FINE STRUCTURE ON NMR LINES IN A PARAMAGNET DUE TO INDIRECT NUCLEAR SPIN-SPIN COUPLING

(1)

HAL Id: jpa-00217824

https://hal.archives-ouvertes.fr/jpa-00217824

Submitted on 1 Jan 1978

HAL is a multi-disciplinary open access

archive for the deposit and dissemination of

sci-entific research documents, whether they are

pub-lished or not. The documents may come from

teaching and research institutions in France or

abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est

destinée au dépôt et à la diffusion de documents

scientifiques de niveau recherche, publiés ou non,

émanant des établissements d’enseignement et de

recherche français ou étrangers, des laboratoires

publics ou privés.

FINE STRUCTURE ON NMR LINES IN A

PARAMAGNET DUE TO INDIRECT NUCLEAR

SPIN-SPIN COUPLING

W. Looyestijn, T. Klaassen, N. Poulis

To cite this version:

(2)

JOURNAL DE PHYSIQUE

Coltoque C6, supplkment au no 8, Tome 39, aolit 1978, page

C6-807

F I N E STRUCTURE ON NMR L I N E S I N A PARAMAGNET DUE TO I N D I R E C T NUCLEAR S P I N - S P I N COUPLING W . J . L o o y e s t i j n , T.O. Klaassen and N . J . P o u l i s

Kamerlingh Onnes Laboratorium der Rijksuniversiteit, Leiden, The Netherlands.

RQsum6.- Nous avons observ4 une s t r u c t u r e f i n e d i s c r s t e dans l e s s p e c t r e s RMN d e s l i g a n d s dans RbpCuClq. 2H20 e t dans l e s c o r p s isomorphes dans 1 ' 6 t a t paramagngtique. P l u s i e u r s r d s u l t a t s expgrimentaux d g o n t r e n t qu'un couplage i n d i r e c t d e s s p i n s nu- c l d a i r e s e s t

B

l ' o r i g i n e d e c e t t e s t r u c t u r e . I1 e s t avanc4 que, dans l e c a s p a r t i - c u l i e r de c e s composgs l a p o r t g e du couplage e s t l i m i t 6 e 1 deux s p i n s .

A b s t r a c t . - A d i s c r e t e f i n e s t r u c t u r e i n t h e l i g a n d

NMR

s p e c t r a i n Rb2CuC14.2H20 and isomorphous compounds i s observed i n t h e paramagnetic s t a t e . S e v e r a l experimental r e s u l t s prove t h a t i n d i r e c t n u c l e a r spin-spin c o u p l i n g i s t h e o r i g i n of t h i s s t r u c - t u r e . It i s argued t h a t t h e range of t h e coupling i s l i m i t e d t o two s p i n s e s p e c i a l l y i n t h e s e compounds.

I n d i r e c t c o u p l i n g of n u c l e a r s p i n s i n ma- g n e t i c m a t e r i a l s h a s been r e p o r t e d u n t i l now only a s an important c o n t r i b u t i o n t o the NMR l i n e width. Suhl 121 and Nakamura / 3 / have shown t h a t t h e ma- g n i t u d e of t h i s i n t e r a c t i o n , which o c c u r s v i a t h e h y p e r f i n e coupling, i s of t h e c o r r e c t o r d e r t o e x p l a i n t h e observed l i n e width.

The h e r e p r e s e n t e d experiments,however, a r e c a r r i e d o u t i n such a s i t u a t i o n , t h a t t h e in- d i r e c t c o u p l i n g i n v o l v e s only two n u c l e i . This c o u p l i n g g i v e s r i s e t o a w e l l r e s o l v e d f i n e s t r u c - t u r e of t h e resonance l i n e s , o n l y when t h e two n u c l e i a r e i d e n t i c a l . The n u c l e a r s p i n h a m i l t o n i a n i s u s u a l l y g i v e n by

