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ESR and endor studies of the VK center in SrF2
Solid State Communications,
Vol. 13, pp. 1131—1 134, 1973.
Pergamon Press.
Printed in Great Britain
ESR AND ENDOR STUDIES OF THE VK CENTER IN SrF2* R. Gazzinellit, G.M. Ribeirot and M.L. de Siqueirat Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, Belo Horizonte, Brasil (Received 3 July 1973 by G.F. Bassani)
The results of electron spin resonance (ESR) and electron nuclear double resonance (ENDOR) studies of a self-trapped hole (VK center) in SrF2 are reported. The g-factor and hyperfine interaction constants were determined for the fluorine nuclei forming the center and for those in the nearest three different sites. The values of hyperfine interaction constants are intermediate to the known values for CaF2 and BaF2.
THE V,~center in fluorite type crystals is formed by a trapped hole sharing two halogen ions in a (001) direction. Its structure is similar to a F~molecule ion. It has an unpaired spin in a o~,orbital and is therefore paramagnetic. VK center was studied resonance previously in fluorite typeThe crystals by electron-spin (E5R) and electron nuclear double resonance 1—3 The ENDOR Study was restricted to (ENDOR). CaF 2 and BaF2. There is some interest in completing the measurements for SrF2, thereby permitting a better comparison with theoretical results.
attempts to form sufficient VK center to do ENDOR with undoped samples were unsuccessful. The measurements were made with a super5 heterodyne, spectrometer describedoperating elsewhere. A cylindricalX-band cavity with movable bottom, in the TE andlocated having inside a Q of aabout was used.011 Themode, sample, quartz5000 fmger in the center of the cavity, is cooled by conduction. The RF that induces nuclear transitions is introduced into the cavity by a pair of loops coupled directly to the tank circuit of an oscillator.
In this communication we report the values of the g factor for the hole, the hyperfine interaction constants between the hole and the pair of nuclei constituting the center,determined by ESR, as well as the hyperfmne interaction constants between the hole and the surrounding fluorine in the three different sites shown in Fig. 1, determined by ENDOR. ASrF 2 crystalwascutalonga(111)planeand hydrogen was diffused4 in by samples a method described by The were irradiated Hall and Schumacher. by X-rays at 80 kV and 25 mA at the temperature of liquid nitrogen for periods as long as 12 hr. Many
The unpaired electron spin interacts strongly with the two fluorine nuclei that form the pseudomolecule and less strongly with the surrounding nuclei. 3 The spin Hamiltonian is: =
(3OS.g.HO+hO~3OK.T.Sh7~K.HO + (I) h ~ I~ A,~S h7~I,~Ho —
where S = 1/2, K
=
K
1 + K2 where K1 = K2 = 1/2 are the nuclear spins of the fluorine forming the center, I the hyperfine interaction tensor of the fluorine pseudo-molecule, I,~and A~the nuclear spin and the hyperfine interaction tensor of the surrounding nuclei.
Work partially supported by Conselho Nacional de Pesquisas, Brasil. t Under Contract of COPERTIDE, Brasil. *
1131
1132
ESR AND ENDOR STUDIES OF THE
VK
CENTER IN SrF2
Vol. 13. No. 8
0
c••
A B
C
0 B
I
C’
0
O
•
FLUORINE
0
STRONTIUM
:i C
o
•
o
0
I
FIG. I. Nuclei surrounding The ESR spectrum may be explained by the first three terms of equation (1). The values ofg~,g~, g2, T~,T~and T2, calculated by a second order
• c’
0 VK
center in SrF2.
where a is the isotropic Fermi contact interaction and B~,B~,B~the diagonal terms of the anisotropic tensor.
perturbation treatment are shown in Table 1.
The hyperfine interaction term for each neighbour nucleus may be written as: h S~AI = alS
+ BXJXSX +
~
+
B21~S2
The nuclear transitions in zero order for a given nucleus are: =
;Ilo
—
—
h
(a + B~cr~+ B~
~.
+
B~c~)~
Vol. 13, No. 8
ESR AND ENDOR STUDIES OF THE VK CENTER IN SrF2
-1.00
-0.50
1133
0.50
1.00
I
~1 . •
10
•
S S S
•
0
S
•
I
•
—
•
THEORY
•EXP. S
•
30
40 S
.S S S
.50
.5
•1
$5
I I
I
S
•
.
