Exchange couplings in the free radical nitroxide tanol suberate determined by static magnetic methods and room temperature proton relaxation

HAL Id: jpa-00209072

https://hal.archives-ouvertes.fr/jpa-00209072

Submitted on 1 Jan 1981

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.

Exchange couplings in the free radical nitroxide tanol suberate determined by static magnetic methods and

room temperature proton relaxation

Cl. Jeandey-Veyret

To cite this version:

Cl. Jeandey-Veyret. Exchange couplings in the free radical nitroxide tanol suberate determined by

static magnetic methods and room temperature proton relaxation. Journal de Physique, 1981, 42 (6),

pp.875-883. �10.1051/jphys:01981004206087500�. �jpa-00209072�

Exchange couplings in the free radical nitroxide tanol suberate determined

by ^static magnetic ^{methods and room} temperature proton ^relaxation

Cl. Jeandey-Veyret (*)

Centre d’Etudes Nucléaires de Grenoble, Département ^{de Recherche} Fondamentale, Section de Résonance Magnétique, 85X, 38041 Grenoble Cedex, ^France

(ReCu ^{le 1 e’’} septembre 1980, révisé le I S décembre, accepté ^{le 19} février 1981)

Résumé.

On montre que les propriétés magnétiques du radical libre nitroxyde subérate de tanol peuvent s’interpréter ^dans

système d’Heisenberg quasi unidimensionnel. Les valeurs des couplages d’échange ^{sont déter-}

minées par des méthodes statiques

fonction de la température ^et par relaxation du protron

fonction de la

fréquence ^à température ambiante. Le couplage d’échange intrachaine J est positif et de l’ordre de 1,1 ^{K. On}

été amené à considérer qu’il existe deux autres couplages d’échange : les chaines proches voisines, reliées par

un

couplage interchaîne J’1 positif ^d’environ 0,09 ^K forment des feuillets. Ces feuillets sont reliés entre eux par

un couplage J’2 négatif ^d’environ 0,03 ^K.

Abstract.

Magnetic properties of the free radical nitroxide tanol suberate _{may be} interpreted ^{in terms of a} quasi-unidimensional Heisenberg system. Temperature dependent static methods and frequency dependent

room

temperature proton relaxation

applied ^{to the} determination of exchange couplings. The intrachain

exchange coupling ^{J is} positive and is about 1.1 K. Two other exchange couplings ^{have to} be considered :

neighbouring chains, ^connected by

interchain coupling J’1 positive of about 0.09 K form sheets. These sheets

are

connected together by

coupling J’2 negative ^of about 0.03 K.

Classification Physics ^Abstracts

75.50E - 76.30R - 76.60E

1. Introduction.

Free radicals are molecules with an odd number of electrons. In the last few _years great interest has been focused on the magnetic pro-

perties of free radicals in the solid state because they

are good ^{models to test} existing theories : they ^can

be considered to approximate ^{the S}

1/2 Heisenberg

model and moreover a great number of them have been found to possess chain like (ID) properties [1].

The intrachain interactions Hamiltonian may be written :

where the summation is taken over nearest neighbour spins ^{and J} is the intrachain exchange coupling. ^In

an ideal 1 D magnetic system, the chains are comple- tely isolated, ^no interaction exists between them. In real magnetic systems, ^{one has to take into account} interactions between chains, ^{which can} be charac- terized by ^an exchange coupling J’( J’ I J). ^The

closer we are in the ideal 1 D situation, the smaller the ratio J’/J 1. Besides, the interchain interactions induce a transition to long range (3D) ^{order at a}

critical temperature Tc’

(*) C.N.R.S. ER 216.

It will be exposed ^{here how} temperature dependent

static magnetic methods and frequency dependent

room temperature proton relaxation time measure- ments provide evidence of the ^one dimensional nature of a magnetic system ^and may give ^{access to J. It}

will be shown how in real magnetic systems it is also

possible ^to estimate the interchain couplings.

The free radical investigated here is tanol suberate.

