USING STANDARD PRB S

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Effect of oxygen nonstoichiometry on electrotransport and low-field magnetotransport property of polycrystalline La

_0.5

Sr

_0.5

MnO

_3À_␦

thin films

J.-M. Liu*

Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, People’s Republic of China and Institute of Materials Research and Engineering, 3 Research Link, Singapore 117602

Q. Huang, J. Li, and C. K. Ong

Department of Physics, National University of Singapore, Singapore 119260

Z. C. Wu, Z. G. Liu, and Y. W. Du

Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, People’s Republic of China 共Received 4 November 1999; revised manuscript received 21 March 2000兲

Polycrystalline La_0.5Sr_0.5MnO_3⫺␦thin films deposited on quartz wafers at 680 °C and various oxygen pressures P by pulsed laser deposition are prepared. The effects of oxygen nonstoichiometry on the microstructural, electrotransport and low-field magnetotransport property of the thin films are investigated in details. A structural distortion from the stoichiometric lattice is identified for the samples deposited at P⬍0.1 mbar. It is verified that the thin-film conductivity over the Curie point follows variable-range hopping. The carrier density at the Fermi surface falls and the metal-insulating transition shifts toward low temperature with decreasing P, with a jump at P⫽0.1 mbar. Enhanced low-field magnetoresistance at low temperature is achieved for P

⬎0.1 mbar. Oxygen overdeficiency at P⭐0.1 mbar essentially prohibits the spin reordering. The temperature dependence of the electro- and magnetotransport properties is explained by the two-channel model where the insulating channels and metallic ones coexist in parallel.

I. INTRODUCTION

The discovery of colossal magnetoresistance 共CMR兲 in doped rare-earth manganese perovskite oxides and others has stimulated intensive research activities.^1,2A high magnetoresistance ratio MR„MR⫽关␳⁽⁰⁾⫺␳^(H)兴/␳^{(0), where}␳^{is the} sample resistivity and H is the applied magnetic field…under high magnetic field has been reported for a number of doped rare-earth manganese oxides. At the same time, several physical approaches to the CMR phenomenon have been proposed.^1,3–7

The stoichiometric La₁_⫺_xCa_xMnO₃ 共LCMO兲 or La₁_⫺_xSr_xMnO₃共LSMO兲shows a ferromagnetic transition at temperature T⫽T_c, where the MR ratio reaches the maximal.⁶At the same time an insulator-metal transition appears at T⫽T_m⬃T_c due to the so-called double- exchange 共DE兲mechanism.³ As T⬎T_c, the conduction follows either the variable-range hopping共VRH兲mechanism⁸for polycrystalline samples or small polaron hopping 共SPH兲 one^9,10 for epitaxial or single-crystal samples.^11,12T_min polycrystalline LSMO or LCMO is much lower than that in single crystal, whereas its low-field MR ratio 共LFMR兲 at low T is much higher than that in single crystals.^2,13,14This excess contribution is believed to mainly originate from spin-polarized tun- neling 共SPT兲 or spin-dependent scattering 共SDS兲 associated with grain boundaries共GBs兲.¹³On the one hand, the double- exchange mechanism is currently used to explain the electrotransport behavior of single-crystal LCMO or LSMO for which the simultaneous hopping of an electron from the Mn³^⫹ site to the central oxygen ion and the other from the oxygen ion to the Mn⁴^⫹ site is responsible. Here oxygen

vacancies are essential for the ferromagnetism and electron hopping. On the other hand, MR⬀( M / M_s)² is satisfied be- fore the magnetic saturation reached for polycrystalline LCMO or LSMO, where M is the magnetization of the sys- tem and M_s is the saturated M.¹⁵ As H is raised over the saturated field, the MR response becomes linear against H, controlled by the spin-disordered layers available, such as GBs.^16,17 Therefore, the generation of a number of spin- disordered sites in the microstructure can be an essential scheme to enhance LFMR.

Nevertheless, LFMR enhancement in these oxides remains a big challenge to us.¹⁸ The embedding of spin- disordered ranges in the microstructure is emphasized, in- cluding grain size refining and grain boundary generation,^17–21 porous microstructure fabrication,²² surface crack processing,²³ and metal-insulator mixed sintering,^24,25 in addition to the lanthanide or alkaline-earth doping^26,27and boundary deoxidization²⁸ as well. In this article we explore the effect of oxygen deficiency on the electro- and magnetotransport properties and thus LFMR in polycrystalline LSMO (x⫽0.5) thin films. A direct argument is that oxygen vacancies 共OV兲frozen in LSMO may change a lot the hopping conduction and hinder the double exchange,^29,30 thus producing number of localized spin-disordered ranges. A correspondence between the density of OVs and LFMR may be available.

