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Paramagnetic resonance study on transition metal ions in phosphate, fluorophosphate and fluoride glasses, part I: Cr3+ and Mo3+
Journal of Non-Crystalline Solids 52 (1982) 135-141 North-Holland Publishing Company
135
PARAMAGNETIC RESONANCE STUDY ON T R A N S I T I O N METAL IONS IN P H O S P H A T E , F L U O R O P H O S P H A T E AND FLUORIDE GLASSES, PART I: Cr 3+ AND Mo 3+ G A N Fuxi, D E N G He and LIU Huiming Shanghai Institute of Optics and Fine Mechanics, Academia Sinica, ShanghaL China
The ESR of Cr 3+ in phosphate, fluorophosphate and fluoride glasses has been studied. The energy level splitting and the effective g value of the Cr 3+ ion have been calculated with the spin-Hamiltonian. It is pointed out that the transition can be found not only within every Kramers doublet, but also between two Kramers doublets. The zero field splitting parameter D has been determined: 0.15-0.4 cm - I . In this paper, the ESR of the Mo 3+ ion in phosphate glass is also reported.
1. Introduction
In recent years, phosphate, fluorophosphate and fluoride glasses have been widely applied in optical and laser technology. However, their structure has not been known sufficiently well compared with oxide glasses. Transition metal ions can be used to probe the glass structure, because their outer d-electron orbital functions have rather broad radial distributions and their responses to surrounding actions are very sensitive. The transition metal ions doped glasses are included in the new laser or luminescence materials, so it is necessary to understand the energy level configuration of these ions in glass in detail. The energy levels of paramagnetic ions are split under the action of the ligand field, therefore, the electron spin resonance (ESR) method can be used to measure the spin Hamiltonian parameters and to get information on energy levels and coordination states. The ESR of transition metal ions in glasses have been investigated for over twenty years, Sands [1] did the pioneer work in this field. Due to theoretical difficulty, he only reported some experimental results without any theoretical interpretation. Using spin Hamiltonian, Castner [2] successfully explained the ESR spectrum of Fe 3+ in glass. Since then the ESR investigation has been steadily intensified. For a long time the investigation was confined to oxide glasses, particularly silicate glasses. The study on the ESR of transition metal ions in fluorophosphate and fluoride glasses is just beginning and very little information has been published so far. The ESR spectra of various transition ions in BeF2 glass was reported by Abdrashitova et al. [3] without any theoretical calculation and analysis. Obviously, it is very important and 0022-3093/82/0000-0000/$02.75 © 1982 North-Holland
136
Can Fuxi et al. / Paramagnetic resonance study on transition metal ions I
interesting to investigate the effect of the ligand field on the ESR spectrum when the surrounding ligands change from oxygen to fluorine.
2. Experimental The chemical compositions of the three glasses used in our experiments are (in mol%): phosphate glass P205 58.14, CaO 8.37, SrO 8.37, BaO 16.74, A1203 8.37; fluorophosphate glass P205 5.55, NaPO 3 7.49, MgF 2 16.45, CaF 2 16.34, SrF2 12.16, BaF2 11.63, AIF3 30.39 in addition to NaPO 3 3.0; fluoride glass BeF2 30, A1F3 25, MgF 2 20, BaF2 15. The raw materials used in preparing these glass samples were AR grade or specific grade (Fe < 10 ppm). The Fe 3+ content in phosphate and fluorophosphate glasses is below the ESR detection limit (the instrumental sensitivity was not below 10-12 DPPH). The iron content in the raw material (NH4)2BeF4 is higher, so the ESR signal of Fe 3÷ in the fluoride glass can be detected. The X-band electron spin resonance spectrometers model ESR-3 made by the Hilger & Watts Co. and model JES-FEIX made by the JEOL Co. were used in our experiments. Samples in the shape of a cylinder having diameters 3-5 x 15 mm were put in a quartz tube (in a quartz cryostat at low temperature) when the experiment was conducted. The spin Hamiltonian describing the electron spin resonance spectra of transition metal ions is as follows: ~ = / 3 H . g . , { + S . D . S + S'A "],
(1)
where the first term is the electron Zeeman term, H is the external magnetic field, g is a second rank tensor, S is the effective spin operator. The second term results from spin-orbit coupling, D is also a second rank tensor. The final term describes the interaction between magnetic nuclei and electron spin, I is the nuclear spin operator, A is the hyperfine interaction tensor, its anisotropic part is a second rank non-trace tensor and can be neglected in glass. Thus, the third term can be written as AioS. If the ground state of the transition metal ions is an orbital singlet, then eq. (1) can be written as:
~s=goflH.S+D[S]-IS(S+ I)] +E(S~-~)+AJ'S,
(2)
where 8a~, go = go
a
,
(3)
here ge is free electron g factor equal to 2.0023, 2~ is the spin-orbit coupling constant, A is the gap between the excited level and the ground level. As a pure constant, the value a (0 ~< a ~< 1) is characterized by the ionic contribution of the chemical bond. The second term in expression (2) reflects the action of the trigonal and tetragonal crystal field; the third term is the field action of lower symmetry.