Synthesis [3] ^and crystallographic ^structure [4] ^of

tanol suberate have been published elsewhere. Each molecule is ended by ^{two N-0} groups where an

odd electron is localized [2] giving ^{rise to two} spins

These molecules are centrosymmetric ^and crystallize

in the monoclinic system, space group P2,/c. ^The

dimensions of the unit cell are

There are two molecules in a unit cell. In order to have a better understanding ^{of the} exchange couplings, figures ¹ and 2 show the neighbourhood ^{of the N-0}

group. Middles of groups labelled 0, 1, 2, ^{on one}

hand and 3, 4, 5, ^{6 on} the other hand lie on two diffe-

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01981004206087500

876

rent planes parallel ^{to the ac} plane ^and separated by ^{2.48 A.} Distances between neighbouring ^chains (1-0-2 ^{and 3-5 or} 4-6) ^{is 5.85} A. There are two layers

of this type, separated by ^8.22 A, ^{in a} unit cell. All the experiments presented ^{here are done on} poly-

crystalline samples.

Fig. ^1.

Projection of tanol suberate molecule

the

plane, showing ^{the first} neighbours ^of

^NO group labelled 0 : (NO-NO)

distances

6.10 A (01 ^and 02), ^{6.45 A} (03 ^and 04), ^{7.20 A} (05 ^and 06). ^Other (NO-NO) ^distances

9 A.

2. Static magnetic investigations.

^{2.1 1} THEORE-

TICAL DESCRIPTION.

J. C. Bonner and M. E. Fisher

[5] have studied the thermal properties ^{of an ideal}

S

1/2 Heisenberg ^{1 D} system for both ferro- and

antiferromagnetic coupling (J > 0 ^{and J 0 res-} pectively). ^{Let us} recall the principal ^{results of their}

study : ^the magnetic specific ^heat Cmag (1) ^{shows a}

broad Schottky-type anomaly ^which depends ^{on the} sign ^{of J at a} temperature T.,. ^The Schottky tempe-

rature Ts depends ^{itself on the} sign ^{and on the value}

of J :

When J is negative ^the susceptibility xM passes

through ^a broad maximum at a temperature Tmax.

The value of this maximum and Tmax depend ^{on the}

value of J :

’%here fl is the Bohr magneton.

When J is positive ^{it is} necessary in order to ana-

lyse experimental results, ^to compare ^two double

log plots : ^one of the measured xM 1 ^{vs. T and the}

other of the reduced susceptibility (Xo,,)-’ - Ng 2 #2 xM

vs. reduced temperature T/J. ^{The « T »} scaling yields

J and the « _{x »} scaling determines g (in ^{fact, in nitroxide}

radicals E.P.R. measurements give for g ^a quasi- isotropic value close to 2 [6]).

(1) Cmag ^{and xM}

molar values.

Fig. ^2.

^{Sheet structure of the} magnetic ^moments in tanol suberate (0 symbolizes ^{the middle} of the NO group). Exchange paths ^J, Ji

and J2

^shown.

At high temperature (T > J I) ^the susceptibility obeys ^the classical Curie-Weiss ^{law :}

where CM is the molar Curie constant value and 0p

is the paramagnetic ^Curie temperature. In the mole- cular field approximation [7] :

where J is the exchange coupling ^{between an electron} spin ^{and its} next nearest neighbours ^{and z is the}

number of next nearest neighbours ^{of an electron} spin.

In a chain, ^z

2. As here S

1/2, ^{one has the}

relation :

2.2 EXPERIMENTAL RESULTS.

Some results have

already ^been published ^on the static magnetic pro-

perties ^of tanol suberate [8].

2.2.1 Magnetic susceptibility ^and magnetization

measurements. - The susceptibility, ^{measured be-}

tween 4.2 K and room temperature ^{on a} magnetic

balance [9] obeys ^the Curie-Weiss law. The molar Curie constant value CM is 0.750. This value is consis- tent with two uncoupled spins ^S

1/2 per molecule in this temperature range. The paramagnetic ^Curie

Fig: ^3.

Magnetization

of tanol suberate at T

80 mK.

temperature 0p ^{is positive} and lies in the range of 1 K ; this positive value indicates that ferromagnetic ^inter-

action is dominant in tanol suberate. In the hypo-

thesis which will be discussed here of a one dimen- sional coupling between electron spins, ^{J would be}

in the _range of 1 K.

