3FeO3

December 2002

Materials Letters 57 (2002) 697 – 702 www.elsevier.com/locate/matlet

Non-adiabatic small polaron hopping conduction in Gd1/3Sr2/3FeO3 Woo-Hwan Jung* Division of Electrical, Electronic and Information Engineering, Howon University, 727, Wolha-Ri, Impi, Kunsan Cho˘n Buk, 573-930, South Korea Received 18 December 2001; received in revised form 7 May 2002; accepted 23 May 2002

Abstract The transport properties of Gd1/3Sr2/3FeO3 have been studied carefully by using resistivity and thermoelectric power. Interestingly, a small polaron hopping model of Emin and Holstein is found to fit the resistivity data above 200 K, and the resistivity data of the high temperature region followed a non-adiabatic hopping conduction mechanism. At high temperatures, a significant difference between the activation energy deduced from the electrical resistivity q(T) and thermoelectric power a(T), a characteristic of a small polaron, is observed. D 2002 Elsevier Science B.V. All rights reserved. Keywords: Adiabatic; Charge-ordering; Hopping process; Non-adiabatic; Small polaron; Thermoelectric power

1. Introduction Recently, interest in transition metal oxides has grown after the discovery of high-temperature superconductivity in cuparates and giant magnetoresistance in manganese oxides [1 – 3]. The metal – insulator transitions that appear in a number of these oxides are fascinating features where change and orbital ordering or disordering have roles of prime importance. In contrast to copper and manganese oxides, iron oxides with perovskite structures have not been so extensively studied, perhaps because of their less spectacular properties. Nevertheless, the perovskite La1
xSrxFeO3, first studied by Waugh [4], is of the highest interest if one bears in mind the charge disproportion of iron shown by Takano and Tekada [5] for the perovskite La1/3Sr2/3FeO3. Using the

*

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Mo¨ssbauer spectroscopy, these authors showed indeed the existence of two kinds of iron species below 200 K: the well-known Fe3+ and the unusual Fe5+. Such an anomalous valence state, as well as the real space ordering of valence-skipping sites, was also observed by electron microscopy measurements [6], which indicated that the ordered layers of Fe3+ and Fe5+ ions are in the sequences of . . .335335. . . along the rhombohedral z direction or the pseudocubic-perovskite [111]c direction. Thus, the valence skipping charge-ordered state in La0.33Sr0.67FeO3 may be viewed as condensation of the hole bipolaron (Fe5+) [7] in the magnetic background of Fe3+ lattice. The existence of a charge-ordering transition in Ln1/3Sr2/3FeO3 (Ln: rare earth) has been inferred from the magnetization, electron diffraction and optical measurements, while Gd1/3Sr2/3FeO3 does not undergo a charge-ordering transition [7,8]. Due to the small size of the Gd3+ ion, Gd0.33Sr0.67FeO3 should be in the region of the x=2/3 phase diagram where there is no transition to a charge-ordering state. Thus,

0167-577X/02/$ - see front matter D 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 5 7 7 X ( 0 2 ) 0 0 8 5 6 - X

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charge localization with strong lattice distortion still exists in Gd0.33Sr0.67FeO3 over the whole temperature range. This localization can result from the absence of any long-range order, or from lattice distortion due to a strong electron – lattice interaction, i.e., small polaron formation [9 –11]. In this article, we report the transport mechanism in Gd0.33Sr 0.67FeO3 using a small polaron hopping model. It is the small polaron hopping transport which, we believe, occurs in Gd0.33Sr0.67FeO3. In order to gain insight into the nature of the transport mechanism, we have applied thermoelectric power to Gd0.33Sr0.67FeO3 over a wide range of temperatures in addition to basic characterization according to electrical resistivity measurements. Thermoelectric power, in contrast to electrical resistivity, is relatively insensitive to the effects of grain boundary and disorder. We will show that for this material, thermoelectric power provides unique insight into the transport mechanism.

