Phason excitations in the SDW state of (TMTSF)2PF6

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Phason excitations in the SDW state of (TMTSF)2PF6

S. Donovan, Y. Kim, L. Degiorgi, G. Grüner

To cite this version:

S. Donovan, Y. Kim, L. Degiorgi, G. Grüner. Phason excitations in the SDW state of (TMTSF)2PF6.

Journal de Physique I, EDP Sciences, 1993, 3 (6), pp.1493-1498. �10.1051/jp1:1993193�. �jpa-00246808�

Classification

Physics

Abstracts

72.15N 75.30F

Phason excitations in the SDW _state of (TMTSF)~PF~

S. Donovan, Y.

Kim,

L.

Degiorgi

and G. GrUner

Department

of

Physics

and Solid State Science Center,

University

of Califomia at Los

Angeles,

Los

Angeles,

CA 90024.1547, U.S.A.

(Received 30 December 1992,

accepted

5

February

1993)

Abstract. We have measured the

frequency dependent conductivity

at various temperatures below the SDW transition in (TMTSF )~PF~. We find _two distinct _resonances which _we ascribe to

intemal deformations and

pinned

mode oscillations of the SDW condensate. Furthermore, the spectral

weight

of the

pinned

mode resonance is found to be

nearly

temperature

independent

below the SDW transition. Our

findings

_are contrasted with various models and

suggestions

_on the

electrodynamics

of the SDW ground state.

Considerable progress has been made

recently

in

exploring

the collective mode

dynamics

of the broken

symmetry

state called the

spin density

_wave

(SDW) [Il.

The

electrodynamical

response ^& of the

ground

state is determined

by

^{both the} collective mode

&s~w

and

single particle

_&~~ excitations. As for _a

superconductor, single particle

excitations _are

expected

for

photon energies

^hw _> 2 A where 2 A is the SDW gap. The collective mode response arises at zero

frequency

^for a

superconductor,

^while for _a SDW

impurities

shift the mode to _a finite

frequency

_wo, the so-called

pinning frequency.

In either _case, in the clean limit

(fir

^'

< A,

where _r~ ^' is the

scattering rate)

at T

=

OK all the

spectral weight,

defined _as

j~

^Re

^&(w

^dw =

~

(I)

