Direct observation of one-dimensional electron spin transport in the organic conductor (FA)2AsF6 by the electron spin echo field gradient technique

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Direct observation of one-dimensional electron spin transport in the organic conductor (FA)2AsF6 by the

electron spin echo field gradient technique

G.G. Maresch, A. Grupp, M. Mehring, J. U. V. Schütz, H.C. Wolf

To cite this version:

G.G. Maresch, A. Grupp, M. Mehring, J. U. V. Schütz, H.C. Wolf. Direct observation of one-dimensional electron spin transport in the organic conductor (FA)2AsF6 by the elec- tron spin echo field gradient technique. Journal de Physique, 1985, 46 (3), pp.461-464.

�10.1051/jphys:01985004603046100�. �jpa-00209985�

Direct observation of one-dimensional electron spin transport

in the organic ^conductor (FA)2AsF6 ^by the electron spin ^echo

field gradient technique

G. G. Maresch, ^A. Grupp, ^M. Mehring, ^{J. U. v. Schütz and H. C. Wolf} Physikalisches Institut, Universität Stuttgart, ⁷⁰⁰⁰ Stuttgart ^{80, F.R.G.}

(Reçu le 8 octobre 1984, accepté ^{le 12 novembre} 1984)

Résumé. 2014 L’anisotropie ^{de la constante de} diffusion D des spins électroniques

été déterminée _pour des

cristaux du sel à radical cationique (fluoranthène)2 + AsF-6 ^{par échos de} spin ^{dans des} gradients ^de champ magné- tique ^à température ambiante. Pour la diffusion parallèle ^et perpendiculaire relative à l’axe d’empilement ^des

molécules de fluoranthène on

obtenu les nombres D~

3,0 cm2 s-1 ^et D

0,01 cm2 s-1.

Abstract

The orientational dependence of the diffusion constant D of electronic spins has been determined for single crystals of the radical cation salt (fluoranthenyl)2+AsF-6 by ^electron spin ^echo experiments ⁱⁿ magnetic

field gradients ^at

temperature. The values D~

^{3.0 cm2 s-1 and D}

^{0.01 cm2 s-1}

obtained for diffusion parallel ^and perpendicular ^{to the} stacking axis of the fluoranthene molecules respectively.

Classification

Physics ^Abstracts

76.30P - 76.30R

1. Introduction.

Fluoranthenyl radical cation salts are a model system for quasi one-dimensional metals with high ^electrical

conductivities of about a ~ 1 000 S/cm ^{at room tem-} perature [1]. ^The crystal ^{structure is wellknown} [2]

and shows stacks of fluoranthenyl cations with a very small lattice constant of a

3.3 A. These stacks are

separated ^{in the} perpendicular directions by ^anions

e.g. PFi, AsF6", ^etc. with lattice constants of about

b -- c =! 14 A.’

In the metal-like region ^{above 180 K an} extremely

narrow ESR line is observed [3, 4], ^which corresponds

to long spin relaxation times T 1 ^and T2 of the mobile electrons [4-11]. From nuclear and electron spin

lattice relaxation times an estimate of the spin hopping

rates parallel (,r ^and perpendicular (,r ^{to the}

stack axis has been obtained. A Pauli-like suscepti- bility ^was determined by ^a modified Schumacher- Slichter method [6, 8].

We have shown earlier that the electron spin ^echo technique with different magnetic ^field gradients ^{is a}

useful tool to observe electron spin ^motion [11].

Recent 13C NMR measurements have established that the conduction band is formed from the highest occupied molecular orbital (HOMO) ^{of the} (FA)’

dimer [12]. ^{In order to} determine the .anisotropy ^of

the spin ^{diffusion of the} mobile electrons in radical cation salts we have performed ^time resolved X-band ESR experiments ⁱⁿ magnetic ^field gradients ^on single

crystals ^of (FA)2AsF6. ^In this paper ^we present ^for the first time measurements of the orientational

dependence of the electronic diffusion constant by

the electron spin echo field gradient technique. ^We

obtained Dii ^{= 3 cm2/s in the} stack axis direction and about Dl

^0.01 CM2/S perpendicular ^{to this}

axis. This determination of the electron spin ^motion anisotropy ^{is in} good agreement ^with conductivity

measurements [13] and with estimates of the spin hopping ^rates [6, 11].