When t h e m a g n e t i z a t i o n i s n e a r l y s a t u r a t e d , t h e e l e c t r o n s p i n system i s d e s c r i b e d by s p i n waves. Then, t h e coupling between t h e n u c l e a r s p i n and t h e e l e c t r o n s p i n , which c o n t a i n e s b e s i d e s hyper- f i n e a l s o d i p o l a r i n t e r a c t i o n , g i v e s a c o r r e c t i o n to* which c a n be r e p r e s e n t e d by an e f f e c t i v e h a m i l t o n i a n

Here, z i s t h e d i r e c t i o n of t h e m a g n e t i z a t i o n and

Huk

i s t h e energy of a Spin wave w i t h wave v e c t o r k.$$i i s o n l y e f f e c t i v e when Ii and I . a r e i d e n t i -

1

c a l s p i n s , and l e a d s then t o a f i n e s t r u c t u r e . Thus, t h e l i n e shape of a p a r t i c u l a r i s o t o p e

depends on t h e abundanceof i d e n t i c a l s p i n s . The i n t e r a c t i o n between n u c l e a r s p i n s i s a p p r e c i a b l e

Ih

o n l y w i t h i n a r a d i u s b a(we/wo)

..

Here, a i s t h e l a t t i c e c o n s t a n t and we and wo a r e t h e e l e c - t r o n a n g u l a r f r e q u e n c i e s r e l a t e d r e s p e c t i v e l y t o t h e exchange i n t e r a c t i o n and t h e a p p l i e d f i e l d , i n c l u d i n g demagnetizing and anosotropy f i e l d s / 3 , 4 / I n most w e l l s t u d i e d magnetic m a t e r i a l s i s b >> a and hence a l a r g e number of n u c l e i ' i n t e r a c t . This l e a d s t o such a complicated f i n e s t r u c t u r e t h a t o n l y a broadening o f t h e n u c l e a r resonance l i n e i s observed. I n Rb2CuC14.2H20 and isomorphous compounds however, t h e exchange i n t e r a c t i o n i s r a t h e r s m a l l / l / . Now t h e r a d i u s bo c a n be made s m a l l e r t h a n a a t moderately s t r o n g e x t e r n a l f i e l d s . I n such a s i t u a t i o n t h e i n t e r a c t i o n i s r e s t r i c t e d t o t h e n u c l e i belonging t o one copper octahedron. The o c t a h e d r a l surrounding of t h e copper i o n c o n t a i n e s two e q u i v a l e n t s t r o n g l y bonded C 1 i o n s denoted C 1 ( I I ) , two weakly bonded C 1 ( I ) i o n s and two H20 molecules, a l s o s t r o n g l y bonded. The l o c a l s y m e -

t r y ismnmp.As o n l y t h e i n t e r a c t i o n between i d e n t i - c a l s p i n s g i v e s r i s e t o a f i n e s t r u c t u r e , o n l y t h e i n t e r a c t i o n between i d e n t i c a l s p i n s g i v e s r i s e t o a f i n e s t r u c t u r e , o n l y t h e i n t e r a c t i o n between two C 1 (11) n u c l e i c a n g i v e an a p p r e c i a b l e f i n e s t r u c - t u r e (The 170 n a t u r a l abundance i s v e r y s m a l l ) . I n f i g u r e I c t h e second d e r i v a t i v e i s shown of t h e c e n t r a l 3 5 ~ 1

NMR

l i n e i n a 98 % e n r i c h e d 3 5 ~ 1 Rb2CuC14.2H20 sample, a t T = 1.2 K and H. = 10 kOe a p p l i e d along t h e c a x i s . Whereas t h i s l i n e shows c l e a r l y a f o u r f o l d s p l i t t i n g , t h e s a t e l i t e l i n e s

( a t 12.7 MHz and 2.5 MHz) e x h i b i t a t h r e e f o l d

(3)

structure. In figure la the same resonance line is

shown in an isotopically non enriched sample.

Fig.

1 :

Central NMR lines in Rb2Cu C14.2H20.

a and b in a sample with 75 %

3 5 ~ 1

and 25

%

3 7 ~ 1 ;

c in a sample with 98

%

3 5 ~ l .

