1. Introduction
κ-(BEDT-TTF)
2 Cu[N(CN)
2]Cl (
κ-ET
2-Cl hereafter) is a layered organic conductor on the borderline of a Mott metal–insulator transition [
1,
2]. The electronic band is effectively half-filled with one hole per two ET molecules. The electronic structure is two dimensional, layers of ET molecules are separated by polymeric anion layers (
Figure 1). Judged from the electrical and magnetic properties of non-irradiated
κ-ET
2-Cl, the following temperature ranges are distinguished: (i) Below
TN = 23 K: weakly ferromagnetic insulator [
3]; (ii) Between 23 and about 50 K: a smooth insulator to a semiconductor transition with an anomalous magnetic field dependent magnetism; (iii) Above 50 K: semiconductor with a very small gap and a temperature-independent paramagnetic susceptibility [
4]. In all three temperature ranges the coupling between layers is extremely weak: in ranges (i) and (ii) magnetic oscillations of adjacent layers are independent in general direction magnetic fields; In range (iii) electron hopping between layers is extremely rare. At ambient temperatures electrons diffuse several tenths of a micrometer confined to a single molecular layer [
5].
Figure 1.
Structure of
κ-ET
2-Cl projected onto the (a,b) plane. Only one type of ET molecule per plane is shown for clarity. In the experiments the external field B is along
, where
denotes the angle from a in the (a,b) plane.
Figure 1.
Structure of
κ-ET
2-Cl projected onto the (a,b) plane. Only one type of ET molecule per plane is shown for clarity. In the experiments the external field B is along
, where
denotes the angle from a in the (a,b) plane.
X-ray irradiation at relatively small doses changes drastically the physical properties in all three temperature ranges. Sasaki
et al. [
6] proposed that the deviation from half filling is the underlying reason for the sensitivity to irradiation. The results and discussion of irradiation induced changes of magnetism in range (i) and (ii) will be presented in a forthcoming paper. This paper is restricted to the discussion of the conducting high temperature range. Here the change by irradiation of the resistivity from a semiconductor to a metallic temperature dependence is the most remarkable phenomenon.
Section 2 is a brief description of experimental details and the high frequency ESR method to determine the interlayer hopping frequency
. The relation between interlayer hopping and resistivity (
Section 3) is most important for the interpretation. Details of the method and the high frequency ESR results in non-irradiated
κ-ET
2-Cl and
κ-ET
2-Br were published in References [
7,
8].
Section 4 presents the experimental results. Irradiation has little effect on both interlayer coupling and intralayer spin relaxation at 250 K and we argue in
Section 4.1 that the concentration of irradiation-induced defects is low. In
Section 5 we discuss possible mechanisms for the qualitative changes in the electronic transport.
2. Experimental
This study follows previous optical, resistivity, static magnetization and low frequency (9 GHz) ESR measurements on irradiated
κ-ET
2-Cl [
6,
9] and
κ-ET
2-Br [
10] crystals at Tohoku University (Sendai, Japan). The method of irradiation has been described earlier [
6]. Irradiation intensities were about 1/2 MGy per hour. ESR was measured on the same crystal with increasing doses. The total doses of 90 h, 180 h, 360 h, 720 h resulted from incremental irradiation after each ESR measurement. The ESR data on the non-irradiated crystal are taken from measurements on a different crystal. We found that the ESR of non-irradiated crystals are well reproducible. Although the non-irradiated crystal in this study is different from the two crystals in the previous ESR study [
7], the results agree well. ESR spectra between 3 K and 250 K were recorded for all irradiation doses in magnetic fields along the crystallographic b and c axes and along
from the a axis in the (a,b) plane. In this paper we present only the
data from which the interlayer hopping rate is determined. The ESR spectra were taken at 111.2 GHz and 222.4 GHz in the BUTE ESR Laboratory [
11].
ρ|| in-plane and
interplane resistivity data were measured on different crystals and with different irradiation doses but under the same conditions as used for ESR. The difficulty of contacting make absolute values of
and in particular of
ρ|| uncertain.