o

8

=

~~~~~

~~

^~

~~~

~'~~' _~ ~~'~ ~Urnber

density

of eie~t~~~ _~

~~~'llb

the bandmass, ^;s e~ ~~~~

to be associated with the collective mode. This is in contrast to that found for

charge density

wave

(CDW)

_systems where, ^due to the

large

effective _{mass m} * of the condensate, the

spectral weight

of the collective mode _resonance is small

[2].

We have

recently

observed

[3]

_a low

lying

resonance at

frequencies

well below the

expected single particle

_gap ^{~ ~} _m 30 cm~ ^'

(as

determined from the temperature

dependence

of the dc

h

conductivity

_«

= «~ exp

(-

^~ in the model

compound (TMTSF~PF~

below the SDW

kT transition

(Ts~w

= I1.5

K).

We

argued

that this _resonance is due to the

oscillatory

_response of

1494 JOURNAL DE PHYSIQUE ^{I N° 6}

the SDW condensate, the _q

=

0

phason

excitation and, in clear _contrast with that

expected

from

equation (I),

_a

strongly

reduced

spectral weight

has been found.

Several models have been

proposed

to account for _our

experimental findings.

One

explanation,

that the effective _mass is

large

due _to

coupling

to

phonons,

_can be ruled out as no

lattice distortion has been found in the SDW state

[4].

It has also been

suggested [5] that,

_as for

superconductors, long

_range Coulomb forces shift the

spectral weight

_away from the

pinning frequency

_{w~ up} to the

plasma frequency _w~.

This

model,

based _on the so-called Anderson-

Higgs

mechanism

[6],

should

apply

in _a

translationally

invariant system

only

to the

longitudinal

mode

(q

iiE while

leaving

the _transverse mode

(q

I E

),

_as

sampled

with

optical

measurements, unaffected. However, ^the transverse and

longitudinal

modes may be mixed due to

anisotropy

effects and the

randomly

situated

impurities [7].

It has also been

suggested [8]

that the mode observed may well be due to internal deformations

[7]

and not to the

oscillatory

response of the SDW. If this is the _case, the

pinned

mode _resonance which should be at

frequencies

well above the

spectral

_range where the modes due to intemal deformations _occur would most

likely

be above the gap, I.e.

hw~

_> 2 A.

Recently,

it has been

suggested

that

commensurability

effects _may

play

an

important

role and that these effects lead _to bound state

resonances below the gap

[9].

These bound state _resonances may have _a

large spectral weight

and thus

(because

of the conservation of total

spectral weight)

_may lead to the reduction of the

intensity

of the

pinned

mode _resonance.

Impurities

_can also lead _to bound states

lo,

I

I],

and in _an

analogous

_way also lead _{to a} reduction of the collective mode

spectral weight. Finally,

it

was also

proposed [12]

that

impurities

_may lead to _a

mixing

^{of the} _{q =} 0 magnon and

phason modes,

and that the low

lying

_resonance observed is _a magnon excitation at the

antiferromagne-

tic _resonance

frequency.

In order to address these

questions

_we have conducted

experiments

at various

temperatures

over an extensive

spectral

_range which spans the audio _to infrared

frequencies.

Standard

radiofrequency (rf~ techniques

_were utilized _{up to} I

GHz,

and the components ^{of the}

optical conductivity

d

= « j + I «~ were evaluated from the time

dependence

of the

discharge

current

[13].

In the micro- and millimeter _wave

spectral

_range resonant cavities

operating

at

3, 7, 9,

12,

35,

60,

loo and 150GHz _were

employed,

and the surface

impedance _2~

=

R~+

iX~

was measured. Our measurement

techniques

and

analysis

_are described elsewhere

[14].

For

a

good

metal R~ ^is

proportional

to the

absorptivity A(w

=

I

R(w ),

where

R(w

is the

reflectivity,

and thus _can be combined with

optical experiments,

conducted between 15 and

10~

_cm~

',

_{to construct} A

(w

over a broad

spectral

_range. The

optical

measurements described

here _were made _on mosaics and the

procedure

^has been described in _more detail in reference

[15].

A

Kramers-Kronig (KK) analysis

_was used to evaluate

«j(w

at various

temperatures.

In

figure

I _we show the

absorptivity

_at two temperatures, one above and _one well below

Tsow.

The

absorptivity

values measured with different

techniques

_are shown

together

with _a

Drude and Lorentz oscillator fit. At

high frequencies

^~°

>100cm~')

_a

temperature

2 _gr

independent

feature is found which is discussed in detail elsewhere

[15].

Above

Ts~w,

at 20

K,

the

frequency dependent conductivity

_can be well described with _a

simple

Drude

expression.

The Drude fit

gives

_a relaxation time

=

3 _cm~

', _placing

_{it well into the clean limit. This}

2 _{gr r}

leads,

with «~~

(20 K)

₌ 3 _x

10~

fl~ ^' _cm~ ^' and _a carrier concentration _n

= 1.4 _x

10~'

_cm~ ^~ _to

a bandmass of m~=

20m~,

in

qualitative

agreement ^{with the bandmass obtained from}

magnetic

measurements

[16].

Below

Ts~w

the measured

absorptivity

can be well

reproduced using

_a Drude oscillator _to model the uncondensed electrons and _an

underdamped

Lorentz

oscillator for the microwave _resonance. An

extrapolation

between the measured

points

is made

by joining

^{the different} sets of data

together using

the oscillator fit _{as a}

guide.

At each

temperature

^A

(w

is transformed

through

_a KK

analysis

to

give

« j

(w ),

_as shown in

figure

2.

TMTSF),PF,

m

~ /

~

~

~ /

~

$

~

~ _~/

~ ~ ~

~

°

~ ^~

' ~~~~~~

~~

)16,°°'' : _ll~l

_{sI do<o}

"

~~~~

^~'~'~~~

lo" lo"' lo° lo' lo' lo' lo'

frequency (cm"')

Fig.

