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Advances in Physics Theories and Applications www.iiste.org
ISSN 2224-719X (Paper) ISSN 2225-0638 (Online)
Vol.19, 2013 - Selected from International Conference on Recent Trends in Applied Sciences with Engineering Applications
130
Effect of Cr doping in Structure and Magneto-transport
Properties of (La0.67Sr0.33)MnO3
Tejas M. Tank*
, Deepshikha Bhargava, S. P. Sanyal
Solid State Physics Laboratory, Department of Physics, Barkatullah University, Bhopal – 462 026, India
*
E-mail: tejas.physics2020@gmail.com
Abstract
The study of perovskite manganites La0.67Sr0.33Mn1-xCrxO3 (0≤ x ≥0.10) has been carried out. The structure and
magneto-transport properties of La0.67Sr0.33Mn1-xCrxO3 manganites are strongly dependent on the doping level x.
Polycrystalline samples of La0.67Sr0.33Mn1-xCrxO3 (0≤ x ≥0.10) were prepared by solid state reaction method. The
little difference between the ionic radii of Cr3+
and Mn3+
causes no change in the structure, the structure remains
rhombohedral. The temperature dependence of the resistivity is measured from 5 – 400 K without and with
magnetic field upto 5 T. The value of metal-insulator (M-I) transition temperature (TP) decreases when resistivity
increases for all the samples while doping level x increases. The value of magnetoresistance (MR %) increases
with increases Cr doping level for all samples. We have calculated energy band gap (Eg) for all samples and it is
revealed that as per doping level increases Eg increases which is comparable with experimental data. So, the
structure and magneto-transport behavior pretentious by Cr doping.
Keywords: Colossal magnetoresistance, metal-insulator transition.
PACS: 75.47.Gk; 71.30.+h;
INTRODUCTION
The physical properties of the hole doped manganites is one of the most studied topics in the last one
and half decade due to the observation of ‘‘colossal’’ magnetoresistance (CMR) [1]. The basic magnetic and
structural properties of R1-xAxMnO3 (R: rare earth, A: Ca, Ba, Sr) were widely studied in the past. Both end
members – LaMnO3 and AMnO3 – of La1-xAxMnO3 (A = Ca, Sr, Pb, Ba, etc) are antiferromagnetic insulators,
but, doped compounds (0.2 < x < 0.4) exhibit metal-insulator transition in concomitant with the ferromagnetic-
paramagnetic transition. The extraordinary electronic and magnetic properties of colossal magnetoresistance
(CMR) materials R1−xAxMn1−yByO3 (where R is a trivalent rare earth and A is a divalent alkali earth, B is
transition metal) have attracted considerable attention during the past decade. In these perovskite compounds,
interplay between magnetism, charge ordering, and electronic transport have been studied in detail [2]. In
manganites Mn ions play a crucial role in shaping the magnetic properties. Effects of Mn site substitution with
different elements such as Fe, Ni, Co etc. on the TC and other physical properties have been reported by some
workers [3]. We report here a thorough study on the effects of the replacement of Mn by Cr in the colossal
magnetoresistive La0.67Sr0.33MnO3. Replacing trivalent Cr ion with Mn ion provides us a system to understand
weakened double-exchange (DE) interaction (Mn3+
- O- Cr3+
) and the effect of co-doping of electrons on the
system with a network of Mn3+
- O- Cr3+
and Mn4+
- O- Cr4+
. In this paper, we report the results of structural and
transport properties and also energy band gap calculation on La0.67Sr0.33Mn1-xCrxO3 (0≤ x ≥0.10) compounds.
This made it possible to determine change in the electrical transport near the metal- insulator transition in this
compound.
EXPERIMENTAL
Polycrystalline samples of La0.67Sr0.33MnO3 (LSMO), La0.67Sr0.33Mn0.95Cr0.05O3 (LSMCO-5) and
La0.67Sr0.33Mn0.90Cr0.10O3 (LSMCO-10) were synthesized by the solid state reaction method. Stoichiometric
mixture of respective oxide powders was ground and reacted at 1100 ºC for 24 h in air. The samples were
reground, pressed into pellets, heated again and sintered at 1300 ºC for 24 h. The structure and phase purity of
samples were confirmed by Powder X-ray diffraction using Cu Kα radiation at room temperature. The
temperature dependence of the resistivity was measured from 5 – 400 K without and with applied magnetic field
upto 5 T. The magnetic field dependence magnetoresistance carried out at various temperatures.
