One and two dimensional high temperature spin diffusion in molecular semiconductors

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One and two dimensional high temperature spin

diffusion in molecular semiconductors

P. Petit, P. Spegt

To cite this version:

1645

One

and

two

dimensional

_high

_temperature

_spin

diffusion in

molecular

semiconductors

P. Petit and P.

_Spegt

Institut Charles _Sadron, 6 rue

_{Boussingault,}

67083

_Strasbourg

Cedex, France

(Reçu

le 8 _janvier 1990, révisé le 30 mars _1990,

_accepté

le 3 avril

₁₉₉₀₎

Résumé. 2014 La

_dépendance

en

_fréquence

du taux de relaxation

_spin-réseau

du _proton montre _que

la diffusion de

_spin

électronique

dans les

systèmes

de

spins

localisés

_{Pc2Y . CH2Cl2}

et

Pc2Lu

est

_{respectivement}

unidimensionnelle et bidimensionnelle. Les mesures des taux de relaxation ont été faites dans la gamme de

fréquence

25-200 MHz. Dans les deux

systèmes,

la

diffusion de

spin

n’a lieu

qu’à

la

fréquence

de Larmor

_{électronique.}

Les taux et les

anisotropies

de diffusion ont été

_{quantitativement}

estimées.

L’anisotropie

de la diffusion de

_spin

dans

Pc2Lu

est très élevée.

Abstract. 2014 The

frequency dependence

of the _proton

_spin

lattice relaxation rate as a

_probe

of the electron

_{spin dynamics}

shows that the

spin

diffusion in the

spin

localized _systems

_{Pc2Y . CH2Cl2}

and

_Pc2Lu

is

_quasi

one- and two-dimensional,

respectively.

The relaxation rates are measured in

the

frequency

range 25-200 MHz. In both systems, the

_spin

diffusion occurs

_only

in the electronic

frequency

range. The diffusion rates and the

anisotropies

in these molecular semiconductors are

quantitatively

estimated and

_comparable

to other

spin

localized systems.

Pc2Lu

is found to be a

«

_highly

two-dimensional »

exchange coupled

paramagnet.

J.

_Phys.

France 51

₍₁₉₉₀₎

1645-1654 1 er AOÛT 1990,

Classification

Physics

Abstracts

75.40G - 76.60 - 76.30

Introduction.

The search for molecular semiconductors has been oriented towards 7T-radicalar neutral

phthalocyanine

derivatives

(lutetium

and

_lithium)

because of their

_exceptional

chemico-physical properties

[1].

Their intrinsic semiconductor

behaviours,

which have led to the obtention of field effect transistors

[2],

are due to their radicalar nature. In addition to their electrical

_properties,

these

compounds

exhibit

_exceptional

and unusual

_magnetic

behaviours

[3,

4].

In two recent _{papers, it has been shown that the}

_spin

diffusion in the lutetium

bisphthalocyanine (Fig.

la)

compounds depends

on the

_stacking

of the molecules

_{[5, 6].}

Indeed,

depending

on the

preparation,

two

_crystalline

structures of this material are

available,

whether it is solvated or not. The solvated

_system,

_{Pc2Lu. CH2Cl2}

_(Pc

=

C32Hl6N8),

shows a

_stacking

of the molecules in

_parallel

chains

_{(Fig. lb) ;}

the unsolvated

system,

Pc2Lu,

exhibits a

stacking

of

parallel planes (Fig. 1 c)

[7,

_8].

The

spin

diffusion has

been shown to be one-dimensional and two-dimensional in the solvated material and the

Fig.

1.

_{- a)}

Structure of the lutetium

_{bisphthalocyanine}

molecule

_{(Pc2Lu). b)}

Schematic view of the

crystal packing

in

_{Pc2Lu . CH 2C’2 (after}

Ref.

_{[7]). c)}

Schematic view of the

crystal packing

in

_Pc2Lu

(after

Ref.

_[8]).

unsolvated one,

_{respectively.}

However,

although they

are

_unambiguous,

these

characteri-zations of the

_spin

diffusion,

determined

_by

ESR on

_single

crystals,

remain

qualitative.

The

_present

paper deals with

quantitative

determinations of the diffusion rates, the cutoff

frequencies

and the

_anisotropies

of the diffusion rates of the unsolvated lutetium

bis-phthalocyanine Pc2Lu

and the solvated

yttrium

bisphthalocyanine Pc2Y .

CH 2C12

[9].

