Journal of Magnetism and Magnetic Materials 324 (2012) 4061–4063

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Journal of Magnetism and Magnetic Materials

0304-88

http://d

n Corr

Advanc

E-m

journal homepage: www.elsevier.com/locate/jmmm

Theoretical investigation of EPR and optical spectra of Mo(V) in[Mo6O19][N(C4H9)4]3 salt

Wen-Lin Feng a,b,c,n

a Department of Applied Physics, Chongqing University of Technology, Chongqing 400054, Chinab Chongqing Key Laboratory of Time Grating Sensing & Advanced Testing Technology, Chongqing 400054, Chinac International Centre for Materials Physics, Chinese Academy of Sciences, Shenyang 110016, China

a r t i c l e i n f o

Article history:

Received 24 December 2011

Received in revised form

13 May 2012Available online 20 July 2012

Keywords:

Electron paramagnetic resonance

Optical spectrum

Crystal-field theory

Mo5þ

[Mo6O19][N(C4H9)4]3 salt

53/$ - see front matter & 2012 Elsevier B.V. A

x.doi.org/10.1016/j.jmmm.2012.07.015

espondence address: Chongqing Key Laborato

ed Testing Technology, Chongqing 400054, Ch

ail address: wenlinfeng@126.com

a b s t r a c t

The electron paramagnetic resonance (EPR) spectral data (the g factors and hyperfine structure

constants) and d–d transition spectra for the tetragonal Mo5þ centre in [Mo6O19][N(C4H9)4]3 salt are

theoretically investigated from the complete diagonalization method (CDM) for a 4d1 ion in tetragonally

compressed octahedron. The theoretical results are in good agreement with the experimental data. The

dependency of the g factors of the ground state on the RJ(MoQO bond length) has been studied. It is

shown that the g factors varied with the RJ approximately in a linear way.

& 2012 Elsevier B.V. All rights reserved.

1. Introduction

The transition-metal (TM) ions doped materials have attractedmore and more attention because of their wide applications suchas magnetic, optical and electronic devices, and so on. Manyinteresting properties including the ferromagnetic resonance,spin paramagnetism, and optoelectronic behavior will occurwhen these materials contain TM ions [1–5]. TM ions such asTi2þ , Ni2þ , V3þ and Mn2þ are important active ions for opto-magnetic and photoelectric materials. However, compared withthe first (3dn) series, the second (4dn) and third (5dn) series inthese materials are relatively less studied. As known, the Mo5þ

(4d1 electron configuration) is an interesting paramagnetic probeto study the local structure by EPR spectroscopy, so we can verifythe local structure parameter of [Mo6O19][N(C4H9)4]3 by fittingEPR spectral data. [Mo6O19][N(C4H9)4]3 salt has potential applica-tions in magnetic cooling and spintronic devices, which use thespin of the particles in addition to their charges. The six oxygenligands around Mo5þ ions are located at the approximately C4v

symmetry site with a distorted octahedron in [Mo6O19][N(C4H9)4]3

salt [6]. The ground state of Mo5þ ions at tetragonal symmetrysites is 2B2g (9dxyS). Che [6] reported the EPR (the anisotropic g

factors and the hyperfine structure parameters) and optical

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spectral data of Mo5þ in [Mo6O19][N(C4H9)4]3. However, the aboveexperimental data have not been theoretically interpreted, andinformation about the local structure of this paramagnetic centrewas not acquired. Thus, theoretical investigations on the EPR andoptical spectra for the tetragonal Mo5þ centre in [Mo6O19][N(C4H9)4]3 are of physical significance. In this work, the EPR,optical spectra and the local structure for Mo5þ in [Mo6O19][N(C4H9)4]3 are quantitatively studied using the complete diago-nalization method (CDM) for a 4d1 ion in tetragonally compressedoctahedron. In the calculations, the experimental values arereasonably explained in a uniform way.

2. Theoretical methods

The energy matrices for the 4d1 configuration ion in a crystalhave been established by using the Hamiltonian [7]

H¼Hf rþHCF ðBkqÞþHSOðzdÞþHZeþHhy ð1Þ

where Hfr, HCF, HSO, HZe, and Hhy represent, respectively, the freeion, the crystal field (CF), the spin–orbit (SO), Zeeman andhyperfine interactions. Bkq are the CF parameters, zd is the spin–orbit coupling coefficient. The Zeeman interaction and hyperfineinteraction terms can be expressed as

HZe ¼ mBðLþgsSÞHM ð2Þ

Hhf ¼ P Lþ4

7�k

� �S�

1

7ðLSÞLþLðLSÞ½ �

� �I ð3Þ

Fig. 1. Energy level diagram for a d1 ion in tetragonally compressed octahedron.

Table 2The EPR spectral data (g factors and hyperfine structure constants Ai, A-values

are in units of 10�4 cm�1) for tetragonal [MoO6]7� clusters in [Mo6O19]-

[N(C4H9)4]3 salts.

gJ g? g AJ A? A

Calc. 1.922 1.930 1.927 74.9 32.3 46.5

Expt. [6] 1.919 1.930 1.926 75.0 32.2 46.5

W.-L. Feng / Journal of Magnetism and Magnetic Materials 324 (2012) 4061–40634062

where mB is the Bohr magneton, gs (¼2.0023) is the g value of thefree ion, k (¼0.98 [6]) is the core polarization constant and therest notations in Eqs. (2) and (3) are defined in literature [8].

