Magnetotransport in Quasi-Two-Dimensional Organic Conductors Based on BEDT-TTF and its Derivatives

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Magnetotransport in Quasi-Two-Dimensional Organic Conductors Based on BEDT-TTF and its Derivatives

M. Kartsovnik, V. Laukhin

To cite this version:

M. Kartsovnik, V. Laukhin. Magnetotransport in Quasi-Two-Dimensional Organic Conductors Based on BEDT-TTF and its Derivatives. Journal de Physique I, EDP Sciences, 1996, 6 (12), pp.1753-1786.

�10.1051/jp1:1996187�. �jpa-00247280�

Magnetotransport in Quasi.Two.Dimensional Organic

Conductors Based

_on

BEDT-TTF and its Derivatives

M.V. Kartsovnik (~>*) and V.N. Laukhin

(~'**)

(~ Institute of Solid State Physics, ^Russian

Academy

of Sciences,

Chernogolovka,

142432 Russia (~) ^{Institute of Chemical}

Physics,

Russian

Academy

of Sciences,

Chernogolovka,

142432 Russia

(Received

28 May 1996. accepted 13

August 1996)

PACS.71.20.Rv

Polymers

and

organic compounds

PACS.71.18.+y

Fermi surface: calculations and measurements; ^effective mass, 9 factor PACS.72.15.Gd

Galvanomagnetic

and other magnetotransport effects

Abstract. In this short _{review we} discuss the magnetotransport

properties

of the most

popular

series of

quasi-two-dimensional organic

metals and

superconductors, namely fl-,

_K- and

cv-salts of BEDT-TTF

(shortly, ET)

and _some

compounds

based _on the ET derivatives, BEDO-

TTF and BEDT-TSeF. We concentrate _on the results of the Fermi surface studies obtained

by

means of Shubnikov-de Haas

as well _{as a new very} informative

angle-dependent

semi-classical

magnetoresistance

oscillations

(AMRO)

experiments. ^{The results}

reported

here _were obtained mainly due to close collaboration of different

physical

and chemical groups in

Chernogolovka (Russia),

which have been

organized

and led

by

Prof. I.F.

Schegolev.

1. Introduction

The orgamc conductors based _on the

bis(ethylenedithio)tetrathiafulvalene

molecule

(BEDT- TTF,

_or,

shorter, ET)

have

initially

attracted attention due to the

discovery

of the ambient

pressure

superconductivity

in _a

layered

cation radical sait

fl-(ET)213

_m 1984 [1]. ^Further extensive efforts _on the

synthesis

^{and studies of} new salts of ET and its derivatives _gave rise to a new

generation

of

quasi-two-dimensional compounds

_[2] with

properties

_rangmg from

magnetic

dielectric to

superconducting, depending

_on the chemical

composition

and external conditions such _as

temperature,

pressure and

magnetic

field.

It is essential to know the electromc band structure of these materials _m order to under- stand the nature and

specific properties

of their normal and

superconducting

states. A direct information _on the Fermi surface

(FS),

_one of the most

important

characteristics of the elec-

tromc

system,

can be obtained from the

magnetic

field studies.

This, however,

_reqmres ^the

fields

strong enough

to

provide

the Larmor

radius,

_{rL '~}

cpfleB (where

B is the

magnetic

field induction, _{pF is} the characteristic Fermi momentum m the

plane perpendicular

to the field

direction,

c is the

light velocity

and _e is the electron

charge) sufliciently

smaller than the

electron _mean free

path

_{1, ~}

= rL

Ii

_« 1. The ratio _rL

Ii

can be estimated from the

resistivity

_p

j*)

Present address: Walther-Meissner-Institut, Walther-Meissner-Str. 8, 85748

Garching, Germany.

(**)

Author for

correspondence.

Present address: Institut de Ciencia de Materials

(CSIC), Campus

de la UAB, 08193 Bellaterra,

Spain. (e-mail: vladimirslicmvax.icmab.es)

©

Les

Éditions

de

Physique

1996

and carrier concentration _n,

using

the standard kinetic

mortel,

_~

r-

pnec/B. Taking

the lowest

resistivity

value known among the ET-based

metals,

_p à

10~~

fl _cm, that is characteristic of

high-quality single crystals

of

flH-(ET)213

and

fl-(ET)2IBr2

at low

temperatures [3],

^and a

typical

concentration _n à 10~~

cm~3,

_one has ~ r-

20/B,

where B is measured in teslas. For many other ET

salts,

such _as

superconductors K-(ET)2X,

this ratio is

expected

to be _even

an order of

magnitude large

because of their

higher resistivity- Therefore, according

to these estimations, the

strong-field limit,

_{~ <} 1 _can be

hardly

achieved in the available

steady fields,

< 20 30 T.

Notwithstanding

the initial

expectations

had been rather

pessimistic, prominent

Shubnikov- de Haas

(SdH)

oscillations _were discovered in 1988 in the

magnetoresistance

of

fl-(ET)2IBr2

_(4]

and

~-(ET)2Cu(NCS)2

_{(5] in} moderate fields of

r- 10 15 T. These observations _gave the first direct evidence for the existence of _a well defined

FS, provided quantitative

information _on the FS parameters

and, hence,

stimulated _a tremendous surge of interest to the

magnetic

field

studies of the

organic

metals based _on the ET molecule and its derivatives.

A

great

^{deal of the}

experimental

data obtained to date

(see,

_{e-g- [fil)} have

considerably

contributed to

understanding

the electromc

properties

^of these materials and, in

particular, proved

that the rather

simple

extended Hiickel mortel calculations in many cases

give

_a

surpris- mgly good description

of the electronic band structures. In spite ^{of their}

complicated

chemical

compositions,

their FS _can be

basically represented by

_{one or} several

slightly warped cylinders

with the _axes

perpendicular

to the

crystal highly conducting plane.

Sometimes the

cylinders

cross the first Brilloum _zone

boundary, giving

rise to a

multiply

connected FS

consisting

of

bath

cylindrical

and _open parts. ^Due to the

extremely high anisotropy (the

ratio between the

in-plane

and

inter-plane

resistivities is

typically

r-

10~~ 10~3),

these

compounds

_may

be

regarded

_as

quasi-two-dimensional (Q2D) metals,

thus

representing

_an intermediate Mass between the conventional three-dimensional metals and artificial two-dimensional structures.

