Experimental evidence of the influence of electron dipole dipole interaction on nuclear spin lattice relaxation

V o l u m e 27A, n u m b e r 1

PHYSICS

ferromagndtique. Les mesures d'absorption opt i q u e de B u s c h et W a c h t e r [3] ont ddj~ m i s en d v i d e n c e c e t o r d r e ~ c o u r t e d i s t a n c e . A t i t r e de c o m p a r a i s o n , n o u s a v o n s r e p r d s e n t d la p o s i t i o n de l ' a r 6 t e d ' a b s o r p t i o n o p t i q u e ( c o u r b e en p o i n t i l l d m i x t e ) en f o n c t i o n de la t e m p d r a t u r e . D a n s l e s l i m i t e s d ' e r r e u r , l e d d p l a c e m e n t de l ' a r 6 t e d ' a b s o r p t i o n s u i t la v a r i a t i o n de v o l u m e du c r i s tal. P o u r E u O , l e p a r a m ~ t r e H de la r e l a t i o n e n t r e l ' d n e r g i e d ' d c h a n g e et l e v o l u m e v a u t - 3.47. C e t t e v a l e u r e s t en a c c o r d a v e c c e l l e o b t e n u e p a r t i r d e s m e s u r e s de l a t e m p 6 r a t u r e de C u r i e en f o n c t i o n de la p r e s s i o n , de S t e v e n s o n et R o b i n son [4]: ~ = - 3.57. De s e m b l a b l e s r d s u l t a t s ont dtd o b t e n u s p o u r EuS, od H = - 6.41. D a n s E u T e , nous n ' a v o n s p a s o b s e r v d la d d f o r m a t i o n m e s u r d e p a r R o d b e l l et al.

EXPERIMENTAL EVIDENCE DIPOLE INTERACTION

LETTERS

20 May 1968

[5]. I1 est p r o b a b l e que p o u r d e s t e m p e r a t u r e s p l u s b a s s e s , EuSe, m o n t r e un c o m p o r t e m e n t complexe. N o n s r e m e r c i o n s l e F o n d N a t i o n a l S u i s s e de la R e c h e r c h e S c i e n t i f i c p o u r son s u p p o r t f i n a n cier.

Rdfdrences 1. B . E . A r g y l e , N. Miyata et T . D , S c h u l t z , P h y s . Rev. 160 (1967) 413.

2. C. P. Bean et D. S. Rodbell, Phys. Rev. 126 (1962) 104. 3. G. Busch et P. Wachter, Phys. kondens. Materie 5 (1966) 232. 4. R.Stevenson et M.C.Robinson, Canad. J. Phys. 43 (1965) 1744. 5. D. S. Rodbell. L.M. Osika et P. E. Lawrence, J. Appl. Phys. 36 (1965) 666.

OF THE INFLUENCE OF ELECTRON DIPOLE ON NUCLEAR SPIN LATTICE RELAXATION

G. M. VAN DEN H E U V E L , C . T . C . H E Y N I N G , T . J . B . S W A N E N B U R G and N. J . P O U L I S

Kamerlingh Onnes Laboratory, Leiden, The Netherlands Received 19 April 1968

The electron dipole dipole interaction in dilute paramagnetic crystals at low temperatures may determine the nuclear spin lattice relaxation rate. Experimental evidence to confirm these ideas is given.

It h a s b e e n shown t h a t t h e s p i n - l a t t i c e r e l a x a tion of n u c l e i in d i l u t e d p a r a m a g n e t i c c r y s t a l s at low t e m p e r a t u r e s i s due to t h e d i p o l e d i p o l e i n t e r a c t i o n of t h e s e n u c l e i with t h e p a r a m a g n e t i c i o n s [1]. In o r d e r to c a l c u l a t e the n u c l e a r r e l a x a t i o n t i m e one h a s to e v a l u a t e t h e s p e c t r a l d e n s i t y of the l o c a l f i e l d due to t h e t i m e d e p e n d e n c e of the z - c o m p o n e n t of t h e e l e c t r o n s p i n S. T h e r e a r e two m e c h a n i s m s w h i c h m a y a f f e c t the o r i e n t a t i o n of t h e s p i n s S, n a m e l y t h e e l e c t r o n s p i n l a t t i c e i n t e r a c t i o n and t h e e l e c t r o n d i p o l e - d i p o l e i n t e r a c t i o n , c h a r a c t e r i z e d by t h e t i m e c o n s t a n t s T l e and T2e r e s p e c t i v e l y . T h e s p e c t r a l d e n s i t y due to t h e f i r s t m e c h a n i s m b e i n g about a d i r e c t energy exchange between the nuclear spin syst e m and t h e l a t t i c e . T h e s e c o n d m e c h a n i s m , h o w e v e r , i n d u c e s a r e l a x a t i o n of t h e n u c l e i to the electron interaction system. F o l l o w i n g P r o v o t o r o v [2], i t i s a s s u m e d t h a t 38

t h e i n t e r a c t i o n s y s t e m of t h e s p i n s S can be d e s c r i b e d by a t e m p e r a t u r e TSS = 1/kl3ss. T h e r e l a x a t i o n e q u a t i o n f o r the n u c l e i can t h e n be w r i t t e n a s [3]: d d-t ~I = - Wl(~I - HL) - W2(HI -/3SS) , w h e r e W 1 and W 2 a r e t h e t r a n s i t i o n p r o b a b i l i t i e s due to t h e a f o r e - m e n t i o n e d m e c h a n i s m s , and can 2 2 1 be deduced tobe[3]: W 1= CTle(I+wITle); z "2 1 . 3 2 W 2 = C T 2 e ( l + c 0 I T 2 e )- w i t h C = i ~ ~ ~,2~2~.6. ~SrI'~o fJS' HI and HL are the inverse temperatures ol m e nuclear Zeeman system and the lattice. The time dependence of Hss is given by .