Gan Fuxi et al. / Paramagnetic resonance study on transition metal ions I
137
Owing to the long-range disorder in the glass structure, the sites of paramagnetic ions are not identical, and have various possible orientations to the external magnetic field. So, in general, the spin Hamiltonian parameters are not constants and have a certain distribution range. Therefore, in experiments the rather wide profile overlapping all the resonance lines is obtained.
3. Results and discussion
Cr 3÷ ions have the d3-electron configuration and have a larger octahedral site preference energy (OSPE) [4]. In an octahedral field, its ground level is 4A2g. Under the field action of a low symmetry component and spin-orbit coupling, the fourfold degenerate spin state splits into two Kramers doublets. The two resonance signals of g - 2 and 5 respectively can be observed at room temperature. Zakharov [5] and Landry [6] investigated the ESR of Cr 3+ in phosphate glass. Based on the spin Hamiltonian, they both found out the energy levels of the paramagnetic ion, then they considered the transitions within each Kramers doublet and calculated or estimated the effective g factor and zero-field splitting parameter D from different points of view. Zakharov estimated that the zero-field splitting is about 300 cm-1. This conclusion is obviously controversial. Later Garif'yanov [7] negated this point of view. Landry calculated the value of the effective g factor, and found that the geff changes from 0 to 3g e with a very wide distribution. However it is not enough to interpret the experimental spectra. The estimation of parameter D is also improper. He pointed out, however, that there were two paramagnetic species. They are the isolated Cr 3+ ions and exchange coupled pairs Cr 3÷ - C r 3+ in glass, and he satisfactorily explained the concentration effect of Cr 3+ ions on ESR spectra. Our experiments were performed at room temperature. The ESR spectra of phosphate (P) and fluorophosphate (FP) glasses with 0.5 (wt)% Cr203 and fluoride (F) glass with 0.5 (wt)% CrC13 are shown in figs. l and 2. It can be found from fig. 2 that the low field spectral intensity of Cr 3+ in fluoride glass is much less than the high field portion. According to the theory of Landry, the low field portion of the spectrum is attributed to the isolated Cr 3+ ions, and the high field portion mainly belongs to the exchange coupled pairs Cr 3÷ - C r 3÷. It indicates that Cr 3+ exists in the manner of an exchange coupled pair in our fluoride glass. We found many tiny inclusions in our fluoride glass. This is obviously due to the incomplete dissolution of CrC13 in fluoride glass. Consequently, the isolated Cr 3÷ ions doped into the glass are rather few. The effective g factors observed in our experiment are: phosphate glass:
gPf = 4.92,
1.97,
fluorophosphate glass:
geVfP = 4.89,
1.97,
fluoride glass:
gF t =
4.69,
1.98.
138
Gan Fuxi et aL / Paramagnetic resonance study on transition metal ions I
g=4.922 G
o£L0
J
1
/
g=1.973
g=1.973 2
Ii
Fig. 1. ESR spectra of Cr 3+ in glasses doped with 0.5 wt% Cr203. 1 - p h o s p h a t e glass, 2 fluorophosphate glass. Fig. 2. ESR s p e c t r u m of Cr 3+ in fluoride glass. " A " is the amplified low field portion.