2. Theory : spin ^echo decay.

The electron spin ^{echo is} usually generated by ^a 7r/2-T-7r-pulse sequence. The spin ^echo decay ^{which is}

observed by varying -r ^is exponential ^{if the} spins ^are

fixed or only slowly moving. ^The accompanying

transverse spin relaxation time T2 ^{has been measured}

this way in radical cation salts [4, 6-11]. ^{In fluoran-} thenyl radical cation salts, however, ^{the diffusion}

constant is so large, ^{that an} additional decay ^{due to}

the diffusion in the magnetic ^field gradient ^{must be}

taken into account.

From Bloch equations ^one gets ^the decay ^{of elec-}

tron spin ^{echoes in} magnetic ^field gradients [14] :

where Mo ^{is the} equilibrium magnetization. ^The

first time dependent ^term describes the usual _expo- nential decay ^{with the} transversal relaxation time T2.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01985004603046100

462

The relaxation function R(G, D, tE) with tE

^{2 i}

modifies this exponential decay ^{and leads to an}

additional decay ⁱⁿ magnetic ^field gradients ^{G in case}

of mobile spins :

The diffusion constant D describes the electronic motion and contains the anisotropy of the diffusion tensor D

where D1, D2, D3 ^{are the} principal values and _a, f3

are the Euler angles ^with respect ^{to the} magnetic

field gradient. ^{In case of axial} symmetry ^{of the ten-}

sor D with diagonal components D.1’ DII ^{the orien-}

tational dependence ^{of D in} equation (2) ^{reduces to}

With Dil >> ^{Dl we expect a} rapid decay ^{of the trans-}

versal magnetization M(tE) ^{if the} stack axis is parallel

to the gradient. Single crystal measurements of the

spin ^echo decay ⁱⁿ sufficiently strong magnetic ^field gradients allow the determination of the spin ^diffusion

tensor.

3. ExperimentaL

The (FA)2AsF6 crystals ^were grown by anodic oxida- tion at - 30 °C [1, 15, 16]. They consist of shiny

black needles with the needle axis corresponding ^to

the stacking direction, along which the radical elec- trons are highly ^mobile.

Measurements of the electron spin ^echo intensity

spectrum ^{are carried out with a} pulsed ^ESR spectro-

meter at 9.7 GHz. Slotted tube resonators [17] ^were

used with gradient saddle coils inside.

The ESR pulse spectrometer is homemade and consists mainly ^of (a) ^low power microwave pulse

units with 160 MHz intermediate frequency, (b) ^{10 W} (8-18 GHz) ^microwave amplifier, (c) receiver with

phase sensitive detector and (d) ^{transient recorder}

and boxcar. The magnetic ^{field is} supplied by ^a

conventional ESR magnet, whereas the gradient

fields are generated by ^a home built current pulse

unit.

4. Results.

In order to calibrate the magnetic ^field gradient, ^we prepared ^a sample ^{with two} single crystals ^of (FA)2AsF6 ^{mounted on a 2.1 mm} glass ^rod (see ^insert

in Fig. 1). ^Field gradients ^of varying strength ^were applied ^{and the} corresponding ^electron spin ^echo spectra ^{were taken as shown in} figure ^1. The observed spectra ^are spin density projections ^{onto the} gradient

axis. This technique ^is well known from NMR imag- ing applications. Figure ¹ also shows the line _sepa- ration Av versus ^a parameter ^{which is} proportional ^to

Fig. ^1.

^{Left :} spin ^echo spectra ^{at four different} gradients, right : spin echo line width

function of the gradient amplitude.

the gradient. ^{From the} separation ^{of the} crystals ^a

calibration of the gradient is obtained. The gradient amplitude ^{was measured as a} voltage drop ^{at a}

resistor in series with the gradient ^coils.

