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Covalency and EPR hyperfine structure constant of Eu2+ in crystals
Volume 119, number 2
PHYSICS LETTERS A
1 December 1986
COVALENCY AND EPR HYPERFINE STRUCTURE CONSTANT OF Eu2~IN CRYSTALS Al. NICULA University of Cluj-Napoca, Faculty of Physics, 3400 Cluj-Napoca, Romania
0. PANA and L.V. GIURGIU Institute ofIsotopic and Molecular Technology, P.O. Box 700, 3400 Cluj-Napoca 5, Romania Received 28 August 1986; accepted for publication 2 October 1986
The covalent reduction of the EPR hyperfine constant of Eu2 + in different crystals is presented as resulting from the exchange polarization mechanism. Free-ion values of hyperfine constants of Eu2 isotope are calculated.
The dependence of the EPR hyperfine constant A on the bonding covalency character was analysed by Simanek and MUller [1] for the Mn2 ± (3d5) ion substituted in a large class of crystals. A similar dependence was evidentiated by us, in the case of S state Eu2~(4f7) ions, considering published reports on the EPR hyperfine structure constants of Eu2~.Values of the hyperfine constant A of these ions, in various host lattices, are indicated in 51Eu2~and ‘53Eu2~isotopes. table 1, for ‘ The covalency was computed using the relation of Hannay and Smyth [18] 2 (1) .
Cr 1
0.16(XEU —XL)
0.035(XEU
XL)
Here,the electronegativities of europium and ligands, designated as XEU and XL, where taken from.the tables of Gordy and Thomas [19]. The covalency parameter was obtained dividing the covalency c by the number of ligands n. In fig. 1 we can observe the monotonic decrease of 2~isotopes, with the hyperfine constants, for both Eu increasing covalency. Different values of the hyper2~—liganddistances in fine constants, for the same covalency parameter, are probably due to[201. different Eu various crystals For qualitative discussions, a calculation could be developed using the LCAO description, Combinations of ligand, øL~and europium, 06s, orbitals give the following bonding and antibonding 92
Table 1 EPR hyperfine structure constants for Eu2 ~ in different host lattices. Host crystal NaCI KCI RbCl 2 SrCl2 PbCI 2 NaBr RbBr KBr Nal KI Rb! CaO SrO CaWO 4 PbMoO4 KTaO3 SrTiO 3 ZnS CdTe CdS CdSe
A(‘ 51Eu) (l0-~cm~) 31.3 31.3
A ( ‘53Eu) (l0-~cm~) 13.8 14.3
Ref.
33.8 32.5 32.5 34.5 30.8 30.3 30.6 30.2 30.6 30.4 30.1 29.9
15.5 14.7
13.4 13.2
[3] [4] [5] [6] [2] [8] [8] [9] [9] [9] [10] [10]
34.8 34.0 36.0 36.2 23.3 23.2 23.0 22.5
15.8 15.0 16.0 17.6 10.3 10.2 10.3 10.0
[11] [12] [13] [14] [15] [16] [17] [16]
15.3 13.2 13.2
[2] [2]
states: ~
— ~
WB—
BkWL+Y6W6S
0375-9601186/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Volume 119, number 2
PHYSICS LETTERS A
ment in eq. (5)
1
-Ax~m
1 December 1986
S~flO3 ~KTCO3
<ØfØn CcWi~
I Vex I øBøf>
=NBNnY 6<øfønsIVexIø4søf>. 30
(6) 2 + nucleus could
Thewritten unpaired spin density at the Eu be
~NoCL ~2 R~CL~ ‘< + f~2 ROt ~Co0 L~t2 ~ Nc,Br~0 R~r ‘
N\
p’(O):=p(O)_[IØ~(O)I2—IØ~(O)l2]
(7) where p(O) is the unpaired spin density for the “free” Eu2~ion and IØ~(0)I2—IØB(0)I2 is the bonding exchange contribution. This contribution is easily calculated from eqs. (5) and (6) giving
ZeS
25 CdS Cd~+~ + 20 SI~t03 KT003
IØ~(0)I2_IØa(0)I2
c~o 4
~5,
_________ ~
SrC 10
=N~Y~(2N2 6 <0f06sE6-EB I Vex Iø6søf> 106s(0) 12
,~
‘
.
