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Fluorescent vibronic transitions in CaF2(Eu++)
Volume 15, number 1
PHYSICS LETTERS
I Mswoh 1965
two different c r y s t a l s for Ag Ka-radD~tion 0.986, and for Mo Kcr-radiation 0.985. In order to obtain these values we have used the t h e o r e t i c a l values for ~D, ~Q and D220 for T = 292°K. The ~gre~ment with the theoretical value/)220 =
Mitchell and J. Turner for their help in the design and construction of the crystal holder.
0,988 is quite good.
1. B . W . B ~ t m mad H.Coleo l ~ v . M o d . P h ~ . 3 8 0964) SSX. ~. B.W.Bed~erman, Phys.Rev.127 (1962) eS6. 3. B.Oklmrse, Phfl.R~.Rep.IT (1962) 464. 4. G.Hfldebrm~dt mid l i . W ~ l d , f$txl~ lutm~.Collgr. ~t~'n.Vaton of Cr~mdlog~sphy, Rome (1963). 5. B.W.Batterman, J.Appl.Phys.$2 (1961) 998. 6. H.Wage~eld, J.Appl.Phys.33 (1962) 2907. 7. W.H. Zschartuen, Proo.Natiolml Academy of Sc~noe (U.S.A.) $8 (19S2) $V8. 8. N.Ka~, J.Phys.Soo.Jspan 10 (1955) 46. 9. G. Hfidebrandt, Z. Krfstallographte 112 (1959) 312. 10. B.W.Batterman and D.R.Chtpm-~, Phys.Rev. 127 (1962) 690. 11. B.W.Battvrman, Phys. Rev.126 (196Z) 1461.
It is obvious from eq. (1) that one has a good chance at low t e m p e r a t u r e of d e t e r m i n i n g experimentally ~D and ~Q (combined with n o r m a l absorptlon m e a s u r e m e n t s ) . The i n c r e a s e in the intensities at low t e m p e r a t u r e leads to the possibility of using the B o r r m a n u effect in o r d e r to ebtaln a ~.ell defined monochromatic and polarized X - r a y beam. The authors would like to express their gratitude to Professor J. M. C o w icy for his support and helpiul discussion, and also to Messrs. G.
FLUORESCENT
VIBRONIC
References
TRANSITIONS
IN C a F 2 ( E u
++)
M. V. HOBDEN R~yal Radar i'stablishment, Malvern, Wares.
Received 4 February 1965
Vibronic sideban,~s of the electronic transition [l'r ,~f Eu-* m CaF 2 at 24206 cm-I have been ~.xa:nmed and some conc!~sions drawn about this transition and the phonon spectrum of C a F 2. Various c r y s t a l s containing 0.05% and 0.005% E,.,*" in CaF 2 were irradiated at temperaL.~res ,qown tc 4°K and their fluorescent s p e c t r a examined with a spectrophotometer with a resolution of 1 c m - i . The s p e c t r a were identical at a given temperature, a p a r t from weak s h a r p lines close to *he fundamental line in heavily doped cry:~tals. The spectrum of a lightly doped c r y s t a l at 20°K is shown in fig. I. The strong line at 24206 cm" I is due to an e!cc:rr:nic transitinn from the lowest excited state of Eu ~" in CaF 2 to the eround state. This :',. is ak~out 2 cm -1 wide b e ~ w 20OK inci-ea~i!~.K _._.y z !:.~-twc~.n 20 ° and 90°K; the associated v~br,,nic spectf~ are correspondingly broadened. 2~is transitio~ ha.~ a small f n u m b e r (~ 2x 10 -~ at 4°K and ~ ~.0-5 at 77oK) suggesting that it m a y ~.. a 4i7 -- 411 transition. However it has been shc,'.vn[2, 3] that it has a large splitting under un~\~.al s~ress and also a Z e e m a n spectrum whica I~
appears the s a m e with light polarized perpendicular to the magnetic field for propagation perpendlcular and parallel to the magnetic field. These two facts euggest that it is an electric dipole transition f r o m 4f65d-- 4f7. This latter assignment is supported by the form of the contlnu u m of this vibronic spectrum within ~ 100 c m - I of the line, due to low energy acoustic phonons. Experimentally this is found to fit the expression (E-Eo)/{exp[(.~-Eo)/kT] - I} where E o is 24206 cm-1, the intensity of this continuum a t.E o being directly proportional to T. This is the form of continuum expected for low energy acoustic phonon vibronic transitions associated with an electronic electric dipole transition [4]. For such transitions associated with electronlc transitions between states of the s a m e parity (forced electric dipole transitions) the form [41 would be (E-Eo)S/{exp[(E-Eo)/k T] - 1}. So the transition is most probably 4i~5d ~ 4f~. Tlle narrowness m a y be due to the upper level having a high energy yet being the lowest excited state. The pea:ms in the vibronic spectrum arc related to peaks in the overall phonon density of
Volume 15, number 1
PHYSICS L E T T E R S ....