This,

of _course,

directly

influences all the

magnetotransport properties,

often

leading

to _{a non-} conventional behaviour of bath the semiclassical

magnetoresistance (MR)

and SdH oscillations and

causing

_a number of novel

phenomena,

for

example,

semiclassical

angle-dependent

MR _os-

cillations

(AMRO)

which have _proven themselves to be _a

powerful

tool for the FS

investigation

of these

compounds-

This _paper presents a brief review of the

magnetotransport

studies of

Q2D organic

metals

based _on the ET molecule and its

derivatives,

which _were carried eut

by

the

Chernogolovka

group

(ISSP

and

ICP)

led

by

I.F.

Schegolev

for _{many years.} Some of recent results _were ob- tained

during

_a close collaboration of the

Chernogolovka

_group and the _groups from the

I<yoto University (Kyoto),

Walther-Meissner-Institut

(Garching),

Laboratoire de

Physique

des Solides et SNCMP

(Toulouse),

Laboratoire de

Physique

des Solides

(Orsay),

and State

University

of New York

(Buflalo).

In Section 2 _we will present SdH oscillations and semiclassical MR studies in

apparently

the

simplest Q2D metals, fl-(ET)2X

with X

=

IBr2 and13,

with the FS

mainly

characterized

by

_a

smgle cyhnder.

We will also

briefly.

_{review our}

understanding

of the AMRO

origmating

from the

specifics

of the electron motion _on the

shghtly warped cyhndrical

FS which _were found for the first time _m

fl-(ET)2IBr2.

In Section 3 the

compounds

of the

~-(ET)~X family

will be discussed. As shown

by

_numerous

experiments,

the FS of the salt with X

=

Cu(NCS)2

consists of bath _a

cylinder

and open sheets

separated

from each other

by

_a small energy gap,

being especially

smtable for

studying magnetic

breakdown

(MB) phenomena,

_m

particular,

the quantum interference eifect _in the coherent MB regime. The semiclassical AMRO demonstrate

a rather

comphcated

behaviour

reflecting

_most

likely

the electron orbits _on the closed

cyhndrical (2D AMRO)

^and open

(1D AMRO)

parts of the FS.

Very

recent results _on the FS studies of

the

highest-Tc

_organic

superconductors, ~-(ET)2Cu[N(CN)2]K

with X

= Cl and Br will be

R~, ^Q

19.94

10 11 12 13 14 15

B, T

Fig.

l. The magnetic ^field dependence of the resistance measured

along

the _a-axis of

fl-(ET)2IBr2

in

magnetic

field tilted, in the plane perpendicular to the _a-axis, by 11° from the normal to the

ab-plane;

T

= 1.45 K.

also

presented

in Section 3. Section 4 is devoted _to the

a-(ET)2MHg(XCN)4 compounds.

Their behaviour in

magnetic

^fields is

currently

of

special

interest due to _a number of

puzzling

anomalies

originated

most

likely

from _a

unique

co-existence of

Q2D

and

quasi-one-dimensional (QID)

FS parts. Section 5 will describe the MR

properties

of _{some new}

compounds,

based _on

the ET derivatives:

(BEDO-TTF)2Re04

_*

2H20, À-(BETS)2FeC14.

2.

p-(ET)2X

Salts with X

=

IBr2

and

13

2-1- SdH OSCILLATIONS IN

fl-(ET)2IBr2.

Since the

discovery

of the

superconductivity

in the salts

fl-(ET)2X

with X

= 13 (1] and

IBr2 (î],

the _{progress m} the

sample preparation technique

led to the

synthesis

of

high quality crystals

of these

compounds

_[8] and enabled the

observation of the SdH oscillations of two diiferent series and other

galvanomagnetic

^eifects

reflecting

the

Q2D

nature of their electromc

systems.

A

general

_view of the fast SdH oscillations _m the

in-plane,

1-e-

parallel

to the

highly

_con-

ducting ab-plane,

is

displayed

in

Figure

1. The oscillation

frequency,

F

=

Fol cos9,

where

Fo

₌ 3900 T and 9 is the

angle

between the field direction and the normal to the

ab-plane, corresponds

to the FS

cylinder

_{occupymg m} 55% of the Brillomn _zone

(BZ)

_[9]. A rather

heavy cyclotron

_{mass, mc} re

4.smo (mû

is the free electron

mass),

and

Dingle temperature,

TD ~S oA

K,

have been estimated from the

temperature

and field

dependencies

of the SdH

amplitude according

to the well-known formula

(see

_e-g-

[10]),

~~

_"

ÎÎÎnhÎÎÎ~ÎÎÎÎÎ~ÎÎÎÎÎÎÎ'

^~~~

where _uJc

=

ehB/mec,

the

cyclotron frequency

and _p is the harmonic index

(in

the

present

case p =

1)-

The

warping

of the FS

cyhnder

^is _very ^{small and has} no considerable eifect _on the

angular dependence

of the oscillation

frequency [9,11].

However, _{as seen m}

Figure 1,

it causes a

promurent beating

with trie

frequency Fbeat(9

=

o°)

re 30 T- This _means that in fact _two

6Ra/Ra

ù-13

o-i

o.i i

o,io

8 10 12 14

B,T

Fig.

2. The superposition ^of the fast and slow SdH oscillations in

fl-(ET)2IBr2

_in the field tilted

by

= 17° from the normal to the

ab-plane

towards the a-axis; T

= 1.45 K.

extremal _areas.

)j~ (Fo Fbeat)

and

)j~ (Fo

₊

Fbeat),

contribute to the SdH eifect.

Assuming

trie electron

dispersion

law in trie

form,

e(k)

=

e(k~, _k~) 2t~ cas(k~à), (2j

where trie _z and y axes are directed in trie

crystal ab-plane,

_z 1 _z, y and d is trie

interlayer spacing,

trie ratio between trie _transverse

overlap integral

tz and trie Fermi energy SF is _es-

timated _as

tzlef

"

Fbeat/2Fo

~S 4 x

10~3.