2.1. Method of Measuring
The measurement of
by ESR is based on the assumption that spin and charge hopping rates are equal. We use the convention
, where 1/
Tx is the spin cross relaxation rate due to hopping from one layer to the two adjacent layers. In
κ-ET
2-Cl
and
, the spin relaxation rates of conduction electrons due to processes intrinsic to layers
A and
B are long (
i.e., in the ns range); consequently the ESR spectrum depends sensitively on interlayer hopping.
can be measured by electron spin resonance (ESR) in materials like
κ-ET
2-Cl where chemically equivalent but structurally different layers (denoted by
A and
B in
Figure 1) alternate [
8]. If the
A and
B layers do not interact, the ESR spectrum is a superposition of two lines at the Larmor frequencies
νA and
νB. Since the
g-factor tensors of
A and
B layers are differently oriented, the
A and
B lines are resolved in sufficiently high magnetic fields. In
κ-ET
2-Cl the splitting is largest in fields oriented along
in the (a,b) plane while it is zero in the (a,c) plane and in the principal crystallographic directions. For a finite interaction between adjacent layers the ESR spectrum depends on the strength of the interlayer interaction,
i.e., on the magnitude of
:
(a)
. The two lines are resolved; the lineshapes differ only slightly from the non interacting case.
(b)
. The spectrum has a complicated lineshape.
(c)
. A “motionally narrowed" line appears at the frequency
. The linewidth depends on
.
The three cases are demonstrated in
Figure 2 for
κ-ET
2-Cl. Here
was increased by applying pressure [
7].
Figure 2.
Motional narrowing of the ESR lines of adjacent
A and
B ET layers in
κ-ET
2-Cl under pressure (after [
7]).
B ||
. The spectra were measured at 420 GHz,
T = 250 K and pressures of 0, 0.32 and 1.04 GPa. KC
60 is an ESR reference.
Figure 2.
Motional narrowing of the ESR lines of adjacent
A and
B ET layers in
κ-ET
2-Cl under pressure (after [
7]).
B ||
. The spectra were measured at 420 GHz,
T = 250 K and pressures of 0, 0.32 and 1.04 GPa. KC
60 is an ESR reference.
To extract
and
, the lineshapes are fitted to spectra calculated from two coupled Bloch equations. The electronic exchange between layers represented by an effective magnetic field is also included in the fit. In this paper all data were obtained by fitting ESR spectra recorded at two frequencies, 222.4 GHz and 111.2 GHz.
gA and
gB were also free parameters, they change little with temperature.
3. Relation between Interlayer Hopping and Resistivity
and
are closely related [
12]. The resistivity is proportional to the hopping time and inversely proportional to the density of available states,
D. The electrical current
j is given by
where
=
is the potential difference between adjacent layers due to the electric field
. The relation is particularly simple if the electrons of molecular layers form a Fermi liquid. Then
D =
D(
EF) is the density of states (DOS) per ET dimer for both spin directions of the metallic layers at the Fermi energy,
EF. The perpendicular conductivity calculated from the hopping rate is
where 1/
F is the two dimensional charge carrier density. Assuming one hole/dimer in
κ-ET
2-Cl,
F = (
ac)/2, where
a and
c are the in-plane,
the out-of-plane lattice constants. The significance of Equation (2) lies in the possibility to determine the DOS from measurements of the perpendicular resistivity and spin cross relaxation time without knowing details of the barrier between layers:
In a simple semiconductor with a gap
U and phonon assisted hopping with attempt frequency
ν0, the hopping rate is given by
and
is replaced by
in Equation (3).
Interlayer hopping measured by ESR in non-irradiated
κ-ET
2-Cl and
κ-ET
2-Br crystals hasbeen discussed in detail in Reference [
7]. At 250 K the interlayer hopping time is
for the Cl compound and the same for the Br compound within experimental accuracy. The conduction is quasi-two-dimensional: at 250 K electrons are confined to single layers for times several orders of magnitude longer than the momentum relaxation time. The density of states estimated from Equation (2) is about a factor of 5 larger than calculated from the band structure. Between 250 K and 50 K
Tx increases rapidly with decreasing temperature in the Cl compound while it is about constant in the Br compound.
4. Interlayer Hopping Rate and Resistivity above the Metal Insulator Transition
The experimental data of the cross relaxation time
and the perpendicular resistivity
above the metal-insulator transition at various irradiation doses are summarized in
Figure 3. The irradiation doses are in the same range in the two experiments. The scales of
Tx and
are chosen in the figure so that the experimental points of
Tx and
coincide at 250 K for the non-irradiated sample.
Figure 4 displays the in-plane and interplane resistivities
ρ|| and
respectively of non-irradiated and 300 h irradiated samples. The resistivities in
Figure 3 and
Figure 4 are similar to the ones measured on a different crystal in Reference [
6]. The resistivity
in this work agrees reasonably well with the measurements of Reference [
13].