II. EXPERIMENTAL DETAILS

The LSMO thin films of variable oxygen concentration were prepared on quartz wafers at adjusted pressure P of oxygen ambient by means of pulsed laser deposition 共PLD兲. PRB 62

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Quartz substrates were chosen for several reasons here. The first is to avoid the potential effect of crystalline substrates on the film orientation. Second, the density of OVs in the films can be enhanced in the polycrystalline sample rather than the epitaxial sample. In fact, our previous work revealed that a modulation of density of OVs over a wide range in epitaxial LSMO is not easy, even if P was reduced to 10^⫺⁶mbar. However, this becomes much easier in polycrystalline LSMO thin films,^28,29 since GBs in polycrystalline LSMO can be seriously oxygen deficient at low P. Finally, the stress effect commonly available in epitaxial growth can be minimized if amorphous wafers are used here.

The PLD experiment was performed by using a KrF ex- cimer laser of 248 nm in wavelength and 30 ns in pulse width. An optimized laser fluency of 1.6 J/cm²and reprate of 5 Hz were utilized and the substrate temperature T_s of 680 °C was kept during the ablation. A dense ceramic LSMO disk was chosen as target. The detailed PLD procedure was described earlier.²⁹The pressure P of the flowing oxygen in the chamber was precisely adjustable from 10^⫺⁶ to 2 mbar.

Films of 800 nm in thickness and 10⫻1.0 mm² in in-plane dimension were deposited and then cooled down to room temperature at the same P. The film thickness was measured by atomic force microscopy 共AFM兲 and confirmed with cross-section profiling.

The microstructure of the films was checked by fine step- mode x-ray diffraction共XRD兲. The grain size was evaluated with AFM. The Oxford superconducting vibrating sample magnetometer共VSM兲was used to characterize the magnetic property of the samples. The electro- and magnetotransport properties were measured by using the standard four-pad probe with the sample temperature well controlled. A triangle-wave ac magnetic field of⫾4 kOe in magnitude and 0.01 Hz in frequency was applied in parallel to the sample surface.

III. EXPERIMENTAL RESULTS AND DISCUSSION A. Microstructural evaluation

The XRD␪^-2␪spectrum for a series of samples deposited at different P is presented in Fig. 1. All films are polycrystalline, and 共110兲,共111兲, 共200兲,共211兲, and共220兲reflections are identified. Starting from P⫽0.5 mbar until P

⫽0.14 mbar, the positions of the XRD peaks show no iden- tifiable difference from those of the target. However, the target is 共110兲 favored, but the films prefer 共111兲. The film lattice parameters remain the same as the target.

At P⫽0.1 mbar, a very strong 共200兲 peak is recorded, whereas共111兲and共211兲reflections almost vanish. However, the peak positions show no identified change. Subsequently, as P⫽60␮bar and lower, a distinct shift of共111兲,共200兲, and 共211兲peaks toward the low-angle direction is found, as indicated by arrows, while the共110兲peak remains stationary. A lattice distortion is probed. The spacing expansion along 关111兴and关211兴is 1.7% and 2.5%, respectively, and 2.2% for 关200兴. The共200兲peak decays sharply down to a comparable level to others and almost vanishes as P⭐10␮bar. Since the 共110兲 peak remains unmoved, one may not be able to give details of the lattice distortion just from the␪^-2␪ ^{scan. Nev-} ertheless, the distortion takes place once P⭐0.1 mbar. It is

small, but imposes a significant influence on the electro- and magnetotransport of the films.

The lattice distortion may be ascribed to several particu- lars in the samples, such as fluctuations of GBs, cation stoichiometry, or strain against the change of ambient pressure P. The AFM observation of grain size for these films does not expose a remarkable change. Coarser grains of⬃100 nm for the films deposited at P⬎0.1 mbar are imaged, but the average grain size for the films for P⫽4␮^{bar is} ⬃80 nm.

