LC

La

b

c

d

a

ARRA

KLL(

1

mlp[tctisotp

tsrdi[A

U

0d

Materials Chemistry and Physics 112 (2008) 690–695

Contents lists available at ScienceDirect

Materials Chemistry and Physics

journa l homepage: www.e lsev ier .com/ locate /matchemphys

ocal lattice structure of Mn2+ ions in (MnO6)10− coordination complex:omplete diagonalization of d5 ions in a trigonal ligand field

u Chenga, Kuang Xiao Yua,d,∗, Zhou Kang Weib,c,d

Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, ChinaDepartment of Physics, Sichuan University, Chengdu 610065, ChinaCCAST (World Laboratory), P.O. Box 8730, Beijing 100080, ChinaInternational Centre for Materials Physics, Academia Science, Shenyang 110016, China

r t i c l e i n f o

rticle history:

a b s t r a c t

A detailed theoretical method for studying the local lattice structure of Mn2+ ions in (MnO6)10− coordi-

eceived 23 March 2008eceived in revised form 22 May 2008ccepted 30 May 2008

eywords:igand field model

nation complex is presented. Using the ligand field model, the formulas relating the microscopic spinHamiltonian parameters with the crystal structure parameters are derived. Based on the theoretical for-mulas, the 252 × 252 complete energy matrices for d5 configuration ions in a trigonal ligand field areconstructed. By diagonalizing the complete energy matrices, the local structure distortion of Mn2+ ions inA(C11H12ON2)6(ClO4)2:Mn2+ (A = Ca, Cd, Mg, Co, Pb) systems have been investigated. It is found that thetheoretical results are in good agreement with the experimental values.

h[tabtbtwthioot(

oT

ocal structureMnO6)10− coordination complex

. Introduction

Impurities in solid have attracted a great deal of attention forany years owing to their important roles from both a techno-

ogical and a theoretical point of view [1,2]. Among the impuritiesarticular attention has been focused on the transition metal ions3–5]. The transition metal Mn2+ ion is perhaps the most inves-igated impurity ion because the Mn2+ ion has a half-filled d5

onfiguration and its ground state is 6S, which suggests that theotal orbital angular momentum is zero. Since the total spin is 5/2,t exhibits an additional interaction, the zero-field splitting, and thisplitting is highly sensitive to the local structure of Mn centers. Inrder to gain more insight into the optical and magnetic proper-ies on the structure of the Mn centers, many studies of electronaramagnetic resonance (EPR) have been achieved [6].

EPR is one of the most important and powerful techniques forhe investigation of interactions of magnetic impurity ion withurroundings, since the spin resonance of a paramagnetic impu-ity is sensitive to its environment and its spectra can provide

etailed experimental information on the chemical identity of the

mpurity ion and its local arrangement within the host crystal7,8]. The EPR spectra of transition metal Mn2+ ions doped into(apy)6(ClO4)2 (apy = C11H12ON2, A = Ca, Cd, Mg, Co, Pb) crystals

∗ Corresponding author at: Institute of Atomic and Molecular Physics, Sichuanniversity, Chengdu 610065, China. Tel.: +86 2885405515; fax: +86 2885405515.

E-mail address: palc@163.com (K. Xiao Yu).

Atssosdd(

254-0584/$ – see front matter © 2008 Elsevier B.V. All rights reserved.oi:10.1016/j.matchemphys.2008.05.102

© 2008 Elsevier B.V. All rights reserved.

ave been experimentally observed by Woltermann and Wasson9]. Their experimental results give important information abouthe ground state of the transition metal Mn2+ ions and form

useful starting point for understanding the inter-relationshipsetween electronic and molecular structures of Mn2+ ions inhe (MnO6)10− coordination complex. However, there has so fareen no systematical theory for their analysis. The reason whyhe previous theoretical results are not in quite good agreementith the observed values may be due to the oversimplifica-

ion of the theoretical method. For instance, Jain and Kapoorave theoretically investigated the local structure of Mn2+ ions

n A(C11H12ON2)6(ClO4)2:Mn2+ (A = Mg, Ca, Pb) complex systemsn the basis of the second-order zero-field splitting parameter b0

2nly [10]. They did not investigate the fourth-order zero-field split-ing parameter b0

