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Article

Spin and Charge Transport in the X-ray Irradiated Quasi-2D Layered Compound: κ-(BEDT-TTF)2Cu[N(CN)2]Cl

1
Condensed Matter Research Group of the Hungarian Academy of Sciences, P.O.Box 91, Budapest H-1521, Hungary
2
Institute of Physics, Budapest University of Technology and Economics, Budapest H-1111, Hungary
3
Interdisciplinary Graduate School of Medicine and Engineering, University of Yamanashi, Takeda 4-4-37, Kofu, Yamanashi 400-8511, Japan
4
Laboratory of Physics of Complex Matter, École Polytechnique Fédérale de Lausanne, Lausanne CH-1015, Switzerland
5
Institute for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan
*
Author to whom correspondence should be addressed.
Crystals 2012, 2(2), 579-589; https://doi.org/10.3390/cryst2020579
Submission received: 23 March 2012 / Revised: 25 April 2012 / Accepted: 11 May 2012 / Published: 24 May 2012
(This article belongs to the Special Issue Molecular Conductors)

1. Introduction

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 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-ET2-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 Crystals 02 00579 i004, where Crystals 02 00579 i005 denotes the angle from a in the (a,b) plane.
Figure 1. Structure of κ-ET2-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 Crystals 02 00579 i004, where Crystals 02 00579 i005 denotes the angle from a in the (a,b) plane.
Crystals 02 00579 g001
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 Crystals 02 00579 i007. 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.

2. Experimental

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 Crystals 02 00579 i004 from the a axis in the (a,b) plane. In this paper we present only the Crystals 02 00579 i004 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 Crystals 02 00579 i001 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 Crystals 02 00579 i001 and in particular of ρ|| uncertain.

2.1. Method of Measuring Crystals 02 00579 i007

The measurement of Crystals 02 00579 i007 by ESR is based on the assumption that spin and charge hopping rates are equal. We use the convention Crystals 02 00579 i008, where 1/Tx is the spin cross relaxation rate due to hopping from one layer to the two adjacent layers. In κ-ET2-Cl Crystals 02 00579 i010 and Crystals 02 00579 i011, 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.
Crystals 02 00579 i007 can be measured by electron spin resonance (ESR) in materials like κ-ET2-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-ET2-Cl the splitting is largest in fields oriented along Crystals 02 00579 i004 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 Crystals 02 00579 i007:
  • (a) Crystals 02 00579 i017. The two lines are resolved; the lineshapes differ only slightly from the non interacting case.
  • (b) Crystals 02 00579 i018. The spectrum has a complicated lineshape.
  • (c) Crystals 02 00579 i019. A “motionally narrowed" line appears at the frequency Crystals 02 00579 i020. The linewidth depends on Crystals 02 00579 i007.
The three cases are demonstrated in Figure 2 for κ-ET2-Cl. Here Crystals 02 00579 i007 was increased by applying pressure [7].
Figure 2. Motional narrowing of the ESR lines of adjacent A and B ET layers in κ-ET2-Cl under pressure (after [7]). B || Crystals 02 00579 i004. The spectra were measured at 420 GHz, T = 250 K and pressures of 0, 0.32 and 1.04 GPa. KC60 is an ESR reference.
Figure 2. Motional narrowing of the ESR lines of adjacent A and B ET layers in κ-ET2-Cl under pressure (after [7]). B || Crystals 02 00579 i004. The spectra were measured at 420 GHz, T = 250 K and pressures of 0, 0.32 and 1.04 GPa. KC60 is an ESR reference.
Crystals 02 00579 g002
To extract Crystals 02 00579 i007 and Crystals 02 00579 i023, 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 Crystals 02 00579 i007 and Resistivity Crystals 02 00579 i001

Crystals 02 00579 i007 and Crystals 02 00579 i001 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
Crystals 02 00579 i028
where Crystals 02 00579 i029 = Crystals 02 00579 i030 is the potential difference between adjacent layers due to the electric field Crystals 02 00579 i031. 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
Crystals 02 00579 i034
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, Crystals 02 00579 i038 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:
Crystals 02 00579 i039
In a simple semiconductor with a gap U and phonon assisted hopping with attempt frequency ν0, the hopping rate is given by Crystals 02 00579 i042 and Crystals 02 00579 i043 is replaced by Crystals 02 00579 i044 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 Crystals 02 00579 i045 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 Crystals 02 00579 i047 and the perpendicular resistivity Crystals 02 00579 i001 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 Crystals 02 00579 i001 are chosen in the figure so that the experimental points of Tx and Crystals 02 00579 i001 coincide at 250 K for the non-irradiated sample. Figure 4 displays the in-plane and interplane resistivities ρ|| and Crystals 02 00579 i001 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 Crystals 02 00579 i048 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 Crystals 02 00579 i001 smoothly increasing as the temperature is decreased. On the contrary, the 180 h and more irradiated samples have a metallic like behavior: Tx and Crystals 02 00579 i001 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 Crystals 02 00579 i001 and ρ|| have similar temperature and irradiation dependence. The ratio Crystals 02 00579 i001/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 Crystals 02 00579 i049 and interlayer resistivity Crystals 02 00579 i050 in κ-ET2-Cl. Left scale: Tx after 0, 90, 180, 360 and 720 h of irradiation. Right scale: Crystals 02 00579 i001 after 0, 100, 150 and 300 h of irradiation.
Figure 3. Comparison of the temperature dependence of the spin hopping time Crystals 02 00579 i049 and interlayer resistivity Crystals 02 00579 i050 in κ-ET2-Cl. Left scale: Tx after 0, 90, 180, 360 and 720 h of irradiation. Right scale: Crystals 02 00579 i001 after 0, 100, 150 and 300 h of irradiation.
Crystals 02 00579 g003
Figure 4. Comparison of in-plane resistivity ρ|| and interlayer resistivity Crystals 02 00579 i001 in non-irradiated and 300 hours irradiated κ-ET2-Cl. ρ|| and Crystals 02 00579 i001 were measured on different samples.
Figure 4. Comparison of in-plane resistivity ρ|| and interlayer resistivity Crystals 02 00579 i001 in non-irradiated and 300 hours irradiated κ-ET2-Cl. ρ|| and Crystals 02 00579 i001 were measured on different samples.
Crystals 02 00579 g004

