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RELAXATION MEASUREMENTS IN THE SYSTEM CaF2 : Fe2+
P. Bonville, J. Chappert, C. Garcin, P. Imbert, J. Régnard
To cite this version:
P. Bonville, J. Chappert, C. Garcin, P. Imbert, J. Régnard. RELAXATION MEASUREMENTS IN THE SYSTEM CaF2 : Fe2+. Journal de Physique Colloques, 1980, 41 (C1), pp.C1-235-C1-236.
�10.1051/jphyscol:1980177�. �jpa-00219746�
JOURNAL DE PHYSIQUE Colloque C1, suppl6ment au n O 1, Tome 41, janvier 1980, page C1-235
2+
RELAXATION MEASUREMENTS
IN THE
SYSTEM CaF2 : FeP. Bonville, J. chappert+, C. Garcin, P. Imbert and J.R. ~6~nard' DPh. G/PSRM, C. E. N. SacZay, B. P. n02, 91190 Gif-sup-Yvette (France)
+
DRF/Groupe Interactions Hyperfines, C.E.N. Grenoble, 85X-38041 G~enoble Ceder (France)I. INTRODUCTION. Miissbauer studies of Fe2+ ions diluted in cubic diamagnetic gave inte- resting results concerning the role played by cova- lency, relaxation and dynamical Jahn-Teller effects (3) within the electronic levels of this ion.
In the eightfold coordinated system CaF2:Fe 2+
,
the Fe2+ ion presents the same electronic level scheme as in tetrahedral sites, i.e, a ground orbital doublet E which splits into five quasi equidistant
g
spin-orbit levels rl(l), r4(3), r3(2), i- (3), r2(1).
A preliminary Miissbauer study of CaF2:Fe showed that it was possible to observe the slow relaxation contribution of the first excited triplet
r4,
as predicted byam'^).
This observation was made around 9K, a temperature high enough to populate appreciably the levelr4,
but avoiding fast relaxation. The con- tribution ofr4
appears then as a quadrupole doublet superimposed on the single line due to the ground state singlet TI. From the thermal variation of the relative intensity of this doublet(5), it was possi- ble to evaluate the energy separation K between the levelsr4
andrl
(K=17t2 cm-l) and a complementary far infrared study gave independently a more accurate determination (Ka15.8 cm-'1.The present paper deals with the detailed analy- sis of the relaxation effects which influence the Miissbauer spectra of caF2:Fe2+ between 10 and 30K.
11. EXPERIMENTS. Sample preparation and experimental conditions have already been described (5)
.
Fig.1 represents the spectra between 4.2 and 27.53. At 4.2K only the ground state T1 is signifi- cantly populated, and the spectrum consists of a single absorption line. At 8 and 1OK the quadrupole doublet due to
r4
is visible ; with a further increase of temperature the doublet broadens and disappears at the same time that the single line considerably broa- dens.111. RELAXATION LINESHAPE THEORY. As shown by Ham, random strains play a crucial role by splitting the
r4
triplet into three singletsr4x, r4y
and r4z, each of them corresponding to equivalent axial electric field gradients (EFG) on the nucleus, respectively along the x,y and z axes. The quadrupole splitting isthus the same value is(3) E
Q
C =
E
for the three sublevels of T4 and its
=6q1cEI with q % 1 and (117) < Y 3 > e2q / [1(21-I)]
.
On the other hand the quadrupole interaction is zero in the ground state level
r
1'In order to resolve the relaxation lineshape problem, we adapted the stochastic theory of Blume and ~ j o n ( ~ ) to the case of a kandomly fluctuating EFG which can jump both between three equivalent values along the x,y and z axes due to relaxation transi- tions inside the triplet
r4,
and between these three finite values and zero because of the relaxation transitions betweenr4
andrl.