We note from
Figure 3 that the interlayer hopping time and the perpendicular resistivity are to a good approximation proportional for all irradiation doses and in the full temperature range above 50 K. The non-irradiated sample has a semiconducting behavior with
Tx and
smoothly increasing as the temperature is decreased. On the contrary, the 180 h and more irradiated samples have a metallic like behavior:
Tx and
decrease with decreasing temperature. In the irradiated samples the abrupt metal-insulator transition is qualitatively different from the smooth transition in the non-irradiated sample. Furthermore, irradiation shifts the transition to lower temperatures.
Figure 4 shows that
and
ρ|| have similar temperature and irradiation dependence. The ratio
/
ρ|| is about 600 independent of temperature for both the irradiated and non-irradiated samples. This ratio, even if uncertain, is typical for measurements in the literature.
Figure 3.
Comparison of the temperature dependence of the spin hopping time
and interlayer resistivity
in
κ-ET
2-Cl. Left scale:
Tx after 0, 90, 180, 360 and 720 h of irradiation. Right scale:
after 0, 100, 150 and 300 h of irradiation.
Figure 3.
Comparison of the temperature dependence of the spin hopping time
and interlayer resistivity
in
κ-ET
2-Cl. Left scale:
Tx after 0, 90, 180, 360 and 720 h of irradiation. Right scale:
after 0, 100, 150 and 300 h of irradiation.
Figure 4.
Comparison of in-plane resistivity
ρ|| and interlayer resistivity
in non-irradiated and 300 hours irradiated
κ-ET
2-Cl.
ρ|| and
were measured on different samples.
Figure 4.
Comparison of in-plane resistivity
ρ|| and interlayer resistivity
in non-irradiated and 300 hours irradiated
κ-ET
2-Cl.
ρ|| and
were measured on different samples.
4.1. Irradiation Dependence of and at 250 K
The 250 K ESR spectra change little under irradiation (
Figure 5a). Even at the highest irradiation dose the interlayer hopping rate remains low since the
A and
B layer lines are well resolved.
Figure 5b shows the cross relaxation
Tx and intrinsic relaxations
and
calculated from the spectra.
Tx decreases by less then a factor of 2 for the largest dose while
and
are not changed significantly by the irradiation.
The mean free path within ET layers is shorter than the molecular separation, implying a very short in-plane electronic momentum lifetime. In contrast, out of plane hopping events are rare,
in
κ-ET
2-Cl is about
and electrons diffuse to long distances without hopping to adjacent layers. Although the irradiation increases somewhat
, electrons remain confined to single molecular layers for long times. In addition,
, the electronic spin relaxation time within the conducting ET layers, is independent of irradiation. Usually charged defects effectively increase the spin relaxation rate in conductors. The insensitivity of
to irradiation and the relatively small decrease in
Tx are in agreement with earlier findings [
9] that the concentration of induced defects is small even under the largest dose.
Figure 5.
(
a) ESR spectra of
κ-ET
2-Cl at 222.4 GHz and 250 K after different doses of X-ray irradiation. There is a small impurity line at 7.935 T in the spectrum of the sample irradiated for 180 h, not present in the other spectra. The signal at 7.943 T is the KC
60 reference; (
b) Irradiation dose dependence of
Tx and
at 250 K.
Figure 5.
(
a) ESR spectra of
κ-ET
2-Cl at 222.4 GHz and 250 K after different doses of X-ray irradiation. There is a small impurity line at 7.935 T in the spectrum of the sample irradiated for 180 h, not present in the other spectra. The signal at 7.943 T is the KC
60 reference; (
b) Irradiation dose dependence of
Tx and
at 250 K.
Figure 6.
(
a) ESR spectra of
κ-ET
2-Cl at 222.4 GHz and 50 K as a function of X-ray irradiation dose. The line at 7.935 T for 180 h irradiation, not present in the other spectra, is an impurity line. The signal at 7.943 T is a KC
60 reference; (
b) Irradiation dose dependence of
Tx and
at 50 K.
Figure 6.
(
a) ESR spectra of
κ-ET
2-Cl at 222.4 GHz and 50 K as a function of X-ray irradiation dose. The line at 7.935 T for 180 h irradiation, not present in the other spectra, is an impurity line. The signal at 7.943 T is a KC
60 reference; (
b) Irradiation dose dependence of
Tx and
at 50 K.
4.2. Irradiation Dependence of and at 50 K
Figure 6 displays the irradiation dependence of the ESR spectra at 222.4 GHz and the spin relaxation times. The interlayer hopping time
Tx decreases rapidly with irradiation, especially at low doses. On the other hand, the intrinsic spin relaxation is not sensitive to the irradiation. The single ESR line at 720 h irradiation has an ESR-frequency-dependent width and illustrates the “motional narrowing” case described in
Section 2.1.
5 Discussion
We first list the main findings of the present and earlier works on the conducting and magnetic properties in the temperature range between 50 K and 250 K. (Below this temperature the properties change).