Low temperature (0.05 ^{K to 4.2} K) ^static magnetic properties ^{have been} investigated by ^{an induction}

method [10]. Temperatures ^{lower than 1.3 K are}

obtained by ^adiabatic demagnetization. ^{The low tem-} perature ^{low field} (20 Oe) susceptibility ^{curve shows}

a peak indicating antiferromagnetic coupling ^at Tc

^{0.38 K} while the magnetization ^{curves below} Teare characteristic of a metamagnet (2) (Fig. 3).

The critical field He lies in the range of 200 Oe. A metamagnet ^{is an} antiferromagnet which upon the

application ^{of a} magnetic ^field (the ^critical field) ^can undergo first order magnetic phase transition to a

state with relatively large magnetic ^{moment. Low}

dimensional ( 1 D ^or 2D) magnetic systems ^with positive (or ferromagnetic) ^short range interactions and negative ^(or antiferromagnetic) long range inter- actions are good examples ^of metamagnets [12].

2.2.2 Specific ^heat measurement.

The specific

heat has been investigated ^{in a} recirculating ^3He cryostat between 0.35 K and 3.2 K, using ^{a heat} pulse technique which has been described in detail elsewhere [13]. ^{A A} anomaly, typical ^{of a} long range transition is observed at 0.38 K. This result has been

previously published [8] ^{as well as an} estimation of the lattice specific heat. The decrease of the magnetic

Fig. ^4.

Specific heat of tanol suberate

function of the tempe-

rature : + measured specific ^heat (lattice ^and magnetic ^contri- butions) ;

estimation of the lattice specific heat ; magnetic specific ^{heat of}

ferromagnetic S

1/2 Heisenberg ^{chain with}

J=1K.

(2) ^Based

preliminary results, ^this compound appeared ^{to be}

ferromagnetic [8]. ^A detailed static magnetic investigation ^below

T, ^{will be} published in the future [11].

878

specific ^{heat for T} > Tc ^is slower than expected ^for

a long range order and an important part (60 %) ^of

the magnetic entropy is removed after (Fig. 4).

This can mask a Schottky anomaly typical ^{of a short}

range ( 1 D) transition of the type usually ^{found in}

free radicals. If there is an overlap between the round maximum of the Schottky anomaly ^{and the} large peak which reflects the long range ordering, ^{the two}

may ^not be resolvable. On figure ^{4 is shown} together

with the experimental ^results, the estimation of the lattice contribution and the magnetic specific ^{heat of}

a ferromagnetic chain with J

1 K.

2.3 ESTIMATION OF LONG RANGE INTERACTIONS.

It appears that the simplest way ^to analyse ^{the sus-} ceptibility measurements is to assume that there are

in tanol suberate interacting chains with a positive

intrachain coupling ^{J, then to} apply ^{a mean field}

correction to describe the other exchange ^interac-

tions J’ [14]. ^One may suppose the chains in the direction joining ^{the nearest} neighbours (all ^the 6.10 A) and the other interactions due to the signi-

ficant neighbouring ^chains (two, z’ ^{at 5.85} A) ^{or sheets}

(two, z2 ^{at 8.22} A). ^Cf. figures ^{1 and 2. The reduced} susceptibility (xr) -1 ^for interacting ^chains may be written (3) :

where (X0,r) -1 is the dimensionless reduced isolated chain susceptibility ^{and A is the mean field} parameter interaction : A

2 z’J/J

where z’ is the number of

significant neighbours ^{of a} chain. The sign of A deter- mines the sign ^{of J’. We} follow the method indicated for ideal ferromagnetic ^{chains to determine J} (§ 2.1),

but we compare the double log plot of the measured

xm 1 ^{vs. T} with the double log plot of (Xr) - 1 ^{vs. reduced}

temperature T/J, where A is adjusted ^{to obtain the}

best fit; ^{in this} way, ^we may determine both J and the mean field correction.

The best fit is obtained for J

1.1 K and for A

+ 0.2 .

The mean interaction between the chains is then

positive. Nevertheless, ^we have established that anti-

ferromagnetic coupling exists between the chains.

Thus we have to consider that two types of interchain interactions must exist : _one, Ji, ^is positive, ^the other, J’2 ^is negative, ^{and one has} I J’2 I J so ^that

J’ oc J1 ⁺ J2 ^{would be} positive. ^{Such an} assumption

is consistent with crystallographic description. ^An

estimation of J2

^the exchange interaction leading

to the antiferromagnetic coupling

may be made from the critical field Hc ^{of the} metamagnetic ^transi-

tion :

(3) ^The method utilized is described in the article of Bonner J. C.

et al. (Ref. [14]). Expressions ^of (X0,r)-1

^given in the article of Swank D. D., ^Landee C. P. and Willett R. D. (Ref. [14] also).

