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Submitted on 1 Jan 1978
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DISTRIBUTION DES VALEURS DES MOMENTS
DIPOLAIRES ELECTRIQUES DANS UN VERRE
L. Bernard, L. Piche, G. Schumacher, J. Joffrin
To cite this version:
JOURNAL DE PHYSIQUE Colloque C6, supplément au n" 8, Tome 39, août 1978, page C6-957
DISTRIBUTION DES VALEURS DES MOMENTS DIPOLAIRES ELECTRIQUES DANS UN VERRE
L. Bernard, L. Piche, G. Schumacher and J. Joffrin ,
Centre de Recherehes sur les Trds Basses Temperatures, C.N.R.S., BP 166 X, 38042 Grenoble Cedex
FRANCE.
Résumé.- Par une méthode d'échos dipolaires électriques, on montre que dans un verre, la distribution des moments électriques longitudinaux statiques d'un paquet de "spins" est une lorentzienne. Ce ré-sultat confirme, d'un autre point de vue, le caractère inhomogène des raies de résonance et il en précise un aspect.
Abstract.- Using the electric dipolar echoes we show that in a glass, the distribution of the longi-tudinal static dipole of the same frequency obeys a Lorentzian law. This result confirms the inhomo-geneous character of a resonance line.
Experiments on electric dipolar echoes in glasses have allowed to measure the mean value of the effective dipole moment, the density of state of these dipoles, the elastic coupling constant to the resonant phonons and the temperature dependan-ces of the longitudinal (Tj) and transverse (T2) relaxation time /l/. The description in terms of two level defects implies that for the dipole mo-ments both the longitudinal (permanent dipole) and the transverse (induced dipole)components must be specified. We had already evaluated p, the effective transverse moment. Here we modified our experimen-tal procedure so as to put in evidence the longitu-dinal component, and to describe it's distribution within a spin packet.
EXPERIMENTAL PROCEDURE.- In an echo experiment, the spin medium is submitted to two consecutive R.F. pulses of same height, of width Atj and At sepa-rated by a time T. An echo appears at time 2 T , and the variation of it's amplitude as a function of T is a measure of T2. Now, in the interval 0,T we apply a static electrical field E for a time At
(fig. 1) ; we observe, T being constant, that the amplitude of the echo decreases when E or At increa-se. The R.F. pulses have widths of Atj = 0.7 y.s and At2 = 1.4 y.s and - 24 dBm peak power : pulse one causes a 90° rotation of the magnetization. We took T = 10 u.s. a value smaller than T2 (T2 = 60 u.s.) ; At varies from 0.5 to 5 y.s. and V, theD.C. voltage1, from 0 to 1 volt. The sample is a disk of
Suprasil I glass which contains 1200 ppm OH ions ;
it is 2 mm(l) thick and metalised on both sides, it constitutes the capacitor of a resonant circuit (co/2ir = 370 MHz) IM ; the ensemble is immersed in the mixing chamber of our dilution refrigerator and the temperature regulated at T = 10 mK.
EXPERIMENTAL RESULTS.- The figures show the decrea-se of the echo intensity with increasing V (fig. 1) and At (fig. 2 ) . One sees without ambiguity that the decrease is exponential so that the amplitude is :
A = exp(- \ At K) (1)
and we deduce K = 7 x 10s M.K.S. from our data.
Fig. 1 :
It must be noted that the position of the D.C. pulse in the interval 0,T or T , 2 T has no influence and also that there is no effect if the D.C. pulse comes before the first (ir/2) R.F. pulse.
* Institut Laue-Langevin, BP 156 X, 38042 Grenoble Cedex, FRANCE.
I
Signal ( d B)A t l At 2
I I I !
200 400 m 800 V(rnV1
*
Fig. 2
:DISCUSSION.- The decrease, as a function of,T of the
amplitude of a spontaneous echo is due to irrever-
sible processes
;effects such as inhomogeneous
broadening of spin packets are compensated by the
time reversal operated by the second
(T)R.F. pulse.
In our experiment, the effect of the D.C. field is
not compensated
;the amplitude of the echo decrea-
ses when V increases. We explain the effect by the
a12 pulse
;for some, the precessing frequency
increases, for others, it decreases. Note that since
this effect is due to a static field (V.C.) we are
concerned with the longitudinal component of the
dipoles (permanent dipoles). In a time At, such a
longitudinal dipole of moment pi encounters aphase
+
-+shift pl.E/$At. It's contribution to the amplitude
A of the echo (unity without the field step) is
+
. t
Pi
cos
(-g
At)
(2)
However in a glass, a spin packet is expec-
ted to have a broad distribution of it's characte-
-+
ristics such as the module of p and it's orienta-
-ftion with regards to E. Let n(6) be the distribu-
+
tion of p which in a glass we shall assume to be
isotropic. Starting from (2) we can write
A
as
:+m
+
+E
A =1
c o s ( k At) n($)
d3$
4 ( 3 )Calling Z the axis of our D.C. field, this becomes
Obviously
(4)
shows that the amplitude of theecho
is the Fourier transform of n
Z
(p
Z
) ;n
Z
(p
Z
)is thus
is a Lorentzian centered on zero
:- 3 0
with ApZ
=$K
=0.7 x 10
M.K.S.
=0.2 Debyes.
This must be compared to an earlier
111
result given for
p
the effective transverse dipole
-
-3 0moment
:p
=1.8 x 10
M.K.S.
=0.5 Debye. It
could be there also that the distribution of the
transverse dipole moments is zero centered andthat
p
and Apz have comparable values even though one is
the transverse and the otherthe longitudinal compo-
nent of the dipole moment.
CONCLUSION.- From n (p
),using
(5) we can describe
z
Zn(
lpl)
the distribution of the modules of the lon-
gitudinal dipole moments. It resembles a Lorentzian
but sharper
;it's width is of the order of ApZ.
We
conclude by saying that n(
l p
1)
being centered on
zero does not show a maximum for any value of
l p
1
like one could have thought in reminicing that the
dipoles originate from OH- ionic impurities.
Reference
/I/ Bernard, L., Piche, L., Schumacher, G., Joffrin
J.,
Graebner, J., J. Physique Lettres,
2
(1978) L- 126.
where n (p
)is the distribution of the component
z z
(pZ) of the longitudinal dipole moment lying along
the field axis
:nZ(pZ) should be symetrical in pZ
and is related of n($)
=n( lpl) through
:m
