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ONE DIMENSIONAL TRANSFER IN CsNiF3
J. Cibert, M. Terrile, Y. Merle d’Aubigné
To cite this version:
ONE DIMENSIONAL TRANSFER IN CsNiF
3J. Cibert, M.C. T e r r i l e and Y. Merle d'Aubigné
Laboratoire de Speotrométrie Physique**, Université Saientifiaue et Médicale de Grenoble, B.P. 87, 38402 Saint Martin d'Hèreê Cedex, France
Résumé - Le déclin de 1 'émission intrinsèque dans le ferromagnétique
unidi-mensionnel CsNiF3 est en excellent accord avec le modèle suivant : 1/
trans-fert rapide, à une dimension, entre ions normaux ; 2/ piêgeage lent, assisté
par les magnons dans le cas des pièges peu profonds.
Abstract - Decay of the intrinsic emission in the one-dimensional ferromagnet
CsNiK3 shows excellent agreement with a model of 1/ fast one-dimensional
transfer between normal ions ; 2/ slow trapping,assisted by magnons for
shallow traps.
One dimensional excitation transfer is of current interest from both a theoretical
and experimental point of view : simple models are amenable to rather complete
ana-l y s i s , and a number of reaana-l systems are known to be fairana-ly ID. A non exponentiaana-l
decay of the intrinsic emission, related to the trapping of the mobile excitation,
is often compared to a exp-(kr+k'/ff) law / l / : the two parameters k and k' are
ex-tracted from a single experimental curve, and their ratio bears information about
the importance of ID transfer (k') relative to 3D motion and one-center
deexcita-tion (k).
We present results on the ID ferromagnet CsNiF3 which clearly disagree with such a
law (§2). Other sources of non-exponential ity - existence of different traps,
bi-exciton decay, long-range transfer - being reasonably excluded, we have developped
twoextreme models of ID transfer and trapping (§1), one of them showing excellent
agreement with our experimental results. We conclude that the excitations in CsNiF3
are characterized by a fast one dimensional transfer between normal ions, over
seg-ments cut on the chains by randomly distributed traps, then trapping at the ends of
the segment. The trapping is slow for deep traps, and for shallow traps when a
ma-gnetic field is applied. A fast transfer to the shallow traps when the mama-gnetic
field is decreased suggests that i t is assisted by the magnons.
I - MODELS
In both models randomly distributed deep traps (no back transfer) cut the chains
in-to independent segments. We consider one dimensional motion along the segments (e.g.
incoherent transfer with hopping rate w from one normal ion to i t s nearest
neigh-bour), and trapping (rate W) from the normal ion at one end of the segment to the
neighbouring trap. Both traps and normal ions have a radiative lifetime T.
Consider a segment with n normal ions ; l e t Pi(t) be the probability that the ion i
is excited at time t if one ion of the segment has been excited at t = 0. The traps
are labelled 0 and (n+1). The probability that the excitation remains untrapped on
the segment a t time t is Pp(t) = 2,", p-j(t). The intrinsic emission from the whole
crystal is given by a statistical average over segments of different lengthes, and
On leave from IFQSC, U. Sao Paulo (Brasil), under grant from CNPq Laboratoire associe au C.N.R.S. (L.A. 08).
C7-136 JOURNAL
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PHYSIQUEi s p r o p o r t i o n a l t o I ( t ) = I.
cm
n c2(1-c) P n ( t ) ( t h e probabi l i t y t h a t a g i v e n i o n i s a normal i o n which belong;=:o a c h a i n o f l e n g t h "is
n c 2 ( 1 - c ) ~ ) ) .Dynamics o f t h e segment i s governed by a master equation :
Po
= - 1 / T Po + Wpl (+Wp-l)tl
= -(W + w+
l / ~ ) p 1+
Wp2 ( 1 )ti
= - ( & + J - / T ) P ~ + w ( P ~ - 1 +L e t us d e f i n e a v e c t o r
fS
= (PI,. .Pi,. .pn). The master equation i s s h o r t l y w r i t t e n i* + +
p.=
-
~ . p-
p / r . The r a d i a t i v e l i f e t i m e gives o n l y an o v e r a l l e x p ( - t / ~ ) fa- t o r ; the f l r s t p a r t i s e a s i l y s o l v e d i f we know the e i genval ues ( h j ) o f t h e * ~ t r i x3,
and the sorresponding l e f t and r i h t eigenvzctors,Zj
= ( a l j,.
