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Maghetic Fields
Seiichi Kagoshima
To cite this version:
Seiichi Kagoshima. Low-Dimensional Organic Conductors under High Maghetic Fields. Journal de Physique I, EDP Sciences, 1996, 6 (12), pp.1787-1807. �10.1051/jp1:1996188�. �jpa-00247281�
Low-Dimensional Organic Conductors under
High Magnetic Fields
Seiichi Kagoshima (*)
Department of Pure and Applied Sciences, University of Tokyo, Komaba 3-8-1, Meguro, Tokyo 153, Japan
(Received 20 May 1996, revised 16 July 1996, accepted 20 August 1996)
PACS.72.15.Gd Galvanomagnetic and other magnetotransport effects PACS.74.70.Kn Organic superconductors
Abstract. Novel electromc properties of Iow-dimensional organic conductors.under high
magnetic fields are briefly reviewed and some topical problems are discussed. Magnetic field effects to electron spins and electron orbital motions
are discussed in the quasi one-dimensional
conductors (RIR2DCNQI)2Cu and (TMTSF)2X and in the quasi two-dimensional conductor
(BEDT-TTF)2XHg(SCN)4. Electronic properties in the anomalous state of (BEDT-TTF)2 KHg(SCN)4 are discussed in the Iight of the angle dependent magnetoresistance oscillations.
Properties of field-induced spin-density waves are studied in relation to the superlattice poten- tiaI made by the anion ordering m (TMTSF)2CI04. Possible origms of the rapid oscillations
m
magnetoresistance of (TMTSF)2X are examined. Introduction is made to theoretical ideas of field-induced superconductivity and experimental triai to find it.
1. Introduction
Low-dimensionality is one of trie most charactenstic properties of organic conductors. It is due to trie shape of constituent molecules far from sphencal symmetry. TMTSF (tetram- ethyltertaselenafulvalene) and BEDT-TTF (bis(ethylenedithio)-tetrathiafulvalene) molecules,
which are most popular ones to make organic conductors and superconductors, usually form columnar or sheet-like structures in crystal because of their planar shape. In those conductors
one obtains quasi one- or two-dimensional conduction electron systems.
Magnetic fields play several roles in electronic properties of low-dimensional organic con- ductors: First, it gives trie Zeeman energy to trie system leading to possible phase changes
due to reduction of trie free energy of spins parallel to trie magnetic field. Second, magnetic fields modify trie orbital motion of electrons by exerting trie Lorentz force. Electrons lose trie freedom of translational motion perpendicular to trie magnetic fields. This provides a due to
investigate electronic structures and their dynamics and, moreover, to control trie electronic state. Under high magnetic fields other kinds of electronic state are formed such as trie Landau
quantized state.
This article reviews trie magnetic field effects to spins and orbital motion in low-dimensional organic conductors followed by discussion on novel electronic states in them under high mag-
netic fields.
(* e-mail: kagosima©komaba.ecc.u-tokyo. ac.jp
© Les Éditions de Physique 1996
LU METALLIC
)
à
Îf iNSULATING
~~
PRESSURE
Fig. 1. Schematic phase diagram of (RIR2DCNQI)2Cu.
2. Basic Properties of Low-Dimensional Electronic Systems under High Magnetic
Fields
2.1. ÀiAGNETIC FIELD EFFECTS TO ELECTRON SPINS A FIELD-INDUCED METAL-INSU-
LAToR TRANSITION. Trie quasi one-dimensional conductor, (DMeDCNQI)2Cu bas columns
of DCNQI molecules interconnected by Cu il,2]. It is metallic in trie high-temperature or low- pressure regime and is insulating in trie opposite one [3] as shown in Figure 1. So-called chemical pressure effects bave been found in deuterated samples: When hydrogen atoms of
a DMeDCNQI molecule are replaced with deuterium, trie sample shows properties similar to those of pristine samples under pressures. This is ascribed to trie C-D bonding shorter than trie C-H one leading to reduction of intermolecular distance. Therefore, replacement of
a suitable number of hydrogen atoms with deuterium makes it possible to bave samples at ambient pressure showing properties of pnstine samples near trie critical pressure below which trie system remains metallic down to trie lowest temperature range.