Now a quarter of the resonant 3 5 ~ 1

nuclei have a

3 7 ~ 1

neighbour, which explains the extra line in

the middle of the resonance pattern. Reversely,

when observing the 3 7 ~ 1

line, figure Ib, only a

quarter of the 3 7 ~ 1

nuclei can interact with an

identical nucleus and hence three quarters of the

line intensity appears in the middle of the reso-

mince pattern. Although less intensive, the four

fine structure lines can also be seen in this fi-

gure. The tensor

d

is rather anisotropic. Typical

1

I

values for 3 5 ~ 1

are /l/

Azz

=

27 MHz,

-ir;

+

=

1

4 MHz

and - A

=

3

MHz,

where Z points along

2h

XX

the Cu

-

C1 (11) bond and Y along the c axis. Only

a weak angular dependence of the fine structure

has been observed in the X-Y plane, whereas the

spectrum along the Z axis shows no fine structure.

This is in accordance with the expression for$.

Since the quadrupolar interaction in com-

parable to the Zeeman interaction

(v =

10.3

MHz

and

q =

0.16) the effect of

%l

on %:annot

be

calculated analytically. In the high field appro-

ximation the observed resonance patterns can be

explained. Also the magnitude of the splitting

is found to be correct. The ratio of the split-

tings in the 3 5 ~ 1 ( ~ ~ )

and 3 7 ~ 1

(11) spectra is

found to be (35~/37~)2,

again in accordance with

The same structure has also been found in the

compounds

/ l / ,

in which RbCl is replaced by KCI,

NHsC1, CsCl or NHsBr, RbBr. As the abundance of

7 9 ~ r

and "Br is equal, the resonance lines of both

isotopes are similar. Again, the ratio of the split-

tings is found to be (79~/81~)2.

The temperature

and field dependence of the fine structure has

been studied extensively in Rb2CuC14.2H20. The ma-

gnitude of the splittings is not temperature

dependent for T <4

K (T

=

I K). For H

.

2

5 kOe

the splitting is proportional to H - ~

,

in accor-

dance with the high field approximation for

1

X

-

.

For H

.

<

5 kOe, the resonance lines are

Wk

broadened by multiple spin-spin interactions, due

to the increase of the interaction radius bo. The

same arguments hold for the line width in the fer-

romagnetic state in zero field.

In addition to the fore mentioned indirect

co~pling,~~contains

also a t e n for i

=

j, which

gives a correction, of the same magnitude as the

fine structure, to the parallel hyperfine interac-

tion and to the quadrupolar interaction

/ 3 , 4 / .

Re-

cently, we reported on the

170

hyperfine interac-

tion in these compounds

/ S / . We observed that the

angular dependence of the quadrupolar splittings

could not be descr2bed on the basis of the usual

hamiltoniana4 Preliminary calculations show thaf

nn

by incorporation of these self energy terms of

-6,

the experimental data can be understood.

In low fields at temperatures near T

C'

a

different kind of nuclear spin-spin interaction

is observed /1.5/. As now

X//

is large, the expec-

tation value <S>

will be influenced markedly by

the Cu nuclear spin. This effect gives a correc-

tion to the larmorfrequency of the ligand nuclei,

proportional to

X

,/

A// (Cu)A// (Cl). A four fold

equidistant pattern is observed in the spectra of

3 5 ~ 1

(11)

,

3 7 ~ 1

(11) and l70 when a weak magnetic

field is applied along the Cu-CI(1) direction,

where A1

1

(Cu) is large /l

/.

Further experimental and theoretical in-

vestigations are in progress.

(4)

References

/l/ Klaassen, T.O., Looyestijn,

W.J.

and Poulis, N.J. Physica 66

(1973) 567. (Com. Kamerlingh Onnes Lab., Leiden No. 4036)T

/2/ Suhl, H., Phys. Rev.

109 (1958) 606.

/3/ Nakamura, T., Prog. Theor. Phys. (Kyoto)

E

(1958) 542.

/4/ de Gennes, P.G., Pincus, P.A., Hartmann-Boutron, F. and Winter,

J.M.,