No remarkable grain refining can be identified. The contribution to sample conductivity due to change of the GB vol- ume fraction is small, taking a note that the GBs contribute to the sample resistivity.

In order to discard the possible cation nonstoichiometry due to the change of P, the chemical constitution of the film deposited at P⫽10␮bar was checked by transmission electron microscopy 共TEM, Philips CM-300兲 equipped with an energy-dispersive x-ray共EDX兲spectrometer. The data show that the relative atomic ratio La:Sr:Mn roughly meets the stoichiometry within the measuring uncertainty, indicating that no cation deficiency or accumulation appears in the films prepared at low P. In fact, it is believed that evaporation of heavy elements like La, Sr, and Mn during laser ablation is not sensitive to the variation of the oxygen pressure. And more, as we mentioned earlier, the effect of stress in the films can be forgotten too since the films are⬃800 nm thick and deposited on quartz substrates. The thin strained layer, if any, neighboring the substrate surface just contributes a neg- ligible part to the shift of XRD probed peaks. Therefore, variation of the oxygen vacancy density depending on the oxygen pressure remains the only factor responsible for the fluctuations of the microstructure and transport property.

B. Electro- and magnetotransport property

A tremendous dependence of the zero-field electrical resistivity ␳0 and magnetic moment M on P is shown. The FIG. 1. XRD spectra for a series of LSMO thin films deposited at different values of P as indicated. The spectrum for the LSMO target is inserted for reference.

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measured ␳0⬃T relation favors the insulating-type conduction for all samples. Figure 2共a兲 presents the data for three samples at P⬎0.1 mbar. The ln␳0⬃T relation is roughly linear at high T, but nonlinear at low T. The occurrence of an insulator-metal transition is clearly indicated by the sublin- earization. Nevertheless, no distinct resistivity peak is observable unless T⬍77 K, the lowest temperature available to us because of existence of GBs. T_m for the samples can be given by an indirect definition.

While the conduction at T⬍T_c共or T_m兲follows the metal- like behavior, it has been established that the polycrystalline LSMO over T_mexhibits the VRH conduction:³¹

␳0⫽␳i0exp共T₀/T兲^1/4, 共1兲 where␳i0 is the prefactor and T₀ the characteristic temperature. The conduction at high T far over T_m may operate in terms of the SPH mechanism:¹²

␳0/T⫽␳p0exp共E_p/kT兲, 共2兲 where ␳p0 is the prefactor, E_p represents the activation energy for small polaron, and k is the Boltzmann constant. The SPH conduction commonly works well for over-room- temperature data. Really, a fitting of the data on the three samples does not support the SPH unless T is close to room temperature 共⬎280 K兲, while the VRH mechanism works quite well for all data. As shown in Fig. 2共a兲, a plot of ln␳0

against T^1/4 produces good linearity once T is higher than a

critical value, which is defined as T_m. The as-defined T_m is really very close to T_cas evaluated from the VSM data. The measured moment M, and 1/M as well, as a function of T for the sample prepared at P⫽0.2 mbar is presented in Fig. 2共b兲. T_c⬃200 K, very close to T_m⬃188 K, is derived from Fig.

2共a兲. The values of T_m for the three samples are given in Table I, from which one sees a downshift of T_m with decreasing P.

As P⭐0.1 mbar, the as-prepared samples show no more magnetization over T⬎77 K, indicating T_c⬍77 K. The measured␳0⬃T relationships are plotted in Fig. 3, from which a big change is observed, referring to the two curves at P

FIG. 2. 共a兲Zero-field resistivity␳0as a function of T and T^⫺1/4 for three LSMO thin films deposited at 0.5, 0.2, and 0.14 mbar and 共b兲magnetic moment M and its reciprocal 1/M as a function of T for LSMO thin film deposited at 0.2 mbar.

TABLE I. Fitted data of T₀, T_c, N(E_F), and E_pfor LSMO thin films deposited at different P.

P共mbar兲 T₀共MK兲 T_m共K兲 N(E_F) 共eV m兲^⫺³ E_P共meV兲

0.50 9.853 201 1.1884⫻10²⁶ 97.84

0.20 12.272 188 9.5418⫻10²⁵ 98.44 0.14 16.080 172 7.2819⫻10²⁵ 100.18 0.10 111.615 ⬍77 1.0491⫻10²⁵ 104.63 0.06 161.177 ⬍77 7.2650⫻10²⁴ 112.38 0.01 170.335 ⬍77 6.8744⫻10²⁴ 132.67 0.004 176.860 ⬍77 6.6207⫻10²⁴ 134.71

FIG. 3. 共a兲Zero-field resistivity␳0as a function of T and T^⫺1/4 for four LSMO thin films deposited at 0.1 mbar, 60␮bar, 10␮bar, and 4 ␮bar, respectively, and 共b兲 ln(␳0/T)⬃1/T relations for the four samples.