The low field spectra can be described by the spin Hamiltonian in eq. (2) (here Icr = 0). We may state it as the sum of two terms, assuming D or E >> gflH. ^ I ~ s = ~ o + ~1~,
(4)
~ o = O[ S ~ - ½ S ( S + 1)] + E ( S f - S~),
(5)
the perturbation term
~C~ = gofln.s
(6)
can be diagonalized in I_+ ~), l+ ½), we can find the zero-field splitting and spin eigenfunctions of the ground level of the Cr 3+ ions. They are two Kramers doublets with the gap 2(D 2 + 3 E Z ) 1/2 (fig. 3). Under the action of the external magnetic field, these doublets produce Zeeman splitting. Taking + I~kl,2), Iq~{,2) as basic vectors, the matrix representation of the perturbation term (6) is: -H
3a z - 1
got~ z 2 - ~ + l ) gofl[
( 31/la
+ l)Hx - ( 31/2a - l ) i H y ]
goa[ (3'/~a + l ) ' x + (3'/~a - I)i/Ye] 3a 2 - 1 - go#l-tz--
2(a2 +1)
and flH
3b z -
1
go zz-~Ti) gofl[ ( 3'/2b + l ) H x - ( 3'/2b - l ) i n y ]
gofl[ ( 31/2b + l)Hx + ( 3'/2b - l ) i H y ] 3b z - 1 -
go~HzZ(b2 + l)
Gan Fuxi et al. / Paramagnetic resonance study on transition metal ions I
139
I ~ > = (1-1a')-÷(~I-3/2>+I 1/2>)
\\-f~ +a~ ~ I'~> = (I+~ r~( b Ia/2>+I-I/2>)
t I~= ( 1+b' ~(b l-a/z>+l I/2>) Fig. 3. Level splitting of the ground state 4A2g of the Cr 3+ ion at zero-field, a = [ D + ( D 2 + 3E2)I/2]/31/2E, b = [ D - ( D 2 + 3E2)l/2]/31/2E.
When the external magnetic field H is parallel to the three principal axes respectively, the effective g value of the resonant transition within each doublet can be found as shown below: 3~/2a + 1
ge~f
a2+l 31/2a- 1 2g o , a2+ 1
3~/2b + 1 b ~ 2go, +1 31/2b- 1 2g o , b2 + 1
geZff
3a 2 - 1 a 2+ 1 go,
3b 2 - 1 b 2+ 1 go"
gefXf
2go,
(7) (8) (9)
Taking E / D <~½, according to Wickman [7], then the various possible values of effective g factor are in the range of 0.3-1.7g 0 or 2 . 2 - 2.7g 0. The values of geff in eqs. (7), (8) and (9) only depend on the ratio between E and D, the values of which cannot be determined yet. We have also investigated the possibility of transition between the two doublets. If D or E >> gflH it is not feasible in terms of the energy. If D and E are of the same order of magnitude as gflH, the transition can certainly be observed. Thus, the Hamiltonian (2) (without A ] - S ) is used and diagonalized in [ +_3 ), [ + ½) after performing coordinate transformation for convenience of calculation (see Part II the following paper). Setting E / D = 4, then the function of the effective g factor and D can be obtained: H II Z;
gcu = go{ l + [(1 + D / g o f l H ) 2 + 3~2(D/goflH)2] 1/2
-[ (1- Z /goB i) HI, X .
-[(1
+
3 (z /goBH)
=go(1 + [ ( 1
"},
' 1-T-3l~ ~ 2 ,
~-ofl ~1-T-3~)2+ 3D2---~-(1-+3~]2]'/2},gofl H ] ]
3 D 2 / 1 +3,~21 '/2
(lO)
where hv = 0.31 cm- i, is the microwave quantum, go can be determined by eq. (3). From the optical spectral data [9], taking A = 15000 cm -~, X = 91 c m - 1 a = 0.70-0.85, hence go = 1.961-1.968.