XPS and infrared studies bave verified that Cu bas trie mixed valence Cu~/~+ in trie metallic
state [4,5]. Therefore, d-electrons of Cu are expected to take part in trie electronic states near
trie Fermi level. Band calculations bave shown this intuitive expectation to be valid [6]. It is formed by one-dimensional ~-like bands originating in DCNQI molecular orbitals and three-
dimensional d-like ones from Cu. Electrical, magnetic and structural studies bave shown that trie insulating state bas paramagnetic spins of Cu~+ and
a three-fold superstructure parallel
to trie one-dimensional c-axis ii,8].
Trie essential mechanism of trie metal-insulator transition is ascribed to trie Peierls instability
in trie ~-like band and trie Mott transition in trie d-hke one [9]. Trie Peierls instability is accompanied by trie three-fold superstructure [10,11]. This superstructure makes trie Mott
transition easy to undergo because trie Brillomn zone is reduced to 1/3 leading to trie half- filled state of trie d-like band.
One of novel properties of this material is trie metal-insulator-metal re-entrant transition observed in trie narrow pressure range shown in Figure Electrical resistance measurements under high magnetic fields and heat capacity ones of partially deuterated samples were made in order to clanfy its ongin [12,13] Trie magnetoresistance is found to be qmte normal unlike that
observed in trie heavy electron system. Trie electronic heat capacity was measured to be about 10 20mJ /mol/K~ at low temperatures. This is also normal as organic conductors suggesting that trie re-entered metalhc slate bas basically trie same properties as ordinary metalhc states far from trie re-entrant regime.
Under high magnetic fields of trie order of10 T, however, we found a field-induced transition from trie metallic state to trie insulating one as shown in Figure 2. This transition occurs
when trie system is close to trie insulating phase. It bas a hysteresis for trie field cycling. By
o,05
~
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~
, ,
'
~ o»o*o *«
'~ *O. O O o
*. ~ ~-
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o2 ,°
. «,. «
, ... .." .
° 33K
o
(a) 0 2 4 6 8 10 12
MAGNETIC FIELD T
16)la
~
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.
~8
À7 "
f .. «
f~
£5
u ~
à É3
m~
É~
o
0 2 4 6 8 10 12
MAGNETiC FIELD T)
Fig. 2. Examples of the field-induced metal-msulator transition m deuterated (DMeDCNQI)2Cu.
(ai Continuous increase of resistance m the 29%-deuterated sample. (b) Sharp increase m the 44%- sample. (Reproduced from Ref. [13j, with kind permis3ion from Elsevier Science S-A-, Lausanne,
Switzerland).
analyzing expenmental results we propose trie following picture: The magnetic field reduces trie free energy of trie insulating state because of a negative contribution of trie Zeeman energy.
Therefore trie metallic state is made unstable by high magnetic fields when trie metallic system is close enough to trie insulating regime. Trie above idea is consistent with theoretical studies
from both phenomenological and microscopic view points [14, lsj.
Trie de Haas-van Alphen effect bas been observed in trie metallic phase of (DMeDCNQI)2Cu
as shown in Figure 3 [16j suggesting trie presence of both one- and three-dimensional Fermi surfaces which are consistent with trie band calculations [6j. However, no Shubnikov-de Haas oscillations bave been found in magnetoresistance. It is presumably too small compared to trie
background resistance.
(ai
fl j
1 0.05K °
j II C Î F=477T
à (o=0° <
0 400 800
0.14 Ô.16 Ô.18 0.20 0.22 0.24
ibi
é
h ~'
ÎÎ
~ é £6
/f à
~
£5
) 0.05
~ ~
262
~ oe=26° ~
0 4000 8000
0.080 0.085 0.090 0.095 Ô.IÔÔ 0.105
1/H (T
Fig. 3. De Haas-van Alphen oscillations of (DAIeDCNQI)2Cu. Trie msets show trie FT spectra.