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⫽0.14 and 0.1 mbar, respectively. Note that the lattice distortion occurred at P⭐0.1 mbar. It is clearly shown that the conduction follows VRH in a much better manner than SPH.

A perfect linear ln␳⬃T^1/4relationship is demonstrated for all samples 关Fig. 3共a兲兴, while no sample fits well the ln(␳0/T)

⬃T relationship关Fig. 3共b兲兴. When T₀for the three samples at P⬎0.1 mbar is⬃10⁷K, a big jump up to 10⁸K is extracted for the samples deposited at P⭐0.1 mbar. The fitted values of T₀ are listed in Table I, from which the carrier density at the Fermi surface, N(E_F), is estimated via³¹

N共E_F兲⫽ 24

␲␰³^kT0

, 共3兲

where ␰ is the localization length for LSMO, i.e., Mn-Mn separation. Taking ␰⫽0.39 nm, one obtains N(E_F) for all samples, as shown in Table I. Noting N(E_F)

⫽10²⁸– 10²⁹eV¹m^⫺³ for stoichiometric LSMO single crystals,³² the as-prepared thin films have a much lower N(E_F), which falls down with decreasing P. If the conduction bandwidth for LSMO remains unchanged at 1.5 eV,³³ the real hole carrier density, which is of the same order of magnitude as N(E_F), decreases with decreasing P. This pro- vides us direct evidence that more oxygen vacancies are frozen in the lattice when the thin film is deposited at a lower value of P. The density will be so high once P⭐0.1 mbar that a lattice distortion appears. A similar phenomenon was reported earlier for La_0.5Sr_0.5CoO₃ thin films.³⁴

On the other hand, the best fitted E_p for different samples are given in Table I just for a qualitative discussion, suppos- ing the SPH mechanism works too. The evaluated E_p, over 90 meV as P⬎0.1 mbar and even reaching 112 and 134 meV as P⫽60 and 4␮bar, respectively, is consistent with the data reported earlier.¹²It is then suggested that the electron-lattice interaction would be greatly enhanced in oxygen-deficient thin films.

It is basically understandable that oxygen vacancies frozen in the samples hinder the localized electron hopping via the DE mechanism. Although the conduction bandwidth data and details of the lattice distortion are unavailable to us, as justified previously¹² and confirmed presently, the oxygen vacancies contribute extrinsically to the VRH conduction.

C. Low-field magnetoresistance

The LFMR effect is strongly dependent on P as P

⬎0.1 mbar, however, seriously damaged once P

⭐0.1 mbar. It is reasonable to correlate this damage with high density of OVs in the samples. As an example, the resistivity␳-H loop at 77 K for the sample at P⫽0.2 mbar is shown in Fig. 4共a兲. The MR⬃H hysteresis 共here MR

⫽␳^/␳0⫺1兲for three samples is plotted in Fig. 4共b兲. First, the MR response to varying H shows typical MR-H hysteresis.

The peak location is the same as the magnetic coercivity H_c. Second, the MR response can be roughly classified into two parts. In part I where兩H兩⭐800 Oe, the response is seriously nonlinear and a sharp decreasing of ␳ is observable once H deviates from H_c. The resistivity reduction at low field 共lower than the field for reaching M_s兲 is attributed to the movement of the ferromagnetic domain walls and spin align- ment inside the domains if any and at the walls, i.e.,^13–15

MR⫽⌬␳^/␳共0兲⬀共M / M_s兲², 共4兲

which is independent of structural defects such as GBs and OVs. A direct verification of Eq.共4兲is given in Fig. 5 where the MR⬃H loop and M -H loop for the sample at P

⫽0.2 mbar are plotted. Equation 共4兲 is roughly satisfied as long as H⭐800 Oe. For part II where 兩H兩⬎2000 Oe, the field dependence of MR becomes roughly linear and the path correlation of the response is no longer remarkable. This is FIG. 4. 共a兲Measured MR ratio (␳/␳0⫺1) for a LSMO thin film deposited at P⫽0.2 mbar together with recorded H and T as a function of time set and 共b兲 measured MR⬃H hysteresis loops measured at T⫽77 K for three LSMO thin films at P⫽0.5, 0.2, and 0.14 mbar, respectively.