I. The

frequency dependence

of the

absorptivity

both above (T

=

20 K) and below (T ₌ ^{2 K} Tsow in

(TMTSF)~PF6. Optical

measurements (solid line) _are shown together with both surface

impedance

(SI) measurements (circles and boxes) and _a

simple

harmonic oscillator (h.o.) fit (dashed and dotted line).

~~~~~'Z~~6

ZOK . tm4

a ,0K 6 _. Ploo÷iWW

~~

~

,,

'~#'~lii~i

_

+ f °,,

-, ^#

. ,

, Jf - fi. _-+

~

' ₊

] ^",

~

'

£ ",,'

u I .

~' I

~ _,

- , ~'~

a I

]-

_,

..~ i

. . ,

. ,

i

^'

lf'

lo"'

io° lo' lo'

lo' id

ftequmcy (cm-')

Fig.

2.- The

frequency dependent conductivity

both above and below Tsow for

(TMTSF)2PF6

determined from _a Kramers

Kronig analysis

of

figure

I. The

single particle

_gap, determined from dc

conductivity

measurements, is indicated in the

figure

with _{an arrow.} The

pluses

(+) _are the values of

« as determined

directly

from _a measurement of both R~ ^and X~ ^{in the microwave}

region.

In the inset, the temperature

dependence

of the normalized

spectral weight

of the various contributions to «sow (w below Tsow are

displayed,

where each has been normalized by the

spectral weight

of the Drude response at

20 K.

1496 JOURNAL DE

PHYSIQUE

I N° 6

A _resonance at temperatures below

Ts~w

is

clearly

evident _near 0. I cm~ ^' This _resonance

was

previously

associated

[3]

with the

pinned

mode _resonance. The

single particle

gap, as

established from the temperature

dependence

of the dc

conductivity,

is indicated

by

the _arrow in

figure

^{2. Earlier}

[3]

_we have associated the increase of «,

(w )

around this

frequency

with the

gap in the SDW state, however, the fact that this structure is also observed well above

Tsow [15]

_suggests that it has _a different

origin

and is most

probably

due to _an interband transition. The _reason for the absence of the gap structure in the

optical conductivity

is the

same as that in _a

superconductor

^{in the} clean limit _«

j

(w )

is small in the

spectral

_range around 2 A, and

consequently

the effect of the removal of this

spectral weight

leads _to

only

minor

changes

in the

reflectivity.

The detailed form of the low

lying

resonance was

explored by combining

^the

optical

^data

with

experiments

in the rf

spectral

_range. Below

Tsow,

^the

conductivity d(w)

has contributions from both the

thermally

excited electrons

d~~(w ⁾

^{and the condensed electrons}

&sow(w )(&(w )

=

&~~(w

⁺

ds~w(w )). ds~w

for

(TMTSF)~PF~, together

with the conduc-

tivity

observed

[17]

in the material

Ko_~MOO~

^{in the CDW} state are

displayed

in

figure

3. In

both _{cases we} find _a broad structure at low

frequencies together

with _a well defined _resonance

in the

high frequency

end of the

spectrum.

^{In the CDW} system ^{the low}

frequency

behavior has been

analyzed

in detail and is _now well understood

[7]

_to be due to the intemal deformations of the collective mode.

Furthermore,

the _resonance which appears ^{at loo GHz for}

Ko_~MOO~

^is due _to the oscillations of the entire collective mode. This _resonance is

usually

referred _{to as} the

pinned

mode _resonance at the

pinning frequency

_wo. Extensive

experiments [2, 18]

_on several materials with _a CDW

ground

state

clearly

establish that _wo is indeed determined

by pinning

to the

impurities,

and that it

represents

^the oscillations of the entire collective mode

subject

to an

average

restoring

force whose

spring

_constant is

given by

k

=

m*

w(.

Much less is known

104

/j

io3

)

jj

₁₀₂