(a) Magnetic fields parallel to the one-dimensional c-axis. (b) Magnetic fields in the ab-plane making the angle uJ from [110j direction. (Reproduced from Ref. [16j with kind permission from American
Physical Society).
2.2. MAGNETIC FIELD EFFECTS TO ORBITAL MOTION ANGLE-DEPENDENT ÀiAGNETORE-
sisTANcE OsciLLATioNs. Examples of magnetic field effects to trie orbital motion of elec-
trons are found in quasi one-dimensional conductors (TMTSF)2X (X = Cl04, PF6 etc.) and
quasi two-dimensional ones (BEDT-TTF)2X (X =13, IBr2, KHg(SCN)4 etc.). When one ro- tates trie direction of magnetic fields, trie electrical resistance oscillates as a function of trie angle between trie field direction and a lattice vector but not of trie field strength. This phe-
nomenon called angle-dependent magnetoresistance oscillations was found for trie first time in
fl-(BEDT-TTF)2IBr2 by Kartsovnik et ai. and in 0-(BEDT-TTF)213 by Ilajita et ai. inde-
pendently il7, 18].
In trie quasi two-dimensional (BEDT-TTF)2X trie resistance perpendicular to trie two-
dimensional plane shows a series of resistance maximum as a function of trie angle b between trie magnetic field direction and trie normal to trie two-dimensional plane as shown in Figure 4.
Trie oscillations were found to be a function of tan b.
X.loloH
ào éo o ào g(degj
Fig. 4. Angle-dependent magnetoresistance oscillations observed in (BEDT-TTF)2IBr2. Trie angle
9 is measured from trie normal to trie two-dimensional plane. (Reproduced from Ref. [17j. with kind
permission from The American Institute of Physics).
(a) (bj
B B
"''''~ ~
' '
j
~
' , /
'--' /
/ i
,
' ' '
' ' ,'
--"
2-DIMENSIONAL PLANE 2-DIMENSIONAL PLANE
Fig. 5. Real space trajectories of an electron at the Fermi level under magnetic fields apphed at
general angles (Ieft) and magic angles (right).
A theoretical idea to explain this phenomenon was given by Yamaji [19]. When trie field direction is general, trie electron trajectory in real space is spiral-like leading to a finite re- sistance perpendicular to trie two-dimensional plane. At magic angles given by trie relation.
tan b
= (kF/c*)(n +1/4) where kF, c* and n are trie Fermi wave number, trie reciprocal lattice vector and an arbitrary integer, respectively, trie real space trajectory becomes a closed loop
as shown in Figure 5. This makes trie perpendicular resistance infinite. Quantum mechanical caiculations of electrouic euergy spectra bave showu that trie baud width at trie Fermi level vanishes at trie magic angles [20]. We consider this corresponds to trie above naive picture of closed orbit in real space.
'
'
P/q
# ~ ~ ~~
à T=1.5K
d é
aj
'4
,fÎ
.l
il ~
t
,
,
(=-4~3-2-)-1-)-j-~-~ 0 l 234
Fig. 6. Angle-dependent magnetoresistance oscillations of (TMTSF)2CI04 for the field rotation
m the b~c*-plane. The angle 9 denotes that between the magnetic field and the c"-axis. Note that second-derivative traces are shown. The hatched peaks correspond to the onset of field-induced spin-
density waves. The angles that satisfy tan 9
= 1.1p/q are shown. Right inset: Plot of trie tangent of peak position vs the fraction p/q. Left inset: Semi-classical electron trajectory on the Fermi surface.
(Reproduced from Ref. [22j, with kind permission from The American Physical Society).
This phenomenon and trie interpretation were found to be universal ones common to quasi two-dimensional conductors such as GsAs/GaAlAs. This phenomenon gives a due to find trie
size and trie shape of trie cross-section of trie warped cylindrical Fermi surface cut by a plane normal to trie cyhnder axis if trie cross-sectional shape is not far from a circle and trie degree
of warping is not too much.