140
Gan Fuxi et al. / Paramagnetic resonance study on transition metal ions 1
According to Wickman, we only need to examine those values of ~ in the range of 0 ~<~ ~<½. As shown above, the measured gefe values in our experiments vary in the range of 4.0-5.0, so from eq. (10) we can obtain: D = 0.15-0.4 cm-J, ~ -- 0.1-0.25, and the zero-field splitting 2(D 2 - 3E2) 1/2 is about 0.3-0.8 c m - ' . This conclusion is consistent with the result obtained by Khudoleev et al. [10] obtained using X-band and Q-band ESR experiments. From eq. (3) it can be considered that the value of a describes the nature of the chemical bond between the central ion and the ligands. The larger the value a, the stronger the ionic contribution of the chemical bond, and the smaller the value of go- The experimental results signify that for the low-field spectra, g~r > g FP > gFf. According to expressions (7), (8), (9) and (10), the value of g~ff is in direct proportion to the value of go [gofl H in brackets in eq. (10) can really be treated as a constant], so, we have gff > gFoV> gFo, which means that the ionic contribution of the chemical bond in these three glasses increases gradually. This result is consistent with the change of the Racah parameter in optical spectra [9]. The high field resonance geff 2 is attributed mainly to exchange coupled pairs Cr 3+ - C r 3+ . This was investigated in detail by Landry, and his results are in good agreement with our experiments. So it is unnecessary to discuss this further. It is more difficult to obtain trivalent ions Mo 3+ in glass. We have only obtained Mo 3+ in phosphate glass, which was prepared under the reducing conditions. The ESR spectra of phosphate glass containing 0.1 wt% and 0.5 wt% MoO 3 are shown in fig. 4. In the glass with 0.1 wt% MoO 3, the effective g factors are g~n = 4.82, 2.00. They both belong to the Mo 3+ ions. In another glass with 0.5 wt% MOO3, besides the spectra g~ff = 4.77 and geff 2 which belong to Mo 3+, there is also a very strong signal in the vicinity of g - 2, which is attributed to Mo 5 + ions. It seems that the ratio between the numbers of Mo 3+ and Mo 5+ ions is in equilibrium. The number of Mo 5 + ions increases with the increase of MoO 3. At liquid nitrogen temperature, the ESR signal intensity of Mo 3+ increases obviously while the value of the g factor remains --
=
g=4.82~ ,500G, / jJ
,,,,
=2.o0
k~. lwt% I
g=4.77
Fig. 4. ESR spectra of Mo3+ in phosphate glass doped with 0.1 and 0.5 wt~ MoO~.
Gan Fuxi et al. / Paramagnetic resonance study on transition metal ions I
141
c o n s t a n t , consequently, the zero-field splitting of the g r o u n d state is larger. M o 3÷ has the same d - e l e c t r o n c o n f i g u r a t i o n as Cr 3÷ , their E S R s p e c t r a also have similar o u t w a r d features, b u t it is m o r e difficult to calculate o r e s t i m a t e the spin H a m i l t o n i a n p a r a m e t e r s of M o 3÷ ions, b e c a u s e M o 3÷ ions have a stronger s p i n - o r b i t c o u p l i n g interaction. In an o c t a h e d r a l field their fourfold spin degenerate state 4A2g has a larger zero-field splitting, the mixing of excited states is so strong that we c a n n o t write out its a p p r o x i m a t e eigenfunctions. In c o m p a r i s o n with Cr 3+ , the s p i n - o r b i t c o u p l i n g c o n s t a n t of M o 3+ is = 272 cm -1, 1 0 D q = 22400 c m - l . W e p r e d i c t that the g factor of M o 3÷ is strongly anisotropic, and its E S R signals m a y be a t t r i b u t e d to the transition in each K r a m e r s doublet.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]
R.H. Sands, Phys. Rev. 99 (1955) 1225. T. Castner, Jr. G.S. Newell, W.C. Holton and C.P. Slechtor, J. Chem. Phys. 32 (1960) 668. E.I. Abdrashitova et al., Dokl. Acad. Nauk. SSSR 175 (1967) 1305. J. Wong and C.A. Angell, Glass Structure by Spectroscopy (Marcel Dekker, New York, 1976) p. 225. B.K. Zakharov et al., Fiz. Tverd. Tela 7 (1965) 1571. R.J. Landry, J.T. Fouruier and C.G. Young, J. Chem. Phys. 46 (1967) 1285. N.S. Garif'yanov et al., Fiz. Tverd. Tela 42 (1964) 1545. H.H. Wickman, M.P. Klein and D.A. Skirlex, J. Chem. Phys. 42 (1965) 2113. Gan Fuxi, J. Chinese Silicate Soc. 6 (1978) 41. A.G. Khudoleev et al., Zh. Prikl. Spectrosk. 12 (1970) 551.