_{Trie absolute values of}

SF and trie bandwidth in trie

z-direction, 4tz,

_can be

roughly

evaluated under trie

assumption

of trie

quadratic isotropic in-plane dispersion,

_SF ~É

ehfo/mec

à

103 K;

4tz à 15 K, _m fair agreement with other

estimations.

In _{contrast to} trie

frequency

of the oscillations, their

amplitude

exhibits

strongly

_non-

monotonous

dependence

_on the

tilting angle

9. In

particular.

_a

strong

enhancement of the

amplitude

_was found at the

angles

9 _re -2î° and +30° when the field _was rotated in the

plane perpendicular

to the a-axis

[9,11].

This

behaviour,

_{as was} first noted

by Yamaji [12j,

_is

closely

related to the

Q2D

nature of the FS and will be discussed later.

In addition to the fast SdH oscillations with the

frequency Fo,

much slower oscillations

were found under the field

applied

at small 9

[4, 9].

^A

typical example

of the

superposition

of the two series _is shown _m

Figure

2. The

periodicity

in scale

1/B, mdependence

of the

phase

_on

temperature

and

gradual

_mcrease of the

amplitude

at

coohng

the

sample

allow _us to attribute the slow oscillations to the SdH eifect- The

frequency, Fsiaw

_re 50 T

corresponds

to the

k-space

area of 4-8 _x 10~3

cm~~

or re o.6% of the BZ cross-section. Trie existence of such _a small FS cross-section _{is not}

predicted by

trie band structure calculations

[13j.

Trie

Shoenberg

^eifect

(magnetic interaction) [loi

_can be ruled _{out as a}

possible explanation

due to trie

following

_reason: trie influence of trie

magnetic

interaction should increase with

lowering

trie

temperature;

^{in trie}

contrary,

^trie

amplitude

of trie slow oscillations

changes

with

temperature

much slower than that of trie fast _ones,

yielding

trie

cyclotron

_mass of

only

m

o-smc [4,9j-

Above 3 K

only

trie slow oscillations bave been detected _so far. Another

possibility

to

explain

R~,

^~

oôs

oôo

o26

O.20

o,iô

oie

Qo5

o

10 _{50 90} 130 170

9, degrees

Fig.

3.

Angular dependence

of the

interlayer

MR of

fl-(ET)2IBr2

in the field B

= 14 T

rotating

_in

the

plane nearly perpendicular

to the a-axis (qJ ₌ 95°); ^T ₌ IA K.

trie slow oscillations coula be _an interference of diiferent

cyclotron

orbits

(this

eifect will be considered in Sect.

3).

This would

imply

_{a more}

complicated multiply

connected FS

that,

agam,

disagrees

with trie theoretical

prediction _[13].

Therefore, although

the existence of _a

slightly warped cyhnder

_{as a} main motif of the FS is

proved by

the SdH

experiments,

some details _are not clear

yet

and need further

investigation.

2.2. SEMI-CLASSICAL MR ANISOTROPY _AND AMRO _IN

fl-(ET)2IBr2.

The _most remark-

able feature found in the semi-classical MR _was

strong

^AMRO

periodic

_m scale of tan 9

[9,11].

These oscillations _are shown _m

Figure

3 for the

magnetic

field

rotating

_m the

bc-plane.

The

position

^of the oscillations does not

depend

_on the field _or

temperature. Increasmg

the tem-

perature

^from 1.5 to 4.2 K reduces their

amplitude by

_a factor of

r- 1.5

[11].

Yamaji [12]

was the first who

suggested

that the

strong periodic

_mcrease in MR of _a

Q2D

metal at

rotating

the

magnetic

^field _may be caused

by

_a

simple geometrical

reason- He noted that at certain

angles satisfying

the

condition,

dk F tan

9n

=

7r(n -1/4),

_n

=

1, 2,.

,

tan 9 _> 1,

(3)

trie _areas ofthe

cyclotron

orbits _on trie FS determined

by

trie

dispersion

law

(2)

with

e(k~, ky)

₌

h~k(/2m

^{do not}

^depend

on trie transverse wave vector

kz,

to trie accuracy of trie ratio

~/ =

tzlef

< 1- Of _course this should lead to _a considerable enhancement ofthe SdH

amplitude

and

disappearance

of the beat-like

behaviour,

in

agreement

^with the

experimental

^result men-

tioned above. As for the semi-classical MR, the numerical calculations

by Yagi

et ai.

[14j

^indeed showed _a

strong

mcrease of the

interlayer

MR at trie

angles (3)- Further,

a detailed

analytical

consideration of _a

Q2D

metal with _a

general

form

in-plane dispersion

made

by Peschansky

et ai. [15] ^{in the} semi-classical

approximation

confirmed this result- A _more

transparent

^inter-

pretation

_was done

by

Yakovenko et ai. in [16] ⁱⁿ the

following

_way- Under the conditions

~/,~ < 1, the transverse

resistivity

_may be written _as

pzz =

~o~

(4)

az~ +

o(~2~2)

where

aÎÎJ

c~

(ù]) (angle

brackets _mean the average over

kz).

At _{a common} field

direction,

_pzz,

is determined

only by

_a finite transverse

velocity, (R)),

and saturates _m

strong

^field.