The use

of these two

_systems

for the

_{reported study}

has been

_{imposed by}

the

_quantity

of

_sample

available.

These characteristics of

_spin

diffusion have been determined

_by

an NMR

_study

of the

proton

relaxation time

Tl

as a function of the irradiation

_frequency

and some measurements of

_{Tl p}

for a fixed

_frequency.

The results of the

_experiments

have been

interpreted

within the

framework of Devreux et al.

_{[ 10]}

and Nechtschein et al.

_{[ 11 ].}

Table 1 summarizes the orders of

magnitude

of the

_parameters

of the

_spin

diffusion for the two

_compounds.

Table I. 2013 Characteristics

1647

Experiment.

The

_{synthesis [12]}

and the structure of the lutetium molecule and its two

_{possible crystalline}

structures have been

_published

elsewhere

_{[7, 8].}

The structure of the solvated

_yttrium

bisphthalocyanine

is

_isomorphous

to that of the solvated lutetium

_compound,

and their electrical behaviours are

_{comparable [9].}

For both

_systems,

the

_experiments

were

_performed

on

_{powder samples}

of about 300 mg,

hereafter referred to as

_{Pc2Lu (unsolvated, planar}

_structure)

and

_{Pc2Y . CH2Cl2 (solvated,}

linear

structure).

NMR measurements have been carried out at

25,

30,

45 and 60 MHz

_using

a Bruker SXP

spectrometer

operating

with a wide _gap

_high

resolution Varian

_magnet

stabilized

by

an

external field lock. At 200

_MHz,

a Bruker CXP200

_spectrometer

has been used.

The

_spin-lattice

relaxation times

_Tl

were measured

by

the

inversion-recovery

method,

with

typically

60

_{equally spaced points}

on the _recovery curves. A

_{preliminar fitting}

of the relaxation curves with two

_{exponentials (5 parameters)}

has shown these curves to be

_strictly

monoexponential

and therefore all the relaxations have been fitted with one

_exponential

(3 parameters) by

a

_non-linear,

least square routine

_{(Fig. 2a).}

The

_given

results are averages

over 10 curves

_sampling

the relaxation at different

_positions

in the first third of the free induction

_{decay (FID).}

The second moments

_M2

of the

_proton

resonances have been

calculated by fitting

the FID’s

after the

_spectrometer

deadtime

_(typically

5

_kts)

to a ten

_degree

even

_polynomial

and

extrapolating

to time 0 taken at the middle of the rf

_{pulse (Fig. 2b).}

This

_procedure

is

described elsewhere

_[13].

The

ESR

_experiments

were

_performed

with a Bruker ESP 300 X-band

_spectrometer

provided

with a

_TE102

cavity,

an NMR

_gaussmeter,

a

frequency

meter and a HP330

computer

for data

_handling

facilities. The

_{reported experiments}

have been

_performed

at lôw

power and modulation

amplitude

in order to avoid saturation and distortion effects. The

magnetic susceptibilities

were determined

_by

numerical double

_integrations

of the ESR

spectra

recorded on 40 times the linewidth.

Fig.

2. - Plots and fits of

a) spin-lattice

relaxation curve ;

b)

free induction

_decay.

Theoretical

_background.

summarized. The

_proton

relaxation rate

_depends

on the

_{spectral density f ( w )}

of the

_spin

motion

_{[10] :}

where

_{X is}

the relative

_{spin susceptibility ( x =}

_{X molar/ N (guB )2), a}

and d are the

_isotropic

and

dipolar electron-proton hyperfine couplings respectively

and _{cv e} =

w N

’Y el ’YN =

658 wN’ The

spectral

density f(w )

reflects the

_{dimensionality}

_{of the diffusion process :}

where

_{Dz, Dy, Dx}

are the diffusion rates; for a one-dimensional _process,

_{DZ > D Y,}

Dx ;

for a two-dimensional process,

_{Dz >}

_{D y > DX.}

At low

_frequency

the low-dimensional

diffusion,

1 D or

_2D,

breaks down because of interchain or out of

_{plane couplings.}

This

crossover between a 1 D or 2D

regime

and a

higher

order one occurs at

_{w c ~- D L .}

The determination of the cutoff

_frequency

_{w c} then allows an evaluation of the

_anisotropy

in the

system

under

_study.

_However,

this

_frequency

is not

_easily

accessible. Another way to evaluate

wc is to determine the

proton

relaxation time in the

_rotating

_frame,

since

_{Tl p}

_depends

on the

spectral density

at _{w c}

_{[ 14] :}

Tht:

measure of

_{Tl p}

at a

given frequency gives

therefore an evaluation of the cutoff

frequency.