4 of Mn2+ ions in the A(C11H12ON2)6(ClO4)2:Mn2+

A = Mg, Ca, Pb) complex systems.It is well known that for a d5 configuration ion in a trig-

nal ligand field, the high-spin ground state is the 6A1 state.o describe the 6A1 ground state splitting of the Mn2+ ions in(C11H12ON2)6(ClO4)2:Mn2+ (A = Ca, Cd, Mg, Co, Pb) complex sys-

ems, the spin Hamiltonian should include three different zero-fieldplitting parameters b0

2, b04 and b3

4. In order to explain the distortiontructure more reasonably, herein, we suggest that the second-

rder zero-field splitting parameter b0

2 and fourth-order zero-fieldplitting parameter b0

4 should be simultaneously considered in theetermination of the local structure distortion of (MnO6)10− coor-ination complex for Mn2+ ions in A(C11H12ON2)6(ClO4)2:Mn2+

A = Ca, Cd, Mg, Co, Pb) systems.

stry an

suteefctac

sc

2

fi

H

wfmts[eg

tbsfi

3

ics

wOttuhfifbCpw

j2 − j

× (j − j2 +m1 + �)!(j − j1 −m2 + �)!]−1

} j1m1

j2m2. (4)

L. Cheng et al. / Materials Chemi

The goal of the present study is two-fold: to elucidate a micro-copic origin of various ligand field parameters which are usuallysed empirically for the interpretation of EPR and optical absorp-ion experiments, and to provide powerful guidelines for futurexperimental studies aimed at pinpointing how actually Mn2+

nters the metal perchlorate complex. The paper is organized asollows: In Section 2, the spin Hamiltonian and energy levels for d5

onfiguration Mn2+ ion in trigonal ligand field are described andhe microscopic formulas of EPR parameters for 6A1 ground statere given. In Section 3, the method how to construct the 252 × 252omplete energy matrices is discussed. In Section 4, the local

tructure distortion for Mn2+ ions in the (MnO6)10− coordinationomplex is investigated. Conclusions are summarized in Section 5.

. The spin Hamiltonian

The EPR spectra of d5 configuration Mn2+ ions in a trigonal ligandeld can be described by the following spin Hamiltonian [11]

ˆ = uB�S · g · �B+ 1

3b0

2O02 + 1

60(b0

4O04 + b3

4O34), (1)

here the first term corresponds to the Zeeman interaction and theollowing terms represent the zero-field interaction. uB is the Bohr

agneton, �S is the spin angular momentum operator, g is the split-ing factor, �B is the external magnetic field, bq

kare the zero-field

plitting parameters, Oqk

are the standard Stevens spin operators12]. From the spin Hamiltonian the explicit expressions of thenergy levels in the ground state 6A1 for a zero magnetic field areiven as follows [11]

�E1 = E(

± 52

)− E

(± 1

2

)= ± 1

3

[(18b0

2 − 3b04)

2 + 910

(b34)

2]1/2

,

�E2 = E(

± 32

)− E

(± 1

2

)= −b0

2 − 92b0

4 ± 16

[(18b0

2 − 3b04)

2 + 910

(b34)

2]1/2

.

(2)

where

E(

±12

)= 1

3b0

2 + 32b0

4 ∓ 16

[(18b02 − 3b0

4)2 + 9

10(b3

4)2]1/2,

E(

±32

)= −2

3b0

2 − 3b04,

E(

±52

)= 1

3b0

2 + 32b0

4 ± 16

[(18b0

2 − 3b04)

2 + 910

(b34)

2]1/2

.

(3)

he positive and negative signs in Eqs. (2) and (3) correspond to02 ≥ 0 and b0

2 < 0, respectively. Some properties of the zero-fieldplitting energies�E1 and�E2 for Mn2+ ion in the trigonal ligandeld are shown in Fig. 1.

. The complete energy matrix

jm =∑m1m2

(j1j2m1m2||j1j2jm) j1m1 j2m2

=∑m1m2

{ım,m1+m2 ×

[(2j + 1)

(j + j1 − j2)!(j − j1 + j2)!(j1 +(j + j1 + j2 + 1)!

×∑�

(−1)�

�![(j1 + j2 − j − �)!(j1 −m1 − �)!(j2 +m2 − �)!

