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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