RESULTS AND DISCUSSION
Figure 1 shows the XRD patterns of La0.67Sr0.33Mn1-xCrxO3 with x=0, 0.05 and 0.10. The XRD analysis
indicates that all samples are single phase with perovskite rhombohedral structure and lattice cell parameters and
unit cell volume are tabulated in Table 1. No impurity phase is observed in the XRD patterns, which suggest that
the doped Cr substitute mainly for Mn. The similarity between the crystal structures of pure and Cr-doped
samples imply that the doped Cr3+
ion does not change the crystalline structure of pure LSMO, which may
mainly result from the similar ionic size of Mn3+
and Cr3+
and the structure remains rhombohedral.
Advances in Physics Theories and Applications www.iiste.org
ISSN 2224-719X (Paper) ISSN 2225-0638 (Online)
Vol.19, 2013 - Selected from International Conference on Recent Trends in Applied Sciences with Engineering Applications
131
TABLE 1. Lattice Parameters and Unit Cell Volume for La0.67Sr0.33Mn1-xCrxO3 samples.
Sample Code Lattice Parameters ( Å ) Unit Cell Volume
(Å)3
a (Å) b (Å) c (Å)
LSMO 5.4797 5.4797 13.4040 402.483
LSMCO-5 5.4767 5.4767 13.3749 401.169
LSMCO-10 5.4741 5.4741 13.3600 400.342
FIGURE 1: X-ray diffraction patterns for La0.67Sr0.33Mn1-xCrxO3 with x=0, 0.05 and 0.10 samples.
Figure 2 demonstrates the temperature dependence of resistivity under 0 T, 1 T, 3 T and 5 T magnetic
fields. When Mn is partly substituted by Cr, the system displays a complicated and interesting transport behavior.
With increasing Cr content, the M–I transition near TP shifts to lower temperature; meanwhile an additional
bump grows up subsequent to it. The coexistence of two bumps of CMR results in CMR remains in a broad
temperature range from the lowest (T2) to above room temperature (T1). The double-peaked feature of ρ-T curve
has been also observed in high doping level (y ≥ 0.07) La0.67A0.33Mn1-yByO3 [4]. In the absence of a magnetic
field LSMCO shows Tmin in the vicinity of 60 K. Assorted possible causes for the low-temperature resistivity
minimum in the LSMCO sample are considered. These include the grain boundary, phase-separation, and
electron-electron localization [5]. To confirm these reasons, work is under process by using theoretical model.
The value of metal-insulator (M-I) transition temperature (TP) decreases when resistivity increases for all the
samples while doping level x increases. The resistivity and TP are listed in Table-2.
TABLE 2. Metal-Insulator Transition Temperature and Resistivity for La0.67Sr0.33Mn1-xCrxO3 samples.
Sample Code M-I Transition (TP) K Resistivity (ρ) Ω*cm
LSMO 373 0.0356
LSMCO-5
351 (T1)
289 (T2)
0.0450
0.0419
LSMCO-10 327 (T1) 0.0548
257 (T2) 0.0506
Advances in Physics Theories and Applications www.iiste.org
ISSN 2224-719X (Paper) ISSN 2225-0638 (Online)
Vol.19, 2013 - Selected from International Conference on Recent Trends in Applied Sciences with Engineering Applications
132
FIGURE 2. Temperature dependence of resistivity of La0.67Sr0.33 Mn1-xCrxO3 with and without magnetic fields.
Therefore, it should be ascribed to the crucial role of Cr. It suggests that Cr element substitution on Mn
site can be a potent way in tuning CMR response. This suggests that it originates from the same mechanism
based on the DE between Mn ions as in undoped La0.67Sr0.33MnO3. As we mentioned that, there is a possibility of
DE through Mn3+
–O–Cr3+
due to the identical electronic configuration between Cr3+
and Mn4+
. The present
results of CMR behavior in La0.67Sr0.33Mn1-xCrxO3 could be supporting evidence to this view. We have calculated
energy bandgap (Eg) of for all samples and it is revealed that as per doping level increases Eg increases which is
comparable with experimental data as well as due to the interruption of well known phenomena of exchange
between Mn3+
and Mn4+
while as the magnetic field increases Eg decreases for each samples which is
theoretically provide evidenced of CMR [6] and Eg values for each samples tabulated in Table 2. One can see
that Cr doping is inefficiency in lowering TP, which imply that there might exist FM interaction between Mn3+
and Cr3+
. Considering those electrical properties, we assume that a FM interaction between Cr3+
and Mn3+
is
similar to the traditional Mn3+
-O-Mn4+
DE process. Because of the different effect of the crystal field over Mn4+
and Cr3+
, this cause an energetic difference between eg orbital levels of Mn3+
and Cr3+
, which becomes strong
enough to result in that electronic exchange between them that is not equivalent to that between Mn3+
and Mn4+
.