In order to shed more light on the local structure of the Mn2+

ons in the (MnO6)10− coordination complex, we will construct theomplete energy matrix of d5 configuration ion within ligand fieldcheme in this section. It is well known that, there are two different

F�

d Physics 112 (2008) 690–695 691

ays which have been developed to construct the complete matrix.ne is Racah’s method, in which the tensor operator is used [13];

he other is Slater’s method, in which the relationships betweenhe matrix of the single d electron and the matrix of the dn config-ration are established [14]. In the present work, Slater’s methodas been employed. For a d5 configuration ion in a trigonal ligandeld, in order to construct the complete matrices, the |J, MJ〉 basic

unctions need to be expanded into the form of the |L, S, ML, MS〉iasic functions. This expansion may be realized in terms of thelebsch–Gordon coefficients which are associated with the cou-ling of two angular moments. In general, the expansion can beritten as [15]

)! × (j1 +m1)!(j1 −m1)!(j2 +m2)!(j2 −m2)!(j +m)!(j −m)!

]1/2

ig. 1. The energy levels of the three Kramers doublets in S = 5/2 spin state.�E1 andE2 are the zero-field splitting energies in the ground state 6A1.

692 L. Cheng et al. / Materials Chemistry and Physics 112 (2008) 690–695

Table 1The observed and calculated optical absorption spectra for �-Fe2O3 and MnO compounds

State �-Fe2O3 MnO

Mineral Powder Thin film �-Fe2O3 on S.S.

Obsda Calc Obsdb Calc Obsdc Calc Obsdb Calc Obsdd Calc

4T1(G) 11,600 11,601 11,614 11,614 11,560 11,560 11,695 11,695 15,890 15,8904T2(G) 16,028 16,050 16,071 16,670 16,682 16,615 16,644 20,210 20,2374A1(G) 4E(G) 23,800 23,803 23,926 23,800 23,803 24,009 23,708 23,7074T2(D) 25,039 26,408 24,987 26,502 25,910 25,9684E(D) 26,700 26,724 28,324 26,670 26,690 29,762 29,822 27,912 27,9744T1(P) 31,800 31,841 32,585 32,596 31,750 31,794 32,101 32,175 32,084

All levels in units of cm−1.a

〈

f

|

w2otc

H

woitcfif

4c

(paTCTpa

wmcWbaZlE

G

tance and the angle between R and C3 axis. � and q� represent the�th ligand ion and its effective charge, respectively. A2 = −eq� 〈r2〉,A4 = −eq� 〈r4〉 and A2/A4 = 〈r2〉/〈r4〉. The ratio of 〈r2〉/〈r4〉 = 0.119328 isobtained from the radial wave-function of Mn2+ ion in complexes[23]. A4 is a constant for the (MnO6)10− coordination complex,

Reference [28].b Reference [26]. (S.S.: Stainless Steel).c Reference [27].d Reference [24].

The relationship of the coefficients between m and −m is

j1j2m1m2||j1j2jm〉 = (−1)j1+j2−j〈j1j2 −m1 −m2||j1j2j −m〉 (5)

From the Eqs. (4) and (5), it is quite easy to get the |J, MJ〉 basicunctions

J,MJ〉 =∑i

Ci|L, S,ML,MS〉i =∑i

∑j

CiCj˚j (6)

here Ci and Cj are the Clebsch–Gordon coefficients,˚j is one of the52 basic Slater determinants. For a d5 configuration ion in a trig-nal ligand field, there are 252 independent wave-functions. Usinghe |L, S, ML, MS〉i functions, we have constructed the 252 × 252omplete energy matrices of the Hamiltonian

ˆ = Hee + Hso + Hlf =∑i<j

e2

ri,j+ �

∑i

li · si +∑i

Vi (7)

here the first term is the electron–electron interactions, the sec-nd term is the spin–orbit coupling interactions, and the third terms the ligand field potentials [16]. The matrix elements are the func-ion of the Racah parameters B and C, Trees correction ˛, Racahorrection ˇ, the spin-orbit coupling coefficient � and the ligandeld parameters B20, B40, Bc43 and Bs43, which are in the following

orms [17]

B20 = 12

∑�

G2(�)(3 cos2 �� − 1),

B40 = 18

∑�

G4(�)(35 cos4 �� − 30 cos2 �� + 3),

Bc43 =

√354

∑�

G4(�)(sin3 �� cos �� cos 3��),

Bs43 = i

√354

∑�

G4(�)(sin3 �� cos �� sin 3��).