Measurements were performed ^on single crystals

for different orientations of the stack axis with respect

to the magnetic ^field gradient. ^{The field} gradient ^was parallel ^{to the static} magnetic field and was turned

on 50 ps before the first pulse ^{and was} turned off 50 ys after the spin echo, ^to eliminate transient effects of the gradient pulse ^{on the} spin echo. This procedure

in addition avoids heating ^{of the} sample. ^The spin

echo experiment ^was performed by using ^{a 150 ns} n/2-pulse, ^{a time} delay ^{L and a 300 ns} Tr-pulse. ^The

echo amplitude ^was measured with a Boxcar Inte- grator ^{at different} pulse spacings ^{i with a 50 ns} Boxcar

gate at tE

²

Figure ^{2 shows the} decay ^{of the} spin ^echo amplitude

Fig. ^2.

Decay ^of magnetization ^{at different} gradients

and two different orientations : top : needle axis parallel ^to

the gradient ^field, bottom : needle axis perpendicular ^{to the}

gradient ^field.

as a function of time at different gradients (G1

18 mT/m, G2

36mT/m ^and G3

72 mT/m) ^and

two different orientations of the crystal.

For orientations of the crystal stack axis parallel

to the gradient ^we expect ^{a much faster} decay ^due

to the part ^{of the} relaxation function containing ^the spin ^motion. Figure ^{2 shows the} rapid magnetization decay ^{when the} unique crystal ^{axis is} parallel ^{to the} gradient ^{field. In} contrast to this fast decay, figure ²

bottom presents ^the very slow magnetization decay

at the same gradients ^{but the} crystal ^rotated by nearly

900.

For large gradients ^the quasi continuous technique

as applied here fails because of limited microwave excitation power. We have therefore supplemented

our measurements by applying ^the following pulsed gradient technique, ^{shown in} figure ^3.

Fig. ^3.

Top : spin ^echo experiment ^with pulsed gradients,

bottom : echo spectrum amplitude

square of the gra- dient maximum Go ^{with fixed} pulse spacing

^at three diffe- rent orientations.

The spin ^echo experiment ^is performed ^{as usual}

with the gradient ^now being ^zero during ^{the micro-}

wave pulses ^and during ^the detection of the spin ^echo.

The gradient pulses are, however, ^{switched on imme-} diately ^{after the} microwave excitation and switched off _{4 [ts} before the second pulse and before the echo maximum. In this _way the fieldgradient contribution to the echo decay ^{due to the} relaxation function

R(G, D, fl, tE) ^{can be} separated ^{from the} T2 ^relaxa-

tion and is unaffected by the microwave pulses.

We detect the echo spectrum by sweeping ^the homogenous ^field Bo ^{with a Boxcar} gate starting ^on

the echo maximum. Figure ³ bottom shows the depen-

dence of the echo spectrum height ^{from the} gradient pulse amplitude Go ^{at different} orientations fl ^and

fixed microwave pulse spacing ^{time r}

5.6 gs.

From figure ^{2 it is} clearly ^{visible that the influence}

of the gradient ^{field is much} larger ^{in the} parallel direction, ^which corresponds ^{to a} larger ^diffusion

constants due to equation (2). Measurements of the orientational dependence ^{of the} spin ^echo decay yield

the anisotropy ^of the, diffusion ^constant D(a, fl) ^of

the mobile electronic spins ⁱⁿ (F A)2AsF 6.

In figure ^{4 we have} plotted ^{the measured diffusion}

constant D versus the angle fl ^{of the} stacking ^axis

with respect ^{to the} magnetic ^field gradient. ^{Note the} large anisotropy ^{of D which} clearly demonstrates the

quasi one-dimensional ^nature of electron spin ^trans- port ^{in this} organic conductor. The principal ^values

Dn ^{and D.L} of the diffusion tensor were obtained to be DII = ^{3 cm2 s-’ and Dl}

^{0.01 cm2 s-1.}

Fig. ^4.

Orientational dependence ^of spin ^diffusion

constant in (FA)2AsF6. ^{The data} (points) ^{were obtained}

from decays ^{similar to} figure ^{2. The} theoretical

(line) corresponds ^to equation (4) ^with D ^II = 3 cm 2 s -

and

Dl = 0.01 CM2 S- 1.