(1) The perpendicular resistivity
is semiconducting-like in non-irradiated
κ-ET
2-Cl. Irradiation decreases
in the full temperature range, the decrease is non-linear with dose. At higher doses the resistivity is metallic,
i.e., it increases linearly with temperature.
(2) The interlayer spin hopping time
Tx and
have the same temperature and irradiation dose dependence. The ratio
is independent of temperature and irradiation dose.
(3) The resistivity anisotropy
/
ρ|| is typically between 100 and 1000. It is independent of temperature and irradiation dose.
(4) The magnetic spin susceptibility is approximately temperature independent and does not change with irradiation [
9].
(5) Theintralayer spin relaxation time
is independent of temperature and dose.
The interpretation of the qualitative change in transport properties by irradiation in κ-ET2-Cl poses a difficult problem. Matthiessen’s rule describes the change of resistivity by defects in usual metals. Impurity scattering in metals increase the resistivity by a temperature independent quantity, the increase is linear with defect concentration and the temperature dependent phonon resistivity is not affected. Clearly, nothing of this applies to κ-ET2-Cl: irradiation decreases the resistivity, the decrease is non-linear with defect concentration and the temperature dependence is drastically changed from semiconducting like to metallic.
At the same time other quantities that depend sensitively on the electronic structure are independent of temperature and defect concentration. In Fermi liquids the magnetic spin susceptibility
and the perpendicular hopping time to resistivity ratio
are both proportional to the density of states. Although
κ-ET
2-Cl is a strongly correlated system and at high temperatures there are no long lifetime quasi-particles, the independence of the susceptibility and the
ratio indicate that the electronic structure is not strongly affected by the irradiation. The defect dose independence of
, the relatively small decrease of
Tx at 250 K with dose and earlier magnetic measurements [
9] indicate that the defect concentration is small.
Sasaki
et al. [
6] proposed that irradiation of organic layered compounds has two effects: it increases the electron momentum scattering rate and at the same time dopes the material. By creating localized electrons at defects in the anion layer and delocalized holes in the conducting molecular layers a charge imbalance from half filling takes place. In metallic compounds far from the Mott transition, like
κ-(BETS)
2 FeCl
4, defects enhance the electron scattering as in other metals. In materials close to the Mott metal-insulator transition, doping of holes changes the electronic properties drastically as the band is no more half filled. At high temperatures the extra holes change the semiconducting behavior to metallic, at low temperatures the metal-insulator and the magnetic ordering transitions are suppressed. To understand the measured electric and magnetic properties one has to assume that the small deviation from half band filling changes the resistivity from semiconducting to metallic-like but has little effect on the band structure in general.
It is not simple to understand within the model the independence of the resistivity anisotropy from irradiation induced defect concentration. Why does adding high mobility carriers increase the in-plane conductivity and the interlayer hopping time in the same way? Kumar and Jayannavar [
12] proposed a mechanism for a temperature independent anisotropy
/
ρ|| in materials where the perpendicular conductivity is incoherent. They showed that if the in-plane scattering time
is much shorter than the interlayer hopping time
, then the ratio
/
ρ|| is independent of
. To understand the doping independence of
/
ρ|| one has to assume that irradiation introduces carriers with an increased
but at the same time the parallel and perpendicular electronic overlap integrals remain unchanged.
A different approach has been proposed by Analytis
et al. [
14]. They assumed that irradiation creates two kinds of defects. Like in the model of Sasaki
et al., some defects increase the electronic scattering rate. There is a further defect-assisted interlayer channel which decreases the interlayer resistivity. This model gives a good description of the irradiation dose dependence of
in
κ-(BEDT-TTF)
2 Cu(SCN)
2, an organic conductor close to the Mott transition. The in-plane resistivity is assumed to be small and without any effect on
. A defect-assisted interplane conductivity has also been proposed [
15] to explain the metallic zero frequency interplane conductivity and the absence of a Drude peak in the optical conductivity in
κ-ET
2-Br. However, it is difficult to understand within this model the irradiation and temperature independence of the anisotropy between 50 and 250 K in
κ-ET
2-Cl. Due to difficulties in contacting and/or macroscopic sample imperfections, the current is usually inhomogeneous in strongly anisotropic conductors and in general the interlayer resistivity affects in-plane measurements. If
ρ|| is very small, the contribution of
might dominate the apparent in-plane resistivity. This would explain that
and
ρ|| have (apparently) the same temperature dependence both for the non-irradiated and irradiated crystal. However, this model does not explain why the anisotropy is independent of irradiation dose.