(8)

. The local structure distortion for Mn2+ ions in (MnO6)10−oordination complex

The molecule 1-phenyl-2,3-dimethyl-5-pyrazaloneC11H12ON2), know as antipyrine, is a crystalline organic com-ound [18]. It can form stable metal complexes via the oxygentom in the carbonyl group, with iron group metal perchlorates.

he crystal structure of A(apy)6(ClO4)2 (apy = C11H12ON2, A = Ca,d, Mg, Co, Pb) has been reported by Vijayan et al. [18–21].he structural information shows that the hexakisantipyrineerchlorate complexes of divalent magnesium, calcium, cobaltnd lead are isomorphous, crystallizing in the space group P3

FAli

ith one molecule in the unit cell. The EPR spectra of transitionetal Mn2+ ions in A(C11H12ON2)6(ClO4)2 (A = Ca, Cd, Mg, Co, Pb)

rystals are extensively studied by Woltermann and Wasson [9].oltermann and Wasson observed that Mn2+ ion is surrounded

y six antipyrine oxygen atoms. The local lattice structure displaystrigonal distortion [9,10]. In order to describe the distortion, theaxis is chosen along three-fold axis, as shown in Fig. 2. Then, the

igand field parameter Bs43 will vanish and the G2(�) and G4(�) in

q. (8) can be expressed as [22]

2(�) =−eq�

⟨r2

⟩R3

= A2

R3, G4(�) =

−eq�⟨r2

⟩R5

= A4

R5. (9)

where the R in Eq. (9) and � in Eq. (8) are the metal–ligand dis-

ig. 2. The local structure of (MnO6)10− coordination complex for Mn2+ ions in(C11H12ON2)6(ClO4)2:Mn2+ (A = Ca, Cd, Mg, Co, Pb) systems. R is the Mn O bond

ength, � is the angle between Mn O bond and C3 axis when Mn2+ ion replaces A2+

on.�� and�R represent the structure distortion.

L. Cheng et al. / Materials Chemistry and Physics 112 (2008) 690–695 693

Table 2The calculated parameters for Fe3+ ions in �-Fe2O3 and Mn2+ ions in MnO compounds

Parameters N B C � ˇ Dq A2 A4

�-Fe2O3

Mineral 0.9266 815.3 2891.2 59.7 −21.4 1393.8 2.9986 30.9133Powder 0.9278 819.5 2906.2 60.0 −21.5 1405.8 3.0244 31.1795Thin film 0.9266 815.3 2891.2 59.7 −21.4 1397.9 3.0074 31.0043on S.S. 0.9286 822.4 2916.2

MnO 0.9694 810.7 2890.4

Where B, C, �, ˇ and Dq are in units of cm−1, A2 and A4 are in units of au.

Table 3The energy levels 4A1, 4E(G) for Mn2+ ions in different ligands

Ligands Compounds 4A1, 4E(G) (cm−1)

H2OMn(ClO4)·6H2Oa 25,000MnSiF6·6H2Oa 25,000

ClMnCl2b 23,825(CH3)4NMnCl3c 23,780

BrMnBr2

b 23,084CsMnBr3

d 23,150

OMnOe 23,708Mn(apy)6(ClO4)2

f 23,708

a Reference [32].b Reference [33].c Reference [34].

ittwpTrsiS(d(tdf�P

R

(be

dlaf

B

bˇAtsMfoNCfPpdtT

irsF�(ttotaf

′

TT

r

C

MCCCP

d Reference [35].e Reference [24].f The energy level 23708 cm−1 is estimated from Mn2+ ions in MnO.