By refining ^the calculation of the mean field para- meter interaction, ^{one obtains i}

As z’

z’ = 2, ^one may determine J’ - ^{0.085 K.}

Theoretical studies [15], ^{on the other} hand, ^{allow us}

to correlate Ji ^and J2 to ^{J and} T,,. Equations (40)

and (44) of reference [15] ^{lead to} the relation :

The set of values I J I

^1.1 K, J’1 I ^{= 0.09 K and} J’2 I

^{0.03 K} satisfies this relation.

In order to have another approach ^{to the deter-}

mination of the exchange couplings lying ^{in tanol} suberate, ^{we have} undertaken proton spin ^lattice

relaxation time (T1) measurements as a function of the frequency ^{at room} temperature. ^{As is shown} below this method provides evidence of the low dimensional nature of a magnetic system ^and gives

access to the anisotropic diffusive coefficients which may be correlated to the anisotropic exchange couplings.

3. Room temperature proton relaxation.

3.1 THEORETICAL DESCRIPTION.

One has, ^{for a} single crystal ^{in the} high temperature ^limit [16] :

where the sum is performed ^{over all the electron} spins Si ^{of the} sample.

Q1À.,(!3

^N, e) ^are geometrical coefficients depend- ing ^{on the} hyperfine ^and dipolar interactions between nuclear and electron spins. They ^are functions of the orientation

determined by ^the angles ^{0 and} 9

of the magnetic field with respect ^to the electron spins chain, ^{and can be} calculated.

The functions fÀ.J.À.’(w) ^{are the} spectral ^{densities or} frequency Fourier transform of the ^two spins ^corre-

lation function F’.,,(t). They depend ^{on the} spin component S’ ^and sf = Sf + iS Y ^{and on the cor-}

relation order n = I À - À’ ^{between two} spins;

n

0 refers to the autocorrelation function and n =1= 0 ^to the cross-correlation functions :

H is the Hamiltonian describing ^the spin system ^and thus contains the exchange couplings between electron

spins. ^{One can} understand why ^these couplings may

be accessible when studying T1 ^vs. frequency. ^When

the spin dynamics ^is governed by ^a Heisenberg Hamiltonian, ^the spin correlation functions and the

spectral ^{densities are} isotropic ⁱⁿ any spin represen- tation and one can write :

Equation (11) shows that T 1 measurements allow

us to probe ^the magnetic fluctuations at two different

frequencies, WN and _we, the nuclear and electron Larmor frequencies, respectively. ^{In our} case, the nuclei studied are protons ^and We/wN

YeIYN

^658.

For a powdered sample, ^a spatial average has ^to be done on equation (11). ^{Since the} spectral ^densities

are spatially isotropic, ^the average bears only ^on

the geometrical coefficients and one can write :

Let us now examine more precisely ^the spectral

densities and the geometrical coefficients. It is shown that because of the one dimensional character of the

magnetic coupling, ^the spatial ^{average in} equation (16)

can be performed easily. We shall consider two

limiting ^cases, corresponding ^to the « low » and

« high » frequency behaviour of f;.,;.,,( w). These fre- quency ranges ^are defined with respect ^{to the fre-}

quency wX

D, ^{where D} is the intrachain spin

diffusion coefficient; ^{for S} = 1/2, ^{one has}

in our case, with J - 1 K, wx - 50 GHz. Experi- mentally, the nuclear Larmor frequency wN varies from 4 to 340 MHz and the electron Larmor fre- quency We (we

⁶⁵⁸ wN) from 2.6 GHz to 224 GHz.

f(wN) ^will always ^be analysed in the low frequency limiting ^{case while} f(we) ^{has to be} analysed ^{in both} high ^{and low} frequency limiting ^{cases (cf.} Fig. 5).

a) ^The spectral density.

