κ-(BEDT-TTF)₂ Cu[N(CN)₂]Cl (κ-ET₂-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-ET₂-Cl, the following temperature ranges are distinguished: (i) Below T_N = 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].

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-ET₂-Cl and κ-ET₂-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.

This study follows previous optical, resistivity, static magnetization and low frequency (9 GHz) ESR measurements on irradiated κ-ET₂-Cl [6,9] and κ-ET₂-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.

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

(1)

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(E_F) is the density of states (DOS) per ET dimer for both spin directions of the metallic layers at the Fermi energy, E_F. The perpendicular conductivity calculated from the hopping rate is

(2)

where 1/F is the two dimensional charge carrier density. Assuming one hole/dimer in κ-ET₂-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:

(3)

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-ET₂-Cl and κ-ET₂-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 T_x increases rapidly with decreasing temperature in the Cl compound while it is about constant in the Br compound.

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 T_x and are chosen in the figure so that the experimental points of T_x 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 T_x and smoothly increasing as the temperature is decreased. On the contrary, the 180 h and more irradiated samples have a metallic like behavior: T_x 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.

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).

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-ET₂-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 T_x 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 FeCl₄, 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-ET₂-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-ET₂-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.

In κ-ET₂-Cl, the interplane spin cross relaxation time measured by high frequency ESR is proportional to the interplane resistivity in the temperature range between 50 and 250 K. The ratio is unchanged in the range of irradiation doses where the resistivity changes from a semiconductor-like behavior to metallic. Since κ-ET₂-Cl is a strongly correlated conductor close to the metal insulator and magnetic ordering transitions, the spin and charge hopping rates could have different temperature or doping dependence. The insensitivity of to doping and temperature makes this unlikely. The qualitative change of the temperature dependence of the resistivity with irradiation and the insensitivity of other quantities depending on the density of states poses a difficult problem, which is not yet satisfactorily resolved.