ts value can be determined from the optical absorption spec-ra and the Mn O bond length of MnO crystal [24,25]. By fittinghe calculated optical absorption spectra to the observed values,e can obtain different optical parameters for different com-ounds [24–29]. The quantitative calculation results are listed inables 1 and 2. From Tables 1 and 2, we can see that the calculationesults are in quite good agreement with the experimental values. Ithould be also noted that A4 for (MnO6)10− coordination complexs obviously smaller than A4 for (FeO6)9− coordination complex.ubstituting A4 = 27.6104 au and A2 = 3.2947 a.u. for Mn2+ ions inMnO6)10− coordination complex into Eqs. (8) and (9), the localistortion structure of Mn2+ ions in A(C11H12ON2)6(ClO4)2:Mn2+

A = Ca, Cd, Mg, Co, Pb) crystals can be determined by diagonalizinghe complete energy matrices. The local structure distortion can beescribed by two parameters�R and�� (see Fig. 2). We used theollowing relationship to evaluate the bond length R and bond anglefor Mn2+ ions in A(C11H12ON2)6(ClO4)2:Mn2+ (A = Ca, Cd, Mg, Co,b) complex systems.

= R0 +�R, � = �0 +�� (10)

where R0 is the A O bond length in A(C11H12ON2)6(ClO4)2A = Ca, Cd, Mg, Co, Pb) crystals. �0 is the angle between A Oond and C3 axis [18–21]. Thus, the trigonal ligand field param-ters (B20, B40, B

c43) are only functions of �R and ��. In order to

tMAob

able 4he ground-state zero-field splitting �E1, �E2 and the EPR parameters b0

2 and b04 for Mn

oom temperature, where 104�E1, 104�E2, 104b02 and 104b0

4 are in units of cm−1

rystals R (Å) � (◦) 104�E1 10

g(C11H12ON2)6(ClO4)2 2.240 53.947 −264.70 −7o(C11H12ON2)6(ClO4)2 2.194 54.292 −244.81 −6d(C11H12ON2)6(ClO4)2 2.292 54.299 −167.48 −4a(C11H12ON2)6(ClO4)2 2.234 54.333 −190.01 −5b(C11H12ON2)6(ClO4)2 2.263 54.619 −50.20 −a Reference [9].

60.2 −21.6 1406.5 3.0259 31.1950

57.4 −115.7 933.8 3.2947 27.6104

ecrease the number of adjustable parameters and reflect the cova-ency effects, we use the Curie et al. covalent theory and take anverage covalence factor N to determine the optical parameters asollowing [30]

= N4B0, C = N4C0, ˛ = N4˛0, ˇ = N4ˇ0, � = N2�0. (11)

The values of the free-ion parameters for Mn2+ ion haveeen obtained as B0 = 918 cm−1, C0 = 3273 cm−1, ˛= 65 cm−1,= −131 cm−1, and �0 = 347 cm−1 [31]. For Mn2+ ions in the(C11H12ON2)6(ClO4)2:Mn2+ (A = Ca, Cd, Mg, Co, Pb) complex sys-

ems, the optical spectra has not been reported. However, for theame ligand, the experiments show that the 4A1 and 4E states ofn2+ ion have the similar energy (see Table 3) [13,32–35]. There-

ore, we can take the average covalency parameter N = 0.9694 of thexygen ligand in the calculation. Substituting the covalence factorinto the Eq. (11), we can get the optical parameters B = 810.7 cm−1,= 2890.4 cm−1, ˛= 57.4 cm−1, ˇ = −115.7 cm−1 and � = 326.1 cm−1

or Mn2+ ions in the A(C11H12ON2)6(ClO4)2:Mn2+ (A = Ca, Cd, Mg, Co,b) complex systems. By using of the Eqs. (7)–(10) and the opticalarameters B, C,˛,ˇ and �, we can calculate the corresponding localistortion structure parameters R and �. The comparisons betweenhe theoretical values and experimental findings are shown inable 4.