[
.1,.
''
z4oo
|
1 March 1965 I
I
a4ooo
I
Fig. 1. Fluorescence spectrum of E u ++ in CaF2 at 20°K. states as m o d i f i e s by selection r u l e s . The initial and final e l e c t r o n i c states being of opposite parity, only t r a n s i t i o n s involving phonons of even parity at th~ defect ion are allowed. F o r this r e a son none of the peaks can be due to the local mode of the Eu ++ Ion (on a calcium site) for this has odd parity. Loudon has shown [5] t h a t in CaF 2 at X and L in m o m e n t u m s p ~ c e o n l y two of the six phonon b r a n c h e s (X~X~ L~ L ~ have the n e c e s s a r y s y m m e t r y a f t e r reduction to the point group. At points of lower s y m m e t r y t h e r e is l e s s r e s t r i c t i o n . At the c e n t r e of the zone the only b r a n c h with positive parity is the Raman active optic branch with s y m m e t r y F~5. This energy has been m e a s u r e d [6] by Raman spectroscopy to be 322 cm -1. The s t r e n g t h of the highest e n e r g y peaks at 341, 383 and 389 cm -1 c o m p a r e d with the weakness of peaks at these e n e r g i e s in a theoretical density of s t a t e s curve, obtained f r o m a band s t r u c t u r e calculation [7], s u g g e s t s that these a r e associated with density of s t a t e s m a x i m a of the highest e n e r g y optical branche~ and that these
have symme
y Xi
Li or
at X or L. The
absence of a peak at 322 cm" shows that although the s y m m e t r y of the F~5 Haman phonons is favourable the density of s t a t e s is very small. The we_a~er peaks at 289, 278, 261, 240, 230 and 197 c m ' " can be associated with density of s t a t e s maxima at points of lower s y m m e t r y on in!.ermediate b r a n c h e s , the s t r o n g e r peak at 1 ~ cm-1 possibly being the fourth of the allowed phonons at X and L. The acoustic phonon vibroaic continuum inc r e a ? s l e s s r a b i d l y at phonon e n e r g i e s g r e a t e r than 100 c m - whereas the phonon density of states a p p r o a c h e s a maximum as the zone boundary is approached. This shows that the coupling becomes w e a k e r as the band edge is approached
where at points X and L the t r a n s i t i o n s a r e forbidden (assuming the forgoing assignment) though the density of s t a t e s goes to a s h a r p peak. The peak at the end of the continuum at 183 cm -1 is thought to be the top of an acoustic b r a n c h in a s y m m e t r y direction most favourable for participation of this acoustic phonon branch. This vibronic s p e c t r u m is superiml~osed upon a continuum extending about 2 000 c m - • presumably due to t r a n s i t i o n s associated with two or m o r e phonons. As t h e r e are no e n e r g y r e s t r i c tions on which p a i r s of phonons can be produced this continuum has virtually no s t r u c t u r e . Weak peaks were se(:a at 680 (±3) cm -1, 728 (+3) cm -1. and 775 ~ 5) cm -1 due to combinations of two opticai phonons. Table 1 Energies of peaks in the phon~n density of states of CaF2(cm'Z). This work