+~-
+2N6 ~
CdSe
n>6
30 m’,. 51Eu2~and Fig. ‘53Eu2~as 1. Thea hyperfine function of interaction the ratio c/n. constant The upper A of ‘curve is for 5’Eu2 + and the lower one for ‘“Eu2 ~ 10
15
20
25
0 6=N6[06S—(y6+S6)OL]
n>6,
Ofl=Nfl(OflS—SflOL),
(3) (4)
where Sn = <Ø,~.I OL> designates the overlap integral. Here 0,, (n> 6) are the up-spin-excited states of the ion—ligands complex. N is a normalisation constant and Y6 is the OL~~O6stransfer parameter. The transfer parameter y,, in eq. (4) was considered zero since the bondings of S-excited states are zero. Also, it is obvious that orbital cannot be included, since thethe 4f 4f orbital is covalency inside the 6s one, and thus a single covalency parameter was used, Via the exchange potential the unpaired Ø~elecirons remove the O~spin degeneracy, giving the Ø~ distorted orbital = OH +
~
nZ~6
I
Vex 100> On.
E~—EB
(5)
Using eqs. (2) and (4) one has for the matrix ele-
<øføns I Vex Iø6søf>Ø* (0)0 (0)) EflEB
(8) In this equation the parameters N~ y~and N~are proportional to the total charge transferred to the 6s state ofthe Eu2 ± ion. By substitution of eq. (8) into eq. (7) these parameters act to reduce the unpaired spin density with increasing covalency. As a consequence, from eq. (8), the observed decrease of the hyperfine structure constants with increasing covalency (fig. 1) arises from the reduction of the unpaired spin density, via the exchange polarization mechanism, of both ion—ligands cornplex bonding orbitals and up-spin-excited states. Extrapolation of the curves from fig. 1 to “zero covalency” gives the possibility to estimate two hyperfine constants which attributed to 2 + free ion: A(‘ 51Eu2are ~) formally = —42.2 x l0~cm—’ the Eu and A (‘“Eu2 ~) = 19.4 x 1 Ø_4 cm—’. The experimental hyperfine structure constant could be expressed in the form [21] —
(9) where Af includes contributions from the break-down A=AS+Af,
of LS coupling and from relativistic effects. A~is the exchange polarization term. For Eu2~,Evans, Sandars and Woodgate [22] consideredA~tobeA~(’”Eu2~)= —6.7xl04cm’ 93
Volume 119, number 2
PHYSICS LETTERS A
andAf(’53Eu2~)=—2.9x l0~cm~. From eq. (9), free ion values for the exchange polarization term, A~, in the case of Eu2~were obtained as A~(’51Eu2~)=35.5x l0~ cm~and A~(’53Eu2~)= l6.5x l0~cm~. Using these values, the hyperfine field parameter x~representing the hyperfine field at europium nucleus per unpaired spin unit, was determined. For both isotopes a value of x = 1.2 au was obtained, corresponding to a hyperfine field of 350 kG, in excellent agreement with the theoretical value obtained by Watson and Freeman [23] using the unrestricted Hartree—Fock method. —
—
—
—
References [1] E. Simanek and K.A. MUller, J. Phys. Chem. Solids 31 (1970) 1027. [2] S. Aquilan and E. Munoz, J. Chem. Phys. 62 (1975) 1197. [3] J.O. Rubio et al., J. Chem. Phys. 72 (1980) 2210.
94
1 December 1986
[4] W. Lowand U. Rosenberger, Phys. Rev. 116(1959) 621. [5] Q.H.F. Vrehen andJ. Volger, Physica 31(1965) 845. [6] J.M. Bekeret al.,et Proc. R. Soc.A247 (1958) [7] V.M. Vinocurov al., Ph.T.L 5 (1963) 1936.141. [8] E. Munoz,J. Chem. Phys. 62(1975) 3416. [9]J.O. Rubio,J. Chem. Phys. 63(1975)4222. [10] W. Low and J.T. Suss, Phys. Lett. 11(1964)115. [11] [12] [13] [14] [15]
J. Bronstein and V. Voltera, Phys. Rev. 137 (1965) A 201. A.A. Antipin et al., Ph.T.T. 7 (1965) 1425. H. Unoki andJ. Sakudo,J. Phys. Soc. Japan 21(1964)1730. L. Rimai et al., Phys. Rev. 133 (1964) A 1123. J. Turkevich and A. Nicula, unpublished.
[16] [17] [18]
R.S. Title, Phys. Rev. 133 (1964) A 198. P.B. Donan, Phys. Rev. 120 (1960) 1190. N.B. 171. Hannay and C. F. Smyth, J. Am. Chem. Soc. 68 (1946)
[19] W. Gordy and W.J.O. Thomas, J. Chem. Phys. 24 (1956) 439. [20] G. Lehmann, J. Phys. Chem. Solids 41(1980) 919. [21] B. Bleaney, in: La structure hyperfine magnetique des atomes et des molecules (CNRS, Paris, 1967). [22] L. Evans, P.G.H. Sandars and KG. Woodgate, Proc. R. Soc. A 289 (1965) 97. [23) R.E. Watson and A.J. Freeman, Phys. Rev. 123 (1961) 2027.