^The spectral density

may be determined by ^a method based on knowledge

of the moments M2n(q) occurring ^{in the} development

of the _space Fourier transform of the correlation function. This method ^is developed in reference [17]

in the ^case of a S = 1/2 Heisenberg ^{1 D} system. ^The autocorrelation spectral density fo(ro) ^vs. (w/J)-1/2

calculated in this _way is shown in figure 6a. Several remarks have to be made :

-

One can define a frequency

such _as, when w > wmax, fo(W) ~ ^0.

-

When

(Vx (low frequency range) ^{one has}

the well known (Dw)-1/2 dependence ^{for the} spectral density ^{of a} purely ^{1 D} system [18]

where the high frequency behaviour introduces the constant term A

1.13/4nJ.

-

One has to note that in the high frequency

range the contribution of the cross-correlation func- tions is negligible ^with respect ^{to the} contribution of the autocorrelation function. It follows that only

the knowledge of the autocorrelation geometrical

coefficients is needed to calculate T1. ^{On the} contrary,

at low frequency, ^one may consider the contribution of the cross-correlation function to be equal ^{to the}

contribution of the autocorrelation function [18]. So,

in this frequency range, all the terms of the geometrical

coefficients are needed to calculate Ti.

In the high frequency range, ^we shall use the

spectral density fo(w) calculated in reference [17]. ^In

the low frequency range, the divergence ^of fo(w) ^is

truncated [19] ^to keep the value of T 1 ^from being

zero at zero frequency. ^{In the} general case, the fol-

Fig. ^5.

^{Low and} high frequency range approximation ^with respect ^to the variation

of wN ^and me for tanol suberate.

880

Fig. ^6.

Autocorrelation spectral density

(w/J)-1/2 ^for

quasi-lD S

1/2 Heisenberg system : a) high frequency range;

b) ^low frequency range. For J

1 K, (we/J)-1/2 varies from 0.002 to 3 and (wN/J)-1/2 ^{from 8 to 75.}

lowing expression ^{can be used as a} reasonable approxi-

mation to describe the long time limit [20]

where Di ^and D’ ^{are the} transverse spin ^diffusion

coefficients and IO(k) ^{is the zero} order Bessel function.

According ^{to this} description, ^{we have made nume-}

rical calculations of fo(w) ^{as a} function of the _para-

meters ç

D1/D and 11

D2/D i . ^{As an} example,

the spectral ^densities corresponding to j

10-’, 10-2, ^{10- 3} and for each value of ç to 11 = 0, 0.1,

0.5 and 1 are drawn on figure ^{6b vs.} (W/J)-1/2.

b) ^The geometrical coefficients.

Their expres- sions _may be found in several sources, in particularly

in [16]. ^{Let us} recall them in an appendix. ^Further-

more, it has been noted that it will be _necessary to have either only ^the autocorrelations terms (in ^the high frequency limiting case) ^{or all the terms} (in ^the

low frequency limiting case). ^{Let us} examine what

happens ^{to the} spatial average in these ^{two cases.}

1) High frequency limiting ^{case :} autocorrelation

terms

The spatial average is _easy to do and one obtains the relations :

d ^{and à are the} dipolar and scalar electron proton couplings respectively

As the intramolecular (2

0) ^{distances are shorter}

than the intermolecular distances, ^a straightforward approximation ^{is to write :}

As tanol suberate structure is known [4] ^one may calculate d 2 ~ 1.1 G2

As far as the scalar electron proton couplings ^are concerned, ^a tanol suberate molecule (Fig. 1) may be considered as two tanol molecules (Fig. 7) ^connected by ^a protonated ^chain.

Fig. ^7.

Tanol molecule.

The scalar electron proton couplings of tanol have

been determined by ^{NMR at 4.2 K} [21] ^{but the uncer-}

tainty ^{is rather} large :

One may consider that the protons of the chain are

sufficiently removed from the electron spins ^{to have}

no scalar coupling ^{with them; for these} protons, only dipolar coupling ^{will be} considered and the scalar elec- tron proton coupling ^of tanol suberate _may thus be considered equal ^{to those} of tanol. One has :

2) ^Low frequency limiting ^{case : all the terms}

The spatial average confines itself to the calculation of three summations :

which have been calculated only in the direction where the magnetic ^{field is} parallel ^to the chain axis.