4.1. Irradiation Dependence of Crystals 02 00579 i007 and Crystals 02 00579 i052 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 Crystals 02 00579 i053 and Crystals 02 00579 i054 calculated from the spectra. Tx decreases by less then a factor of 2 for the largest dose while Crystals 02 00579 i053 and Crystals 02 00579 i054 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, Crystals 02 00579 i007 in κ-ET2-Cl is about Crystals 02 00579 i055 and electrons diffuse to long distances without hopping to adjacent layers. Although the irradiation increases somewhat Crystals 02 00579 i007, electrons remain confined to single molecular layers for long times. In addition, Crystals 02 00579 i056, 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 Crystals 02 00579 i056 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-ET2-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 KC60 reference; (b) Irradiation dose dependence of Tx and Crystals 02 00579 i056 at 250 K.
Figure 5. (a) ESR spectra of κ-ET2-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 KC60 reference; (b) Irradiation dose dependence of Tx and Crystals 02 00579 i056 at 250 K.
Crystals 02 00579 g005
Figure 6. (a) ESR spectra of κ-ET2-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 KC60 reference; (b) Irradiation dose dependence of Tx and Crystals 02 00579 i056 at 50 K.
Figure 6. (a) ESR spectra of κ-ET2-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 KC60 reference; (b) Irradiation dose dependence of Tx and Crystals 02 00579 i056 at 50 K.
Crystals 02 00579 g006

4.2. Irradiation Dependence of Crystals 02 00579 i007 and Crystals 02 00579 i023 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 Crystals 02 00579 i001 is semiconducting-like in non-irradiated κ-ET2-Cl. Irradiation decreases Crystals 02 00579 i001 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 Crystals 02 00579 i001 have the same temperature and irradiation dose dependence. The ratio Crystals 02 00579 i058 is independent of temperature and irradiation dose.
  • (3) The resistivity anisotropy Crystals 02 00579 i001/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 Crystals 02 00579 i056 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 Crystals 02 00579 i059 and the perpendicular hopping time to resistivity ratio Crystals 02 00579 i058 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 Crystals 02 00579 i058 ratio indicate that the electronic structure is not strongly affected by the irradiation. The defect dose independence of Crystals 02 00579 i056, 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 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 Crystals 02 00579 i001/ρ|| in materials where the perpendicular conductivity is incoherent. They showed that if the in-plane scattering time Crystals 02 00579 i060 is much shorter than the interlayer hopping time Crystals 02 00579 i061, then the ratio Crystals 02 00579 i001/ρ|| is independent of Crystals 02 00579 i060. To understand the doping independence of Crystals 02 00579 i001/ρ|| one has to assume that irradiation introduces carriers with an increased Crystals 02 00579 i060 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 Crystals 02 00579 i001 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 Crystals 02 00579 i001. 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 Crystals 02 00579 i001 might dominate the apparent in-plane resistivity. This would explain that Crystals 02 00579 i001 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.

6 Conclusions

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 Crystals 02 00579 i058 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 Crystals 02 00579 i058 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.

Acknowledgements

We acknowledge the Hungarian National Research Fund OTKA NN76727, CNK80991, CK84324, the New Hungary Development Plan TÁMOP-4.2.1/B-09/1/KMR-2010-0002.

References

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MDPI and ACS Style

Antal, Á.; Fehér, T.; Yoneyama, N.; Forró, L.; Sasaki, T.; Jánossy, A. Spin and Charge Transport in the X-ray Irradiated Quasi-2D Layered Compound: κ-(BEDT-TTF)2Cu[N(CN)2]Cl. Crystals 2012, 2, 579-589. https://doi.org/10.3390/cryst2020579

AMA Style

Antal Á, Fehér T, Yoneyama N, Forró L, Sasaki T, Jánossy A. Spin and Charge Transport in the X-ray Irradiated Quasi-2D Layered Compound: κ-(BEDT-TTF)2Cu[N(CN)2]Cl. Crystals. 2012; 2(2):579-589. https://doi.org/10.3390/cryst2020579

Chicago/Turabian Style

Antal, Ágnes, Titusz Fehér, Naoki Yoneyama, László Forró, Takahiko Sasaki, and András Jánossy. 2012. "Spin and Charge Transport in the X-ray Irradiated Quasi-2D Layered Compound: κ-(BEDT-TTF)2Cu[N(CN)2]Cl" Crystals 2, no. 2: 579-589. https://doi.org/10.3390/cryst2020579

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