W o o dand Kaiser [8]
Kiss [9]
Hayes and Macdonald [10]
183 197 230 24o 261 278 289 341 383 389
184 199 228 239 259
183 196 227 238 253
183 196 228 238 279
289 339 379 389
339 389
Tal,le 1 c o m p a r e s this data with that of Wood and I~xiser (Sin ++ in CaF2) [8], Kiss (Tin ÷+ in C a F 2) [9], and Hayes and Mactlonaid (H" in CaF2) [10]. The f i r s t c a s e is very s i m i l a r to Eu ++ in CaF2, the t r a n s i t i o n being an e l e c t r i c dipole transition. The t r a n s i t i o n i'~ Tm ++ in C a F 2 i~ a 4f13 -. 4f13 magr, etic dipole transition ~r,d so the 11
Volume 15, number 1
PHYSICS
.~minuum :and the phonon _ e l e c t i o n r u l e s a x e diff e r e n t . H o w e v e r o n e s t r o n g line a p p e a r s 359 c m - 1 f r o m the m a i n l i n e . We have a s s i g n e d t h i s p o s i tive p a r i t y and s o it should be w e a k in t h i s c a s e . T h i s m a y be due to a s p u r i o u s d e g e n e r a c y of two • , r e l a t e d phonon d e n s i t y of s t a t e s m a x i m a o r o u r a s s i g n m e n t is w r o n g . The d a t a of H a y e s a n d M a c donald a r e c o n c e r n e d w i t h side b a n d s d u e to l a t t i c e phonon a b s o r p t i o n a s s o c i a t e d with l o c a l i s e d m o d e s of the H- ions on F si£e. T h e r e a r e n o s e l e c t i o n r u l e s in t h i s c a s e a n d all phonons m a y p a r t i c i p a t e .
D YNAMIC
POLARIZATION
OF
T. J. B. S W A N E N B U R G ,
1 M a r c h 1965
LETTERS
PROTONS
References
1. A.A.KaplyanskV.. and P.P.Feofllov, Optics and Spec~oscopy 13 (1962) 129. 2. W.A.Runctman and C.V.Stager, J.Chem. Phys.3$ (1963) 279. 3. B.P.Zakharchenya and A.Ya.Ryakin, Optics and Spectroscopy 14 (1963) 163. 4. R. Loudon, private communication. 5. R.Lc~don, Proc.Phys.Soc.84 (1964) $79. 6. V. Ansmth~mraysmnn, Z. Phys. 167 (1962) 39. 7. F.A. Johnson, privs~te communication. 8. D.L.Wood and W. Kaiser, Phys.Rev. 126 (1962)2079. 9. Z.J.Kiss, Phys.Rev.127 0962) 718. 10. W.Hayes, G.T.Jones, H.Macdonald, R.J.Elltott and C.T.Sennet,, Proc.Roy.Soc., to be published.
IN
N.J. P O U L I S
(La, C e ) 2 M g 3 ( N O 3 ) 1 2
• 24H 2 °
and L. J. A N C H E R
Kamerl ingh On,tes Laborator~um , Leiden, Netherlands
Received 4 F e b r u a r y 1965
The be,ha~-iour of the nuclear dynamic po'arization as a function of the induced transitiov, probabihty has been cxlculated by Leifson and Jeffries [I]. from the rate equation for the populations of ch~" Z e e m a n levels. A few years later A b r a g a m :~-d Borghini g a v e a m o r e r i g o r o u s d e s c r i p t i o n of -~':s s ,lid s t a t e e f f e c t on the b a s i s of R e d f i e l d ' s spin t e m p e r a t u r e t h e o r y [2]. The d e s c r i p t i o n by A b r a g a m and Bc'rghini t a k e s irto ac-ount the presence of "impurity" electron spins, which contribute only to the nuclear rela.xation and not to the polarization. The steady state value of the nuclear polarization enhancemere factor E is given by 0~eA wn E ......................