The fluctuating qua- drupole hamiltonian may then be written~ ~ ( t ) = ~ c ~ ~ x [ 1 - ( 1 / 4 ) ' f ~ ( t ) 1 {[1-f~(t)1(31;-1~)+
where the random function of time f(t) takes on the four possible values 2,1,0,-1. The relaxation matrix W whose off-diagonal elements are the transition probabilities per unit time between these values of
W represents the transition rate from one sublevel to another inside the triplet
r,,
and W' the transition rate from any sublevel ofr4 t o r l s t a t e
A straightforward generalization of relation (15) of ref.6 gives the lineshapeW(w)u Re
C
<j (~(p) ~1+3a~(m~)~(p)~(p) I - ~ P I ~ >i,j,ml
with ~ ( ~ ) = [ p - i a ( m ~ ) F ~ - w ] ' ~ ; ~ ( p ) = ~ ~ [ p + i a ( m ~ ) ~ p=-iwrr/2 ; a(ml=ti)=J
lcel
and o(ml=fB)=-QjcEl
:2 F =
1
-1
(P is the density matrix of the electronic system).
IV. DISCUSSION. Fitting a given relaxation spectrum requires only two adjustable parameters, the transi- tion rates W and W'. As for the constrained para- meters, we used the values Kz16 cm-';
I
~ Q I ~3.78 -.it17 Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980177
(21-236 JOURNAL DE PHYSIQUE (from the slow relaxation quadrupole splitting at 8K)
and 2P0.34 mrn.9-' (from the mean width of the cen- tral line below 10K).
This analysis revealed several interesting fea- tures :
-
1. Both the traasition rates W and W' are needed to fit the intermediate relaxation spectra (Fig.l), and the thermal variation of each of these rates is given in Fig.2. As W/W1=5 at 15K, the transition processes which act inside the triplet
r
4 are dominant compared to the transition processes betweenr
4 andrl.
Both Wand W ' can be fitted as these two relaxation rates
affect the lineshape in a different way : the pro- cesses internal to the
r4
level (rate W) do not broaden the central line due torl,
whereas the processesr4+rl
(rate W' orr1+r4
(rate EW' ) broaden both the quadrupole doublet and the central line before mixing them into a single line at higher temperatures.2. The thermal variation of W measured between 10 and 27.5K is less rapid than a T' type variation, but approaches this law towards the higher temperatures, which shows that the Raman processes then become dominant.
3. The W' measurements, although they are less pre- cise and concern a narrower temperature range, are roughly compatible with a T~ type law (dotted line, Fig.2) due to Raman processes.
4. W' becomes smaller than the inverse nuclear life time l/T for T-15K. From this observation we can predict an interesting consequence on the source spectra expected for the system c ~ F ~ : ~ ~ c o below 15K.
Namely the excited level Th of ~ e should then ~ + appear out of thermal equilibrium after the decay of 57~o. Such a behaviour has alreadv been observed in the system Z ~ S : ~ ~ C O where the quadrupole doublet due to
r4
presents a finite intensity down to zero-.
~elvin'~' ' I .
REFERENCES
(1) T. RAY and J.R. REGNARD, Phys. Rev. 14, 1796 (1976)
J.R. REGNARD and T. RAY, Phys. Rev.
g ,
1805 (1976) and references therein(2) C. GARCIN, P. IMBERT and G. JEHANNO, Solid State Coma. 2l, 545 (1977)
P. IMBERT, C. GARCIN, G. JEHANNO and A. GERARD, Internat. Conf. Miissbauer Spectroscopy, Buchareet 1977; Proceed.I1,123
(3) F.S. HAM, J. Physique
25
Colloq., C6-121(1974) (4) J.R. REGNARD and J. CHAPPERT, J. Physique 37,Colloq. C6-611 (1976)
(5) J.R. REGNARD and U. DURR, J. Physique (accepted for publication)
(6) J.A. TJON and M. BLUME, Phys. Rev.
165,
456 (1968).( 7 ) P. BONVILLE, C. GARCIN, P. IMBERT and G.
JEHANNO, Same Conference.
Fig.l- Mgssbauer spectra with fitted relaxation curves. (slight misfits around zero velocity are due to absorption by iron impurities in the Be windows of the dewar ; the corresponding channels were eliminated when fitting the spectra)
FCg.2
