Colloque C1, suppMment au n " 1, Tome 41, janvier 1980, page Cl-243. &SBAUER. STUDY OF THE FREQUENCY DEPENDENCE OF PARAMAGNETIC ...
Colloque C1, suppMment au n " 1 , Tome 41, janvier 1980,page Cl-243
JOURNAL DE PHYSIQUE
&SBAUER STUDY OF THE FREQUENCY DEPENDENCE OF PARAMAGNETIC R E W T I Q N OF DY MOMENTS I N TYPE I SUPERCONDUCTOR THORIUM W. Wagner, G.M.
+
Kalvius and V.D.
+
Gorobchenko
Physik Dept. TU Mnchen, 0-8046 Garching, Fed. Rep. Gemany. Kurehatov I n s t i t u t e of Atomic Energy, Moscow, USSR.
Mossbauer spectroscopy may be s a i d to be well established a s a method f o r the inves-
t r y the q dependence may be skipped) : (;(t)$(0))
= Td&$(t))(0)1
= ( ~h3 (t)
t i g a t i o n of paramagnetic r e l a x a t i o n of dil u t e r a r e e a r t h (RE) impurities i n metals. A t an e a r l i e r conference we have reported
the system Dy:=.
W e have extended t h i s
study to the temperature range where Th be-
. (i)
Thermal averaging i s done with the d e n s i t y matrix
cB =
exp(-Di$)/~rr exp(-D%)]
with
D= l / k B ~ .A l l time dependent func t i o n s 2 i n (i, f 1 ~ l i ' , f )may be c o l l e c t e d i n an i n t e g r a l
comes a superconductor ( T = I . 3 3 ~ ) . Contrary to a normal conductor the r e l a x a t i o n r a t e was found to be strongly dependent on the amount of energy transfered i n the relaxat i o n process. I n t h i s paper we have to renounce d e t a i l s already given i n Ref.
1 fo-
w r e p r e s e n t s the v e l o c i t y s c a l e and E i s 0 an unperturbed hf l e v e l . On the o t h e r hand, the s p e c t r a l d e n s i t y function of the thermal bath i s given by the Fourier transform
cusing on r e l a x a t i o n i n a superconductor. A n a l l o y of 500 ppm of r a d i o a c t i v e I6OT'b
( ~ ~ / ~ d) = 7i n 2 Th was used as a source f o r the 87 keV (2++ ) ' 0 resonance i n I 60Dy. The hyperfine ( h f ) spectra of t h i s source was analyzed with a s i n g l e l i n e absorber
1 6 0 ~ . q ~ c . 6 ~held 2 a t 16 K.
refrigerator.
The e l e c t r o n i c gTbund s t a t e of Dy3+ i n Th i s an i s o l a t e d
r7 Kramers
exponential term i n Eq.
doublet with an
( 2 ) , the frequency
spectrum of the bath turns o u t to be r a t h e r f l a t (white n o i s e ) i n the range of i o n i c hf frequencies.
Source tempera-
t u r e s ( 1 -52 to 0.79 K ) were obtained with a continous~lyoperating 'He
I f h ( t ) f a l l s off r a p i d l y compared with the
This i s c a l l e d the "white
noise approximation'' = WNA.
I t was widely
used i n the p a s t because one i s l e f t with one r e l a x a t i o n parameter I ( 0 ) . The WNA i m p l i e s the i d e n t i t y of the s p e c t r a l d e n s i t y of the bath (evaluated a t zero frequency)
e f f . s p i n ~ = 1 / 2giving r i s e to an i s o t r o p i c paramagnetic hf i n t e r a c t i o n
fihf
= A~(?-;).
The excited s t a t e (Ii=2) c o n s i s t s of two l e v e l s ?'i=?it$ 5/2, 3/2 separated by 154mR while the ground s t a t e ( I f = O )
n(4nf=
remains
u n s p l i t . The degeneration of the energy l e v e l s allows 20 y-transitions.
Fig.
1
'
shows the r e s u l t i n g hf s t r u c t u r e . The r e l a x a t i o n c o n s i s t s of an e l e c t r o n i c s p i n - f l i p which couples d i f f e r e n t y-transitions (i-f (i,f
and 2 4 ' ) .
The r e l a x a t i o n matrix
I R ~i , f ) represents t h i s process. The
ion-bath i n t e r a c t i o n i s commonly f a c t o r i z e d by the Hamiltonian
$=
5 kqGq . The bath
v a r i a b l e s F ( t ) e n t e r the Mossbauer l i n e 9 shape expression a s parameter only through the c o r r e l a t i o n functions ( i n cubic symme-
Fig. 1 : M E s p e c t r a above and below Tc=l . 3 3 K
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980181
(21-244
JOURNAL DE PHYSIQUE
with the r e l a x a t i o n parameter i n the M E l i n e shape expression.
g
one has t o pay a t t e n t i o n t o the spectros-
G; 400-
copic "time window" ( i n our case the nucle-
I-
a r l i f e time). The c a l c u l a t i o n of M E spec-
d
z
: 3
t r a may be s i m p l i f i e d i n the slow relaxat i o n regime by the " s e c u l a r approxima tiontt: f i ' I n s e t t i n g PIW II Eo-Eo i n Eq. (2) one neg-
200 T, = 1.33K
4w
l e c t s intermediate r e l a x a t i o n frequencies out of resonance.