polarizing spins S 1 and impurity spins S 2. R is assumed that T n c, Te~ ' as m e a s u r e d by Leifson and geffries in (La. Ce)2Mg3(NO3)12 • 24H~O. A s e r i e s of e x p e r i m e n t s is c a r r i e d out to m e a s u r e the f a c t o r E f o r p r o t o n s in s i n g l e c r y s t a l s of La2Mg3(NO3)12 • 2 4 H 2 0 c o n t a i n i n g d i f f e r e n t c o n c e n t r a t i o n s of C e 3+ and ei i m p u r i t i e s . F i g . 1 s h o w s E in a c r y s t a l c o n t a i n i n g 2% C e , at a t e m p e r a t u r e of 1.be'K, a s a function of the m i c r o w a v e p o w e r P in the c a v i t y . T h i s p o w e r P is p r o p o r t i o n a l to the i n d u c e d t r a n s i t i o n p r o b a b i l i t i e s Wo, W o and W o. T h e g e n e r a l b e h a v l o u r of the c u r v e s is in a g r e e m e n t with the c a l c u l a t i o n s
2WL2 Tn. 1
(1)
. . . . . . . . . . . . . . . . . . . . . "..... A2 + 2WL-2 ..........
[! - (wo-~ woo r e + - 7 . ~ ,/-i + (w o + w d Tel[X + --~G-~--~:.-- W c Tel w h e r e ;:'c" W~, W ° - allowed and f o r b i d d e n ia~aced t r a n s i t i o n p r o b a b i l i t i e s ; COL, con - e l e c t r o n ~,.~ a u c i e a x Laz-mor l r e q u e n c i e s m the i n t e r n a l ,~ield Ho: a: L - e l e c t r o n L a r m o r f r e q u e n c y in the lqcal field: _X = ¢Oe-a~ - d i f f e r e n c e b e t w e e n e l e c tron L a r m o r f r e q u e n c y coe and i r r a d i a t i o n f r e quency ~; Te - s p i n - l a t t i c e r e l a x a t i o n 0.me of ,~,:4~-i::ation s p i n s S l l 1 / T n , 1, 1 / T n 2 - c o n t r i bu i'~ns t n the nuclear relaxation r a t e I / T n from
on the b a s i s of fo, m u l a (1). The n u m e r i c a l v a l u e s of Te and Tn. 1 w e r e t a k e n f r o m L e f f s o n and J e f fries [I]. Ho~vever, two major discrepancies are observed. First o! all, the curve for A = 68 M H z leads to a b~zeater enhancement than the curve for A = 25 M H z at high microwave power levels, whereas according to formula (1) the m a x i m u m enhancement is expected for A = 25 M H z . For the other curves the mutual agreement with theory is
PHYSICS LETTERS
I Mswoh 1965
two different c r y s t a l s for Ag Ka-radD~tion 0.986, and for Mo Kcr-radiation 0.985. In order to obtain these values we have used the t h e o r e t i c a l values for ~D, ~Q and D220 for T = 292°K. The ~gre~ment with the theoretical value/)220 =
Mitchell and J. Turner for their help in the design and construction of the crystal holder.
0,988 is quite good.
1. B . W . B ~ t m mad H.Coleo l ~ v . M o d . P h ~ . 3 8 0964) SSX. ~. B.W.Bed~erman, Phys.Rev.127 (1962) eS6. 3. B.Oklmrse, Phfl.R~.Rep.IT (1962) 464. 4. G.Hfldebrm~dt mid l i . W ~ l d , f$txl~ lutm~.Collgr. ~t~'n.Vaton of Cr~mdlog~sphy, Rome (1963). 5. B.W.Batterman, J.Appl.Phys.$2 (1961) 998. 6. H.Wage~eld, J.Appl.Phys.33 (1962) 2907. 7. W.H. Zschartuen, Proo.Natiolml Academy of Sc~noe (U.S.A.) $8 (19S2) $V8. 8. N.Ka~, J.Phys.Soo.Jspan 10 (1955) 46. 9. G. Hfidebrandt, Z. Krfstallographte 112 (1959) 312. 10. B.W.Batterman and D.R.Chtpm-~, Phys.Rev. 127 (1962) 690. 11. B.W.Battvrman, Phys. Rev.126 (196Z) 1461.
It is obvious from eq. (1) that one has a good chance at low t e m p e r a t u r e of d e t e r m i n i n g experimentally ~D and ~Q (combined with n o r m a l absorptlon m e a s u r e m e n t s ) . The i n c r e a s e in the intensities at low t e m p e r a t u r e leads to the possibility of using the B o r r m a n u effect in o r d e r to ebtaln a ~.ell defined monochromatic and polarized X - r a y beam. The authors would like to express their gratitude to Professor J. M. C o w icy for his support and helpiul discussion, and also to Messrs. G.