FIG. 5. Measured MR⬃H and M⬃H hysteresis at T⫽77 K for a LSMO thin film prepared at P⫽0.2 mbar.

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attributed to the spin-disordered ranges centered at GBs and OVs. Since the grain size for the three samples remains similar, OVs represent the main source for the difference in the MR response.

As P⫽0.5 mbar, the MR effect in part II is very weak so that an almost horizontal line is obtained. The sample at P

⫽0.2 mbar shows the maximal LFMR, up to 21% at H⫽

⫾4 kOe. The field for prohibiting the path correlation is the lowest at P⫽0.5 mbar and highest at P⫽0.14 mbar. A higher field predicts more spin-disordered sites in the sample. To get insight into the role of OVs, we plot d␳^/dH against H and ␹⫽(d␳^/dH)/(d␳^/dH)H⫽H_c against H/H_c in Fig. 6. Note here that␳⫽␳0 at H⫽H_c. A good coincidence of the three ␹⬃H/H_c curves over H/H_c⫽1 – 2.5 confirms once more that Eq.共4兲is satisfied no matter with how much the oxygen vacancy density in the sample is. The coercivity H_c is slightly enhanced with decreasing P, confirmed by a shift of the d␳/dH peak toward high field. This is also an indication of the appearance of more spin-disordered sites.

The same argument applies when noting that on the right of (d␳^/dH)H⫽H_c, d␳/dH takes the highest at P⫽0.14 mbar and the lowest at P⫽0.5 mbar. If this tendency is retained, a higher MR ratio is expected at a much higher field for the sample deposited at lower P. Once P⭐0.1 mbar, the samples show no more ferromagnetic moment at T⬎77 K, and LFMR at 77 K falls down to a few percent 共⬃4%兲, as presented in Fig. 7.

From all of the results presented above, it can be con- cluded that oxygen vacancies as induced by low-pressure deposition produce a number of spin-disordered sites at low T. These disordered sites can be reordered at a higher field so that part II of the MR response can be enhanced. However, overoptimized OVs weaken ferromagnetism and damage the electrotransport property. Especially, as P⭐0.1 mbar, the induced high-density OVs result in lattice distortion and pro- hibit the ferromagnetic state at all. The LFMR and high-field MR are intrinsically prohibited.

D. Two-channel model

The oxygen-vacancy-induced spin-disordered sites may form insulating chainlike clusters that distribute randomly,

but uniformly, in the microstructure and coexist with the other ranges that are metallic like. When the density of OVs increases up to some value, percolating spin-disordered net- works may form in the microstructure. Such a configuration can be described by the two-channel model proposed by An- dres et al.²⁰We give here a modified physical picture for this model. Two types of conduction channels, insulating conduction channels 共ICCs兲 and metallic conduction channels 共MCCs兲, are supposed to align in parallel. From the authors’

opinion, the interfacial layers between the two types of channels remain spin disordered at zero field or very low field.

Part of these spin-disordered interfacial layers may be reordered at a field enough low, but much higher than, H_c. In addition, GBs can be viewed as a mixing of the two types of channels. Those GBs with intimately contacted grains may be metallic ones and other GBs with heavy OVs are thought to be insulating, as proposed in the original model.²⁰

The conduction for the ICCs and MCCs follows, respectively,

␳i⫽␳i0exp共T₀/T兲^1/4,

␳m⫽a⫹bT, 共5兲 where␳iremains the same as Eq.共1兲and␳mis the resistivity for MCCs, a and b are constants to be determined. The total resistivity␳ is then written as

␳⫽共␳i⫺1⫹g␳m⫺1兲^⫺¹, 共6兲 where g represents the geometrical parameter, which de- pends not only the applied field, but also the two-channel configuration. Substituting Eq. 共5兲into Eq.共6兲, one obtains

␳⫽

再

^␳ⁱ⁰^exp^共¹^T⁰^/T^兲^1/4^⫹¹^⫹^g/a^共^b/a^兲^T

冎

^⫺¹^. ^共⁷^兲

Equation 共7兲 is used to fit our data at zero field and H

⫽4 kOe in order to evaluate four parameters␳i0, T₀, g/a, and b/a. Because ICCs make little contribution to the MR effect, Fig. 8共a兲just presents the fitted g/a and b/a, whereas T₀ at zero field is given in Table I. It is revealed that ␳i0

decreases rapidly, but T₀ is raised with decreasing P. They shift slightly up and down, respectively, once the field is applied.