135
PARAMAGNETIC RESONANCE STUDY ON T R A N S I T I O N METAL IONS IN P H O S P H A T E , F L U O R O P H O S P H A T E AND FLUORIDE GLASSES, PART I: Cr 3+ AND Mo 3+ G A N Fuxi, D E N G He and LIU Huiming Shanghai Institute of Optics and Fine Mechanics, Academia Sinica, ShanghaL China
The ESR of Cr 3+ in phosphate, fluorophosphate and fluoride glasses has been studied. The energy level splitting and the effective g value of the Cr 3+ ion have been calculated with the spin-Hamiltonian. It is pointed out that the transition can be found not only within every Kramers doublet, but also between two Kramers doublets. The zero field splitting parameter D has been determined: 0.15-0.4 cm - I . In this paper, the ESR of the Mo 3+ ion in phosphate glass is also reported.
1. Introduction
In recent years, phosphate, fluorophosphate and fluoride glasses have been widely applied in optical and laser technology. However, their structure has not been known sufficiently well compared with oxide glasses. Transition metal ions can be used to probe the glass structure, because their outer d-electron orbital functions have rather broad radial distributions and their responses to surrounding actions are very sensitive. The transition metal ions doped glasses are included in the new laser or luminescence materials, so it is necessary to understand the energy level configuration of these ions in glass in detail. The energy levels of paramagnetic ions are split under the action of the ligand field, therefore, the electron spin resonance (ESR) method can be used to measure the spin Hamiltonian parameters and to get information on energy levels and coordination states. The ESR of transition metal ions in glasses have been investigated for over twenty years, Sands [1] did the pioneer work in this field. Due to theoretical difficulty, he only reported some experimental results without any theoretical interpretation. Using spin Hamiltonian, Castner [2] successfully explained the ESR spectrum of Fe 3+ in glass. Since then the ESR investigation has been steadily intensified. For a long time the investigation was confined to oxide glasses, particularly silicate glasses. The study on the ESR of transition metal ions in fluorophosphate and fluoride glasses is just beginning and very little information has been published so far. The ESR spectra of various transition ions in BeF2 glass was reported by Abdrashitova et al. [3] without any theoretical calculation and analysis. Obviously, it is very important and 0022-3093/82/0000-0000/$02.75 © 1982 North-Holland
136
Can Fuxi et al. / Paramagnetic resonance study on transition metal ions I
interesting to investigate the effect of the ligand field on the ESR spectrum when the surrounding ligands change from oxygen to fluorine.
2. Experimental The chemical compositions of the three glasses used in our experiments are (in mol%): phosphate glass P205 58.14, CaO 8.37, SrO 8.37, BaO 16.74, A1203 8.37; fluorophosphate glass P205 5.55, NaPO 3 7.49, MgF 2 16.45, CaF 2 16.34, SrF2 12.16, BaF2 11.63, AIF3 30.39 in addition to NaPO 3 3.0; fluoride glass BeF2 30, A1F3 25, MgF 2 20, BaF2 15. The raw materials used in preparing these glass samples were AR grade or specific grade (Fe < 10 ppm). The Fe 3+ content in phosphate and fluorophosphate glasses is below the ESR detection limit (the instrumental sensitivity was not below 10-12 DPPH). The iron content in the raw material (NH4)2BeF4 is higher, so the ESR signal of Fe 3÷ in the fluoride glass can be detected. The X-band electron spin resonance spectrometers model ESR-3 made by the Hilger & Watts Co. and model JES-FEIX made by the JEOL Co. were used in our experiments. Samples in the shape of a cylinder having diameters 3-5 x 15 mm were put in a quartz tube (in a quartz cryostat at low temperature) when the experiment was conducted. The spin Hamiltonian describing the electron spin resonance spectra of transition metal ions is as follows: ~ = / 3 H . g . , { + S . D . S + S'A "],
(1)
where the first term is the electron Zeeman term, H is the external magnetic field, g is a second rank tensor, S is the effective spin operator. The second term results from spin-orbit coupling, D is also a second rank tensor. The final term describes the interaction between magnetic nuclei and electron spin, I is the nuclear spin operator, A is the hyperfine interaction tensor, its anisotropic part is a second rank non-trace tensor and can be neglected in glass. Thus, the third term can be written as AioS. If the ground state of the transition metal ions is an orbital singlet, then eq. (1) can be written as:
~s=goflH.S+D[S]-IS(S+ I)] +E(S~-~)+AJ'S,
(2)
where 8a~, go = go
a
,
(3)
here ge is free electron g factor equal to 2.0023, 2~ is the spin-orbit coupling constant, A is the gap between the excited level and the ground level. As a pure constant, the value a (0 ~< a ~< 1) is characterized by the ionic contribution of the chemical bond. The second term in expression (2) reflects the action of the trigonal and tetragonal crystal field; the third term is the field action of lower symmetry.