d

NIW}

2

~tt HSS = - W2 J-,NsW---~~ S S - HI) - --T1 e 03ss - HL) ' 2 2 w h e r e Niwi/NsW L i s t h e r a t i o of t h e h e a t c a p a c -

Volume 27A, number 1

S_~

PHYSICS LETTERS

I

'

10' -

20 May 1968

10 ~ $i

I T = 3.0 °K

0=9.3

/ No= 9.3 kO¢

kOe

.5 ° ld

5 °

2

10 2

1.0

-T

TI n

I o .3

10-3

Tt n

\

I J I 0 -3 N d / L o

m,

0.2

Fig. 1. Concentration dependence of Tln1 for different temperatures. The horizontal scale indicates the amount of Nd in the crystal. i t i e s of the n u c l e a r Z e e m a n s y s t e m and the e l e c tron interaction system. The g e n e r a l solution for flI exhibits two t i m e c o n s t a n t s ; t h r e e s p e c i a l solutions will be p r e sented: 1) W1 >> W2; The n u c l e a r r e l a x a t i o n t i m e T l n i s given by W~I; T l n is p r o p o r t i o n a l to T l e and to N s 1; 2) W 2 >> Wl; 2 / T l e >> (Nio;f/Ns w2) W2, 2 / T l e > > W2. Then T l n = W~1. T l n i s independent of t e m p e r a t u r e , and the c o n c e n t r a t i o n dependence is d e t e r m i n e d by that of T2e[1]; 3)2W2 >>2WI; N I ~ / / N s ~

>> 1;

\

tO-4

I I 0 -a

1

(NIOgI/NsO)L)W2 >> 2/T1 e. T l n i S given by T~n = = W 1 + (NsCO2/NIW2) • 2 / T l e , so that Tln i s again p r o p o r t i o n a l to Tle, w h e r e a s the c o n c e n t r a t i o n dependence v a r i e s f r o m N s l for s m a l l c o n c e n t r a tions to T l n c c Ns3 for l a r g e r v a l u e s of N s. D u r ing the n u c l e a r r e l a x a t i o n p r o c e s s the i n t e r a c t i o n s y s t e m i s heated to a t e m p e r a t u r e different f r o m that of the lattice. M e a s u r e m e n t s of the proton spin l a t t i c e r e l a x a t i o n t i m e T l n have been p e r f o r m e d in s i n g l e c r y s t a l s of La2Mg3(NO3)12.24H20 cont a l n i n g a v a r y i n g p e r c e n t a g e of Nd 3+, in fields f r o m 2.5 kOe to 14 kOe. Calculation shows that for t h e s e c r y s t a l s the conditions mentioned in "3" a r e fulfilled. All m e a s u r e m e n t s show for

\ -1 I

T -~ . 0.4

,

"7-0.6 °K-~

-i Fig. 2. Temperature dependence of Tin for crystals containing various amounts of Nd. Here the concentrations indicated refer to those of the solutions.

s m a l l N d - c o n c e n t r a t i o n s a l i n e a r dependence on N d / L a , w h e r e a s for l a r g e r v a l u e s of the conc e n t r a t i o n this dependence v a r i e s between Ns3. An example is given, in fig. 1, for a field of 9.3 kOe. The t e m p e r a t u r e dependence of T l n is the s a m e for all v a l u e s of Ns, and equal to that of T l e as shown in fig. 2. The c o n c e n t r a t i o n of Nd in the c r y s t a l s was d e t e r m i n e d by X - r a y f l u o r e s c e n c e and activation a n a l y s i s *. A m o r e e l a b o r a t e d i s c u s s i o n of the e x p e r i m e n t a l r e s u l t s in the whole f i e l d - and t e m p e r a t u r e - r e g i o n will be given in a f o r t h c o m i n g a r t i c l e . The c o n s e q u e n c e s of t h e s e concepts on the d y n a m i c p o l a r i z a t i o n p r o c e s s have been d i s c u s sed before [4].

References 1. N . B l o e m b e r g e n , P h y s i c a 15 (1949) 386. 2. B . N . P r o v o t o r o v , Z h . E k s p . i T h e o r . F i z . 41 (1961)

1582; Soviet Physics JETP 14 (1962) 1126. 3. T.J.B. Swanenburg, Thesis, Leiden 1967. 4. W. Th. Wenckebach et al., Phys. Letters 26A (1968) 203.

* We are very much indebted to Dr. Addink and Mr. A. W. Witmer of Philips Research Laboratory for performing this analysis.

39