However,

at the

special

field directions at which the

cyclotron

orbit _area does not

depend

_on the

position

of the orbit

plane Kz

the time

averaged

transverse

velocity

for _any of the orbits vanishes:

"~~~~~ ~~~~~~~ ~~~~ÎÎÎÎ~~~ ~~~ÎÎ~ÎÎ~~~~'

~~~

and _so does

aÎÎl.

_{In that}

case, the

resistivity,

_pzz, is determined

by

the small second term in

the denominator of

(4)

and grows up as ~~ c~

H~. Indeed,

the

sharp change

to _a

non-saturating

field

dependence

_was found in the transverse resistance of

fl-(ET)2IBr2

at

turning

the field to the

angles corresponding

to the AMRO

peaks

_{[11] k}

The condition

(3)

for the critical

angles 9n

_was

generalized

in [16] ^{for the}

dispersion

law written in trie

form,

e =

e(kz, _ky) 2tz cos(kzd

₊

k~u~

+

kyuy), (6)

characteristic of _a

low-symmetric system

_m which electrons

hop

between trie 2D

layers along

trie vector h

=

(u~,

_uy,

d):

[tan

_Ùni

=

lR(n -1/4)

+

(k~~~~~, U)i/Lt~~~d, (7)

where _u

=

(u~, uy),

k)j~~~~ ^{is the Fermi wave vector}

component

in the 2D

plane

whose pro-

jection

_on the field rotation

plane, kf~~~,

is

maximal,

and the _signs +

correspond

to the

positive

and

negative 9, respectively- Using

the relation

(7),

it is

possible

to determme the FS cross-section and the direction of trie electron

hopping

vector from trie A&lRO

positions

found in the experiment

[16]. Figure

4 sho~vs the result for

fl-(ET)2IBr2 _(16j

which is in

good agreement

with the SdH data and the band structure calculations. Later detailed studies of the

angular dependence

of the dHvA effect [17] have also confirmed the

predicted

behaviour of the quantum oscillations at the critical

angles (î).

Worth of

noting,

the

periodicity

of AMRO in tan 9 is found

experimentally

to hold _even better than

predicted by theory.

The conditions

(3)

and

(7)

_are obtained

assuming

tan 9 _> 1.

However,

the AMRO observed in

fl-(ET)2IBr2 keep

trie

periodicity

down to trie lowest critical

angles

for ~vhich tan 9 < 1

[16]

Turnmg

_now to the

dependence

of trie _transverse MR _on trie field direction _m trie

highly conducting ab-plane,

a

surprismgly _{strong amsotropy}

bas been found for

fl-(ET)2IBr2 _[11].

As

is seen m

Figure

à, trie _maximum to minimum MR ratio _{is r-} 10. This result _was

reproduced

_on

several

samples

and _can be

hardly explained

within the

isotropic

relaxation time

approximation

for _a

simple cylindrical

FS

presented

in

Figure

4. A

possible

_reason for this

amsotropy

_may be _a

highly

anisotropic in the

ab-plane

relaxation time. On the other

hand,

_a

qualitatively

diiferent character of the field

dependencies

of the MR

[11j,

may reflect

changes

_m trie electron orbit

topology, depending

_on trie field orientation _m trie

ab-plane-

Another

argument

^{in favor} of _a

topological

reason of the

amsotropy

_may be _a sudden

vanishing,

at _some field

orientations,

a

[1$él)/2

1 /

' ' / / / / ,

©cm-' _//

/ ^°

/ / 1 /

b

'

1 ' '

1 '

' '

1 1

1

Fig.

4. The transverse cross-section of the FS

cylinder

in

fl-(ET)2IBr2 (thick fine)

deduced from

the AMRO parameters

using

the equation

(7).

The thin fine

interpolates

the

experimental

points

kf~~l(Ù) (see text).

of the

sharp peak

in the

R(9)

_curves which is

normally

observed at 9 _- 90° and

corresponds

to

switching

from closed to open orbits

[16j.

Thus,

like in the SdH

studies,

the results _on the semi-classical

MR, establishing

the

weakly corrugated

FS

cyhnder

_{as a main} motif of the

FS, suggest

^{the existence of fine details which}

are not

yet

resolved.

2-3- THE

fl-(ET)213

SALT. It is well known that this

compound

_can exist at low tem-

peratures

m either of two states,

3L-

and

flH-states,

which _are characterized

by

_very different

superconducting

transition temperatures,

Tc

_m 1.4 and 8 K,

respectively [18,19j.

The differ-

ence in

Tc

is caused

by

_a small difference in the

crystal

structures; ^{whereas the}

positions

of the terminal

ethylene

_groups of the ET molecules _are

completely

ordered in the

flH-state [20],

there is _an mcommensurate

superstructure

_[21]

leading

to a weak disorder of these

positions and; hence,

to a weak random

potential

in the

@L-state.

The existence of the

cylindrical

FS in the

flH-(ET)213

_was established

by Kang

et ai. [22]

by

means of the SdH

expenment-

The

frequency

of the fundamental

harmonic,

F

= 3î00

T,

beat- hke

behaviour, cyclotron

_{mass, mc re} 4

4.smo

and _even the

Dingle temperature, TD

_* o-à K

are very similar to those obtained for the

fl-IBr2 salt, reveahng

the

similarity

of their FS.

ARjR~

eo

1 1

1

ôo

'

à

1

~°

i

1 1

20

ja

~izo° ~80° ~vo° o 40° ào°

~p°

Fig.

5. The

interlayer

MR of

fl-(ET)2IBr2

_{as a} function of the orientation of the field

rotating

_in

the 2D

ab-plane-

The inset shows the

sonne

dependence

_in the

polar

co-ordinates.

QÎ

100/B, T'~

Fig.

6. The

oscillatory

_part of the MR in

flL-(ET)213

~s. the inverse field.

The AMRO have not been observed

directly

_m the

flH-(ET)213

but the

angular

behaviour of the dHvA oscillations [fil

suggests

the

hkely

existence of the critical

angles (7).

The giant

amplitude

of the SdH oscillations and their

U-shape

form

[22]

at re 0.4 K reflect _most

hkely

a

high two-dimensionality

of the

FS,

however _no

quantitative explanation

have been

proposed

as

yet.

The

relatively strong scattering

_on the random

potential resulting

in the _mcrease of trie

resistivity

_m trie

PL-Phase,

_is most

likely responsible

for trie lack of trie fast SdH oscillations.

On trie other

nana, _promurent

slow oscillations with trie

frequency Fsiow

~É 110 T [23] ^bave been observed

(see Fig. 6).

Like _m trie _case of

fl-(ET)2IBr2,

trie small FS parts which coula

give

use to these oscillations _are not

predicted by

trie extended Hiickel mortel calculations

(see

e-g.

[24]

^{and their}

origin

is not clear. One coula suppose them to come from _a minor _anion

Bllc*

a

Blla

20 10 0 10 20

CT

Bllc* ~

Bila

50

F, T

Fig.

7. Polar co-ordinate plots of the

angular dependence

of the slow SdH oscillation frequencies

in

fl-(ET)2IBr2 (a)

and

flL-(ET)213

16) for the field

rotating

_in the

ac*-plane,

where c* is the normal to the

ab-plane.

contribution to trie

conducting system. (Trie

contribution of trie

Ii

anion to trie DOS at SF was

suggested by first-principle

band structure calculations

[25j.

however trie main structure of the FS

predicted by

these calculations is

unlikely reahstic.)

In that _case, the choice of anion

should

considerably

affect the parameters of the slow oscillations. The considerable diiference in the absolute values of the

frequencies

and their

angular dependencies

shown _m

Figure

7

might

support ^this

supposition.

Î

A B

/

O O

~

E

~~

O

'

>

Fig.

8. A schematic _view of the FS of

~-(ET)2Cu(NCS)2.

Enumerated filled circles denote the MB

junctions. Solid _arrows and dashed Iine show the classical

(o)

and MB

(fl)

electron

orbits, respectively.

We should note that

although

trie results of trie SdH studies of trie

flL-

and

flH-states

_are

very

different,

this does not

necessarily

_mean trie considerable difference of their FS. As _men- tioned

above,

trie absence of trie fast oscillations in trie

flL-state

_is most

likely

caused

by

trie

higher scattering.

On trie other

hand,

trie slow

oscillations, having

lower

cyclotron

_{mass, may}

easily

be hidden behind trie

extra-ordinarily strong

^fast oscillations in trie

low-temperature

measurements of trie

pH-Phase _[22].

3.

~z-(ET)2X

Salts

3.1.

QUANTUM

INTERFERENCE _IN

~-(ET)2Cu(NCS)~.

Trie

~-(ET)~Cu(NCS)~

Salt bas been

subjected

_extensive

magnetic-field

studies

revealing

various kinds of

magnetic

oscillations.

This includes trie conventional SdH [SI and dHvA