The theoretical expressions obtained for the spatial

average of the geometrical coefficients have the same

form as previously; ^{however, the} dipolar ^electron proton coupling ^{d2 has to be} exchanged ^with

N w

One determines :

We shall examine our experimental results in the two limiting ^{cases of} high ^{and low} frequencies. ^{In the} high limiting ^case (m > wx).

while in the low limiting ^case (w wx)

3.2 EXPERIMENTAL RESULTS.

Nuclear relaxation times are measured with pulse sequences n, n/2 ^{in a}

conventional pulsed ^NMR spectrometer. The spec- trometer is piloted by ^a computer [22] : ^{the interval T}

between the two pulses ^{is increased} automatically,

then the proton spin lattice relaxation time T

^is

calculated from the measured value of the magnetiza-

tion M(T) ^{for at} least fifteen different values of T. T

is measured at the beginning ^{of the recovery of the} magnetization (T between 70 _ps and T1/2).

We have measured T1 ^vs. frequency (FN

^{4 MHz-}

340 MHz) ^{for a} polycrystalline sample of tanol sube- rate at room temperature. T1-1 ^is plotted ⁱⁿ figure ⁸

vs. FN -1/2, in the usual way in order ^to display ^{the ID}

diffusive process. The change ^of slope which appears

corresponds ^{to the} change ^of regime ^for f(we) :

labels (I) ^and (II) correspond ^{to the} high ^{and low} frequency limit, respectively (see § 3. la ^and Figs. ⁵

and 6).

Fig. ^8.

^Proton spin lattice relaxation rate at

temperature

frequency (+) ^and calculated

for J

1.15 K, ç = 5 X 10-2 and il

0.7; f(co.) ^is analysed ^{in both} high (I) ^{and low} (II) frequency limiting ^cases; f(wN) ^is always analysed ^{in the low} frequency limiting

(cf. Fig. 5). (1) ^{is for a2}

^0.8 G’ ; (2) ^{is for a2 = 1.25} G2 ; (3) ^{is for} a2 = 1.70 G’.

3.3 EVALUATION OF THE EXCHANGE COUPLINGS.

To evaluate the exchange couplings, ^{we have} compared

two double log plots : ^one of the measured 1/TB ^vs.

F Ñ 1/2 and the other of calculated J/T1 ^vs. (F N/J)-1/2 (cf. Eq. (11)). ^The frequency dependence ⁱⁿ f(we)

and f(wN) is introduced using figure 6a for the high frequency limit and figure 6b for the low frequency

limit. The

x » and _{o y »} scaling determines J while the best fit allows adjustment of ç ^and q. In this way,

we have obtained J

1.15 K, ç

^{5 x 10-2 and}

tj

0.7. An uncertainty exists in the determination of the geometrical coefficients De ^and De, ^{due to the}

unaccurate knowledge ^{ofii2 .} This is taken into account

by drawing ^three calculated curves in each case consi- dered for the values of the parameters ç and q : ^the

first corresponds ^to the lowest possible ^{value of} a2 (0.8 G2), the second to the mean value (1.25 G2)

and the third to the greatest possible ^value (1.70 G2).

At high frequency (set ^{of curves} I), the values of the parameters J, ç and tj ^{are, in fact,} determined without reference to the precise ^{value of a2.} Nevertheless to

have a good ^{fit at low} frequency (set ^{of curves} II)

882

with the values of J, ç and q determined by ^the high frequency ^fit, it is necessary ^to have a2 nearer 1.70 G2 than 0.8 G’.

We now discuss the interchain couplings. ^{The rela-}

tion between the spin diffusion coefficients D, D’1, D2 obtained from T 1 and the interchain exchange couplings J i ^and J’2 ^{is not} direct. Self consistent treatments have been done in the two limiting ^cases of n

¹ (J’

J 1

J’2) by ^Reiter [23] ^and Laggen- dijk [24] ^and of il

⁰ (J’

Ji ; J2

0) by Laggen- dijk. ^{As the} experimental determination of il ^{is nearer 1}

than 0, ^we have calculated what would be J’ in the

limiting case q

1. From Reiter’s calculation we

have determined J’ = 0.10 K and from Laggen- dijk’s calculation J’ - 0.18 K. These values ^are in

good agreement with the static results.

