Theory of neutral-ionic transition in mixed stack compounds

Synthetic Metals, 19 (1987) 497--502

497

THEORY OF NEUTRAL-IONIC TRANSITION IN MIXED STACK COMPOUNDS

N. NAGAOSA Institute for Solid State Physics, University of Tokyo, Tokyo (Japan) J. TAKIMOTO Institute for Molecular Science, Okazaki (Japan)

ABSTRACT The microscopic theory of the neutral-ionic (NI) transition found in mixed-stack charge transfer compounds is developed.

Quoting the results of the quantum Monte

Carlo simulations, we sketch the physical picture of this transition.

The neutral-

ionic domain wall (NIDW) on a chain plays the major role in explaining the optical and electrical properties found experimentally. structures

Its relationship with soliton

is also discussed.

INTRODUCTION Neutral-ionic transition [1,2] is a distinguished phenomenon accompanied by many anomalous features.

Experiments have revealed that charge, spin and lattice

degrees of freedom are nonlinearly coupled by the strong electron-electron and electron-lattice interactions which originate from the localized nature of the electron in this system.

We have investigated the one dimensional model including

these strong interactions by the quantum Monte Carlo simulatlons.[3]

In this paper,

we sketch the physical picture of this transition in TTF-Chloranil (TTF-CA) quoting the simulation results.[4]

PICTURE OF THE NI TRANSITION IN TTF-CHLORANIL Model We discuss the NI transition by the following one dimensional Hamiltonian. t

t

A

H = - Z t £ , £ + 1 (C£oC£+1o + C£+1oC£o) + ~ Z (-1)£n£ £o £ + U [ n£+n£+ + V £

0379-6779/87/$3.50

(i)

2 ! (u£ - U£+l ) 2 n£n£+ I + -ff

© Elsevier Sequoia/Printed in The Netherlands

498 t where C~o ( C ~ )

is the annihilation

(creation)

operator of the electron at site

with spin o .

U and V are on-site and nearest neighbor site Coulomb interactions,

respectively.

A is the effective

and acceptor

(even £) molecular

site energy difference between donor

(odd £)

orbitals and expressed by

& = I - A + U - 4V

(2)

where I is the ionization energy of the donor and A is the electron affinity of the acceptor.

The transfer

integral t£,~+ 1 is given by

t£,£+ I = T + u£ - uz+ 1

(3)

where u£ is the displacement

of the £-th molecule

in the appropriate unit.

dependence of t£,£+ 1 on u£ and u£+ 1 gives the electron-lattice strength is represented by S.

From the experimental

The value of S will be determined later.

interaction whose

results and theoretical

lations, we take the following values for each parameter. V = 0.7eV.

The

T=0.2eV,

calcu-

U=I.5eV

and

We change g across the tran-

sition. Without

the transfer

We first neglect

t£,£+ I.

The ground state is neutral

(each donor site is occu-

pied by two electrons while acceptor site is empty) when I - A > 2V, and is ionic (each site is occupied by one electron)

when I - A < 2V.

Lowering temperature

or

Ec'r

Ionic

V

Neutral

EMAe

>

2V

I-A

Fig. i. The three excitation energies ECT, hVcT and EMA C as functions of I-A. These energies are related to the electrlcal(~onduction~, optical and magnetic properties of the system, respectively.

499

applying pressure contracts the ionic phase.

increases V and drives the system into

Three excitation energies govern the physical properties

system (Fig.l). infinitely

the lattice,

far from, and to the neighboring

is the energy required to flip one spin.

site o $ the hole

this simple picture which ignores the transfer happens in the real system TTF-CA. to O N = 0 . 3

interpreted

(ii) The activation

is about 0.1eV which is much smaller than V [6]. (iii)

Experiments

shape

(inhomogeneous

[5] or by applying pressure

(iv) The magnetic

susceptibility

ESR signal of the remaining

These experimental

lattice interaction

[8] with

in the ionic

phase shows that there is a gap for the spin flip, and Mitani et al. the motional-narrowed

[7]. hvCT is

(ionic) domain into the

show that this domain structure

is introduced by impurity doping

much lower energy than hVcT ( = V).

--

However,

is unable to describe what

as the energy required to introduce a neutral phase.

EMA G

(i) The degree of charge transfer jumps from

spectrum shows a broad band, with an unsymmetric

ionic (neutral) structure)

(Fig.l)

respectively.

[5] not from 1.0 to 0.0 at the transition.

energy for the conductivity The absorption

respectively.

ECT, h~CT and EMA G are related to the

electrical (conduction), optical and magnetic properties,

Pl =0"7

of the

ECT and h~CT are the energies required to transfer an electron

[9] attributed

spin species to the spin soliton.

facts show that the electron hopping and the electron =

are essentialjabout

which we discuss below.

The effects of the transfer First, we consider only the electron transfer charge transfer P jumps from Pl =0"85 iments

(p I =0.7,

ON = 0 . 3 )

into account, because

to ON = 0 . 4 5 .