CT
This approach d i s i n t e -
1 2 3 REDUCED TEMPERATURE TIT=
g r a t e s I ( @ ) i n t o a number of r e l a x a t i o n parameters
I(w.) J
determined by the i o n i c
energy d i f f e r e n e i e s
w The r e l a x a t i o n r a t e 3'
W of a ~ = 1 / 2e l e c t r o n i c system a t tempera-
W = ig;.1(u,~). m e evaluation of r e l a x a t i o n s p e c t r a i n metals
t u r e T i s given by
i s based on the exchange coupling
-
fiex -
-2(gJ-1 )Jsf (3.2) between the conduction e l e c t r o n spin 3 and the R E impurity moment a
J with the s-4f
exchange i n t e g r a l Jsf.
Fig.2:
Relaxation r a t e s W from hf s p e c t r a
sponds t o the l a r g e s t l i n e broadening observed i n the S-state and therefore the sec u l a r approximation can be adopted. I n order to remove the s i n g u l a r i t y of
( 6 ) we make use of the ani s o t r o p y of the gap A(T) over the Fermi surface by the s u b s t i t u t i o n A + A.(l+a).
I ~ ( w = o )i n Eq.
As a f i r s t approach we average IS(@,T) by
The decay ( c o r r e l a t i o n ) time of h ( t ) i n 10-16s Eq. ( 1 ) i s f o r a normal conductor t C
(fi/Fermi energy E ~ ) .That i s why the WNA i s v a l i d l e a d i n g to the wellknown Korringa law 41t gJ-'
I
I
-
Giving up the WNA,
a second i n t e g r a t i o n with a normalized rec-
,
tangular d i s t r i b u t i o n function3 ~ ( a )what makes ( I ~ ( o , T ) ) , v f i n i t e . I n t h i s way the mean square anisotropy ( a2) of the Fermi
with the d e n s i t y of s t a t e s p(EF) a t EF and
surface e n t e r s ( I ~ (,T)kV a s only f r e e parameter! (J P ( ~ F ) i s known from the Nsf s t a t e ) . I n t h i s s o l u t i o n (a 2 ) i s connected
~ ( a ) / ( l - a ) ' takes i n t o account electron-
with gap anisotropy, n e v e r t h e l e s s , i t can
JN(T)
= Tk;.(-
Jsf p(EF))2
~ ( akgT ) ~ (4) (1-4
g~
electron interactions.
Indeed, i n Fig.
2
the r a t e deduced f o r
TC (open c i r c l e s ) follows well the Korringa r e l a t i o n . For an i d e a l BCS superconductor ( s ) the bath Hamiltonian i s given by
be regarded more than t h a t a s an averaging parameter r e f l e c t i n g the spectroscopic time window and the f i n i t e l i f e time of the su-
.
perconduc t i n g q u a s i p a r t i c l e s I n the l i n e shape c a l c u l a t i o n the matrix
elements fI, = ko'k -1 .6+ka , 8ko , - $ A ( B & E ; ~ , , + ~' (- 5~) ~ ~ ~ ~ )
6:k c and a r e c r e a t i o n and a n n i h i l a t i o n operators
The energy gK i s measured from EF;
f o r e l e c t r o n s i n the (E?,a) one p a r t i c l e s t a t e (cr=
1,~).
The energy spectrum of the
bath i s now governed by the e l e c t r o n quasip a r t i c l e s with e x c i t a t i o n energy ( E2+ A2 ) 1/2, i.e.
the d e n s i t y of s t a t e s i n c r e a s e s rapid-
l y f o r energies near the energy gap A(?'). On b a s i s of
gex
and the new eigenfunctions
4
of HB we obtain f o r the r e l a x a t i o n function with a small energy t r a n s f e r TiW c 2A(T) :
meters connected with w 0 (AF=O)
and W-%f ( ~ F = f l ) .The r e s u l t of a f i t t o our d a t a
f o r T < T Ci s shown i n Fig.
trum a t 'k1.33 K shown i n Fig.
1 corre-
2.
W e f i r s t cal-
culated (I~(~A$.,~,T)&~ ( d o t s on s o l i d l i n e ) and used (I,(o,T)&
a s f r e e parameter ( b i g
d o t s with e r r o r b a r s ) . The dashed l i n e i s a t h e o r e t i c a l curve with (a2 )=0.021 taken 4 from tunneling experiments
.
The hf constant A
d i d n o t change f o r TtT
C*
References 1 2
Here f ( ~ )i s the Fermi function. The spec-
of the e l e c t r o n i c s p i n determine
the occurrence" of the two r e l a x a t i o n para-
3 4
W. Wagner, J.Physique ~ o 1 1 . 1974) ~ ( ~6-133 S.Dattagupta,G.K.Shenoy,B.D.IXlnlap and L.Asch, ~ h y s . ~ e v . 197713893 a( R.J.Clem, ~nn.~hys.4q(1966)268 B.A.Haskell,W.J.Keeler and D.K.Finnemore, phys.Rev.a( 1972)4364