4. Conclusion.

Tanol suberate is the only-known purely organic compound ^where ferromagnetic exchange interactions have been discovered. As a

considerable number of free radicals, it has been found to possess chain-like properties; however with a

ratio J1 /J ~ 0.1, ^it may ^not be considered as a very

good example ^{of 1 D} magnetic system. ^In addition,

we have developed ^a calculation method that allows

a systematic interpretation ^of T1

measurements vs.

frequency : ^{with this} method, ^{one is no} longer ^limited

to consideration of purely ^1D systems, ^{but one can} take into account the different anisotropy parameters in spin diffusion. The evaluation of interchain coupl- ings from interchain spin diffusion coefficients is not

straightforward; however nuclear relaxation is a

powerful method for studying systems ^{where the} presence of ^a transition of structural type makes static methods unusable [25] for, ^{here an} exploration ^{as a}

function of frequency ^{at a} given temperature is substitu- ed for the measurements as a function of temperature used in static methods.

Acknowledgments.

^{J. P. Boucher} and M. Nech- tschein are highly acknowledged ^for many stimulating

discussions. Thanks ^are due to G. Chouteau, ^{M. Saint}

Paul and R. Tournier, from the « Centre de Recherche

sur les Tres Basses Temperatures » for the availabi-

lity ^{of low} temperatures experiments ^{and for} helpful cooperation.

Appendix.

^The geometrical coefficients are given by ^the following expressions :

2022 xl xc is the ratio of the static susceptibility ^{of the} sample ^to the Curie static susceptibility ^{at the same} temperature : .1... = _{Xc p} ; ^{as in tanol suberate,}

op - ^{1 K, we} shall take this ratio equal ^{to 1 at room} temperature.

2022

N /1 is the number of protons considered.

2022 The km ^are expressed ^{in terms} of the scalar elec- tron proton coupling aÀ/1 ^{and the} dipolar ^electron proton couplings; these last terms depend ^{on the}

electron proton ^distance r Àu ^{and on the} angles (e À/1’

cp À/1) ^between r À/1 ^{and the} magnetic ^{field H :}

The Ym ^{are the} spherical harmonics, ^{defined as :}

Let us define 0.,, ^and wi, ^{as the} angles ^between _r.

and the electron spins chain and use the known relation between spherical ^harmonics

R is the rotation which _passes from the axis where rÀIl is referenced by ^the angles (e ÀIl’ ø ÀIl) ^{to the axis where}

ri, is referenced by ^the angles «() ÀIl’ qJ ÀIl)’

A spatial average ^on the geometrical coefficients is

equivalent ^{to an} average ^on the rotations.

References

[1] Non exhaustive list.

MC CONNEL, ^{H. M. and} LYNDEN-BELL, ^R. M., ^{J. Chem.} Phys.

36 (1962) ^2393.

HAMILTON, ^W. O. and PAKE, G. E., ^{J. Chem.} Phys. ³⁹ (1963) 2694.

EDELSTEIN, A. S., ^{J. Chem.} Phys. ⁴⁰ (1964) ^488.

DUFFY Jr., W. and STRANDBURG, D. L., J. Chem. Phys. ⁴⁶ (1967) 456.

LEMAIRE, H., REY, P., RASSAT, A.,

COMBARIEU, ^{A. and} MICHEL, J. C., ^Mol. Phys. ¹⁴ (1968) ^201.

KARIMOV, ^Y. S., Sov. Phys. JETP 30 (1970) ^1062.

YAMAGUCHI, Y., FUJITO, T., NISHIGUCHI, H. and DEGUCHI, Y., Proc. 12th Int. Conf. ^Low Temp. Phys., Kyoto (1970) ^805.

SAITO, S., KUMANO, ^{M. and} KANDA, E., idem, p. 809.

HONE, D. W., Proc. 17th Ann. Conf. Magn. Magn. Materials, Chicago (1971) (AIP Conf. ^Proc. 5, 413).

DUFFY Jr., W., DUBACH, ^J. F., PIANETTA, ^P. A., DECK, J. F., STRANDBURG, D. L. and MIEDEMA, A. R., ^{J. Chem.} Phys.

56 (1972) ^2555.

VEYRET, ^{C. and} BLAISE, A., Mol. Phys. ²⁵ (1973) ^873.

BLAISE, ^{A. and} VEYRET, C., ^ICM 2 (1973) ^278.

BOUCHER, ^J. P., FERRIEU, F. and NECHTSCHEIN, M., Phys. ^Rev.

9 (1974) ^3871.