S
70
____
___________________ -1.00
I
__
60 80 0 90
___________________ -0.50 ~
S
I
0.50
j
__________________
.00
(MI.4~)
FIG. 2. Angular dependence of ENDOR lines of the C nuclei in SrF2 for rotation of H0 on the (110) plane (~is the angle between H0 and the molecule axis). Table]. Parameters of the ESR spectrum of the VK center in SrF2 ~
H~and the axes of the defect, are made for rotation
ofH0 in (110) and (100) planes. One such plot is shown in Fig. 2.
~
2.0192 2.0024 46.3 ±0.0003 ±0.0003 ±0.5 T~,T~,7’2 are given in gauss.
897.9 ±0.5
Symmetry arguments allow an unambiguous 3 assignment of each set ofinteraction equivalentconstants neighbourand nuclei Values of to each of setthe of hyperfine lines on the angular dependence plots. the direction of principal axes are calculated approximately and fed to a computer program that diagonalizes
whereas. as., ct~are direction cosines ofH 0 in the principal axes system. These transitions are observed by ENDOR. Plots of r y~H0 vs E. the angle between —
the spin Hamiltonian matrix. By fitting the calculated and experimental spectra one obtains the best values for the hyperfine interaction constants and principal axes directions. These values are shown in Table 2.
1134
ESR AND ENDOR STUDIES OF THE VK CENTER IN SrF2
Vol. 13, No.8
Table 2. Parameters ofthe ENDOR spectrum of the VK center in SrF2 forfluorine nuclei in sites A, B, C Nucl:ar
a
B~
B~
A B C D
5.43 —0.38 —0.45 —0.80
—6.73 4.33 —0.70 —0.78
—6.13 —1.62 1.40 1.52
a, B~,B~,B~are measured in MHz;
~fi,0,
B~
— — —
12.87 2.72 0.71 0.73
0 90 81.5 90 90
—45 81.5 —45 —45
—90 0 —101 —105
&, defined in reference 3, are measured in degrees.
Nucleiplane, labelled anddetermination C have two principal axes in the(lIO) thusAthe of cosine directions of principal axes is immediate. Nuclei labelled B have no principal axes determined by symmetry due to the pressence of alkaline earth neigh. bours in an asymmetric way. Therefore the values listed for nuclei are the notdirection accurate.of the principal axes for these
3 where the lattice parameter they vary roughly as l/d, d is 5.64,5.86 A and 6.20A for CaF 2, SrF2 and BaF2 respectively. The negative values for the contact interaction a indicate the existence of exchange polarization of 6 the ligand cores by the unpaired electron of the center. Acknowledgements The authors thank Dr. R. Williams (RCA, Princeton) for the samples used in —
The values of the anisotropic hyperfine interaction constants for SrF 2 are intermediate to the known values for CaF2 and BaF2 This should be expected because
this research.
.~
REFERENCES 1.
HAYES W. and TWIDELL J.W.,Proc. Phi’s. Soc. (London), 74, 1295 (1962).
2. 3.
HAYES W., KIRK D.L. and SUMMERS G.P., Solid State Commun. 7, 1061 (19691). MARZKE R.F. and MIEHER R.L.,Phvs. Rev. 182,453 (1969).
4.
HALLJ.L. and SCHUMACHER R.T.,Phvs. Rev. 127, 1892 (1962).
5.
GAZZINELLI R., MARRA J.G. and RIBEIRO G.M., Rev. Brasileira. Fis. 2, 39 (1972).
6.
ICKENBERRY D., JETTE A.N. and DAS T.P., Phys. Rev. BI, 2785 (1970).
Nous relations les resultats Ic l’étude en Resonance paramagnétique electronique (EPR) et en resonance double electronique-nucleaire (ENDOR) d’un centre VK dans SrF2. Le facteur g cc les constants de l’interaction hyperfine ont Cté dCterminCs pour les noyaux de fluor form ant Ic centre, aiiisi que ceux situCs dans le trois couches les plus proches. Les valeurs obtenues pour les constantes de l’interaction hyperfine sont intermédiaires entre les valeurs deja connues pour CaF2 et BaF2.