It can be seen from Table 4 that the theoretical results aren good agreement with the experimental values. The calculationesults have indicated several interesting features of the electronictructure for Mn2+ ions in the (MnO6)10− coordination complex.rom the calculation, the local lattice structure R = 2.194–2.292 Å,= 53.947◦–54.619◦ for Mn2+ ions in A(C11H12ON2)6(ClO4)2:Mn2+

A = Mg, Co, Cd, Ca, Pb) complex systems are determined. Theseheoretical results may provide a satisfactory and unified explana-ion for the experimental findings of the EPR spectra. By comparingur theoretical results (R = 2.194–2.292 Å, � = 53.947◦–54.619◦) withhe results (R = 2.054–2.462 Å, � = 51.98◦–54.47◦) obtained by Jainnd Kapoor [10], it is noteworthy to mention that the empiricalormulas Ri(Rj) = (RH + R′)/2 (where RH is the cation-ligand bond dis-

ance in the pure crystal, R = 2.2 Å is the Mn O bond distance for

n2+ ions coordinated with six oxygens) are not suitable for the(C11H12ON2)6(ClO4)2:Mn2+ (A = Mg, Co, Cd, Ca, Pb) systems andnly considering the second-order zero-field splitting parameter02 in the structure investigation is imperfect.

2+ ions in A(C11H12ON2)6(ClO4)2:Mn2+ (A = Mg, Co, Cd, Ca, Pb) complex systems at

4�E2 104b02 104b0

4 (104b02)

expa (104b0

4)exp

a

8.11 −44.33 −2.20 −44.35 −2.208.61 −41.13 −2.81 −41.09 −2.808.29 −28.09 −1.63 −28.11 −1.642.91 −31.94 −2.25 −31.93 −2.248.32 −8.64 −1.81 −8.68 −1.81

694 L. Cheng et al. / Materials Chemistry and Physics 112 (2008) 690–695

F rs 104

( Mg2+

a

tidCMipClnRw(tmHd

5

iadstfcoop

olp

A

fStC

R

[[

[[

[

ig. 3. The local distortion structure parameters R, � and zero-field splitting paramete

A = Mg, Co, Cd, Ca, Pb):Mn2+ systems when the host metal ion radius increase from (

nd 104b04 are in units of cm−1.

In addition, we can find that the absolute values of the local dis-ortion structure parameter � increased with increasing host metalon radius, and the Mn O bond distance R of the (MnO6)10− coor-ination complex for Mn2+ ions in A(C11H12ON2)6(ClO4)2 (A = Mg,o, Cd, Ca, Pb):Mn2+ systems is nearly the same as R′ = 2.2 Å forn2+ ions coordinated with six oxygens (see Fig. 3) [11,13]. Accord-

ng to Fig. 3, we can see that the fourth-order zero-field splittingarameters b0

4 of Mn2+ ions in A(C11H12ON2)6(ClO4)2 (A = Mg, Co,d, Ca, Pb):Mn2+ complex systems are strongly dependent on the

ocal distortion structure parameter R. From Fig. 3, we can alsoote that the change of the local distortion structure parameterand the zero-field splitting parameter b0

4 are almost the samehen the host metal ion radius increase from (Mg2+ ion) 0.66 Å to

Pb2+ ion) 1.20 Å. These results may be attributed to the fact thathe crystals A(C11H12ON2)6(ClO4)2 (A = Mg, Co, Cd, Ca, Pb) are iso-

orphous and have the similar physical and chemical properties.owever, the above results remain to be checked by other moreirect experimental methods.

. Conclusion

Using the complete diagonalization method, we establish thenter-relationships between electronic and molecular structures,nd study the local molecular structure of the (MnO6)10− coor-ination complex. By solving the energy matrices, the zero-fieldplitting parameters b0

2 and b04 have been derived and the local dis-

ortion structure parameters R = 2.194–2.292 Å, � = 53.947◦–54.619◦

or Mn2+ ions in A(C11H12ON2)6(ClO4)2:Mn2+ (A = Mg, Co, Cd, Ca, Pb)omplex systems are determined. It is worth noting that these the-retical results are of significance in broadening our understandingf the physical and chemical properties of metal perchlorate com-lex. Of course, careful experimental investigations, especially

[[[[[

b02, 104b0

4 of (MnO6)10− coordination complex for Mn2+ ions in A(C11H12ON2)6(ClO4)2

ion) 0.66 Å to (Pb2+ ion) 1.20 Å. Where R is in units of Å, � is in units of degree, 104b02

ptical absorption experiment, are required in order to clarify theocal structure around the Mn2+ ions in the metal perchlorate com-lex in detail.

cknowledgments

The authors express their gratitude to Dr. Du He for many help-ul discussions. This work was supported by the National Naturalcience Foundation (No.10774103 and No.10374068) and the Doc-oral Education Fund of Education Ministry (No. 20050610011) ofhina.

eferences

[1] C. Rudowicz, P. Gnutek, M. Karbowiak, Phys. Rev. B 76 (2007) 125116.[2] E. Malguth, A. Hoffmann, W. Gehlhoff, O. Gelhausen, M.R. Phillips, X. Xu, Phys.