~~~~~~~~~~~

S~ ~~

E T=2K

~~~ /.

i

^~

j

^loo

§~

( _K0.3MO°3

" °

T=40K

io-2

/

o-3

ioi io2 io3 io4 ios io6 io7 io8 io9 trio ion

Frequency(Hz)

Fig.

3. -The

frequency

dependence of the real part of the SDW conductivity

dsow(w)

for (TMTSF )~PF6 and

&~ow(w

) for the CDW compound KO~MOO~. The measured

conductivity

is shown (boxes and circles)

together

with the output ^of the KK

analysis

(solid and broken lines). The

measurements shown _were made _at different temperatures, ^{but in each} case the measurement was made

well below the transition temperature.

about the

electrodynamical

_response of the SDW materials.

Experiments

_on SDW

samples

with

varying impurity

concentrations _are

currently underway

in order to determine the

dependence

of

«j(w)

on

impurity

concentration.

However,

the

striking similarity

of the

frequency dependent

_response of these two systems seen in

figure

3

strongly

_suggests that the low

frequency

mode in

(TMTSF _)~PF~

is due _to internal oscillations of the SDW and the mode

around o-I

cm~'

_{is the response of the}

pinned

SDW.

Therefore,

_we conclude that for

KO~MOO~

^and

(TMTSF)~PF~

both the intemal mode deformations and the

pinned

mode

resonance appear well within the

single particle

_gap,

hwo

_< ² A, ⁱⁿ contrast to the

suggestion

of reference

[7].

The temperature

dependence

of the

spectral weight

of the

pinned

SDW mode _was evaluated

by fitting

the observed

conductivity

with _a function of the form

&

~

~ _~ ~

n(T)

^e~ _r ^I

ill

w

~~ ~~~

mb(

' I_{W T}

)

₄

7r

1(w I

w 2) ^1w r

j

^~~~

where the first _term

d~~

^{is the Drude} response of the

thermally

excited

electrons,

taken from the

temperature dependent

dc

conductivity

_«~~

=

~~~ _~

below the

transition,

and the second m~

Lorentzian _term

&s~w

describes the

pinned

mode _resonance, with

D~

^{the SDW}

^plasma frequency

and r the SDW

damping.

A temperature

independent

_r has been used for

T<Ts~w.

The

spectral weight

associated with the _two contributions in

equation (2)

is

displayed

in the inset of

figure

2 _{as a} function of temperature. ^{It is clear from the}

figure

that in

contrast to the temperature

dependent

Drude

contribution,

the

spectral weight

of the

pinned

mode _resonance is

only weakly

temperature

dependent

and is

significantly

reduced from the

spectral weight

associated with the Drude

conductivity

above the SDW transition. Our observations therefore rule _out the

Anderson-Higgs

mechanism

[5]

_as it would lead to an

exponential

freeze out of the

spectral weight

of the

pinned

mode _resonance with

decreasing

temperature. ^The strong ^{reduction in the}

spectral weight

of the

pinned

mode has been

independently

confirmed with the measured low

frequency

dielectric constant e

[13].

Just below

Tsow,

_e ^{is dominated}

by

low

frequency excitations,

but _at T

= 2 K these low

frequency

modes freeze out and

e is determined

by

the

pinned

mode _resonance. The

spectral weight

obtained

by

this method is also

displayed

in the inset of

figure

2 and it is more than _two orders of

magnitude

below the

spectral weight

associated with the Drude response at 20 K.

Presently

we can

only speculate

on the

origin

of the

missing spectral weight

in the SDW

state. As the total

spectral weight

must be the _same both below and above the transition

lgrne~

^CC

(~,

T

»

Tsow

~'°

"

~

^~~~

°'