..a .) w i t h a . x j =Xj
Xj
,
and Y j = (Bjl ....,Bjn) w i t hfjd
= i j y j ; we can normalize &de vectors, i .e..Za a a i B j a = 6 i j . Then, a f t e r a u n i f o r m e x c i t a t i o n o f t h e segment, we have P n ( t ) = Ca,b,j a a j e x ~ ( - i j t ) B j b .
I a
-
Rode1 A : u n i f o r m d i f f u s i o nWe take t h e t r a p p i n g r a t e W equal t o t h e hopping r a t e w between normal i o n s . Then t h e m a t r i x
%
i s e a s i l y diagonal i z e d : a a j = Bj, =1
/
v
s i n ( n a j / ( n + l ) ))
x j
= 4w s i n 2 ( a j / Z ( n t l ) ) .A f t e r s t r a i g h t f o r w a r d c a l c u l a t i o n we get w i t h o u t approxi mation :
I ( t ) = I,C 2 c2(1-c) c o t 2 a j exp -4 w t s i n 2 a j (2)
n
n + l j=1,3,5...
For low concentrations and wt >> 1, t h e d i s c r e t e sums a r e replaced by i n t e g r a l s and t h e t r i g o n o m e t r i c f u n c t i o n s l i n e a r i z e d , w i t h t h e approximate r e s u l t ( f i g . 1) :
As expected, t h e o n l y r e l e v a n t parameter i s wczt, and t h e c h a r a c t e r i s t i c time (wc2)-? Note t h a t eq. 3 i s v a l i d o n l y f o r wt >> 1 ; e.g. f ( o ) / I ( o ) i s i n f i n i t e u s i n g eq. 3, b u t equal t o -2 wc (as expected) from eq. 2.
For incoherent motion t h i s model i s governed by t h e same master equation ( e q . l ) , b u t w i t h f a s t hopping between normal ions, and slow t r a p p i n g . I f ld = 0, t h e problem i s a c l a s s i c a l one : segment w i t h r e f l e c t i v e b a r r i e r s /2/. Then the m a t r i x
2
has ( n-
1) e i genval ues s i m i l a r t o t h e e i genval ues o f model A ( r a n g i n g from win2 t o w),
and one eigenvalue equal t o zero ( t h e p o p u l a t i o n o f t h e segment i s constant). For times l o n g compared t o w/n2, t h e p o p u l a t i o n i s uniform, i .e. pi = l / n . I f we i n t r o - duce a slow t r a p p i n g ( W << w/n), t h e ( n-
1) non-vanishing eigenvalues a r e o n l y s l i g h t l y modified, and a n t h eigenvalue (= 2 w/n) describes t h e t r a p p i n g from t h e normal ions a t b o t h ends o f t h e segment w i t h u n i f o r m p o p u l a t i o n over t h e segment. A s i m i l a r r e s u l t should be obtained f o r coherent t r a n s f e r (Frenkel e x c i t o n s ) which a l - so leads t o a u n i f o r m p o p u l a t i o n over t h e normal i o n s o f t h e segment. The same ap- proximation, i f a p p l i e d t o three-dimensional systems (e.g. I"nF2) 131, leads t o an exponential decay w i t h a time constant wcz, where z i s the n u t h e r o f n e a r e s t neigh- bours. For one dimensional systems t h e segments are independent ; as f o r model A, a s t a t i s t i c a l average gives f o r l o n g times ( i .e. wczt >> 1)and f o r low .concentrations ( f i g . 1 ) .
I ( t ) = I, ,-x ,-2 Wct/x dx = 4 Wct K2 ( 2 m ) where K2 i; a-modi,fied Bessel f u n c t i o n o f t h e second k i n d .
