Physica 143 B ( I ()8¢~) 41241 i~ 412 Norfl~-ftolland, Amsle~dam

NESTING VECTOR, AMPLITUDE and ANISOTROPY OF SDW IN (TMTSF)2X_ OBTAINED BY NMR

J.M. DELRIEU, M. ROGER, Z. [OFFANO, E. WOPE MBOUGUE, P. FAUVEL, R. SAINI JAMES and K. BECHGAARD. S . P . S . R . M . CEA, CENS, 9 1 1 9 1 G i f s u r Y v e t t e Cedex , F r a n c e

~epar tment of General and Organic Chemistry H.C. Oersted I n s t i t u t e DK 2100 Copenhagen, Denmark

From a d e t a i l e d ana lys i s of the methyl proton N.M.R. l i n e shape, in the S.D.N. s ta te of the organ ic conductors (TMTSF)2PF6 and (TMTSF)2CI04, we determine the loca l f i e l d s at each methyl s i t e and separate the d i p o l a r c o n t r i b u t i o n from the hype r f i ne contac t term; we deduce both the ampl i tude ~ = 8.5 ::. ± 2 ~i;; ~ ( in u n i t ~ p e r melecule ) J o t ~ 6 and S : 12~L f o r ClO 4, and wave vec to r ~ of the S.D.W. Q = 0.5 a ; ( 0.20 * 0.05 ) , ? (a~ b~ c~ rec i p roca l l a t t i c e basis vec to r ) f o r PFG. in agreement w i th r e a l i s t i c t i g h t b ind ing band c a l c u l a t i o n s . The O vec to r Is d i f f e r e n t in (TMTS~2CI04: ~ = "~ ~ ? c ~ 0.5 a , O.3b , w i th very d i f f e r e n t hype r f i ne contact f i e l d s . The exper imenta l o r i e n t a t i o n s of an i so t ropy ax is of SDW are t h e o r e t i c a l y exp la ined a!~ as a f u n c t i o n of the nest ing vector .

I . INTRODUCTION

]he i n t e r p l a y of d i f f e r e n t phase

t r a n s i t i o n s in organ ic conductor~ l i k e

s u p e r c o n d u c t i v i t y and spin dens i t y wave (SDW)

is f a r from being comple te ly understood ( l i .

Up to t h i s date, nea r l y no i n fo rma t i on i?ad

been obta ined on the microcospic parameters of

the SDW s ta tes of the d i f f e r e n t compounds. We

present in t h i s paper NMR measurements (2 )o f

nes t ing vec to r , o rder parameter, hype r f i ne and

d i p o l a r f i e l d s in the SDW.

2. RESULTS

2 . l . M e t a l l i c paramagnetic s ta te

F i r s t , we s tud ied the normal l ine-shape of

methyl protons in (TMTSF) 2 X in t i le

paramagnetic s ta te . [he f as t r o t a t i o n a l

t unne l i ng of the two unequ iva len t methyl

groups s p l i t s the l i n e i n t o one cen t ra l l i ne

and two pa i rs of s a t e l l i t e s wi th s h i f t s

d =3/4 ( ~ ) 2 / ~ H ( l - 3 c ° s ~ i ) depending c,n

f i e l d angle C~. w i th respect to the ax ls

normal to the plane of each methyl groups i .

The fou r groups form two pa i rs w i th d i f f e r e n t

o r i e n t a t i o n s and thus very d i f f e r e n t s h i f t s .

For the f i r s t t ime (2) we are able to separate

e x p e r i m e n t a l l y the i n d i v i d u a l l i n e - w i d t h of

each methyl l i n e , in good agreement w i th our

0 3 7 8 - 4 3 6 3 / 8 6 / $ 0 3 . 5 0 © Elsevier Science Publ ishers B. \" (North-Holland Physics Publishing Division ) and Y a m a d a Science F o u n d a t i o n

second moment c a l c u l a t i o n s ( 2 ) , so tha t the f i t

of exper imenta l l ines i,; d r a s t i c a l l y improw_~d,

2..]. Magnetic SOW s ta te and exper imenta i

iocal f i e l d s

in the SDI4 s ta te , t i le local f i e i d s due t,~

the ordered magneti~ s t ruc tu re lead t an

impor tan t broadening .3-5 bf the i,~,~

depending on the fi~:l,d o r i e n t a t i u ~ , ~ se

perpendi cu lar tc the! ,~ a,~, i!; [h,~ ~,bserve,:1

i ineshapes ~_~re presenter **~i f i g . ~ o ~ ¢ ie id~

below the sp in - f ] ~p f i e l d 1.487 fo r PF 6 ( ( ] . ~ i

t o r (1(!4 i . ihey have been compa~ed ~ f i g . t l

of re f2) to t h e o r e t i c a l (urves corresponding t~)

commensurate and incommensurat, e SOW; the be~t.