Il 7,26]

effects and

magnetic-breakdown (MB)

oscillations

[27, 28] revealing

trie FS

consisting

of _a

cylinder

_{occupying m}

16%

of trie BZ _area and _a

pair

of

corrugated

_open sheets extended

parallel

to trie

kak~-plane

and

separated

from trie

cylinder by

_a small gap of

+~ 5 6 mev

[29].

Here _we will concentrate on a

specific phenomenon, namely

quantum interference

(QI)

of electrons

traversing

^different

patins

in

magnetic

field.

A

particular

_case of

QI

between trie electrons _passing

through

_open orbits

connecting

two MB

junctions

was

investigated

in detail

by

Stark and co-workers

[30].

^A

generalized theory

of

QI

oscillations of kinetic coefficients

in a common case of _a coherent MB network _was

developed

by Kaganov

and Slutskin

[31]. Recently Kishigi

et ai.

[32], basing

_{on a} numencal

analysis

of hnear chain MB

networks, proposed

trie

QI

oscillations _to exist aise _in

thermodynamic

_prop-

erties. From trie

experimental

point of vie~v,

QI

remains _an exotic

phenomenon. Among

trie conventional

metals, only

_pure

Mg

and _some of its diluted

alloys

bave shown _a

simplest

_case of

QI,

so-called Stark interferometer

[30].

^{Trie main} reason for trie lack of trie

expenmental

observations _is that trie MB networks

normally

include orbits too

large

to achieve trie electron

phase

coherence _{on a} sufficient part of trie FS

including

several MB

junctions. Besides,

trie

strong

^3D

dispersion

leads to _an

exceptionally high sensitivity

of trie effect to trie field _orien-

tation: _a small

tilting

of trie field from _a

symmetry

direction breaks trie total orbit

periodicity,

smears trie

phase

and hence results

m a

rapid dampmg

of trie oscillations

[30].

Trie FS of

~-(ET)2Cu(NCS)2 depicted schematically

_in

Figure

8 is

particularly

suited for trie observation of trie

QI effect, representing

_a hnear chain MB network coherent within ai least _one whole _unit cell of trie

reciprocal

_space and almost

independent

of

kz. Indeed,

besides two fundamental

frequencies, Fa

_m 600 T and

Fp

m 3850

T, corresponding

to trie

3.30K

2.99K 2.41K

f

o

_2.llK

À

.1

2

0.072 0.074 0.076 0.078

llB,

T"~

Fig.

9. Trie oscillatory. part ^{of trie}

interplane

resistance of

~-(ET)2Cu(NCS)2

at different temper-

atures.

Rapid (fl 20)-oscillations

^attributed to trie

QI

effect _are

clearly

_seen.

classical

la)

and MB

(fl) orbits, respectively,

and their

higher harmonics,

^small signs of trie differeiice

frequency

harmonics,

Fp ^nF«,

^with n =

1,

2 bave been detected in

low-temperature experiments [2î, 28, 33].

^{However their}

engin

_was unclear because their very low

amplitudes,

which _were

superimposed by

much

stronger

fundamental

harmonics,

^did net allow to

get

a

reliable

quantitative

information on them.

Very recently,

trie oscillations with trie

frequency Fp 2Fa

_were

directly

observed in MR studies at

temperatures

^{above 2 K}

[34], Figure

9 shows trie

oscillatory

^MR in trie field normal to trie

highly conducting bc-plane,

at different

temperatures. ^{Trie slow} SdH

oscillations, Fa

= 605

T,

^{which dominate below 2}

K,

^fade _away as

trie

temperature

increases and _new

rapid

with trie

frequency

of

F~-2a

_" ^{2630 T become}

^clearly

visible. Trie

amplitude

of trie

rapid

oscillations is very lo~v., +~

10~~

_{of trie}

background resistance,

nevertheless

they

bave been

reproduced

on ail trie studied

samples

bath in trie inter- and in-

plane

resistance. As discussed in detail in

[34],

^{trie difference}

frequency

^harmonic

F~ 2Fa

cari be realized in trie MB network shown _in

Figure

8 if trie electrons

keep

^trie

phase

coherence within at least _Due unit cell of trie

k-space.

^Trie

oscillatory amplitude

estimated

according

trie

theoretical models

[30, 31]

is in

good agreement

^{with that found in trie}

experiment [34].

A remarkable feature of trie

(fl 2a)-oscillations

is that

they

_are characterized

by

_{an ex-}

tremely

small effective _mass.

Indeed,

as noted in

[31],

^trie

temperature dependence

^of trie

QI

oscillation

amplitude

_is

determined,

^like in trie standard Lifshitz-Kosevich

(LK) theory, by

trie energy

dependence

^{of trie} oscillation

phase.

In trie

QI

_case that is trie _energy

dependence

^of

trie difference between trie

phase changes

on trie

interfenng trajectories

and

À',

lai

4~

4~,

)j jô4~ jô4~,

2~c

j~

_~~, j~~

ôe

~

ôe

~

ôe ~~ ehB ^{~ '}

where

#~

and #~> are trie

changes

of trie

quasi-classical phase

of trie electron _wave

packet

at

1.2 kbar _{cz m} ~"-~

fi fl

~~

.)

q ~5 ;."q=3o° ^'

~

cÎÎ ^~~~~

~~

lp =36°

0, degrees

Fig.

10. Trie

angular dependence

of trie

interplane

MR of

~-(ET)2Cu(NCS)2

at P

= 1.2 kbar.

Inset:

fragments

of AMRO for two field rotation

planes forming

the

angles

_çS

= 30° and 36° with the

ac-plane,

respectively.

its evolution

along

trie

patins

and

À',

#~

₌

/ _k~dky

Therefore trie

corresponding

thermal factor contains trie effective _mass

equal

to trie

dijference

between trie

cyclotron

_{masses on} trie

patins

and À'. For trie

(fl 2a)-oscillations,

trie effective

mass

mj_~~

= m~ ma, in

agreement

^{with trie}

experiment _[34],

in which trie oscillation effective _{mass was} obtained to be

0.9mo,

a factor of 4 smaller than trie

cyclotron

_mass of trie classical

a-orbit,

_ma m

3.smo.

It is

interesting

to note that

mj_~~

cari be further reduced and

likely

_even tuned _{to zero}

by applying

_a moderate

quasi-hydrostatic

_pressure. As found

by

Caulfield et ai.

[35],

trie _areas of trie _a- and

fl-orbits

bave

considerably

different

dependencies

_{on pressure.}

Therefore,

_{one con}

expect trie relation between trie _masses to

change

with pressure.

Indeed, mj_~~

_was found to decrease under _pressure and constitute <

0.3mo

at P

= 3 kbar [34] ^{that is at} least _an order of

magnitude

lower than _mû This

extremely

low effective _mass allows _{one to}

directly

observe trie

(fl 2a)-oscillations

_{up to} temperatures as

high

_as 9 K whereas ail trie

thermodynamic

quantum oscillations _are

essentially damped

above 2-3 K due to trie temperature _smeanng of trie Fermi level.

3.2. AMRO _IN

~-(ET)2Cu(NCS)2.

At ambient pressure, trie AMRO _{are net very pro-} nounced in this

compound

at fields below 15

T, partly

due to trie

masking

effect of trie _su-

perconducting

transition which _causes

rapid vanishing

of trie resistance _at trie

angles

0 above

> 60° at 1.5 K and _m 70° _at 4.2 K

[36].

^{A moderate} _pressure

effectively

_suppresses trie _su-

perconductivity

and enables _one to observe

relatively complicated

AMRO

[36].

^An

example

of these

angular

oscillations _is shown

in

Figure

10. Trie

positions

of most of trie MR

dips

_are found to

satisfy

_a

simple relation,

tan

°~

_COS~J

= C°t

fl

+ n

A-ÎÎn _~,

^{n =}

^{°, +1,}

⁺²

¹⁹⁾

where

0~

is

tlle _{polar angle}

_{between trie field direction and trie normal to trie}

_conducting

_bc-

plane giving

^{trie n-th MR}

dip,

_çJ is trie azimuthal

angle

between trie field rotation axis and trie

crystal b-axis, Ka

and

K~

_are trie

reciprocal

lattice

periods

and

fl

is trie

angles

between

them. These

dips

_can be

fairly explained by

_a semi-classical lD AMRO model

proposed

by

Maki [37]

and, independently, by

Osada et ai.

[38], predicting

that MR of _a

QID

metal measured

perpendicular

to trie lD axis should exhibit

Sharp

minima at

rotating

trie

magnetic

field in trie

plane parallel

to trie FS

plane,

_i-e-

perpendicular

to trie ID axis. A

qualitative interpretation

of this result _was first _given in

[39. 40]

^{and trier}

reproduced

in several works

(see

e.g.

[6]).

^{Trie critical}

angles

_were

predicted

to be determined

by

trie

reciprocal

lattice

periods

in trie FS

plane,