~~

~~~~(w

dw

=

~

~~ _"°~~~~

there _must be excitations associated with the SDW response in addition _to those found in the microwave

region

and below. One

likely explanation

is that the

missing spectral weight

is associated with bound _states

accompanying

the SDW condensate. In _{contrast to}

CDW'S,

it is

expected

that bound _states due _to

impurities

_can

readily

_occur, and the

reasoning

is _as follows

[10].

In _a CDW the

periodically

modulated

charge density

_can

adjust

_to the electrostatic

impurity potentials by adjusting

its local

phase

to minimize the total energy

(electrostatic

₊

elastic) gain.

On the other hand, the SDW

ground

state can be viewed _{as two}

CDW'S,

one for each

spin direction,

with _a CDW modulation _on the sublattices which differs

by

_gr. As the

pinning

in _an SDW is also due _to electrostatic forces

lo, 19],

_a full

adjustment

of the

phase

cannot _occur

simultaneously

for both

spin sublattices, leaving

_a net energy

gain

which is much

larger

than for _a CDW.

However,

the electrostatic energy can be lowered

by removing

1498, JOURNAL DE

PHYSIQUE

I N° 6

electrons from the condensate _to form _a bound _state about the

impurity.

In

addition,

the

spectral weight

of these bound states is

expected

to be

significantly larger

than in CDW systems. ^The

spatial

extension of _a bound state is

given by

the coherence

length

hv~

f ₌ ,

-, and with _a Fermi

velocity

_{v~ m} lo

cm/s,

and

single particle

_gap A/h

m 15 cm~

WA ,

f _m

10~ h,

which is

significantly larger

than the coherence

length

for

typical

CDW systems.

As the matrix element for

optical

transitions of the bound _state is

proportional

_to its

dipole

moment and hence f, a

large

coherence

length

leads to a

large optical spectral weight

associated with that transition.

Several

microscopic

models also suggest a broad spectrum ^of

impurity

induced bound states

lo,

I

I]

below the

single particle

_gap. An altemative model

[9]

_suggests that _as these materials

are near to

commensurability,

soliton excitations could _occur below the gap. These excitations

hv~

would also have _a

spatial

extension of

f

=

and therefore would have _a

large spectral

WA

weight.

At present we do _not have clear

spectroscopic

evidence for states below the

single particle

_gap. Furthermore, since the

missing spectral weight

is much smaller

(m

5 fb than that associated with the temperature

independent

feature above the gap, we cannot

experimentally

determine whether the

missing weight

is above _or below the continuum of

single particle

excitations.

Acknowledgments.

This research _was

supported by

the National Science Foundation grant ^{DMR 89-13236. Useful}

discussions with

H.Fukayama, K.Maki,

G.

Mihdly,

and A.Zawadowski _are

gratefully

acknowledged.

References

Ill GRUNER G. and MAKI K., comments condensed Matter Phys. IS (1991) 145.

[2] GRUNER G., Rev. Mod. Phys. 60 (1988) l129.

[3] QUINLIVAN D., KIM Y., HOLCzER K., GRUNER G. and WUDL F., Phys. Rev. Lett. 65 (1990) 1816.

[4] POUGET J. P.

(private

communication).

[5] MAKI K. and GRONER G., Phys. Rev. Lett. 66 (1991) 782.

[6] ANDERSON P. W., Basic Notions of Condensed Matter

Physics (Benjamin/Cummings,

CA, 1984).

[7] LITTLEWOOD P.,

Phys.

Rev. B 36 (1987) 3108 _; WONNEBERGER W.,

Synthetic

Metals 43 (1991) 3793.

[8] LITTLEWOOD P.

(private

communication).

[9] WONNEBERGER W., Solid State commun. 80 (1991) 953.

[lO] T0TTo1. and ZAwAoowsKi A.,

Phys.

Rev. Lett. 60 (1988) 1442.

[I Ii ZAwADowsKi A. and T0TTo 1.,

Synthetic

Metals 29 (1989) F 469.

[12] FUKAYAMA H.

(private

communication).

[13] MIHALY G., KIM Y. and GRUNER G., Phys. Rev. Len. 66 (1991) 2806.

[14] DONOVAN S., KLEIN O., HOLCzER K. and GRUNER G., to be

published.

[15] DONOVAN S., DEGIORGI L., KIM Y. and GRUNER G., submitted _to Europhys. ^Lett. 19 (1992) 433.

[16] MORTENSEN K., TomKiEwicz Y. and BECHGAARDK.,

Phys.

Rev. B 25 (1982) 3319.

Using

the measured value of _X for _{a one} dimensional free electron gas

gives

mjm~ ₌ ^3.

[17] MIHALY G., KIM T. W. and GRIjNER G.,

Phys.

Rev. B 39 (1989) 13009.

[18] KIM T. W., DONOVAN S., GRONER G. and PHILIPP A.,

Phys.

Rev. B 43 (1991) 6315.

j19] TVA P. F. and RuvALos J.,

Phys.

Rev. B 32 (1985) 4660.