Now t h e o n l y r e l e v a n t parameter i s Wct, and t h e c h a r a c t e r i s t i c time (!&lc)-l. I 1
-
EXPERIKENTAL RESULTSCsNiF3 i s a one-dimensional ferromagnet where s h o r t range o r d e r i s c o n t r o l l e d by temperature and a p p l i e d magnetic f i e l d s /4/. Emission i n the near i n f r a r e d ( z e r o phonon l i n e s
+
v i b r o n i c band) i s e x c i t e d ( g e n e r a l l y w i t h i n t h e v i b r o n i c band) u s i n g a KC1 :TI0 pulsed l a s e r . The o v e r a l l time r e s o l u t i o n ( l a s e r+
d e t e c t o r + e l e c t r o n i c s ) i s 0.6 1.1s. Due t o t h e c r y s t a l s t r u c t u r e , and t o t h e magnetic d i p o l e c h a r a c t e r o f t h e t r a n s i t i o n , we expect a s t r o n g 1D t r a n s f e r o f t h e e x c i t a t i o n . !<any samples o f two d i f f e r e n t o r i g i n s (L from L E T I - C r i s t a l t e c , Grenoble ; C k i n d l y given by Pr. Chapelle) have been s t u d i e d .A t moderately low temperatures (2K t o 4K), we observe /5/ emission from normal ions, from a shallow t r a p (AE = 12 cm-l) and from deep t r a p s . E x c i t a t i o n s p e c t r a show t h a t t h e shallow t r a p i s t h e dominant one : deepertraps have a lower concentration. A very shallow t r a p i s a l s o detected on the e x c i t a t i o n spectra, b u t n o t i n emission : p o s s i b l y t h i s t r a p and t h e 12 cm-1 t r a p are the next-nearest and t h e nearest neigh- bours o f a d e f e c t ; then they c o u l d r a p i d l y reach therttal e q u i l i b r i u m , and we can i g n o r e t h e very s h a l l ow t r a p .
Thermal e q u i l i b r i u m between normal i o n s and shallow t r a p s i s reached r a p i d l y ( < l US). When back t r a n s f e r i s s i g n i f i c a n t they s l o w l y decay, due t o t r a n s f e r t o deeper t r a p s A t lower temperature no back t r a n s f e r i s p o s s i b l e (exp (-AE/kT) = 5 f o r
T = 1.4 K) and t h e i n t r i n s i c emission disappears ( f i g . 2 ) . Applying a mannetic f i e l d slows t h e dynamics down : we now observe a r i s i n g time on the shallow t r a p s i g n a l , which corresponds t o t h e decay o f t h e i n t r i n s i c emission ( f i g . 2).
C7-138 JOURNAL
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PHYSIQUE TRAP- .
-- 0 T I M E ( m s ) 1 H z 0 Tzl.4K H = 4 T Tz1.3K 6 7 7 0 ENERGY (cm-I ) 6 8 0 0F i g . 2
-
Sample C : e x c i t o n and shallow t r a p a t low temperature ; R i g h t : spectra w i t h and w i t h o u t a p p l i e d magnetic f i e l d . Due t o t h e f a s t r e p e t i t i o n r a t e , t h e r a t i o o f t h e t r a p t o e x c i t o n i n t e n s i t i e s i s underestimated. L e f t : dynamics w i t h a p p l i e d f i e l d ( B = 4.2 Teslas, T = 1.54 k ) .Fig. 3
-
Sample C-
Experimental decay o f t h e e x c i t o n ( d o t s ) a t T = 1.K,
B = 3.8 Teslas
-
L e f t : f i t t o model B (one a d j u s t a b l e parameter ( w c ) - j = 110 u s )-
Right : t e n t a t i v e f i t o f t h e experimental data t o a e x p - ( k t t k ' f i ) law;a
good f i t should r e s u l t i n a s t r a i g h t l i n e .The c o n c e n t r a t i o n has been estimated i n r e f . 5 : c = . 4
lom3.