Vol. 13, pp. 1131—1 134, 1973.
Pergamon Press.
Printed in Great Britain
ESR AND ENDOR STUDIES OF THE VK CENTER IN SrF2* R. Gazzinellit, G.M. Ribeirot and M.L. de Siqueirat Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, Belo Horizonte, Brasil (Received 3 July 1973 by G.F. Bassani)
The results of electron spin resonance (ESR) and electron nuclear double resonance (ENDOR) studies of a self-trapped hole (VK center) in SrF2 are reported. The g-factor and hyperfine interaction constants were determined for the fluorine nuclei forming the center and for those in the nearest three different sites. The values of hyperfine interaction constants are intermediate to the known values for CaF2 and BaF2.
THE V,~center in fluorite type crystals is formed by a trapped hole sharing two halogen ions in a (001) direction. Its structure is similar to a F~molecule ion. It has an unpaired spin in a o~,orbital and is therefore paramagnetic. VK center was studied resonance previously in fluorite typeThe crystals by electron-spin (E5R) and electron nuclear double resonance 1—3 The ENDOR Study was restricted to (ENDOR). CaF 2 and BaF2. There is some interest in completing the measurements for SrF2, thereby permitting a better comparison with theoretical results.
attempts to form sufficient VK center to do ENDOR with undoped samples were unsuccessful. The measurements were made with a super5 heterodyne, spectrometer describedoperating elsewhere. A cylindricalX-band cavity with movable bottom, in the TE andlocated having inside a Q of aabout was used.011 Themode, sample, quartz5000 fmger in the center of the cavity, is cooled by conduction. The RF that induces nuclear transitions is introduced into the cavity by a pair of loops coupled directly to the tank circuit of an oscillator.
In this communication we report the values of the g factor for the hole, the hyperfine interaction constants between the hole and the pair of nuclei constituting the center,determined by ESR, as well as the hyperfmne interaction constants between the hole and the surrounding fluorine in the three different sites shown in Fig. 1, determined by ENDOR. ASrF 2 crystalwascutalonga(111)planeand hydrogen was diffused4 in by samples a method described by The were irradiated Hall and Schumacher. by X-rays at 80 kV and 25 mA at the temperature of liquid nitrogen for periods as long as 12 hr. Many
The unpaired electron spin interacts strongly with the two fluorine nuclei that form the pseudomolecule and less strongly with the surrounding nuclei. 3 The spin Hamiltonian is: =
(3OS.g.HO+hO~3OK.T.Sh7~K.HO + (I) h ~ I~ A,~S h7~I,~Ho —
where S = 1/2, K
=
K
1 + K2 where K1 = K2 = 1/2 are the nuclear spins of the fluorine forming the center, I the hyperfine interaction tensor of the fluorine pseudo-molecule, I,~and A~the nuclear spin and the hyperfine interaction tensor of the surrounding nuclei.
Work partially supported by Conselho Nacional de Pesquisas, Brasil. t Under Contract of COPERTIDE, Brasil. *
1131
1132
ESR AND ENDOR STUDIES OF THE
VK
CENTER IN SrF2
Vol. 13. No. 8
0
c••
A B
C
0 B
I
C’
0
O
•
FLUORINE
0
STRONTIUM
:i C
o
•
o
0
I
FIG. I. Nuclei surrounding The ESR spectrum may be explained by the first three terms of equation (1). The values ofg~,g~, g2, T~,T~and T2, calculated by a second order
• c’
0 VK
center in SrF2.
where a is the isotropic Fermi contact interaction and B~,B~,B~the diagonal terms of the anisotropic tensor.
perturbation treatment are shown in Table 1.
The hyperfine interaction term for each neighbour nucleus may be written as: h S~AI = alS
+ BXJXSX +
~
+
B21~S2
The nuclear transitions in zero order for a given nucleus are: =
;Ilo
—
—
h
(a + B~cr~+ B~
~.
+
B~c~)~
Vol. 13, No. 8
ESR AND ENDOR STUDIES OF THE VK CENTER IN SrF2
-1.00
-0.50
1133
0.50
1.00
I
~1 . •
10
•
S S S
•
0
S
•
I
•
—
•
THEORY
•EXP. S
•
30
40 S
.S S S
.50
.5
•1
$5
I I
I
S
•
.