~~~ ~

Îl'

_~'~

_{~' ~'~'}

_~~~~

where y- and _{z-axes are} normal to trie ID axis. In _{a more}

general

_case, when trie field rotation axis forms _an

angle

_çJ with trie ID axis and trie

elementary

translation vectors,

Ki

and

K2, lying

in trie FS

plane

do trot coincide with trie

orthogonal

_g- and _z-axes, trie condition

(10)

is

obviously

modified to trie form

[40]

tan 0 _cas çJ =

~~~~

~

~~~~

PKiy

+

qK2y iii

or, if

Kiy

_"

0,

tan 0 _{cos çJ}

= cot

fl

+ ~

~~

,

ii ia)

q

K2

sin

fl

where

fl

is trie

angle

between

Ki

and

K2. Taking

into accourt

that,

if trie FS

corrugation

_in trie z-direction _is much smaller than in trie

y-direction, only

trie

integer

index

AMRO,

_{q =}

i,

are

expected [3i],

_{we come} to trie

experimentally

observed relation

(9). Thus,

trie AMRO

dips

observed in trie

R(0) dependence

of

~-(ET)2Cu(NCS)2 directly

indicate trie existence of trie open FS sheets

parallel

to trie

kak~-plane.

We note that, besides trie ID

AMRO,

additional features associated most

hkely

with trie

Q2D

FS

cylinder,

bave been found in

[36].