Depending

on the

_spectral

width at which the electronic

_spin

diffusion takes

_place

and on

the value of _wc

_compared

to that of _wN and _{w e,} three different situations can occur for the

frequency dependence

of the

_{spectral density,}

which lead to three different

_frequency

dependences

of the

_proton

relaxation rate. These situations are resumed in

figures

3a and 3b

for a one-dimensional diffusion process.

If

_{w c : {û N : D Il : {û e’ (case 1 )}

i.e. the diffusion takes

_place

at _{w N}

_only,

or if

{w c : {û N : {û e : DU , (case 2)

i.e. the diffusion takes

_place

_{at w N} and _{w e,} the relaxation rate is

directly proportional

to

_{f ( w ) .}

If

_{W N W c ’ W,, D 11, (case 3)}

i.e. the diffusion takes

_place

at _{W e}

_only.

The

_spectral

density

at W N is constant,

leading

to a non-zero

_{extrapolation}

of the

_Tl

=

_{f (w - 1/2)}

_plot,

proportional

to

_{f ( W N).}

In this

_situation,

an evaluation of _{(û c} is then

_possible

as

f({wN) = f({wc).

It is then

_possible,

before _any calculation to estimate in which

_regime

the

_spin

diffusion takes

_place

and to evaluate the _{range of} the cutoff

_{frequencies (it}

is also a _way to

_verify

the

coherence of the

_{experimental results).}

In the case of a two-dimensional

_spin

diffusion

_regime,

the

_intercept

between the

Tl

1 = f (Ln

( 1 / w ) )

line and

_Tl

1 axis at Ln

_{( 1 lw )}

= 0 is non-zero in the three cases.

However,

it is

_{straightforward}

to estimate the

_frequency

range in which the diffusion takes

1649

Fig.

3.

_{- a) Spectral}

densities for a one dimensional

_spin

diffusion in the three

_{possible frequency}

ranges

(see text). 1)

Wc WN

DI

We.

2)

Wc WN We

DI. 3)

0) N Wc : We :

DI. b) Spin-lattice

relaxation rates as a function of

W - 1/2

for the three cases of

a).

formal

_expression

of the constant term

_(in

_Eq.

₍₃₎₎

must lead to the same value deduced from the

_plot.

Moreover,

when the

_suspected

range of the diffusion is not the one at which

_spin

diffusion occurs, the calculated diffusion rate will lead to a cutoff

_frequency

inconsistent with the initial

_hypothesis.

Results.

Bearing

in mind that the

spin

diffusion in

_Pc2Lu.

_CH2CI2

and

_Pc2Lu

have

_{qualitatively}

been shown

by

ESR studies to be one- and two-dimensional

_respectively

and that

_{Pc2Y .}

_{CH 2C12}

and

_{Pc2Lu . CH 2CI2}

are

_{isostructural,}

the

proton

relaxation rates

Ti

1 have

been

_plotted

as a

function of

_{(w /2}

_{71’)- 1/2}

for

_{Pc2Y .}

_CH2CI2,

and

_{Ln (2}

71’

_{/w )}

for

_PC2Lu.

These results are

shown in

_figures

4a and 4b. Least _square fits of the

_experimental

data indicate that for both

systems,

spin

diffusion occurs in the electronic

_frequency

range

only.

However,

no

breakdowns of the lines are observed and then no cutoff

frequency

can be determined from

these curves. The diffusion rates _{may be calculated from the}

_slopes

of the fits :

Pc2Y . CH 2CI2:

Pc2Lu :

where

_Dp

_II is the intrachain diffusion rate for

_{PC2y .}

_CH2C12

and the

_in-plane

diffusion rate for

Pc2Lu (Pc2Lu

is

assumedy to

be a

_{« good »}

2D

_system

where

_Dz

=

D y

=

D

_|| in the notation of

Eq. (2)).

As the first and the second moments of the

_proton

_absorption

line are

_proportional

to the

Fig.

4. - Variation of the _proton relaxation rate as a functidn of

_(ca

_/2

7r )- 1/2

in

_{PC2y -}

_{CH2Cl2 (a)}

and

as a function of Ln

_(m

_/2

_{’TT )-1}

1 in

_Pc2Lu

_(b).

