared with the observed values in table 2.

Table 1 The normalization coefficients, the spin-orbit parameters, the orbital reduction factors and the dipolar hyperfine

constants for CuAlS2: Ni+

Nt Ne ζ(cm-1-) ζ’ (cm-1) k k’ P (10-4cm-1) P’ (10-4cm-1)

0.7275 0.6353 283 239 0.6260 0.5627 74.20 69.34

Table 2 The optical absorption (d-d transition) and ESR spectra of CuAlS2: Ni+ crystal. (a Calculations based on the

omission of the ligand contributions. b Calculations based on the inclusion of the ligand contributions.)

Transition (cm-1) Calc.a Calc.b Expt. [8] ESR spectra Calc.a Calc.b Expt. [8] 2B1g 0 0 0 g// 2.013 2.052 2.051 2Eg 692 692 g⊥ 2.372 2.330 2.330

2B2g 3519 3519 3566 A// (10-4cm-1) -8.4 -6.9 ≦13

2A1g 4026 4026 3984 A⊥(10-4cm-1) 63.6 61.3 61

3 Summary

It can be found from table 2 that the calculated optical and ESR spectra based on the two SO coupling parameters are in good agreement with the experiment data. There are several points that may be discussed here. 1 The ESR measurement can not determine solely the signs of hyperfine structure constants [24, 25]. So the

signs of A// and A⊥ in CuAlS2: Ni+ obtained by ESR experiment are actually the absolute values although they are written as positive in [8]. From the above calculations, we suggest that A// is negative and A⊥ is positive.

2 From table 2, one can find that the Ni+ replaces Cu+ site, the calculated results are coincident with the observed values. This point can be further supported by the mechanism of the charge balance because Ni+ and Cu+ have equal charge.

3 The ESR results are better than those under neglecting of the ligand contributions ( 00

pζ = ), which

indicates that the impurity-ligand orbital admixtures are significant and cannot be neglected.

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