Rev. B 74 (2006) 165202.[3] S. Dhanuskodi, A. Pricilla Jeyakumari, Mater. Chem. Phys. 87 (2004) 292.[4] R. Davydov, B.M. Hoffman, J. Biol. Inorg. Chem. 13 (2008) 357.[5] W. Ouellette, A.V. Prosvirin, J. Valeich, K.R. Dunbar, J. Zubieta, Inorg. Chem. 46

(2007) 9067.[6] R. Kripal, V. Mishra, J. Magn. Reson. 172 (2005) 201.[7] B. Yasoda, R.P. Sreekanth Chakradhar, J.L. Rao, N.O. Gopal, Mater. Chem. Phys.

106 (2006) 33.[8] R. Kripal, M. Maurya, Mater. Chem. Phys. 108 (2008) 257.[9] G.M. Woltermann, J.R. Wasson, J. Phys. Chem. 77 (1973) 945.10] V.K. Jain, V. Kapoor, J. Phys. Chem. Solids 53 (1992) 1171.11] A. Abragam, B. Bleaney, Electron Paramagnetic Resonance of Transition Ions,

Clarendon Press, Oxford, 1970.12] K.W.H. Stevens, Proc. Phys. Soc., London, Sect. A 65 (1952) 209.13] J.S. Griffith, The Theory of Transition-Metal Ions, Cambridge University Press,

London, 1964.14] J.C. Slater, Quantum Theory of Molecules and Solids, vol. I, McGraw-Hill, New

York, 1963.15] R.N. Zare, Angular Momentum, John Wiley & Sons, New York, 1988.16] M.T. Hutchings, Solid State Physics 16 (1964) 227.17] D.J. Newman, W. Urban, Adv. Phys. 24 (1975) 793.18] M. Vijayan, M.A. Viswamitra, Z. Kristallogr. 122 (1965) 153.19] M. Vijayan, M.A. Viswamitra, Acta Cryst. 21 (1966) 522.

stry an

[[[[[[[[[

[

[30] D. Curie, C. Barthon, B. Canny, J. Chem. Phys. 61 (1974) 3048.

L. Cheng et al. / Materials Chemi

20] M. Vijayan, M.A. Viswamitra, Acta Cryst. 23 (1967) 1000.21] M. Vijayan, M.A. Viswamitra, Acta Cryst. B 24 (1968) 1067.22] J.H.V. Vleck, Phys. Rev. 41 (1932) 208.

23] M.G. Zhao, G.R. Bai, H.C. Jin, J. Phys. C: Solid State Phys. 15 (1982) 5959.24] D.R. Huffman, R.L. Wild, M. Shinmei, J. Chem. Phys. 50 (1969) 4092.25] S.K. Nayak, P. Jena, Phys. Rev. Lett. 81 (1998) 2970.26] R. Guillamet, M. Lenglet, F. Adam, Solid State Commun. 81 (1992) 633.27] L.A. Marusak, R. Messier, W.B. White, J. Phys. Chem. Solids 41 (1980) 981.28] D.M. Sherman, Phys. Chem. Miner. 12 (1985) 161.

[[[[[

d Physics 112 (2008) 690–695 695

29] T. Droubay, K.M. Rosso, S.M. Heald, D.E. McCready, C.M. Wang, S.A. Chambers,Phys. Rev. B 75 (2007) 104412.

31] X.Y. Kuang, W. Zhang, I. Morgenstern-Badarau, Phys. Rev. B 45 (1992) 8104.32] Lawrence L. Lohr Jr., D.S. McClure, J. Chem. Phys. 49 (1968) 3516.33] R. Pappalardo, J. Chem. Phys. 33 (1960) 613.34] K.E. Lawson, J. Chem. Phys. 47 (1967) 3627.35] G.L. Mcpherson, H.S. Aidrich, J.R. Chang, J. Chem. Phys. 60 (1974) 534.