FLUORESCENT
VIBRONIC
References
TRANSITIONS
IN C a F 2 ( E u
++)
M. V. HOBDEN R~yal Radar i'stablishment, Malvern, Wares.
Received 4 February 1965
Vibronic sideban,~s of the electronic transition [l'r ,~f Eu-* m CaF 2 at 24206 cm-I have been ~.xa:nmed and some conc!~sions drawn about this transition and the phonon spectrum of C a F 2. Various c r y s t a l s containing 0.05% and 0.005% E,.,*" in CaF 2 were irradiated at temperaL.~res ,qown tc 4°K and their fluorescent s p e c t r a examined with a spectrophotometer with a resolution of 1 c m - i . The s p e c t r a were identical at a given temperature, a p a r t from weak s h a r p lines close to *he fundamental line in heavily doped cry:~tals. The spectrum of a lightly doped c r y s t a l at 20°K is shown in fig. I. The strong line at 24206 cm" I is due to an e!cc:rr:nic transitinn from the lowest excited state of Eu ~" in CaF 2 to the eround state. This :',. is ak~out 2 cm -1 wide b e ~ w 20OK inci-ea~i!~.K _._.y z !:.~-twc~.n 20 ° and 90°K; the associated v~br,,nic spectf~ are correspondingly broadened. 2~is transitio~ ha.~ a small f n u m b e r (~ 2x 10 -~ at 4°K and ~ ~.0-5 at 77oK) suggesting that it m a y ~.. a 4i7 -- 411 transition. However it has been shc,'.vn[2, 3] that it has a large splitting under un~\~.al s~ress and also a Z e e m a n spectrum whica I~
appears the s a m e with light polarized perpendicular to the magnetic field for propagation perpendlcular and parallel to the magnetic field. These two facts euggest that it is an electric dipole transition f r o m 4f65d-- 4f7. This latter assignment is supported by the form of the contlnu u m of this vibronic spectrum within ~ 100 c m - I of the line, due to low energy acoustic phonons. Experimentally this is found to fit the expression (E-Eo)/{exp[(.~-Eo)/kT] - I} where E o is 24206 cm-1, the intensity of this continuum a t.E o being directly proportional to T. This is the form of continuum expected for low energy acoustic phonon vibronic transitions associated with an electronic electric dipole transition [4]. For such transitions associated with electronlc transitions between states of the s a m e parity (forced electric dipole transitions) the form [41 would be (E-Eo)S/{exp[(E-Eo)/k T] - 1}. So the transition is most probably 4i~5d ~ 4f~. Tlle narrowness m a y be due to the upper level having a high energy yet being the lowest excited state. The pea:ms in the vibronic spectrum arc related to peaks in the overall phonon density of
Volume 15, number 1
PHYSICS L E T T E R S ....
[
.1,.
''
z4oo
|
1 March 1965 I
I
a4ooo
I
Fig. 1. Fluorescence spectrum of E u ++ in CaF2 at 20°K. states as m o d i f i e s by selection r u l e s . The initial and final e l e c t r o n i c states being of opposite parity, only t r a n s i t i o n s involving phonons of even parity at th~ defect ion are allowed. F o r this r e a son none of the peaks can be due to the local mode of the Eu ++ Ion (on a calcium site) for this has odd parity. Loudon has shown [5] t h a t in CaF 2 at X and L in m o m e n t u m s p ~ c e o n l y two of the six phonon b r a n c h e s (X~X~ L~ L ~ have the n e c e s s a r y s y m m e t r y a f t e r reduction to the point group. At points of lower s y m m e t r y t h e r e is l e s s r e s t r i c t i o n . At the c e n t r e of the zone the only b r a n c h with positive parity is the Raman active optic branch with s y m m e t r y F~5. This energy has been m e a s u r e d [6] by Raman spectroscopy to be 322 cm -1. The s t r e n g t h of the highest e n e r g y peaks at 341, 383 and 389 cm -1 c o m p a r e d with the weakness of peaks at these e n e r g i e s in a theoretical density of s t a t e s curve, obtained f r o m a band s t r u c t u r e calculation [7], s u g g e s t s that these a r e associated with density of s t a t e s m a x i m a of the highest e n e r g y optical branche~ and that these