^{These features} are,

however, supenmposed by

trie

considerably _stronger

ID AMRO that makes their accurate

analysis problematic.

Trie further increase of _pressure leads to trie enhancement of AMRO

[41].

^An

example

of trie

angle-dependent

MR at P

= 8.5 kbar is illustrated in

Figure

ii. Trie behaviour of these oscillations _{is even more}

complicated

thon _at lower _pressure most

likely

due to trie

reducing

^of

trie MB gap under _pressure and consequent ansiig of

cyclotron

orbits with different

topologies.

3.3. FS STUDIES OF

~-(ET)2Cu[N(CN)2]X

WITH X

= Cl AND Br. Trie

crystal

struc-

tures of trie

highest-T~ organic superconductors ~-(ET)2Cu[N(CN)2]X

with X

= Cl and Br

(hereafter

referred to _as trie Cl and Br

salts, respectively)

are very similar to that of trie

~-(ET)2Cu(NCS)2. Therefore,

their FS _are

expected

to be similar as well [2].

However,

in

contrast to trie latter

compound,

neither

quantum

nor classical MR oscillations bave been

found in these two salts at ambient pressure up to trie fields

+~ 40 T. It is trot surprising for trie Cl sait which is known to be _a

magnetically

ordered dielectric at ambient pressure

[42].

Recent measurements under pressure above 2 kbar bave revealed clear SdH oscillations in trie metallic state of this sait

[43].

^Trie

oscillatory

part ^{of MR shown for several} pressures

in

Figure

12

clearly

exhibits two different

frequencies,

_in accordance with trie baud structure calculations

[44].

^{Trie lower}

frequency extrapolated

to P

= 0 kbar

equals

to 540 T

correspond- ing

to trie classical orbit _{a on} trie FS

cyhnder

_occupying

14.4%

of trie BZ, and trie

higher

frequency, F(P

_-

0)

= 3150

T,

_comes ^{from trie MB}

fl-orbit

hke that shown _in

Figure

8 and

160

140

#120

~

é100

~ fi

⁸⁰

jj

~ ₆₀

ce

ce ~~

/É

20

0

.80 60 -40 20 0 20 40 60 80

0, degrees

Fig.

Il. AMRO in

~-(ET)2Cu(NCS)2

_at P

= 8.5 kbar.

6

5 9.skbar

m

§

4 _8kbar

£

3 éf

)

6kbar

0 3.8kbar

0.070 0.075 0.080 0.085

l18,

T"~

Fig.

12. SdH oscillations in

~-(ET)2Cu[N(CN)2)CI

at different _pressures, at T

= IA K, B 1ac.

envelopes 100%

of trie BZ cross-section _area. Both SdH

frequencies

and trie

cyclotron

_masses

as well _as their _pressure

dependencies

_[43] resemble those found earher _on

i-(ET)2Cu(NCS)2,

in

agreement

^{with trie} theoretical

predictions.

Trie

only

considerable difference between trie calculations [44] ^and

experiment

_[43] consists _in trie existence of _a limite MB gap between trie open and

cylindrical

FS that is reflected in trie promirent a-oscillations _{seen in}

Figure

12. This

discrepancy might

be

explained by

trie

spin-orbit

interaction n>hich _{was trot} taken into accouiit

1-o

j)

,

/~

^{;. z}

> .:;

~~~j*fi

~. j#'~Î~'

^1.45K

Î~ j#

_~

~,;

~ ^w

~~~

~f~ ~ j~ ^j

~ ~

'

'

W

~Î~

^~~

~~

ÎÎ~

~~

°<~/

O.o ' 2.3K

°1'

~~

0.07 0.08 0.09 O.lO

i/B,T~~

Fig.

13. The SdH oscillations in

~-(ET)2Cu[N(CN)2)Br

at P

= 9 kbar, B1ac.

in trie calculation

[44].

^On trie other hand. _one could propose that _pressure lowers trie

crystal

symmetry, ^thus

removing

trie band

degeneracy

at trie BZ

boundary.

Trie latter

supposition

is corroborated

by

_{a very} recent observation of.trie 2D AMRO associated with trie MB

fl-orbit

in trie Cl sait under _pressure

[45].

^Their

analysis

reveals trie direction of trie

interlayer hopping

vector h

=

(ux,

_uy,

d) (see (î))

to be tilted from trie normal to trie 2D

ac-plane.

This _means that trie orthorhombic

symmetry

charactenstic of trie

room-temperature crystal

structure is

most

hkely

broken at low

temperatures land

under

pressure)

that

gives

rise to _a limite _gap between trie FS

cylinder

and open sheets

[45].

Unhke trie Cl

sait,

its

Br-containing analog

is metallic

already

at ambient pressure. Nev- ertheless,

only

under

high

_pressure, above

+~ 8

kbar,

weak oscillations attributed to trie SdH effect bave been found in trie latter

compound _[46].

A

typical example

of these oscillations at three different

temperatures

is shown in

Figure

13.

Surprisingly

trie oscillation behaviour

is

quite

^different from that observed in trie isostructural Cl sait _or similar

n-(ET)2Cu(NCS)2.

Trie oscillation

frequency

at 9 kbar _is

only

m 160 T

(in

trie field normal to trie

ac-plane),

_corre-

sponding

to FS

cyhnder

with trie cross-section _m 4.4Sl of trie BZ _{area; a} factor of 4 smaller than

expected

from trie calculations

[47].

^Trie

cyclotron

_{mass, ma m}

0.95mo,

is also

considerably

lower than _in trie _case of trie other

n-phase

salts.

Again, despite

trie

predicted degeneracy

of trie

conducting

bauds at trie BZ

boundary,

trie

high-frequency

oscillations

corresponding

to trie

fl-orbit

become visible

only

at very

high fields,

above 23 T

[48].