We should remark, however, ^{that the} measurement

of the diffusion constant by ^{the field} gradient ^tech- nique ^{can become} complicated ^if multiple spin

echoes due to radiational feedback are observed. We have indeed observed these multiple ^{echoes in} (FA)2X crystals (X

AsF6, SbF6). ^{However, their} ampli-

tudes were in the current investigation ^small enough

to be neglected.

Another remark concerns the degradation ^{of the} sample ^after exposure ^to air. Our experiments ^were

all performed ^on freshly grown samples, ^{which were} kept ^under N2 atmosphere ^{in the} refrigerator. ^After

exposure ^to air for several weeks we noted a drastic decrease of the diffusion constant, ^{as measured} by

the field gradient technique, whereas the T1 ^and T 2

values did not show any appreciable change.

5. Discussion.

The anisotropy of the diffusion constant of electronic transport ⁱⁿ (FA)2AsF6 ^as determined by ^{the field} gradient technique ^{allows to} draw direct conclusions

on the electron motion. This has to be contrasted with relaxation measurements where one needs to know the type ^and strength ^of the electron spin

interaction as well as the spectral density ^function

before _any conclusion can be made concerning ^the

transport parameters. On the other hand the know-

ledge ^{of the} diffusion coefficient alone does not supply

any clue to the microscopic details of the motion.

464

One might therefore invoke a simple hopping

model with D

d2 j’t ^where 1 /i ^{is the} hopping ^rate

over the distance d. If we assume d

6.6 A to be the dimer separation ^for hopping parallel ^{to the}

stack direction we obtain i

1.5 X 10-15 s and with d

14 A for the interstack separation ^{we arrive}

at a transverse hopping ^{time of} ’t 1- = 2.0

10-12 s.

These data are in fair agreement ^{with our earlier} estimates [11].

If on the other hand a coherent electron motion

including ^a phonon scattering time T. is invoked, ^the appropriate definition would be Djj V2 ^{Ts, with vF} being the Fermi velocity. The Fermi energy ^was estimated to be 0.22 eV [8]. Using ^this parameter together with the free electron mass a phonon ^scat- tering ^time of ’ts

^{3.9 x 10-15 s} results. The corres-

ponding ^{mean free} path length ^A

vF iS is À

¹¹ A.

In addition the transverse integral t 1- may be estimated

from t.

h(Ts T _L) - 1/2 [18], which leads to t, ^{= 7 meV.}

Using ^these parameters ^an estimate of the conduc- tivities _6" and _{u 1-} based on microscopic parameters

can be obtained as On

1600 S cm-1 and _{J 1- =} SScm-1.

There is, however, ^an alternative interpretation ^as

was recently pointed ^out by E. Dormann [19]. Sup-

pose is is much larger ^than estimated from Dl,, ^i.e.

the electron motion is much more coherent and the diffusion constant D ^II is dominated by ^incoherent

motion across chain defects. For a rough ^estimate

we invoke D II = (Al)2/Tl ^{where we assume the jump}

rate across the chain defects to be equivalent ^{to the}

interchain jump ^rate ’C.L 1. ^{From the} known values of D ^{1, and zl we arrive at Al}

^{240 A} which is about 74a. This ^seems to be a reasonable _average distance between chain defects. Which one of the models

presented ^{here is} appropriate ^cannot be decided on

the basis of the experiments performed ^{so far. We} remark, however, ^{that the} defect model has some

advantages ^with respect ^to the others. At least it allows the condition EE is » h to be fulfilled much better than in the other models. Further experiments

have to be designed ^{to test} these ideas.

We note, that after completion ^{of the} manuscript,

we received a preprint by G. Sachs et al. [19] ^{in which} proton T1 measurements, performed ^on (FA)2PF6

at different magnetic ^fields yield very similar _para- meters for DII, Tr ^{and ’C 1. as} determined here. Stocklein

et al. [5b] also noticed a gradient dependence ^{of the} spin ^echo decay.

Acknowledgments.

We would like to thank D. Schweitzer, ^{M. Schwoerer} and E. Dormann for valuable discussions and for

sending ^us preprints ^{of their} manuscripts prior ^to publication. ^The Stiftung Volkswagenwerk ^has given

financial support.

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