f i t rot ' responds to an iu(ommensurate SD~q. ]ht~

local magne t i za t i ] n S o~ a molecule at s i t e i~

: #a ; ' .5.#kcos(d.R' j- f i t,, 1 ,cai f,e ds J

k~ on each methyl groups i , which ( ,onw;luted

wi th the normal l inesnape of each methyl i in~

(using the d i f f e r e n t ;,Jldths obta ined Ir~ the

paramagnetic s ta te ) g ives the best f i ;

presented on f i g . l wi~:i~ the values H~

shown un f i g . 2 . ~n the commensurate case; (i

(1 /2 , 1/2, 1.,'2) two ,equences are poss ib le

along a: ~ - - ~ - - witi~ four' 1 or,,, I f i e l d s

associated to the four l n e q u i v a l e n t methyls

s i tes and +0-0~0-w i t i~ e iqh t iocal f i e l d s . ,

J.M. Delrieu et al. / Nesting vector, amplitude and anisotropy of SDW 413

the incommensurate case, the f ie lds H i being a

l inear function of magnetization (valuable for

dipolar and hyperfine f i e l ds ) , are spa t ia l l y

s inusoidal ly modulated. Thus the projection of

the local f i e lds on the applied external f i e l d

is given by h i (B).cos(Q.Rj+ ~i) , with

four f ields hi(8) for each orientation of

the magnetic f ie ld . The best f i t s for the

incommensurate case, shown in f i g . l , gives the

experimental local f ie ld hi(B) presented in

f ig . 2, as function of angle 8 of external

f ie ld for PF6 and ClO 4. These experimental

f ie lds are maximum along'b' in PFfibut two of

them are maximum for direct ions d i f fe rent of

for CI0 4 , showing that these two compounds

have d i f ferent properties. We emphasize that

the two local f i e lds seen by one methyl pair

PI =(C4'C15) are to ta l ly separated

experimentally from those seen by the other

pair P2=(C5,C14 ), owing to the very different

NMR line shape of each of these pairs in the

paramagnetic state (due their different

orientations as shown in the insert of f i g .2 ) .

3. DETERMINATION OF NESTING VECTOR

To explain the observed local f ields of f ig

2, we have calculated the dipolar f ields seen

by the different methyl groups ~ fo r different

transverse wave vectors Qh=~b~2 (with

Qa = I/2~), as shown on f ig . 3. We have used

the theoretical spin density distr ibution

calculated by Metzger(6) and the fact that the

easy axis of the magnetization is

approximatively along b in PF 6, as measured

for the similar compound AsF6(7,8); deviations

from these values do not change drastical ly

the theoretical f ie lds; the Q~ component

along "c'~has nearly no effects (maximum I0%) so

that the c component cannot be determined. The

local f ie ld is

Hi(Rj) = H~cos(~.R.+~ i ) j + H~siR(Q.Rj+~ i)

on methyl group i , where the f ie lds ~'. and 1

H i are the f ie lds seen by the methyl groups

in molecules with maximum magnetization ( ~ = ~

and zero magnetization respect ively. The

observed hi(B) projection of ~i(Ri ) on the

direct ion ~o of the external applied f i e l d is ~' (~#^~)2) I /2 given by h i(~)= ((H i .~o)2+ ..

1 Besides Qb we have the order parameter~

and the Knight shi f t K i of the hyperfine

contact f ie ld HC~.~.juB/~p~ (parallel to

the magnetization ~ ). In the sinusoidal

experimental curves hi(8), we measure three

parameters: the mean value, the amplitude and

the angle of the maximum. Thus for a given

arbitrary Qb , i t is not possible to f i t with

the two ~ and K i theoretical parameters, the

three experimental parameters of hi(e) for

each of the four methyls groups i , excepted

for the particular Qb corresponding to the

real i ty .