VEYRET, C., Thesis, ^Grenoble (1975).

[2] DOUADY, J., ELLINGER, Y., RASSAT, A., SUBRA, ^{R. and BER-}

THIER, G., ^Mol. Phys. ¹⁷ (1969) ^27.

DAVIS, T. D., CHRISTOFFERSEN, R. E. and MAGGIORA, G. M., J. Am. Chem. Soc. 97 (1975) ^1347.

[3] BRIÈRE, R., DUPEYRE, ^R. M., LEMAIRE, H., MORAT, C., RASSAT, A. and REY, P., Bull. Soc. Chim. France (1965) ^3290.

[4] CAPIOMONT, A., ^Acta Crystallogr. ^{B 28} (1972) ^2298.

[5] BONNER, ^{J. C. and} FISHER, ^M. E., Phys. ^{Rev. 135A} (1964) ^640.

[6] CAPIOMONT, A., CHION, B., LAJZEROWICZ-BONNETEAU, ^{J. and} LEMAIRE, H., J. Chem. Phys. 60, 5 (1974) ^2530.

[7] ^For example SMART, S., Effective Field Theories of Magnetism (W. B. Saunders Company) 1960, p. 25.

[8] ^SAINT PAUL, ^{M. and} VEYRET, C., Phys. ^Lett. 45A, 5 (1973) ^362.

[9] LEMERCIER, P., Thesis, Grenoble (1968).

[10] CAREAGA, ^J. A., LACAZE, A., TOURNIER, ^{R. and} WEIL, L., Proc. 10th Int. Conf. ^Low Temp. Phys., ^Moscow (1966) 4, 295.

[11] CHOUTEAU, ^{G. and} JEANDEY-VEYRET, Cl., ^{To be} published.

[12] STRYJEWSKI, F. and GIORDANO, N., ^Adv. Phys. 26, 5 (1977) ^553.

[13] GOBRECHT, K. and SAINT PAUL, M., ^{Proc. Third} I.C.E.C., Berlin (1970) ^235.

[14] ^MC ELEARNEY, ^J. N., LOSEE, D. B., MERCHANT, ^{S. and} CARLIN,

R. L., Phys. ^{Rev. B 7} (1973) ^3314.

BONNER, ^J. C., WEI, T. S., ^HART Jr., H. R., INTERRANTE, ^L. V., JACOBS, ^I. S., KASPER, J. S., WATKINS, ^G. D. and BLÖTE,

N. W. J., J. Appl. Phys. 49, 3 (1978) ^1321.

SWANK, ^D. D., LANDEE, C. P. and WILLETT, ^R. D., Phys.

Rev. B 20, 5 (1979) 2154.

[15] HENESSY, ^M. J., Mc ELWEE, ^C. D., RICHARDS, ^P. M., Phys.

Rev. B 7 (1973) 930.

[16] DEVREUX, F., BOUCHER, J. P. and NECHTSCHEIN, M., J. Phy- sique ³⁵ (1974) ^271.

[17] FERRIEU, F., ^J. Physique ^{Lett. 38} (1977) ^L-381.

[18] ^TAHIR KHELI, R. A. and Mc FADDEN, D. G., Phys. ^{Rev. 182} (1969) 604.

[19] SOOS, ^Z. G., HUANG, T. Z., VALENTINE, J. S. and HUGHES, R. C., Phys. ^{Rev. B 8} (1973) ^993.

HUANG, ^{T. Z. and} Soos, ^Z. G., Phys. ^{Rev. B 9} (1974) ^4981.

[20] BUTLER, ^M. A., WALKER, L. R. and Soos, Z. G., J. Chem.

Phys. ⁶⁴ (1976) ^3592.

[21] FERRIEU, ^{F. and} NECHTSCHEIN, M., Chem. Phys. ^Lett. 1, ¹¹ (1971) 46.

[22] BARJHOUX, Y., Thesis, ^Grenoble (1979).

[23] REITER, G., Phys. ^{Rev. B 8} (1973) ^5311.

[24] LAGENDIJK, A. and

RAEDT, H., Phys. ^{Rev. B 16} (1977) ^293.

[25] JEANDEY, ^{Cl. and} NECHTSCHEIN, M., ^J. Mag. Mag. ^Mat. 15,

18 (1980) ^1053.