Least square fits

(solid lines) give : a)

T1,-1

1 =

1.7 X 105 x

_{(w /2 ’TT )-1/2 +}

8.81 ;

b)

Tll

= 6.1 _x Ln

(2 ’TT /Cd) +

130.4.

where H is the

_magnetic

field.

However,

the

_absorption

line

_{being symmetrical, only}

the second moment, and then the

_{dipolar hyperfine coupling,}

has been determined.

The room

_temperature

molar

_{paramagnetic susceptibilities}

of the

_yttrium

and lutetium

compounds

have been found to be 1.4 x

10 - 3 emu/mole

and 1.3 x

10 - 3 emu/mole

respec-tively,

i.e.

_{they correspond}

to _{the presence of} one electronic

spin

per

bisphthalocyanine

molecule. These

_high

values show that both

_systems

are

_spin

localized

_paramagnets.

The

susceptibilities

follow a Curie-Weiss law on the

_temperature

_range 140-380 K

_{(Fig. 5a}

and

5b).

For a better accuracy in the determination of the

_{dipolar hyperfine coupling}

constant, the second moments of the NMR line have been measured as a function of

_temperature

in the same

_temperature

_range as that used for the ESR

_experiments.

The results are

plotted

as a

1651

Fig.

5. -

Variation of the inverse of the normalized ESR

susceptibility

of

Pc2Y . CH2CI2 (a)

and

Pc2Lu

(b)

as a function of the _temperature.

From the

_slope

_{of the least square fits of the variations of}

_M2

versus

X 2,

the

_dipolar

hyperfine coupling

constants are found to be :

For the

_isotropic

_part

of the

_{hyperfine coupling}

we have taken the

value d 2 =

a 2/4

which is

commonly

reported

for a

_{2 pZ}

orbital

_[14,

_15].

With these

_values,

the

_spin

diffusion rates of

Pc2Y .

CH 2C12

and

_Pc2Lu

are estimated to be 5.5 x

1013

_rad/s

and 6.3 x

10 l2

_{rad/s respectively.}

In order to evaluate

_{quantitatively}

the

_anisotropy

of the

_spin

diffusion in these

_systems,

the

Tl p

have been measured at 60 MHz in a rf field of about 6 G. The values found are

Tl P

= 12 _ms for

Pc2Y .

CH 2C12

and

Tl p

= 21 ms for

_Pc2

Lu. With these values and from

equation (3),

the evaluated cutoff

_frequencies

are 5.5 x

_{109 rad/s}

and 1.7 x

_{109 rad/s}

for

Pc2Y .

CH 2C12

and

_{Pc2Lu respectively.}

The cutoff

_frequency

determined from the

extrapol-ation of the

_Ti

₌

_{f(W -}

_1/2)

_plot

for the

_{yttrium compound}

is of about 2 x

101° rad/s,

which is

close to the one derived from the

_{T1 P}

measurements.

Assuming

that _wc is the

_frequency

at which a transverse diffusion _appears, i.e.

wc is the

spin exchange frequency

in the

perpendicular

direction to

_{Dj ,}

it is

_possible

to

_give

an

estimate of the

_anisotropy

of the

_spin

diffusion. In a linear chain of

_{spin 1/2,}

the

_exchange

frequency

is related to the diffusion rate D

_by

_{wex, = D / 1. 15}

_{[ 16, 17].}

The

_anisotropy

in

Pc2Y . CH 2C12

is then found to be

_{’wex /wc ~}

1 x

104.

In the case of

_{Pc2Lu, assuming}

that

D 1- =

1.15 w c, the

_anisotropy

is estimated to

_{Dp /D 1}

.-- 3.2 x

10 3.

These

_{exchange frequencies}

determined

_by

NMR

_experiments

_(w

_ex = 4.8 _x

1013

rad/s

for

Pc2Y . CH 2C12

and _weX = 5.4 _x

10 l2

rad/s

for

PC2LU)

should be related _to the _one derived from the

_temperature

_dependence

of the ESR

_{susceptibilities.}

The Curie-Weiss

_temperatures

deduced from the

_plots

of the inverse of the

_{susceptibilities}

versus T are of about 25-30 K and

5-7 K for the

_yttrium

and the lutetium

_{compounds respectively. Using}

the relations between the Curie-Weiss

_{temperature 0}

and the

_{spin exchange}

_temperature

J

_[19]

and between the

spin exchange

temperature

and the

_{spin exchange frequency [16] :}

the

_{spin exchange frequencies}

in

_{Pc2Y .}

_CH2Cl2

and

_PC2Lu

are found to be of about 8 x

1012

_rad/s

and 9 x

1011

rad/s respectively. Taking

the

_experimental

incertitudes into

account, these values are in

_good

_agreement

with the one

_reported

above.