For PF 6 the~experimental f ie ld hi(8) is

quite small for ~h~perpendicular to l I so that

the dipolar f ie ld must be nearly parallel to

~. This happens for Qb = 0.2# (2), otherwise

the observed strong minimum would be

suppressed or displaced as observed for ClO 4

in f ig . 2. The possibi l i ty of very small

dipolar f ields with large hyperfine f ields is

ruled out by the large broadening observed in

the spin flop phase (2, 9), when the

magnetization is parallel to the intermediate

axis near a, i .e . perpendicular to the applied

f ie ld % , (so that the hyperfine f ields do not

contribute to hi(e) in this case (2, 9)). Thus

our best f ie ld for PF 6 corresponds to

Qb = 0.2 b~ • The contact terms are 24 G and 14

G for the le f t and right side of the molecule

respectively and the order parameter is

~=8.5 % ~ 2 %~LBIn a very preliminary paper(1)

we reported the same order of magnitude

=25% jL~/2, which is a natural unit for I/2

electron hole per molecule. The corresponding

414 J.M. Delrieu et al. / Nesting vector, amplitude and anisotropy oJSDW

(TMTSF)2 ClOz,

80(

(TMTSF) 2 PF 6

e_-

80G

FIGURE l Comparaison of theore t i ca l f i t (dashed l ine ) to experimental NMR l ines ( f u l l curves) in (TMTSF)2PF6 and (TMTSF)2CIO 4 as funct ion of angle'@ fo r incommensurate SDW. The best f i t is obtained in the incommensurate phase, for the maximum local f i e l d s hi(B) shown in f i g . 2 .

\\ % \ ~i \\ ~I

,, ,, , ooo c,o

% = 0 '\ 0-I \, 0.45 \\

FIGURE 3 Theoret ical methyl d ipo la r f i e l d s in (TMTSF) Cl04 with magnetizat ion at 30 ~ from ~' towards -~ for d i f f e r e n t values of nest ing vector Qb • The upper part presents H' on the molecule carry ing maximu_mm magnetizat ion S = ~ and the lower part H" ,the f i e l d s on the molecule with zero magnetizat ion in the incommensurate SDW.

4L~.] ~ hob'.

hi(g) (TMTSF)2PF6 I~(O) .~_ #.~,.. ,_~. a/~,,

• 20 P 2 \ ~ m ~ r ~

90 0 90 (9 °- 90 0 90 ra~

FIGURE 2 Experimental amplitj#de h~(@) of the s inusoidai local f i e l d s ~.i d i s t r i b u t i o n in the incommensurate SDW phase obtained from the f i t s of f i g . l at various @ : al for' (TMTSF)zPF6 ;b) fo r (TMTSF)zCIO 4 below the sp in f lop f i e l d . The f i e lds seen by methyT pairs Pl and P2 are completely resolved.

'; "" ".:': k...

, 12G

D;

FIGURE 4

Best so lu t ion fo r local f i e l d s with ClO~ :~=0.12 , Q=O.I ~ - ~D and ~ d ipo la r f i e l d s of f i g . 3 (dashed l i n e ) , ~ c i hyperf ine co#tact f i e ] d ~ (dotted l i n e ) , 4@ G on the l e f t to 0 G on the r i gh t side of the molecule; H' and ~' t o t a l t heo re t i ca l f i e l d ( f u l l l i ne ) compared to the experimental values represented by the dashed area.

J.M. Delrieu et al. / Nesting vector, amplitude and anisotropy of SDl¢ 415

Knight sh i f t ~(i are -I0 ppm and -7 ppm

respectively on the l e f t and r ight side of the

molecule.

With ClO 4 , the in terpre ta t ion is more

d i f f i c u l t , because the measured or ientat ions

of the easy axis are contradictory; the

reference 7 finds the easy axis at 60°from --a

and the reference 8 f inds i t at 48°from +~,

with a project ion on the plane perpendicular

to -a wi th in I0 o f ~ ' . We t r ied to f i t with

these two possibi l i t ies. On the experimental

f i g 2, we remark that one f i e l d of the pair P2

has a minimum at 45 ° of b" towards the

molecular axis X'. Unfortunately the dipolar

f ie lds ~' of pair PZ' shown in f i g .3 , are

p rac t i ca l l y perpendicular to b" for a l l -Q

vector, so that we cannot f i t perfect ly the

minimum at 45 ~ of pair P2 for any ~ value.

Nevertheless, in f i g 4, we can f i t reasonably

the other character ist ics of f i g .2 , i . e . the

amplitude and angle of maximum of hi(O). In

this case the order parameter is ~=12 %~. Due

to an coincidence, we cannot determine the

easy axis or ienta t ion; for the easy axis at

60 from -a (7), we f ind Qb=0"25 b and for

60 ° from ~ (8) we obtain Qb=O.l ~ with a

s l i gh t l y better f i t of f i e lds of pair P2; for

these two case the dipolar f ie lds are very

s imi lar , but reference 8 has s l i gh t l y more

chances to be exact. The contact terms are

very d i f fe ren t from that in PF 6 as shown in

f i g . 4; th is can be related to the ordering of

the counter ions CIO 4 nearly suppressing the

electronic density on the methyl closest to a

counter ion.