From t h e f i t on fig.3, (wc)-1 = 140 ps, we g e t f o r t h e t r a p p i n g r a t e w-1=
60 ns. Once t h e dynamics has slowed down, t h e measured t r a p p i n g r a t e does n o t change very much w i t h f i e l d (3T t o 5T) and temperature.I1 b
-
Samples LE x c i t a t i o n s p e c t r a reveal a deeper t r a p (AE = 63 cm-l) which a l s o dominates the low temperature emission. As i n samples C, a shallower t r a p (AE = 40 cm-l) appears i n
T = 12 ms.
h i g h e r temperatures. Hence o n l y deep t r a p s a r e r e l e v a n t .
Emission from these deeps t r a p s ( f i g . 4) f i r s t r i s e s , then decays w i t h a l i f e t i m e (12 ms) equal t o t h e r a d i a t i v e l i f e t i m e measured f o r
~
i
as i m p u r i t y i n diamagnetic~
+
f l u o r i d e s . Even a t "high" temperature and w i t h o u t a p p l i e d f i e l d , t h e decay o f t h e i n - t r i n s i c emission f o l l o w s model B. The c h a r a c t e r i s t i c time changes o n l y smoothly w i t h temperature ( f r o m (wc)-1 = 20 ps a t 1.4 K t o 30 us a t 7K), o r w i t h a p p l i e d f i e l d .111
-
CONCLUSIONThe decay o f t h e i n t r i n s i c emission i n CsNiF n i c e l y agrees w i t h the p r e d i c t i o n s o f our model 1 : f a s t 1D t r a n s f e r between norma? i o n s o v e r segments l i m i t e d by randomly d i s t r i b u t e d t r a p s , and slow t r a p p i n g a t t h e end o f t h e segment. This i s v e r i f i e d :
-
when deep t r a p s (e.g. 63 cm-l) are dominant,-
when shallow t r a p s ( e .g. 12 cm-l) a r e dominant and a magnetic f i e l d i s applied. I n the absence o f a p p l i e d f i e l d , t h e t r a n s f e r t o shallow t r a p i s f a s t . However, t h e f i e l d i s o f no i n f l u e n c e on t h e over- a1 1 dynamics when o n l y deep t r a p s a r e present. This suggests t h a t the t r a n s f e r t t o shallow t r a p s i s a s s i s t e d by one o r more magoons : a p p l y i n g a f i e l d opens a gap i n the magnon d i s p e r s i o n curve, and t h e number o f thermal magnons d r a m a t i c a l l y decreases. These experiments bear no i n f o r m a t i o n about t h e n a t u r e o f t h e motion between normal i o n s : coherent o r incoherent. L e t us j u s t mention t h a t i n t r i n s i c emission w i t h crea- t i o n o f a zone boundary magnon has been detected and i d e n t i f i e d through i t s behaviour under a p p l i e d f i e l d . I t s s h i f t from t h e zero-magnon l i n e i s equal t o t h e d i s p e r s i o n o f the magnon /6/ : hence t h e d i s p e r s i o n o f t h e e x c i t e d s t a t e i s very weak;
assuming t h a t S t e i n e r ' s model and parameters /6/ describe c o r r e c t l y t h e energy o f t h e zone boundary magnon, we deduce an upper bound o f I 1 cm-I f o r t h e d i s p e r s i o n o f t h e e x c i - t e d s t a t e .REFERENCES
/1/ Wieting, R.D., Fayer, M.D. and D l o t t , D.D., J. Chem. Phys. 69 (1978) 1996 Mc Pherson, G.L., Auerbach, R.A., Kwawer, G.N. and T a l l u t o , T . F . , 3 . Luminesc. 31-32 (1984) 296
C7-140 JOURNAL
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PHYSIQUE/3/ Hegarty, J., t h e s i s (Galway, I r e l a n d , I9 76)
/4/ C i b e r t , J., and Merle d1Aubign6, Y
.,
Phys. Rev. L e t t . 46 (1981) 1428/5/ Soscip, M., C i b e r t , J., T e r r i l e , M.C. and Merle d1Aubi*e, Y., J. Luminesc.