In Eq. (1), the crystal-field parameters Bkq (B20, B40 and B44) canbe calculated from the superposition model [9] for tetragonaldistorted octahedron as

B20 ¼ 4A2ðR0ÞR0

R?

� �t2

�R0

RJ

� �t2

" #

B40 ¼�12A4ðR0ÞR0

R?

� �t4

�16A4ðR0ÞR0

RJ

� �t4

ð4Þ

B44 ¼�2ffiffiffiffiffiffi70p

A4ðR0ÞR0

R?

� �t4

in which the power-law exponents t2 (¼3) and t4 (¼5) can bedetermined in many reports [10–12]. RJ and R? are the bondlengths which are, respectively, parallel with and perpendicularto the z-axis in the [MoO6]7� cluster. A2ðR0Þ and A4ðR0Þ are theintrinsic parameters with the reference distance R0 (¼R¼ 1.953 Afor [Mo6O19][N(C4H9)4]3 [6]). The ratio A2ðR0Þ/A4ðR0Þ for 4dn

clusters is 672 and 8 is taken here [12].The 10�10 complete energy matrix related to the Hamilto-

nian of Eq. (1) is established. By diagonalizing the completeenergy matrix, d–d transitions can be calculated and EPR g factorsand hyperfine structure constants A are determined as follows:

gJ ¼DEZeðzÞ

mBHz, g? ¼

DEZeðxÞ

mBHxð5Þ

AJ ¼DEhf ðzÞ

I, A? ¼

DEhf ðxÞ

Ið6Þ

where DEZe(i) [¼EZei (1/2)�EZe

i (�1/2), i¼z or x] is the Zeemansplitting under the external magnetic field Hi along the i direction.Similarly, the hyperfine structure constants A can be obtained byhyperfine splitting and nuclear spin quantum number.

Thus, the isotropic EPR parameters can be calculated by

g ¼ g ¼ ðgJþ2g?Þ=3, A¼ A¼ ðAJþ2A?Þ=3 ð7Þ

In order to describe the covalence effect of mdn ions in crystals,an average covalent reduction factor K is introduced in the aboveformulae [13–15]. Thus, we have

z¼ K2z0d , P¼ K2P0 ð8Þ

For [MoO6]7� clusters under study, we have z0dE1030 cm�1

[15,16], P0E68.2�10�4 cm�1 [17].Thus, in the above formulae of Hamiltonian, there are three

adjustable parameters RJ, A4ðR0Þ and K. These values of RJ, A4ðR0Þ

and K, which are best fitted to the experimental values of d–dtransitions and EPR spectral data for Mo5þ in [Mo6O19][N(C4H9)4]3,are collected as follows:

RJ � 1:746 A, A4ðR0Þ � 868 cm�1, K � 0:511 ð9Þ

The comparison between the calculated results and experi-mental ones is shown in Table 1.

Table 1The d–d transition spectra (optical absorption bands, in cm�1) for tetragonal

[MoO6]7� clusters in [Mo6O19][N(C4H9)4]3 salts.

Transitions 2B2g-2Eg

2B2g-2B1g

2B2g-2A1g

Calc. 2148 2435 11,605 20,400

Expt. [6] – 11,600 20,400

3. Discussions

As known, the stronger is the covalence of dn cluster, thesmaller will be the factor K. In this case, the high valence of Mo5þ

leads to the stronger Mo¼O bond, thus, the covalent effect isdistinct and the K value (E0.511) exhibited is very small.

From Fig. 1, the effect of an Table 2 octahedral environment onthe d orbitals of a TM ion may be treated as a splitting of theoriginal group of five orbitals into three lower 2T02g and two upper2E0g orbitals under cubic field. There are many reports on the C4v

crystal field [18–21], the 2T2g level is further split into 2B2g (9dxyS)and 2Eg (9dxzS, 9dyzS) levels, and 2E0g level into 2B1g (9dx2�y2S)and2A1g (9dz2S) levels. Thus, the assigned transitions of the literature[6] may be inaccurate. In the present work, two bands (11,600and 20,400 cm�1) of the assignments are, respectively, 2B2g-

2B1g

and 2B2g-2A1g transitions. The d–d transitions obtained from the

above calculations are consistent with many research results for ad1 ion in tetragonally compressed octahedron [18–21] and can beregarded as rational. g factors varied with the RJ as shown inFig. 2. It is shown that the g factors varied with the RJ approxi-mately in a linear way.

Fig. 2. g factors varied with the RJ.

W.-L. Feng / Journal of Magnetism and Magnetic Materials 324 (2012) 4061–4063 4063

4. Conclusions

From the above calculations, the three optical spectral absorp-tion bands and six EPR spectral data calculated by the CDMmethod are in reasonable agreement with the experimentalvalues. In addition, the present research work about the defectstructure and electronic properties of paramagnetic ions would beuseful to understand the optical properties of [Mo6O19][N(C4H9)4]3

(and other similar oxomolybdenum salt) doped with transition-metal ions.

Acknowledgments

Project supported by the National Science Foundation of China(Grant no. 11104366), the Natural Science Foundation Project ofCQ (Grant nos. CSTC2011jjA50015, KJ120826 and KJ120804), theKey Project of Chinese Ministry of Education (No. 212139).

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