S
70
____
___________________ -1.00
I
__
60 80 0 90
___________________ -0.50 ~
S
I
0.50
j
__________________
.00
(MI.4~)
FIG. 2. Angular dependence of ENDOR lines of the C nuclei in SrF2 for rotation of H0 on the (110) plane (~is the angle between H0 and the molecule axis). Table]. Parameters of the ESR spectrum of the VK center in SrF2 ~
H~and the axes of the defect, are made for rotation
ofH0 in (110) and (100) planes. One such plot is shown in Fig. 2.
~
2.0192 2.0024 46.3 ±0.0003 ±0.0003 ±0.5 T~,T~,7’2 are given in gauss.
897.9 ±0.5
Symmetry arguments allow an unambiguous 3 assignment of each set ofinteraction equivalentconstants neighbourand nuclei Values of to each of setthe of hyperfine lines on the angular dependence plots. the direction of principal axes are calculated approximately and fed to a computer program that diagonalizes
whereas. as., ct~are direction cosines ofH 0 in the principal axes system. These transitions are observed by ENDOR. Plots of r y~H0 vs E. the angle between —
the spin Hamiltonian matrix. By fitting the calculated and experimental spectra one obtains the best values for the hyperfine interaction constants and principal axes directions. These values are shown in Table 2.
1134
ESR AND ENDOR STUDIES OF THE VK CENTER IN SrF2
Vol. 13, No.8
Table 2. Parameters ofthe ENDOR spectrum of the VK center in SrF2 forfluorine nuclei in sites A, B, C Nucl:ar
a
B~
B~
A B C D
5.43 —0.38 —0.45 —0.80
—6.73 4.33 —0.70 —0.78
—6.13 —1.62 1.40 1.52
a, B~,B~,B~are measured in MHz;
~fi,0,
B~
— — —
12.87 2.72 0.71 0.73
0 90 81.5 90 90
—45 81.5 —45 —45
—90 0 —101 —105
&, defined in reference 3, are measured in degrees.
Nucleiplane, labelled anddetermination C have two principal axes in the(lIO) thusAthe of cosine directions of principal axes is immediate. Nuclei labelled B have no principal axes determined by symmetry due to the pressence of alkaline earth neigh. bours in an asymmetric way. Therefore the values listed for nuclei are the notdirection accurate.of the principal axes for these
3 where the lattice parameter they vary roughly as l/d, d is 5.64,5.86 A and 6.20A for CaF 2, SrF2 and BaF2 respectively. The negative values for the contact interaction a indicate the existence of exchange polarization of 6 the ligand cores by the unpaired electron of the center. Acknowledgements The authors thank Dr. R. Williams (RCA, Princeton) for the samples used in —
The values of the anisotropic hyperfine interaction constants for SrF 2 are intermediate to the known values for CaF2 and BaF2 This should be expected because
this research.
.~
REFERENCES 1.
HAYES W. and TWIDELL J.W.,Proc. Phi’s. Soc. (London), 74, 1295 (1962).
2. 3.
HAYES W., KIRK D.L. and SUMMERS G.P., Solid State Commun. 7, 1061 (19691). MARZKE R.F. and MIEHER R.L.,Phvs. Rev. 182,453 (1969).
4.
HALLJ.L. and SCHUMACHER R.T.,Phvs. Rev. 127, 1892 (1962).
5.
GAZZINELLI R., MARRA J.G. and RIBEIRO G.M., Rev. Brasileira. Fis. 2, 39 (1972).
6.
ICKENBERRY D., JETTE A.N. and DAS T.P., Phys. Rev. BI, 2785 (1970).
Nous relations les resultats Ic l’étude en Resonance paramagnétique electronique (EPR) et en resonance double electronique-nucleaire (ENDOR) d’un centre VK dans SrF2. Le facteur g cc les constants de l’interaction hyperfine ont Cté dCterminCs pour les noyaux de fluor form ant Ic centre, aiiisi que ceux situCs dans le trois couches les plus proches. Les valeurs obtenues pour les constantes de l’interaction hyperfine sont intermédiaires entre les valeurs deja connues pour CaF2 et BaF2.