Similar phenomena bave been found also in quasi one-dimensional conductors. When mag- netic fields are rotated in trie plane perpendicular to trie one-dimensional a-axis of (TMTSF)2
Cl04, trie transverse resistance shows a series of local minimum as a function of trie angle
between trie magnetic field and a crystalline axis perpendicular to trie one-dimensional axis as shown in Figure 6 [21,22].
,~
This type of angle dependent magnetoresistance oscillations bas been ascribed to a commen-
surability effect between trie electron trajectory in momentum space and trie reciprocal lattice.
Trie left inset of Figure 5 depicts trie trajectory on trie Fermi surface. When trie field direction
is general, trie trajectory reduced to trie first Brillouin zone covers all over trie Fermi surface.
Transverse components of trie Fermi velocity of electrons are averaged out leading to trie net electron motion parallel to trie one-dimensional axis.
When trie field direction satisfies trie relation tan b
= pb'/qc', trie trajectory gives only a finite number of lines on trie Fermi surface in trie first Brillouin zone. Here p and q are arbitrary integers and b' and c' are projections of trie lattice vectors b and c onto trie plane perpendicular
0.35
1~
O.30 o5K 8T
@,, ," b
025
~ o
~~
~
[0.20
o~~o.15 4T
3T O.lO
0.05 ~~
0.00
~~ ~~ ~ ~~ ~~
8(degree)
Fig. 7. Angle-dependent magnetoresistance oscillations observed in (TMTSF)2CI04 at 0.5 K for trie field rotation in the ac-plane. Trie angle 9 is measured from trie a-axis. The 2 T and 1 T traces
exhibit superconductivity at smaller angles. (Reproduced from Ref. [30j, with kind permission from The American Physical Society).
to trie one-dimensional a-axis, respectively. As trie cancellation of trie transverse components becomes imperfect, trie trajectory of electrons in real space bas trie component perpendicular
to trie one-dimensional axis causing trie local minima in trie transverse resistance. A fully quantum mechanical calculation bas given a result consistent with experimental results and this interpretation [23].
Different interpretations bave been proposed for this phenomenon: Une of them assumes presence of "bot spot" area on trie Fermi surface where electrons suffer strong scattering due to some origins [24]. When magnetic fields are applied at trie magic angles, some amount of
electrons do not go through trie bot spot leading to trie resistance minima. It is dillicult to find at trie present stage which interpretation is more adequate. Other ideas are also proposed stressing trie role of electron-electron interactions or non-Fermi liquid behavior [25-29].
Other types of angle dependent magnetoresistance oscillations bave been found for magnetic
fields rotated in trie plane containing trie one-dimensional a-axis and one of two other axes.
When trie field is rotated from trie a-axis toward trie c in trie ac-plane, trie resistance shows many local maxima near trie a-axis followed by a large peak as shown in Figure 7 [30] Trie data pattem is nicknamed as "Batman-type." Trie angular position of trie "Batman ears" grues
an excellent measure of tb/kF where tb is trie transfer integral parallel to trie b-axis and kF trie Fermi wave number.
When trie rotation is made from trie a-axis to trie b in trie ab-plane, trie resistance shows a minimum at a field direction nearly parallel to trie one-dimensional a-axis. This phenomenon
was first found in (DMET)21~, as shown in Figure 8 [31], which is considered to bave an elec- tronic structure similar to (TMTSF)2X, and was verified to occur also in (TMTSF)2Cl04 (32].
This magic angle bas been interpreted as trie angle above which no closed orbit is formed on trie Fermi surface [32].
1.5 .-«
«*
-
~ ~
e .
- .
~ .
~- " x x
x x e
#1i~ "x . . .
CC
.
~
. x
" , i Î
x o
o o ~
0
PI
o-(BEDT-TIF)~KHg(SCN)~ 0kbar 1,6K 12T
-120 -90 60 -30 0 30 60 90 120
ANGLE fl(degree)
Fig. 10. Angle dependent magnetoresistance oscillations of (BEDT-TTF)2KHg(SCN)4 at ambient
pressure. Trie angles 9 and # denote trie polar angle measured from trie normal of trie two-dimensional
plane and trie azimuth one from the a-axis, respectively. (Reproduced from Ref. [39[, with kind permission from Physical Society of Japan).