Gan Fuxi et al. / Paramagnetic resonance study on transition metal ions I
137
Owing to the long-range disorder in the glass structure, the sites of paramagnetic ions are not identical, and have various possible orientations to the external magnetic field. So, in general, the spin Hamiltonian parameters are not constants and have a certain distribution range. Therefore, in experiments the rather wide profile overlapping all the resonance lines is obtained.
3. Results and discussion
Cr 3÷ ions have the d3-electron configuration and have a larger octahedral site preference energy (OSPE) [4]. In an octahedral field, its ground level is 4A2g. Under the field action of a low symmetry component and spin-orbit coupling, the fourfold degenerate spin state splits into two Kramers doublets. The two resonance signals of g - 2 and 5 respectively can be observed at room temperature. Zakharov [5] and Landry [6] investigated the ESR of Cr 3+ in phosphate glass. Based on the spin Hamiltonian, they both found out the energy levels of the paramagnetic ion, then they considered the transitions within each Kramers doublet and calculated or estimated the effective g factor and zero-field splitting parameter D from different points of view. Zakharov estimated that the zero-field splitting is about 300 cm-1. This conclusion is obviously controversial. Later Garif'yanov [7] negated this point of view. Landry calculated the value of the effective g factor, and found that the geff changes from 0 to 3g e with a very wide distribution. However it is not enough to interpret the experimental spectra. The estimation of parameter D is also improper. He pointed out, however, that there were two paramagnetic species. They are the isolated Cr 3+ ions and exchange coupled pairs Cr 3÷ - C r 3+ in glass, and he satisfactorily explained the concentration effect of Cr 3+ ions on ESR spectra. Our experiments were performed at room temperature. The ESR spectra of phosphate (P) and fluorophosphate (FP) glasses with 0.5 (wt)% Cr203 and fluoride (F) glass with 0.5 (wt)% CrC13 are shown in figs. l and 2. It can be found from fig. 2 that the low field spectral intensity of Cr 3+ in fluoride glass is much less than the high field portion. According to the theory of Landry, the low field portion of the spectrum is attributed to the isolated Cr 3+ ions, and the high field portion mainly belongs to the exchange coupled pairs Cr 3÷ - C r 3÷. It indicates that Cr 3+ exists in the manner of an exchange coupled pair in our fluoride glass. We found many tiny inclusions in our fluoride glass. This is obviously due to the incomplete dissolution of CrC13 in fluoride glass. Consequently, the isolated Cr 3÷ ions doped into the glass are rather few. The effective g factors observed in our experiment are: phosphate glass:
gPf = 4.92,
1.97,
fluorophosphate glass:
geVfP = 4.89,
1.97,
fluoride glass:
gF t =
4.69,
1.98.
138
Gan Fuxi et aL / Paramagnetic resonance study on transition metal ions I
g=4.922 G
o£L0
J
1
/
g=1.973
g=1.973 2
Ii
Fig. 1. ESR spectra of Cr 3+ in glasses doped with 0.5 wt% Cr203. 1 - p h o s p h a t e glass, 2 fluorophosphate glass. Fig. 2. ESR s p e c t r u m of Cr 3+ in fluoride glass. " A " is the amplified low field portion.