Discussion.

The two

_systems

studied here are molecular

_compounds,

i.e.

_composed

of

_only

one

_type

of

molecule,

unlike radical ion

_salts,

_charge

transfer

_complexes,

etc. As shown

_{by paramagnetic}

susceptibility,

there is one

_{unpaired spin}

_per molecule. In such localized

_spin

systems,

the local field seen

_by

the electronic

_spin

is very

weak,

as

compared

to d-electron

_spins.

The

estimate of the

_{hyperfine coupling}

constant shows that the

_spin

in

_mainly

localized on the

protons.

Indeed,

using

the McConnell

relation,

an average

spin density

of

1 p 1 = 1 al

1 IQ

= 0.043

per

proton

is derived for

_{Pc2Y .}

_{CH 2CI2}

_and

_{1 p 1 =}

0.068 for

Pc2Lu,

where

_Q

= 23.4 G. These estimates of the

spin

densities on the

_protons

are closed and

to be

_compared

to those

recently

obtained

_by

Xa calculations on the radicalar lithium

monophthalocyanine

[18]. They

show that the wave function of each

spin

has a

large spatial

1653

local

_fields,

_favoring

the

_exchange

between

_spin

states. This is a

_prerequisite

to obtain narrow

ESR

_{linewidths ;}

the

_peak-to-peak

widths of the

_single

ESR

_lines,

close to the free electron

resonance,

of Pc2Y .

CH2C12

and

_Pc2Lu

are 0.7 G and about 1 G

_{respectively.}

In

addition,

the

exchange

between

_spins

is also increased

_by

the

_{high spatial}

extension of the

_2p,

orbitals which

overlap

each other between

adjacent

molecules of the same chain or of the same

_{plane (the}

distance between the

_macrocycles

of two

_adjacent

molecules is close to the Van der Waals

distance).

These

_arguments

_may

_explain

that the

_high

value found for the diffusion rate is

comparable

to those determined for other

_spin

localized

systems

such as TMMC

[17].

On the other

hand,

there is no

_overlap

between two

_adjacent

molecules in the direction

_{perpendicular}

to the chain

_stacking.

_{This may}

_explain

the estimated

_magnitude

of the

_{anisotropy, specially}

in

the lutetium

_compound.

_Moreover,

the measured ESR linewidths are about two orders of

magnitude

less than the estimated cutoff

_{frequencies, indicating}

that the ESR linewidth of

Pc2Y . CH2C12 (Pc2Lu)

is

governed

by

intrachain

_{(in plane) dipolar}

interactions whereas the cutoff

_{frequency originates}

from interchain

_(out

of

_{plane) spin exchange.}

Conclusion.

The two

_systems

used in this

_study

are molecular

_{semiconductors,}

_composed

of

_only

one

_type

of molecule. Each molecule of the material is a neutral 7T-radical. The characteristics of the

spin

diffusion in these two

_spin

localized

_systems,

_{namely Pc2Y . CH2C12}

and

_Pc2Lu,

have been

_{quantitatively}

estimated

_by

a

_study

of the

_proton

NMR relaxation rates as a function of

frequency.

The

analysis

of these two

_systems

in terms of one and two-dimensional

spin

diffusion have been made in view of the

_qualitative

ESR results

_{previously reported.}

The solvated

_{yttrium bisphthalocyanine}

is a

_quasi

one-dimensional

system,

whose characteristics

are

_comparable

to those of

_inorganic

materials. The unsolvated lutetium

_{bisphthalocyanine}

is

a two-dimensional

_system

with a

_{high (in plane/out}

of

_{plane) anisotropy.}

The latter

_compound

is one of the _very few materials for which the two-dimensional nature of the

_spin

diffusion has been established.

Acknowledgements.

A. De Cian is

_{gratefully acknowledged}

for the

_supply

of the

_{yttrium compound}

and R. Even for the

_supply

of the lutetium

_sample.

We are indebted to J.-J. André for his

_stimulating

interest

_during

this work and to J.-P. Boucher for its criticism of the

_manuscript.

References

[1]

TUREK Ph., PETIT P., ANDRÉ J.-J., SIMON J., EVEN _R., BOUDJEMA B., GUILLAUD G. and

MAITROT M., J. Am. Chem. Soc. 109

₍₁₉₈₇₎

5119.

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