PHYSICS LETTERS A
1 December 1986
COVALENCY AND EPR HYPERFINE STRUCTURE CONSTANT OF Eu2~IN CRYSTALS Al. NICULA University of Cluj-Napoca, Faculty of Physics, 3400 Cluj-Napoca, Romania
0. PANA and L.V. GIURGIU Institute ofIsotopic and Molecular Technology, P.O. Box 700, 3400 Cluj-Napoca 5, Romania Received 28 August 1986; accepted for publication 2 October 1986
The covalent reduction of the EPR hyperfine constant of Eu2 + in different crystals is presented as resulting from the exchange polarization mechanism. Free-ion values of hyperfine constants of Eu2 isotope are calculated.
The dependence of the EPR hyperfine constant A on the bonding covalency character was analysed by Simanek and MUller [1] for the Mn2 ± (3d5) ion substituted in a large class of crystals. A similar dependence was evidentiated by us, in the case of S state Eu2~(4f7) ions, considering published reports on the EPR hyperfine structure constants of Eu2~.Values of the hyperfine constant A of these ions, in various host lattices, are indicated in 51Eu2~and ‘53Eu2~isotopes. table 1, for ‘ The covalency was computed using the relation of Hannay and Smyth [18] 2 (1) .
Cr 1
0.16(XEU —XL)
0.035(XEU
XL)
Here,the electronegativities of europium and ligands, designated as XEU and XL, where taken from.the tables of Gordy and Thomas [19]. The covalency parameter was obtained dividing the covalency c by the number of ligands n. In fig. 1 we can observe the monotonic decrease of 2~isotopes, with the hyperfine constants, for both Eu increasing covalency. Different values of the hyper2~—liganddistances in fine constants, for the same covalency parameter, are probably due to[201. different Eu various crystals For qualitative discussions, a calculation could be developed using the LCAO description, Combinations of ligand, øL~and europium, 06s, orbitals give the following bonding and antibonding 92
Table 1 EPR hyperfine structure constants for Eu2 ~ in different host lattices. Host crystal NaCI KCI RbCl 2 SrCl2 PbCI 2 NaBr RbBr KBr Nal KI Rb! CaO SrO CaWO 4 PbMoO4 KTaO3 SrTiO 3 ZnS CdTe CdS CdSe
A(‘ 51Eu) (l0-~cm~) 31.3 31.3
A ( ‘53Eu) (l0-~cm~) 13.8 14.3
Ref.
33.8 32.5 32.5 34.5 30.8 30.3 30.6 30.2 30.6 30.4 30.1 29.9
15.5 14.7
13.4 13.2
[3] [4] [5] [6] [2] [8] [8] [9] [9] [9] [10] [10]
34.8 34.0 36.0 36.2 23.3 23.2 23.0 22.5
15.8 15.0 16.0 17.6 10.3 10.2 10.3 10.0
[11] [12] [13] [14] [15] [16] [17] [16]
15.3 13.2 13.2
[2] [2]
states: ~
— ~
WB—
BkWL+Y6W6S
0375-9601186/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Volume 119, number 2
PHYSICS LETTERS A
ment in eq. (5)
1
-Ax~m
1 December 1986
S~flO3 ~KTCO3
<ØfØn CcWi~
I Vex I øBøf>
=NBNnY 6<øfønsIVexIø4søf>. 30
(6) 2 + nucleus could
Thewritten unpaired spin density at the Eu be
~NoCL ~2 R~CL~ ‘< + f~2 ROt ~Co0 L~t2 ~ Nc,Br~0 R~r ‘
N\
p’(O):=p(O)_[IØ~(O)I2—IØ~(O)l2]
(7) where p(O) is the unpaired spin density for the “free” Eu2~ion and IØ~(0)I2—IØB(0)I2 is the bonding exchange contribution. This contribution is easily calculated from eqs. (5) and (6) giving
ZeS
25 CdS Cd~+~ + 20 SI~t03 KT003
IØ~(0)I2_IØa(0)I2
c~o 4
~5,
_________ ~
SrC 10
=N~Y~(2N2 6 <0f06sE6-EB I Vex Iø6søf> 106s(0) 12
,~
‘
.
