Addendum - A landau theory for the displacive phase transitions in TTF-TCNQ

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Addendum - A landau theory for the displacive phase transitions in TTF-TCNQ

M. Weger, J. Friedel

To cite this version:

M. Weger, J. Friedel. Addendum - A landau theory for the displacive phase transitions in TTF-TCNQ.

Journal de Physique, 1977, 38 (7), pp.881-882. �10.1051/jphys:01977003807088100�. �jpa-00208652�

881

ADDENDUM

A LANDAU THEORY FOR THE DISPLACIVE PHASE TRANSITIONS

IN TTF-TCNQ

M. WEGER and J. FRIEDEL

Laboratoire de

Physique

^des

Solides,

Université

Paris-Sud,

⁹¹⁴⁰⁵

Orsay Cedex,

^France

(Reçu

^{le 11 mars}

1977, accepté

^{le 23 mars}

1977)

LE JOURNAL DE PHYSIQUE TOME 38, JUILLET 1977,

Classification

Physics ^Abstracts

7.158 ^- 7.396 ^- 7.488 ^- 8.260

In our paper

(J. Physique

³⁸

(1977) 241)

^{it was shown} that the interaction between

neighbouring TCNQ

chains in the a-direction vanishes

(or nearly vanishes)

^{for a}

quarter

^filled

band,

and thus is _very small for TTF-

TCNQ (0.29

^filled

band).

The actual

period of 2 a,

observed between 48 K and 54

K,

^was attributed to devia- tions from this

cancellation,

^{due to} molecular

polarization,

^or thermal fluctuations.

Actually,

the interaction between the CDW on the

TCNQ chain,

_pQ, ^and the libration on the TTF

chain,

xF

(section 3),

is sufficient

by

itself to account for the 2 a

period

^{in this} temperature range.

Let :

where :

pQ(u, ^v)

⁼ pQ ^cos

(2 nvbla

⁺ lpl

+ ka ua)

and similar

expressions

for the other components. ^These

expressions

^are

applicable

^{above 38 K.}

The

expression

^{for the} Free energy in Landau

theory

^is

given by :

with d ⁼ 0 or

al2 (i.e.

^{here we}

^neglect All { a } altogether,

^{in contrast with the}

previous work).

^{The +}

sign applies

^{for two modes of the same} type

(both

^{CDW’s or both}

librations)

^{and the -}

sign applies

^{for two modes of}

opposite types. A13 { 0 }

^and

A24 { 0 }

^vanish

by symmetry.

^{For the fourth order terms, we} shall restrict our-

selves to terms with i

= j

^{= k =}

l, except

^for

C3434

⁼

34

^{which is}

big

^and

important

ⁱⁿ

making

the Peierls transition

temperatures

^{of the}

TCNQ

^{and TTF} chains close

together (48

^{K and 54}

K;

^{see section}

4). Thus,

where (P 12 (P 1 - CfJ2, etc. ;

C11 = C1111,

^etc.

This

expression applies

^above 38 K. Above 48

K,

_PF ⁼

0,

_XQ ^{= 0.}

Therefore,

Substituting

^this

value,

^{the term}

quadratic

ⁱⁿ _pQ ^{is :}

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01977003807088100

882

This term

gives

^a clear minimum for

ka

⁼

7r/a,

^{i.e. a 2 a}

period (see Fig.

⁵

!).

^{This term} should dominate near

the

TCNQ

transition

temperature,

^{and have a} considerable influence also ^at lower

temperatures.

Thus,

^{the 2 a}

period

follows in a

straightforward

and natural _way from the

opposite parity

^{of the} p

and x

modes under reflection in the

plane perpendicular

^to the a-direction. The

staggered positions

^{of the}

TCNQ nitrogen-TTF sulphur bonds,

and the short

period

^{of the}

CDW,

^{ensure that}

A 14

^is

big enough,

^{so that in}

the second order it ^can overwhelm terms like

All 1 a }, Cl 4,

^{or other terms, which}

might give

^{rise to other}

structures

already

in first order.