The low field spectra can be described by the spin Hamiltonian in eq. (2) (here Icr = 0). We may state it as the sum of two terms, assuming D or E >> gflH. ^ I ~ s = ~ o + ~1~,
(4)
~ o = O[ S ~ - ½ S ( S + 1)] + E ( S f - S~),
(5)
the perturbation term
~C~ = gofln.s
(6)
can be diagonalized in I_+ ~), l+ ½), we can find the zero-field splitting and spin eigenfunctions of the ground level of the Cr 3+ ions. They are two Kramers doublets with the gap 2(D 2 + 3 E Z ) 1/2 (fig. 3). Under the action of the external magnetic field, these doublets produce Zeeman splitting. Taking + I~kl,2), Iq~{,2) as basic vectors, the matrix representation of the perturbation term (6) is: -H
3a z - 1
got~ z 2 - ~ + l ) gofl[
( 31/la
+ l)Hx - ( 31/2a - l ) i H y ]
goa[ (3'/~a + l ) ' x + (3'/~a - I)i/Ye] 3a 2 - 1 - go#l-tz--
2(a2 +1)
and flH
3b z -
1
go zz-~Ti) gofl[ ( 3'/2b + l ) H x - ( 3'/2b - l ) i n y ]
gofl[ ( 31/2b + l)Hx + ( 3'/2b - l ) i H y ] 3b z - 1 -
go~HzZ(b2 + l)
Gan Fuxi et al. / Paramagnetic resonance study on transition metal ions I
139
I ~ > = (1-1a')-÷(~I-3/2>+I 1/2>)
\\-f~ +a~ ~ I'~> = (I+~ r~( b Ia/2>+I-I/2>)
t I~= ( 1+b' ~(b l-a/z>+l I/2>) Fig. 3. Level splitting of the ground state 4A2g of the Cr 3+ ion at zero-field, a = [ D + ( D 2 + 3E2)I/2]/31/2E, b = [ D - ( D 2 + 3E2)l/2]/31/2E.
When the external magnetic field H is parallel to the three principal axes respectively, the effective g value of the resonant transition within each doublet can be found as shown below: 3~/2a + 1
ge~f
a2+l 31/2a- 1 2g o , a2+ 1
3~/2b + 1 b ~ 2go, +1 31/2b- 1 2g o , b2 + 1
geZff
3a 2 - 1 a 2+ 1 go,
3b 2 - 1 b 2+ 1 go"
gefXf
2go,
(7) (8) (9)
Taking E / D <~½, according to Wickman [7], then the various possible values of effective g factor are in the range of 0.3-1.7g 0 or 2 . 2 - 2.7g 0. The values of geff in eqs. (7), (8) and (9) only depend on the ratio between E and D, the values of which cannot be determined yet. We have also investigated the possibility of transition between the two doublets. If D or E >> gflH it is not feasible in terms of the energy. If D and E are of the same order of magnitude as gflH, the transition can certainly be observed. Thus, the Hamiltonian (2) (without A ] - S ) is used and diagonalized in [ +_3 ), [ + ½) after performing coordinate transformation for convenience of calculation (see Part II the following paper). Setting E / D = 4, then the function of the effective g factor and D can be obtained: H II Z;
gcu = go{ l + [(1 + D / g o f l H ) 2 + 3~2(D/goflH)2] 1/2
-[ (1- Z /goB i) HI, X .
-[(1
+
3 (z /goBH)
=go(1 + [ ( 1
"},
' 1-T-3l~ ~ 2 ,
~-ofl ~1-T-3~)2+ 3D2---~-(1-+3~]2]'/2},gofl H ] ]
3 D 2 / 1 +3,~21 '/2
(lO)
where hv = 0.31 cm- i, is the microwave quantum, go can be determined by eq. (3). From the optical spectral data [9], taking A = 15000 cm -~, X = 91 c m - 1 a = 0.70-0.85, hence go = 1.961-1.968.