have symme
y Xi
Li or
at X or L. The
absence of a peak at 322 cm" shows that although the s y m m e t r y of the F~5 Haman phonons is favourable the density of s t a t e s is very small. The we_a~er peaks at 289, 278, 261, 240, 230 and 197 c m ' " can be associated with density of s t a t e s maxima at points of lower s y m m e t r y on in!.ermediate b r a n c h e s , the s t r o n g e r peak at 1 ~ cm-1 possibly being the fourth of the allowed phonons at X and L. The acoustic phonon vibroaic continuum inc r e a ? s l e s s r a b i d l y at phonon e n e r g i e s g r e a t e r than 100 c m - whereas the phonon density of states a p p r o a c h e s a maximum as the zone boundary is approached. This shows that the coupling becomes w e a k e r as the band edge is approached
where at points X and L the t r a n s i t i o n s a r e forbidden (assuming the forgoing assignment) though the density of s t a t e s goes to a s h a r p peak. The peak at the end of the continuum at 183 cm -1 is thought to be the top of an acoustic b r a n c h in a s y m m e t r y direction most favourable for participation of this acoustic phonon branch. This vibronic s p e c t r u m is superiml~osed upon a continuum extending about 2 000 c m - • presumably due to t r a n s i t i o n s associated with two or m o r e phonons. As t h e r e are no e n e r g y r e s t r i c tions on which p a i r s of phonons can be produced this continuum has virtually no s t r u c t u r e . Weak peaks were se(:a at 680 (±3) cm -1, 728 (+3) cm -1. and 775 ~ 5) cm -1 due to combinations of two opticai phonons. Table 1 Energies of peaks in the phon~n density of states of CaF2(cm'Z). This work
W o o dand Kaiser [8]
Kiss [9]
Hayes and Macdonald [10]
183 197 230 24o 261 278 289 341 383 389
184 199 228 239 259
183 196 227 238 253
183 196 228 238 279
289 339 379 389
339 389
Tal,le 1 c o m p a r e s this data with that of Wood and I~xiser (Sin ++ in CaF2) [8], Kiss (Tin ÷+ in C a F 2) [9], and Hayes and Mactlonaid (H" in CaF2) [10]. The f i r s t c a s e is very s i m i l a r to Eu ++ in CaF2, the t r a n s i t i o n being an e l e c t r i c dipole transition. The t r a n s i t i o n i'~ Tm ++ in C a F 2 i~ a 4f13 -. 4f13 magr, etic dipole transition ~r,d so the 11
Volume 15, number 1
PHYSICS
.~minuum :and the phonon _ e l e c t i o n r u l e s a x e diff e r e n t . H o w e v e r o n e s t r o n g line a p p e a r s 359 c m - 1 f r o m the m a i n l i n e . We have a s s i g n e d t h i s p o s i tive p a r i t y and s o it should be w e a k in t h i s c a s e . T h i s m a y be due to a s p u r i o u s d e g e n e r a c y of two • , r e l a t e d phonon d e n s i t y of s t a t e s m a x i m a o r o u r a s s i g n m e n t is w r o n g . The d a t a of H a y e s a n d M a c donald a r e c o n c e r n e d w i t h side b a n d s d u e to l a t t i c e phonon a b s o r p t i o n a s s o c i a t e d with l o c a l i s e d m o d e s of the H- ions on F si£e. T h e r e a r e n o s e l e c t i o n r u l e s in t h i s c a s e a n d all phonons m a y p a r t i c i p a t e .
D YNAMIC
POLARIZATION
OF
T. J. B. S W A N E N B U R G ,
1 M a r c h 1965
LETTERS
PROTONS
References
1. A.A.KaplyanskV.. and P.P.Feofllov, Optics and Spec~oscopy 13 (1962) 129. 2. W.A.Runctman and C.V.Stager, J.Chem. Phys.3$ (1963) 279. 3. B.P.Zakharchenya and A.Ya.Ryakin, Optics and Spectroscopy 14 (1963) 163. 4. R. Loudon, private communication. 5. R.Lc~don, Proc.Phys.Soc.84 (1964) $79. 6. V. Ansmth~mraysmnn, Z. Phys. 167 (1962) 39. 7. F.A. Johnson, privs~te communication. 8. D.L.Wood and W. Kaiser, Phys.Rev. 126 (1962)2079. 9. Z.J.Kiss, Phys.Rev.127 0962) 718. 10. W.Hayes, G.T.Jones, H.Macdonald, R.J.Elltott and C.T.Sennet,, Proc.Roy.Soc., to be published.