4. THEORY OF THE ANISOTROPY IN ORGANIC

CONDUCTORS.

No even qua l i ta t i ve theory of the

anisotropy f i e lds of the organic conductors

has been achieved already. We present here a

simple and natural model explaining the

or ientat ion of anisotropy axis and values of

antiferromagnetic resonances. In sul fur

compounds, the spin orb i t coupling being

small, the dipolar anisotropy alone is

suf f ic ient to explain the experimental

or ientat ions (7, I0) of hard, intermediate and

easy axis respectively along ~, ~ a n d b l w i t h

s ign i f icant deviations in the plane (a,b),

function of the exact value of Qb component as

shown in table 1 in agreement with experiment.

This open the poss ib i l i t y to determine Qb from

anisotropy measurement.

On the contrary, in the selenium compound

the spin orb i t coupling is ( Z s ~ Z s ) ~ 3 7

larger than in with sul fur ; i t favors an

or ientat ion perpendicular to the molecular

plane (deduced from anisotropy of g factor ) ,

and is of the same order as the dipolar

coupling, so that the intermediate and hard

axis are permuted, explaining natura l ly the

experimental results (7,8), and in par t icu lar

the very fast change of or ientat ion of easy

axis in the plane (~,b) as function of Qb "

Only when Qb = 0.16 b we explain that the easy

axis is along-~ . For ClO 4 the large deviation

toward ~ (7) or away from ~ (8) can be

explained with a Qb vector respectively

s l i gh t l y below or above .16~ .Un fo r tuna te ly

both cases are in agreement with our

preceeding NMR determination of Qb, but our

f i t favors s l i gh t l y ~L=O.Ib ; th is would be in u

better agreement with band calculat ions and

nesting models (11,2). This simple model

explains the main properties of the

anisotropies of the SDW in both TMTTF and

TMTSF compounds, in par t icu lar the permuted

or ientat ions of hard and intermediate axis

between sulfur and selenium compounds, and the

large var iat ions of of or ientat ions of easy

axis in selenium compounds for r e l a t i ve l y

small changes of Qb component. From

experimental spin f lop f ie lds and

416 J:M. Delrieu et al. /Nesting ~,ector, ampli tude and a#Usotropy oJSDI¥

an t i fe r romagne t i c resonance f requencies a l l

these compound have order parameter in the

range 0. ] to 0 . 2 ~ , as al ready pointed out !u

re f . 7. The O b component var ies between 0

and 0.3 b~

CONCLUSION

We have determined the microscopic:

parameters of organic conductors (TMTSF)2X fo~

X - PF 6 and Cl04, using a very precise and

de ta i l ed f i t of the NMR l i nes . The t ransverse

nest ing vector component Q bchanges wi th the

nature of counter ion X as expected from the

simple theory of nest ing vector ( l ] , 2), based

on Fermi surface s t r uc tu re . The d i p o l a r energy

alone exp la in near ly a l l p roper t i es of

an isot ropy in su l fu r compounds; in the

selenium compounds the compet i t ion between

spin o r b i t and d i p o l a r an isot ropy exp la ins the

permutat ion of hard and in te rmed ia te axis and

the large changes of o r i e n t a t i o n of easy axis

w i th the t ransverse component Qbof the nest ing

vector . In a l l cases, from exper imental

an isot ropy p r o p e r t i e s ( ] O ) , the t ransverse Qb

component var ies between 0 and 0.3 b, and the

an t i fe r romagne t i c order parameter is between

O.l to 0.2, even in (TMTTF)2SCN which from

r e s i s t i v i t y measurements(12) is l oca l i zed

below 16OK; at f i r s t sigh~ nest ing vector

theory of SDW seems d i f f i c u l t to apply fo r t h i s

i n s u l a t i n g phase; a more complex theory ot

l o c a l i z a t i o n and nest ing i n t e r p l a y seems

necessary to exp la in t h i s qu i te small order

parameter w i th l oca l i zed e lec t rons .

"ABLE i ~ang le of easy axis with d towards .::"

_/14¢f2AFR frequency r a t ' o

Qb 'M/TF)2X I t l M , J Z" I ~ pure d i p o l a r ~ d i p o l a r ; suin r b ] t

O.lO / 8.8 1.371SCN II a7 / .47 ~- a ' 0 . ]5 1 8 1.37 Br ? 2.~ 2.49

f .20 .25

I0.50

-5.1 i i . 3 8 - I I . 6 I 1.41 -17.911-46 -30. ] ] .65 - 44 . ] 2 . 3 8

! e o

i ~ u9

-35 . t4 -4~ ] .29 -53 1 , I ] -62 1.06 -73 ' ]5

>

m .

I

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