(hopping).

The degree of the

The discrepancy with the exper-

can not be get rid of as long as only transfer

(p l + p N ) / 2

is always larger than 0.5 in this case.

remains zero in the ionic phase, jumps at the transition 0.1eV and steeply increases

in the neutral phase.

is taken ~AG

to the value of about

ECT has a sharp minimum at the

transition point with the minimum value 0.28eV which is about one-fifth of 2V. On the contrary,

hVcT (the central energy of the absorption

0.8eV and is almost unchanged

spectrum)

The inversion of these two energies ECT and hVcT, which violates al exciton picture,

is explained as follows.

put the system at the transition point. degenerate. ground state,

First, neglect

the transfer T and

(CT-) excitons

from the ionic (neutral)

the excitation energy is the same value V irrespective

the CT-excitons

the convention-

The ionic and neutral ground states are

When we create charge transfer

of the CT-excitons

is about

from V.

as long as they are connected.

of the number

This means that the number of

is not a good quantum number when we introduce

the transfer T.

We should instead choose the domain wall between the neutral and ionic phases (NIDW) as the more fundamental

elementary

excitation.

are the two domain wall states, while the electron-hole

The connected

CT-excitons

pair is the four domain

500

I(~)

I(~) CT-Exciton e.h pair >

>

t w ECT ' h 2El) = 4 Eow

hVcr < Ecr

T-V

Fig. 2. The absorption spectrum I(~) in the two pictures - (a) the conventional exciton picture and (b) the NI-domain wall picture.

wall state.

By this picture,

the absorption spectrum forms a broad band reflecting

the band motion of the domain wall (Fig.2). width is about 4T.

domain wall), and ECT = 4EDw. explains semiquantitatively tron-lattice

Its center hVcT is around V.

The

The lowest edge is 2EDw (EDW is the excitation energy of the

interaction,

This value can be smaller than hVcT.

This picture

our simulation results on our model without

which, however,

is insufficient

the elec-

to describe the real

system TTF-Chloranil.

The effects of the electron-lattice

interaction

Now, we discuss the effects of the electron-lattice

interaction.

In the ionic

ground state, the lattice is always dimerized however small the electron-lattice interaction S is. dimerization

This is due to the gapless spin wave in the absence of S.

This

reduced p in the ionic phase, shifts the transition point to larger

A and diminishes

the jump (PI - PN ) and the average

(PI + p N )/2"

Comparing the exper-

imental results of p and our simulation results, we conclude that S is abour 0.2eV for TTF-Chloranil.

At this value of S, the alternation of the transfer is about

10% of the original value. In the dimerized

ionic phase, the ground states are doubly degenerate,

are connected by two kinds of kinks. solitons)

are schematically

shown in Fig.3.

cussed above, and ESS is EMAG/2 and is zero. of charge soliton

(Ecs) is a decreasing

that of spin soliton (Ess) an increasing point D, these energies

intersect.

into two lattice relaxed NIDW's. located on DC.

which

The energies of these kinks (spin and charge When S = 0, ECS is ECT/2 which we disAlong the transition line, the energy

function of S vanishing at point C, while function of S from zero at point B.

At

Along BC, the charge soliton is dissociated The NI transition of TTF-CA with S = 0.2eV is

The ESS is about 0.1eV and ECS is smaller.

The energy of the NIDW

501 ( =half

of ECS) is of the order of the room temperature,

which explains the pecul-

iar coexistence phenomena found under pressure or by impurity doping.

The compe-

tition between the thermal excitation of the NIDW's and the three dimensional Madelung

interaction

determines

the continuity or discontinuity

and the phase diagram in the Pressure-Temperature picture.

The NIDW

has

a fractional

to the d.c. conductivity,

however,

of the transition,

plane can be interpreted by this

charge and can carry current.

To contribute

charge soliton or NIDW alone is insufficient.

We propose a combined conduction mechanism of charge and spin solitons which gives ESS = 0 . 1 e V as the activation energy.

CONCLUSIONS The degeneracy of the ground states and the quasi one dimensionality the peculiar features of the system.

The excited states which connect these degen-

erate ground states play the major role.

In addition to the two dimerized

ground states, we have the third o n e - - t h e have introduced

the NIDW.

optical excitations

neutral state.

Various dynamical problems

and nonlinear

bring about

conductivity

Correspondingly,

ionic we

such as the relaxation after

are related to these excited states

and are left for the future study.

I sS

l[I . •

<1 Fig. 3. The energies of the charge soliton Ecs and spin sollton E~S (schematic). On the discontinuous transition line BC, E_ S is a decreasing functlon of S and is zero on the continuous transition line ~ Broken line beyond C ). ESS is, on the other hand, a increasing function of S.

502 ACKNOWLEDGEMENTS The authors thank Drs. Y. Tokura, T. Kaneko and Profs. Y. Toyozawa, T. Mitani, T. Koda and J. Tanaka for discussions.

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