+~-
+2N6 ~
CdSe
n>6
30 m’,. 51Eu2~and Fig. ‘53Eu2~as 1. Thea hyperfine function of interaction the ratio c/n. constant The upper A of ‘curve is for 5’Eu2 + and the lower one for ‘“Eu2 ~ 10
15
20
25
0 6=N6[06S—(y6+S6)OL]
n>6,
Ofl=Nfl(OflS—SflOL),
(3) (4)
where Sn = <Ø,~.I OL> designates the overlap integral. Here 0,, (n> 6) are the up-spin-excited states of the ion—ligands complex. N is a normalisation constant and Y6 is the OL~~O6stransfer parameter. The transfer parameter y,, in eq. (4) was considered zero since the bondings of S-excited states are zero. Also, it is obvious that orbital cannot be included, since thethe 4f 4f orbital is covalency inside the 6s one, and thus a single covalency parameter was used, Via the exchange potential the unpaired Ø~elecirons remove the O~spin degeneracy, giving the Ø~ distorted orbital = OH +
~
nZ~6
I
Vex 100> On.
E~—EB
(5)
Using eqs. (2) and (4) one has for the matrix ele-
<øføns I Vex Iø6søf>Ø* (0)0 (0)) EflEB
(8) In this equation the parameters N~ y~and N~are proportional to the total charge transferred to the 6s state ofthe Eu2 ± ion. By substitution of eq. (8) into eq. (7) these parameters act to reduce the unpaired spin density with increasing covalency. As a consequence, from eq. (8), the observed decrease of the hyperfine structure constants with increasing covalency (fig. 1) arises from the reduction of the unpaired spin density, via the exchange polarization mechanism, of both ion—ligands cornplex bonding orbitals and up-spin-excited states. Extrapolation of the curves from fig. 1 to “zero covalency” gives the possibility to estimate two hyperfine constants which attributed to 2 + free ion: A(‘ 51Eu2are ~) formally = —42.2 x l0~cm—’ the Eu and A (‘“Eu2 ~) = 19.4 x 1 Ø_4 cm—’. The experimental hyperfine structure constant could be expressed in the form [21] —
(9) where Af includes contributions from the break-down A=AS+Af,
of LS coupling and from relativistic effects. A~is the exchange polarization term. For Eu2~,Evans, Sandars and Woodgate [22] consideredA~tobeA~(’”Eu2~)= —6.7xl04cm’ 93
Volume 119, number 2
PHYSICS LETTERS A
andAf(’53Eu2~)=—2.9x l0~cm~. From eq. (9), free ion values for the exchange polarization term, A~, in the case of Eu2~were obtained as A~(’51Eu2~)=35.5x l0~ cm~and A~(’53Eu2~)= l6.5x l0~cm~. Using these values, the hyperfine field parameter x~representing the hyperfine field at europium nucleus per unpaired spin unit, was determined. For both isotopes a value of x = 1.2 au was obtained, corresponding to a hyperfine field of 350 kG, in excellent agreement with the theoretical value obtained by Watson and Freeman [23] using the unrestricted Hartree—Fock method. —
—
—
—
References [1] E. Simanek and K.A. MUller, J. Phys. Chem. Solids 31 (1970) 1027. [2] S. Aquilan and E. Munoz, J. Chem. Phys. 62 (1975) 1197. [3] J.O. Rubio et al., J. Chem. Phys. 72 (1980) 2210.
94
1 December 1986
[4] W. Lowand U. Rosenberger, Phys. Rev. 116(1959) 621. [5] Q.H.F. Vrehen andJ. Volger, Physica 31(1965) 845. [6] J.M. Bekeret al.,et Proc. R. Soc.A247 (1958) [7] V.M. Vinocurov al., Ph.T.L 5 (1963) 1936.141. [8] E. Munoz,J. Chem. Phys. 62(1975) 3416. [9]J.O. Rubio,J. Chem. Phys. 63(1975)4222. [10] W. Low and J.T. Suss, Phys. Lett. 11(1964)115. [11] [12] [13] [14] [15]
J. Bronstein and V. Voltera, Phys. Rev. 137 (1965) A 201. A.A. Antipin et al., Ph.T.T. 7 (1965) 1425. H. Unoki andJ. Sakudo,J. Phys. Soc. Japan 21(1964)1730. L. Rimai et al., Phys. Rev. 133 (1964) A 1123. J. Turkevich and A. Nicula, unpublished.
[16] [17] [18]
R.S. Title, Phys. Rev. 133 (1964) A 198. P.B. Donan, Phys. Rev. 120 (1960) 1190. N.B. 171. Hannay and C. F. Smyth, J. Am. Chem. Soc. 68 (1946)
[19] W. Gordy and W.J.O. Thomas, J. Chem. Phys. 24 (1956) 439. [20] G. Lehmann, J. Phys. Chem. Solids 41(1980) 919. [21] B. Bleaney, in: La structure hyperfine magnetique des atomes et des molecules (CNRS, Paris, 1967). [22] L. Evans, P.G.H. Sandars and KG. Woodgate, Proc. R. Soc. A 289 (1965) 97. [23) R.E. Watson and A.J. Freeman, Phys. Rev. 123 (1961) 2027.