^Une cari propose that these

discrepancies

are associated with trie

high

_pressure used in trie

experiment [46]. Indeed,

trie pressure of

+~ 9 kbar _may be

enough

to induce trie lattice deformation

leading

to _a consider- able gap ^at trie BZ

boundary,

thus

depressing

trie

fi-oscillations- However,

trie

large

difference between trie

predicted

and observed _sizes of trie a-orbits _can be

hardly explained by

_a smooth variation of trie

crystal

lattice

parameters

^under pressure. Trie calculated

[44]

^{for trie isostruc-} tural Cl sait and

experimentally

obtained for both trie Cl sait [43] aiid

~-(ET)2Cu(NCS)2 _[35]

pressure

dependencies

of trie band structure

yield only

at most 30% variation of trie FS _size at

kc

kù

Fig.

14. Trie 2D

plane

cross-section of trie FS in

a-(ET)2MHg(XCN)4 according

to trie band structure calculations [50].

P _m 10 kbar.

Therefore, assuming

that trie ambient _pressure band structure of trie Br sait is similar to those of trie other two

compounds,

trie present ^result

suggests

either _an

unusually high sensitivity

of trie electronic

system

to trie pressure or a

pressure-induced phase

transition.

Turning

to trie very low

amplitude

of trie oscillations which constitutes

only

+~

10~~

_of trie

background resistance,

^it _can ^be caused

by magnetic

correlations in trie Br sait.

Indeed,

recent

experiments

_[49]

give

evidences for _a

low-temperature magnetic ordering

at trie ambient

pressure. This may lead to a

highly non-homogeneous

local

magnetic

induction in trie

sample,

thus

killing

trie SdH effect. Une _cari

imagine

that trie low

amplitude

of trie oscillations at 9 kbar _is also related _to trie

magnetic

correlations which _may be trot

completely suppressed by

this _pressure.

It is

interesting

to note

that,

_assuming trie Br sait to be _a

compensated

metal and bave trie

same FS

topology

_as trie Cl and

Cu(NCS)2

salts and

taking

into _account trie very small a-orbit

area, we come to _a FS

consisting

of _a very narrow

cylinder

with cross-section

elongated along

k~ and

only

_very

weakly corrugated

_open sheets

along

trie

kakb-Plane.

Trie flattened form of trie FS would

provide

favorable

nesting

conditions and therefore be unstable

against

trie

charge-

or

spin-density-wave

formation. This could _cause trie above mentioned

magnetic ordering.

To

clarify

trie nature of trie electronic state _in Br sait and its difference from trie Cl and

Cu(NCS)2

ores, further experiments

including

detailed structure

analysis, magnetotransport

^{studies and}

baud structure

calculations,

ail at various _pressures and

temperatures,

are necessary.

4.

Magnetotransport

in the

m-(ET)2MHg(XCN)4 Family,

M

=

K, Tl, Rb;

X

=

S,

Se

The

family

of isostructural

compounds a-(ET)2MHg(XCN)4

with M

=

K, Tl, Rh, NH41

X

=

S,

Se bas been of

special

interest

during

trie last years,

challenging

trie

capabilities

of trie

magnetotransport

and other

magnetic

field methods _in

probing

trie electronic

system

of trie

Q2D organic

^metals.

According

to trie baud structure calculations

[50,51],

^these

compounds

_are charactenzed

by

_a FS

consisting

of _a

slightly warped cyhnder

and open

sheets,

thus

representing

a unique combination of

Q2D

and

QID

electronic

systems (Fig. 14).

As it

stands,

this

family

cari be subdivided into two groups:

ii)

salts with M

=

NH4,

X

= S

[52]

^{and M} = Tl,

K,

3. 5

~~

o 1"

3. 0

1<~

2. 5

~

(

~

_{2. 0}

~n

5

B=14T 1. 0

T=1.3K

o. 5

-1où -50 o 50 1oo

fl, degrees

Fig.

15.

Angular dependence

of MR of

a-(ET)2TIHg(SeCN)4.

Both SdH oscillations and 2D

AMRO _{are seen.} Inset shows the cross-section of the

slightly warped

FS

cylinder,

calculated from the

AMRO experiment.

X

= Se

[53, 54] (hereafter

referred _{to as} trie

NH4,

Tl-Se and K-Se

salts, respectively)

which exhibit _a "normal metallic"

behaviour,

trie former

compound becoming

_a

superconductor

below

+~ 2 K

[55, 56]; iii)

salts with M

=

I<, Tl, Rh,

X

= S

[50, 52,5i]

which

undergo

a

low-temperature phase

transition

entailing

a

variety

^of

puzzling

anomalies in

magnetic

field.

In order to understand which anomalies of trie latter group

really originate

^{from trie}

specific low-temperature (LT)

electronic state, ^{it is natural to discuss} first trie

properties

of trie "normal metallic"

compounds.

4.1. SALTS wiTHouT THE LT PHASE TRANSITION. Here _we will concentrate on trie Tl-

Se salt _as a

typical representative

of trie group

(il.

Trie resistance of this salt exhibits _a smooth behaviour [53] characteristic of _many other stable ET based metals. Trie

only specific

feature of trie

R(T) dependence

consists in a small

upturn

^{below 2-3 K observed in} some

samples

and attributed to a

partial charge

localization in trie radical cation

layer.

Both SdH and semiclassical AMRO _cari be

readily

seen in trie

low-temperature angular

_sweep ^of trie

interlayer

MR shown _in

Figure

15. Trie semi-classical MR [58] ^is

fairly explained by

trie 2D AMRO model

(see

Sect.

2.2)

and

yields

a

slightly warped

FS

cyhnder

^with trie cross-section shown in trie inset in

Figure 15,

in

good agreement

^{with trie baud structure} calculations.

Trie SdH oscillations _are found to be very strong,

amounting

to _more than

20%

of trie

background

resistance

already

at 1.3

K,

14 T

[58].

^Their

frequency, (650 +10)[T]/cos0,

is consistent with trie AMRO data.

Temperature

^{and field}

dependencies

of their

amplitude

measured in trie range T

= 1.3 4.2

K,

H

= 3 14 T

yield

trie values _m~

=

(2.05

+

0.05)mo

and TD ₌ 0.6 K. As noted in

[58],

^trie very

strong

oscillation

amplitude implies

_an

extremely

weak warping of trie FS

cylinder, namely

smaller than trie Landau level

separation already

at fields 10-14

T;

trie transverse

overlap integral,

tb < huJ~

/4

% 1.5 K. In this _case, trot

only

trie