MÖSSBAUER STUDY OF THE FREQUENCY DEPENDENCE OF PARAMAGNETIC RELAXATION OF DY MOMENTS IN TYPE I SUPERCONDUCTOR THORIUM

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MÖSSBAUER STUDY OF THE FREQUENCY

DEPENDENCE OF PARAMAGNETIC RELAXATION OF DY MOMENTS IN TYPE I SUPERCONDUCTOR

THORIUM

W. Wagner, G. Kalvius, V. Gorobchenko

To cite this version:

W. Wagner, G. Kalvius, V. Gorobchenko. MÖSSBAUER STUDY OF THE FREQUENCY DE- PENDENCE OF PARAMAGNETIC RELAXATION OF DY MOMENTS IN TYPE I SUPER- CONDUCTOR THORIUM. Journal de Physique Colloques, 1980, 41 (C1), pp.C1-243-C1-244.

�10.1051/jphyscol:1980181�. �jpa-00219774�

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JOURNAL DE PHYSIQUE

Colloque

C1,

suppMment au n "

1 ,

Tome

^41,

janvier

1980,

page

Cl-243

&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 i g a t i o n of paramagnetic r e l a x a t i o n of di- l 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:=. We have extended t h i s study to the temperature range where Th be- 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 relaxa- t i o n process. I n t h i s paper we have to re- nounce d e t a i l s already given i n Ref. 1 fo- 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 ( ~ ~ / ~ = 7 2 d) i n Th was used as a source f o r

I 60

the 87 keV (2++ )'0 resonance i n _Dy. 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 ~ 2 held a t 16 K. Source tempera- t u r e s ( 1 - 5 2 to 0.79 K ) were obtained with a continous~ly operating 'He r e f r i g e r a t o r . 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 doublet with an e f f . s p i n ~ = 1 / 2 giving 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

n(4nf=

154mR while the ground s t a t e ( I f = O ) 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-transi- t i o n s ( i - f and

2 4 ' ) .

The r e l a x a t i o n matrix ( i , f

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-

t r y the q dependence may be skipped) :

(;(t)$(0)) = Td&$(t))(0)1 = ( ~h ( t ) 3

. ⁽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

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

I f h ( t ) f a l l s off r a p i d l y compared with the exponential term i n Eq. ( 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. 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)

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

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(21-244 JOURNAL DE PHYSIQUE

with the r e l a x a t i o n parameter i n the ME I I

l i n e shape expression. Giving up the WNA,

-

one has t o pay a t t e n t i o n t o the spectros-

copic "time window" ( i n our case the nucle-

_G; g

400- a r l i f e time). The c a l c u l a t i o n of ME spec- I-

d

t r a may be s i m p l i f i e d i n the slow relaxa- z t i o n regime by the " s e c u l a r approxima tiontt :

:

²⁰⁰

^-

f i'

3

^T, ^{= 1.33K}

I n s e t t i n g PIW II Eo-Eo i n Eq. (2) one neg-

l e c t s intermediate r e l a x a t i o n frequencies

4

w

CT

out of resonance. This approach d i s i n t e - ₁ 2 3

g r a t e s I ( @ ) i n t o a number of r e l a x a t i o n REDUCED TEMPERATURE TIT=

parameters

I ( w . )

determined by the i o n i c

J Fig.2: Relaxation r a t e s W from hf s p e c t r a

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 / 2 e l e c t r o n i c system a t tempera- t u r e T i s given by _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 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 J a with the s-4f exchange i n t e g r a l Jsf.

The decay ( c o r r e l a t i o n ) time of h ( t ) i n Eq. ( 1 ) i s f o r a normal conductor t 10-16s

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

sponds t o the l a r g e s t l i n e broadening ob- served i n the S-state and therefore the se- c 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 I ~ ( w = o ) i n Eq. ( 6 ) we make use of the an- i 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).

As a f i r s t approach we average IS(@,T) by 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 ( a 2 ) of the Fermi 41t gJ-'

J N ( T ) =

Tk;.(-

Jsf p(EF)) 2

~ ( a ) ~

kgT ( 4 ) surface e n t e r s ( I ~ ( ,T)kV a s only f r e e par-

g~ ( 1 - 4 ameter!

(J

P ( ~ F ) i s known from the N-

s f

with the d e n s i t y of s t a t e s p(EF) a t EF and 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 e l e c t r o n i n t e r a c t i o n s . Indeed, i n Fig. 2 be regarded more than t h a t a s an averaging the r a t e deduced f o r T (open c i r c l e s ) parameter r e f l e c t i n g the spectroscopic time

C

follows well the Korringa r e l a t i o n . window and the f i n i t e l i f e time of the su- For an i d e a l BCS superconductor ( s ) the perconduc t i n g q u a s i p a r t i c l e s

.

bath Hamiltonian i s given by I n the l i n e shape c a l c u l a t i o n the matrix

fI,

⁼^ko'k

^-1

^.6+,^ka^{8 ,}^ko

- $

A ( B & E ; ~ , , + ~ - ~ ~ ~ ~ ~ ) ' ( 5 ) The energy gK i s measured from EF;

6:

and

k c 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 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 quasi-

2 2 1/2 p a r t i c l e s with e x c i t a t i o n energy ( E

+ A

)

,

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 of HB 4 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) :

Here f ( ~ ) i s the Fermi function. The spectrum a t 'k1.33 K shown i n Fig. 1 corre-

elements 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 parameters 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 C i s shown i n Fig. 2. We 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 (a )=0.021 taken 2 from tunneling experiments 4

.

The hf constant A d i d n o t change f o r TtT

C *

References

1 W. Wagner, J.Physique ~ o 1 1 . ~ ( 1974) ~ 6 - 1 3 3 2 S.Dattagupta,G.K.Shenoy,B.D.IXlnlap and

L.Asch, ~ h y s . ~ e v . a ( 197713893 3 R.J.Clem, ~nn.~hys.4q(1966)268 4 B.A.Haskell,W.J.Keeler and