FIG. 6. d␳/dH⬃H and␹⬃H/H_crelations at T⫽77 K for three LSMO thin films deposited at P⫽0.5, 0.2, and 0.14 mbar.

FIG. 7. MR ratio at H⫽4 kOe as a function of T for a series of LSMO thin films prepared at different values of P as indicated.

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The fitting shows that the parameter b/a remains unchanged around 8.4⫻10^⫺⁴K^⫺¹, no matter what the field or P is. This is reasonable, noting that once one oxygen vacancy is frozen at some site, the local electron hopping is hindered so that MCCs no longer apply to this site. The parameter g/a both at zero field and H⫽4 kOe, however, falls rapidly over three orders of magnitude as P decreases from 0.5 to 0.06 mbar and then remains stable for further descending P. A slight upshift of g/a is observed as H⬎0, which reflects the change of magnetotransport under the applied field.

Equation共6兲can be rewritten in terms of conductivity:

␴⫽␴i⫹g•␴m, 共8兲 where␴⫽1/␳^{, and}␴i and␴mare the conductivity for ICCs and MCCs. Since␴idoes not change much against H and we always have ␴iⰆg␴m at low temperature as shown in Fig.

8共b兲, the MR ratio can be written as

MR⬵ ⌬␴m

␴m共H兲⫹ ⌬共g/a兲

共g/a兲共H兲, 共9兲

where ␴m(0)⬃␴m(H) is taken since ⌬␴Ⰶ␴ 共⌬␴^/␴⬍2

⬃3% at 77 K and 4 kOe for epitaxial LSMO兲.^13,15

The first term on the right side of Eq. 共9兲takes accounts of the MR ratio at very low field (H⬃H_c), i.e., Eq. 共4兲, independent of g/a. The second term is mainly the contribution at HⰇH_c and much higher than that required for M

⫽M_s. Noting that⌬␴m/␴mⰆ⌬(g/a)/(g/a), Eq.共9兲can be simplified as

MR⬇ ⌬共g/a兲

共g/a兲共H兲. 共10兲

A plotting of the measured MR ratio at 77 K and calculated MR ratio via Eq.共10兲 at H⫽4 kOe yields a good coincidence between them, as shown in Fig. 8共c兲. The model predicts a serious damage of the MR effect once P

⭐0.1 mbar, whereas enhanced LFMR is acquired at an optimized pressure of P⫽0.20 mbar. Taking into consideration several approximations, the two-channel model seems to be a quite reasonable description of the electro- and magnetotransport phenomena in oxygen-deficient LSMO polycrystalline thin films.

IV. CONCLUSION

In conclusion, we have investigated the microstructure and electro- and magnetotransport properties of oxygen- deficient LSMO polycrystalline thin films deposited at reduced pressures of oxygen, by pulsed laser deposition. A significant influence of oxygen nonstoichiometry on these properties has been demonstrated. The lattice distortion from the pseudocubic perovskite for the thin films deposited at P

⭐0.1 mbar has been identified from the fine XRD checking, and contributes to the electron-hopping prohibition. The as- deposited thin films show typical VRH conduction over the metal-insulating point. The carrier density at the Fermi surface is found to fall down about three orders of magnitude as the oxygen pressure decreases from 0.5 mbar to 4 ␮^{bar. An} enhanced 77 K LFMR of 21% at H⫽4 kOe is demonstrated for the film deposited at P⫽0.2 mbar. A higher density of oxygen vacancies, however, results in serious damage of LFMR down to 2–3%. The two-channel model where insulating channels and metallic ones coexist is used to explain the electro- and magnetotransport. A good consistency between the measured and calculated LFMR is presented.

ACKNOWLEDGMENTS

The authors would like to acknowledge financial support from the National Natural Science Foundation of China through special and normal projects, the National Key Project for Basic Research, and LSSMS of Nanjing Univer- sity.

*Email address: [email protected]

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