140
Gan Fuxi et al. / Paramagnetic resonance study on transition metal ions 1
According to Wickman, we only need to examine those values of ~ in the range of 0 ~<~ ~<½. As shown above, the measured gefe values in our experiments vary in the range of 4.0-5.0, so from eq. (10) we can obtain: D = 0.15-0.4 cm-J, ~ -- 0.1-0.25, and the zero-field splitting 2(D 2 - 3E2) 1/2 is about 0.3-0.8 c m - ' . This conclusion is consistent with the result obtained by Khudoleev et al. [10] obtained using X-band and Q-band ESR experiments. From eq. (3) it can be considered that the value of a describes the nature of the chemical bond between the central ion and the ligands. The larger the value a, the stronger the ionic contribution of the chemical bond, and the smaller the value of go- The experimental results signify that for the low-field spectra, g~r > g FP > gFf. According to expressions (7), (8), (9) and (10), the value of g~ff is in direct proportion to the value of go [gofl H in brackets in eq. (10) can really be treated as a constant], so, we have gff > gFoV> gFo, which means that the ionic contribution of the chemical bond in these three glasses increases gradually. This result is consistent with the change of the Racah parameter in optical spectra [9]. The high field resonance geff 2 is attributed mainly to exchange coupled pairs Cr 3+ - C r 3+ . This was investigated in detail by Landry, and his results are in good agreement with our experiments. So it is unnecessary to discuss this further. It is more difficult to obtain trivalent ions Mo 3+ in glass. We have only obtained Mo 3+ in phosphate glass, which was prepared under the reducing conditions. The ESR spectra of phosphate glass containing 0.1 wt% and 0.5 wt% MoO 3 are shown in fig. 4. In the glass with 0.1 wt% MoO 3, the effective g factors are g~n = 4.82, 2.00. They both belong to the Mo 3+ ions. In another glass with 0.5 wt% MOO3, besides the spectra g~ff = 4.77 and geff 2 which belong to Mo 3+, there is also a very strong signal in the vicinity of g - 2, which is attributed to Mo 5 + ions. It seems that the ratio between the numbers of Mo 3+ and Mo 5+ ions is in equilibrium. The number of Mo 5 + ions increases with the increase of MoO 3. At liquid nitrogen temperature, the ESR signal intensity of Mo 3+ increases obviously while the value of the g factor remains --
=
g=4.82~ ,500G, / jJ
,,,,
=2.o0
k~. lwt% I
g=4.77
Fig. 4. ESR spectra of Mo3+ in phosphate glass doped with 0.1 and 0.5 wt~ MoO~.
Gan Fuxi et al. / Paramagnetic resonance study on transition metal ions I
141
c o n s t a n t , consequently, the zero-field splitting of the g r o u n d state is larger. M o 3÷ has the same d - e l e c t r o n c o n f i g u r a t i o n as Cr 3÷ , their E S R s p e c t r a also have similar o u t w a r d features, b u t it is m o r e difficult to calculate o r e s t i m a t e the spin H a m i l t o n i a n p a r a m e t e r s of M o 3÷ ions, b e c a u s e M o 3÷ ions have a stronger s p i n - o r b i t c o u p l i n g interaction. In an o c t a h e d r a l field their fourfold spin degenerate state 4A2g has a larger zero-field splitting, the mixing of excited states is so strong that we c a n n o t write out its a p p r o x i m a t e eigenfunctions. In c o m p a r i s o n with Cr 3+ , the s p i n - o r b i t c o u p l i n g c o n s t a n t of M o 3+ is = 272 cm -1, 1 0 D q = 22400 c m - l . W e p r e d i c t that the g factor of M o 3÷ is strongly anisotropic, and its E S R signals m a y be a t t r i b u t e d to the transition in each K r a m e r s doublet.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]
R.H. Sands, Phys. Rev. 99 (1955) 1225. T. Castner, Jr. G.S. Newell, W.C. Holton and C.P. Slechtor, J. Chem. Phys. 32 (1960) 668. E.I. Abdrashitova et al., Dokl. Acad. Nauk. SSSR 175 (1967) 1305. J. Wong and C.A. Angell, Glass Structure by Spectroscopy (Marcel Dekker, New York, 1976) p. 225. B.K. Zakharov et al., Fiz. Tverd. Tela 7 (1965) 1571. R.J. Landry, J.T. Fouruier and C.G. Young, J. Chem. Phys. 46 (1967) 1285. N.S. Garif'yanov et al., Fiz. Tverd. Tela 42 (1964) 1545. H.H. Wickman, M.P. Klein and D.A. Skirlex, J. Chem. Phys. 42 (1965) 2113. Gan Fuxi, J. Chinese Silicate Soc. 6 (1978) 41. A.G. Khudoleev et al., Zh. Prikl. Spectrosk. 12 (1970) 551.