ture was ground and calcined at 1373 K for 24 h. The calcined powder was pressed into pellets, and finally sintered in pure flowing oxygen at 1573 K for 1 day. X-ray powder diffraction at several different points of the pellets confirmed sample homogeneity. The X-ray diffraction was consistent with a rhombohedral cell. The room temperature unit cell parameter and edge ˚ and 60.22j, respecangle are given as aR=5.38 A tively. The magnetic resistivity in the temperature range 80 –373 K was investigated in the heating process using the four-probe method. The maximum magnetic field available in the present apparatus is 0.85 T. A thermoelectric power measurement was carried out below 373 K on a sample placed between two blocks of oxygen-free high conductivity copper. Both ends of the specimen were coated with platinum paste and then placed in contact with thin copper plates. Copper –constantan thermocouples were then welded to the reverse sides of the copper plates to measure the temperature and thermoelectric power.

2. Experimental procedure 3. Results and discussion The sample of Gd1/3Sr2/3FeO3 (abbreviated hereafter as GSF) was prepared by a solid-state reaction method starting with high purity Gd2O3, SrCO3, and Fe2O3 powder in the required proportions. The mix-

In Fig. 1, the temperature dependence of the resistivity in the zero fields and 0.85 T is shown. The resistivity shows an insulating feature without any

Fig. 1. Resistivity (q) of GSF as a function of temperature in a zero field and in a magnetic field of 0.85 T.

W.-H. Jung / Materials Letters 57 (2002) 697–702

distinct anomaly or jump over the whole temperature range, i.e., charge-ordering is not observed. The temperature and magnetic field dependencies of thermoelectric power (a) are demonstrated in Fig. 2. A positive sign is observed throughout the temperature range measured, and the thermoelectric power of GSF decreases gradually with increasing temperature, which indicates that GSF is a p-type semiconductor. Furthermore, the levels of thermoelectric power measured at different fields are almost indistinguishable, that is, almost no magnetic-field dependence is observed over the whole temperature range. In our previous study, on the dielectric properties of GSF, the dielectric loss anomaly was found at around 170 K [12]. That loss peak is an essential feature of the small polaron hopping transport [13 – 15]. Conduction in a narrow polaronic band takes place through the thermally activated hopping of carriers with an activated resistivity [16 – 19]: 

WH q=T ¼ q0 exp kB T c



ever, rather difficult to identify the type of small polaron, adiabatic or non-adiabatic, if only the temperature dependence of conductivity is used, because the conductivity subject to the adiabatic small polaron conduction also currently satisfies the temperature dependence of the non-adiabatic conduction. Furthermore, a hopping process of non-adiabatic small polarons requires several restrictions on the electron transfer integral between the neighboring hopping sites. These restrictions are then to be the criteria of judgement whether the hopping conduction is termed adiabatic or non-adiabatic. The resistivity data can be fitted to Eq. (1) equally well for c=1 and 1.5. With results from the fit alone, it is difficult to decide whether the polaron hopping is adiabatic (see Fig. 3(a)) or non-adiabatic (see Fig. 3(b)). A check on whether the hopping is adiabatic or non-adiabatic can, in principle, be made by using Emin and Holstein’s conditions [20]. Emin and Holstein give the inequality

ð1Þ

where q0 is a constant and WH is the hopping energy for a small polaron. In Eq. (1), c=1 for the adiabatic small polaron hopping, and c=1.5 in the case of nonadiabatic small polaron hopping [16 – 19]. It is, how-

699

hX0 ¼ J

2



p 4WH kB T

1=2 bhx0

ð2Þ

as the condition for validity of the non-adiabatic limit, where J is the electron-transfer matrix element and x0

Fig. 2. Thermoelectric power (a) as a function of temperature. The inset shows Arrhenius relation between (a) and 1/T.