IN
N.J. P O U L I S
(La, C e ) 2 M g 3 ( N O 3 ) 1 2
• 24H 2 °
and L. J. A N C H E R
Kamerl ingh On,tes Laborator~um , Leiden, Netherlands
Received 4 F e b r u a r y 1965
The be,ha~-iour of the nuclear dynamic po'arization as a function of the induced transitiov, probabihty has been cxlculated by Leifson and Jeffries [I]. from the rate equation for the populations of ch~" Z e e m a n levels. A few years later A b r a g a m :~-d Borghini g a v e a m o r e r i g o r o u s d e s c r i p t i o n of -~':s s ,lid s t a t e e f f e c t on the b a s i s of R e d f i e l d ' s spin t e m p e r a t u r e t h e o r y [2]. The d e s c r i p t i o n by A b r a g a m and Bc'rghini t a k e s irto ac-ount the presence of "impurity" electron spins, which contribute only to the nuclear rela.xation and not to the polarization. The steady state value of the nuclear polarization enhancemere factor E is given by 0~eA wn E ......................
polarizing spins S 1 and impurity spins S 2. R is assumed that T n c, Te~ ' as m e a s u r e d by Leifson and geffries in (La. Ce)2Mg3(NO3)12 • 24H~O. A s e r i e s of e x p e r i m e n t s is c a r r i e d out to m e a s u r e the f a c t o r E f o r p r o t o n s in s i n g l e c r y s t a l s of La2Mg3(NO3)12 • 2 4 H 2 0 c o n t a i n i n g d i f f e r e n t c o n c e n t r a t i o n s of C e 3+ and ei i m p u r i t i e s . F i g . 1 s h o w s E in a c r y s t a l c o n t a i n i n g 2% C e , at a t e m p e r a t u r e of 1.be'K, a s a function of the m i c r o w a v e p o w e r P in the c a v i t y . T h i s p o w e r P is p r o p o r t i o n a l to the i n d u c e d t r a n s i t i o n p r o b a b i l i t i e s Wo, W o and W o. T h e g e n e r a l b e h a v l o u r of the c u r v e s is in a g r e e m e n t with the c a l c u l a t i o n s
2WL2 Tn. 1
(1)
. . . . . . . . . . . . . . . . . . . . . "..... A2 + 2WL-2 ..........
[! - (wo-~ woo r e + - 7 . ~ ,/-i + (w o + w d Tel[X + --~G-~--~:.-- W c Tel w h e r e ;:'c" W~, W ° - allowed and f o r b i d d e n ia~aced t r a n s i t i o n p r o b a b i l i t i e s ; COL, con - e l e c t r o n ~,.~ a u c i e a x Laz-mor l r e q u e n c i e s m the i n t e r n a l ,~ield Ho: a: L - e l e c t r o n L a r m o r f r e q u e n c y in the lqcal field: _X = ¢Oe-a~ - d i f f e r e n c e b e t w e e n e l e c tron L a r m o r f r e q u e n c y coe and i r r a d i a t i o n f r e quency ~; Te - s p i n - l a t t i c e r e l a x a t i o n 0.me of ,~,:4~-i::ation s p i n s S l l 1 / T n , 1, 1 / T n 2 - c o n t r i bu i'~ns t n the nuclear relaxation r a t e I / T n from
on the b a s i s of fo, m u l a (1). The n u m e r i c a l v a l u e s of Te and Tn. 1 w e r e t a k e n f r o m L e f f s o n and J e f fries [I]. Ho~vever, two major discrepancies are observed. First o! all, the curve for A = 68 M H z leads to a b~zeater enhancement than the curve for A = 25 M H z at high microwave power levels, whereas according to formula (1) the m a x i m u m enhancement is expected for A = 25 M H z . For the other curves the mutual agreement with theory is