When X is K, however, trie compound bas an anomalous state in trie low-temperature (< 8 K)-low-pressure (< 5 kbar)-low-magnetic-field (22 T) regime as shown in Figure 9 [37].
Trie magnetoresistance bas a broad peak around 10 T accompanied by a kink-like structure at about 22 T while trie NH4 compounÀl bas no broad peak nor trie kink in magnetoresis-
tance [38]. In addition trie angle dependent magnetoresistance oscillations show a feature quite different from NH4 compound and Yamaji's model.
To investigate possible origins of trie anomalous state angle dependent magnetoresistance oscillations were measured under high magnetic fields and high pressures. Figure 10 shows an
example of trie angle dependent magnetoresistance oscillations obtained by rotating a sample
around two axes perpendicular to each other and to trie magnetic field [39]. One finds a
serres of resistance minimum. This suggests trie presence of a quasi one-dimensional Fermi
surface rather than quasi two-dimensional one. However, trie geometry of thus expected quasi one-dimensional Fermi surface is different from that of trie band calculation [40]
Kartsovnik et ai. ascribed trie origin of trie observed quasi one-dimensional Fermi surface to a possible nesting of trie original one due to trie Peierls instability as shown in Figure 11 [41].
,
' '
i j
i
,
i
i
/ ~
a) b)
Fig. ii. Fermi surface of (BEDT-TTF)2KHg(SCN)4. a) Nesting of the quasi one-dimensional
Fermi surface with the vector Q. T > Tp. b) Reconstruction of the Fermi surface giving rise to a
new quasi one-dimen~ional one, T < Tp. (Reproduced from Ref. [41], with kind permission from Les Editions de Physique, Les Ulis, France).
Blundel et ai. showed that trie reconstructed quasi one-dimensional Fermi surface explains qualitatively trie observed results [42].
This idea seems to be consistent with trie possible anti-ferromagnetism suggested by trie
anisotropy of magnetic susceptibility measured by Sasaki et ai. [43j Magnitude of magnetic
moment is measured by ~SR to be of trie order of1o~3~B (44]. Trie Fermi surface nesting
is considered to cause SDW rather than CDW. Under high pressures above about 5 kbar
(o.5 GPa) trie angle dependent magnetoresistance shows trie presence of both trie quasi one- and two-dimensional Fermi surfaces in consistent with trie band calculation [33j.
In trie intermediate pressure range of trie anomalous state trie angle dependent magnetore- sistance shows predominantly trie presence of trie quasi one-dimensional Fermi surface made by trie nesting. However, as shown in Figure 12, another serres of resistance minima was found [39j.
We verified that its angular position is really angle dependent rather than field-strength depen-
dent although its magnitude increases with increasing trie field strength. Figure 12 sugges_ts that trie possible origins for this resistance minimum bave some circular symmetry in trie two-dimensional plane. However, trie Fermi surface predicted by trie baud calculation cannot explain trie presence ofsuch circular symmetry. Therefore, trie origin of this anomaly is remain- mg puzzhng. Some unknown mechanisms are expected to work in trie intermediate pressure
range.
It bas been proposed that more comphcated phases are present in trie anomalous state [45, 46j. Actually magnetic susceptibility measurements bave shown a hysteretic nature suggesting
presence of several first-order-like changes in trie anomalous state. Moreover recent studies suggest that trie phase separation curve in trie temperature-magnetic-field plane shown in
Figure 9 is related to transport properties and another curve should be drawn to specify magnetic properties. One can expect possible presence of more novel electronic states in relation to trie anomalous state.
3.2. FIELD-ÎNDUCED SPIN-DENSITY ÀÀÎAVES IN THE SUPERLATTICE POTENTIAL OF (ÎÙM
TSF)2Cl04. (TMTSF)2PF6 undergoes trie Peierls transition at 12 K accompanied by trie
onset of SDW [4î-soi. Trie wave vector of SDW was measured by ~H NMR as (o.5, o.24,
o). Under high pressures above about 6 kbar (o.6 GPa) it becomes superconducting below