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Fig. 3. Temperature dependencies of resistivity in a zero field. (a) Arrhenius plot of q/T vs. 1/T, (b) Arrhenius plot of q/T1.5 vs. 1/T. The inset shows Arrhenius relation between q vs. 1/T1/4.

is the relevant optical-mode lattice fluctuation. In this limit, however, the resisitivity is given by the hightemperature form:  1=2 cð1
cÞe2 J 2 p q¼ expðWH =kB T Þ 4WH kB T hkB Ta

ð3Þ

For consistency, Eqs. (2) and (3) imply that, in the non-adiabatic limit,

X0 ¼

qakB T expðWH =kB T Þbx0 cð1
cÞe2

ð4Þ

W.-H. Jung / Materials Letters 57 (2002) 697–702

where c is the Sr2+ doping concentration. Taking a from the lattice spacing (assumed in this discussion as equal to ac) and the hopping energy WH from the fits to the measured dc conductivity data (see Fig. 3(a)), that energy does not differ so much even if nonadiabatic Arrhenius plot is used. One obtains the value X0i1012 Hz. The optical phonon frequencies for similar transition metal based materials lie in the range x0i1013 – 1014 Hz. This suggests that for the nonadiabatic limit, Eq. (4) is applicable to that material, thus c=1.5. A least-squares fit based upon Eq. (1) gives a hopping energy of 0.20 eV. Below about 200 K, as shown in Fig. 3(b), the nonArrhenius behavior is found. Miller and Abrahams [21] suggested that non-Arrhenius behavior occur as a result of the charge transport between impurity states. In such a case, a multi-phonon process is replaced by a single-phonon process [22], and disordered energy in a system plays a dominant role in a conduction mechanism, resulting in a variable range hopping with the T
1/4 law [11]. In fact, this type of electrical transport is observed in GSF (see inset of Fig. 3(a)). However, Emin [23,24] argued that the onset of a nonArrhenius temperature dependence as temperature is lowered is general feature of small polaron hopping. It arises as multi-phonon jump processes are frozen out. Without acknowledging the magnitude for the disordered energy, however, a quantitative analysis to determine the conduction mechanism below about 200 K is difficult. Since the high temperature region transport is governed by thermally activated polarons, we have also tried to fit the high temperature thermoelectric power data with Mott’s equation [25], a¼


kB e



 Ea þ aV , kB T

ð5Þ

where Ea is the activation energy for thermoelectric power and aV is a constant of proportionality between the heat transfer and kinetic energy of electrons or holes. The other symbols have their conventional meanings. For aV<1, small polaron hopping transport occurs. For aV>2, conduction is due to the large polarons. From the fit of the high temperature data (linear part in inset of Fig. 2), the value of aV is 0.61 indicating small polaron hopping conduction valid for GSF. From the slop of a versus 1/T (see inset of Fig.

701

2), the estimated value of activation energy Ea is 0.03 eV. From the inset of Fig. 2, we see that the transport gap from thermoelectric power is much smaller than the gap derived from resistivity measurements. In a simplified picture, thermoelectric power measures the heat current associated with charge motion, which for usual semiconductors is the activation energy across the kinetic gap. If transport is dominated by one type of carrier, this results in an equality of the transport and the thermoelectric power gap. In the oxides where the hopping motion of small polarons dominates electrical transport, Ea is the potential difference between identical lattice distortions with and without a hole and/or electron, thus WH Ea. A large difference in the magnitudes of WH and Ea is a hallmark of the polaronic transport [25].

4. Conclusion Thermoelectric power and electrical resistivity experiments, performed in the paramagnetic phase of Gd1/3Sr2/3FeO3, provide evidence for polarondominated conduction in transition metal perovskite materials. We find that the electrical resistivity in the paramagnetic phase has an activated form, whereas the activation energy is not compatible with the formation of thermoelectric power. The large difference between the activation energies, deduced from the electrical resistivity q(T) and thermoelectric power a, is a characteristic of small polaron. The resistivity at the high temperature range is dominated by hopping of localized non-adiabatic small polaron.

Acknowledgements This work was supported by Howon University.

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