Hence, the DE interaction between Mn3+
and Cr3+
is similar to the DE interaction between Mn3+
and Mn4+
but the
former is weaker than the latter.
Advances in Physics Theories and Applications www.iiste.org
ISSN 2224-719X (Paper) ISSN 2225-0638 (Online)
Vol.19, 2013 - Selected from International Conference on Recent Trends in Applied Sciences with Engineering Applications
133
FIGURE 3: The Temperature vs. MR % for La0.67Sr0.33Mn1-xCrxO3 at various magnetic fields.
Sample
Magnetoresistance
1T 3T 5T
MR% T (K) MR% T (K) MR% T (K)
LSMO
LSMCO-5
LSMCO-10
8
9
11
371
354
327
10
12
13
372
353
327
17
18
20
372
354
327
TABLE 3. Temperature dependent MR % at 1, 3 and 5 T magnetic fields for La0.67Sr0.33Mn1-xCrxO3 samples.
The samples show a significant change in resistance with the applied magnetic field. In other words,
they bear varying amount of MR. We show in Fig. 3, the variation of MR value with applied magnetic field at
different temperatures. It is clear from Fig. 3 that the prominent MR at very low temperature, the low-field (< 1
T) MR for Cr doped samples of about 32 % may be attributed to the intergranular spin polarized tunneling (SPT)
of carriers [7]. Thus, it is noted that, at low temperatures, the grain boundary has a significant contribution to the
electrical resistivity of the bulk sample. This is usually observed in polycrystalline samples and may result from
the grain boundary effect. MR value increases gradually with magnetic field for all samples.
CONCLUSION
In conclusion, Cr doping at Mn site weakened double-exchange interaction is reflected in the
progressive decrease in metal-insulator transition (TP) and transport and magneto transport properties in
manganite and FM interaction between Cr3+
and Mn3+
is similar to the traditional Mn3+
-O-Mn4+
DE process.
ACKNOWLEDGEMENTS
The Authors are thankful to Dr. R. Rawat, Dr. V. Ganesan and Dr. M. Gupta of UGC-DAE CSR, Indore for
help in experimental work and to UGC, New Delhi through the research project (No. F. No. 37-90/2009 (SR))
and Special Assistance Programme (SAP). Tejas M. Tank would like to acknowledge UGC-SAP, New Delhi,
India for award of UGC (SAP) – JRF.
Advances in Physics Theories and Applications www.iiste.org
ISSN 2224-719X (Paper) ISSN 2225-0638 (Online)
Vol.19, 2013 - Selected from International Conference on Recent Trends in Applied Sciences with Engineering Applications
134
REFERENCES
1. C. N. R. Rao and B. Raveau, Colossal Magnetoresistance, Charge Ordering and Related Properties and
Manganese Oxides, first ed., World Scientific, Singapore (1998).
2. N. Gayatri, A. K. Raychaudhuri, S. K. Tiwary, R. Gundakaram, A. Arulraj and C. N. R. Rao, Phys. Rev. B
56, 1345 (1997).
3. B Raveau, Phil. Trans. R. Society A 366, 83 (2008).
4. N. Paunović, Z. V. Popović, A. Cantarero, F. Sapina, Science of Sintering 40, 55 (2008).
5. B. L. Altshuler and A. G. Aronov, in Electron-Electron Interaction in Disordered Systems, edited by A. L.
Efros
and M. Pollak, North Holland, Amsterdam (1985).
6. M.F.Thorpe, Physics of Manganites, edited by T. Kalpan and S. Mahanti, New York (2002).
7. H. Y. Hwang, S. W. Cheong and B. Batlogg, Phys. Rev. Letter 77, 2041 (1996).
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Effect of cr doping in structure and magneto transport properties of (la0.67 sr0.33)mno3

  • 1. Advances in Physics Theories and Applications www.iiste.org ISSN 2224-719X (Paper) ISSN 2225-0638 (Online) Vol.19, 2013 - Selected from International Conference on Recent Trends in Applied Sciences with Engineering Applications 130 Effect of Cr doping in Structure and Magneto-transport Properties of (La0.67Sr0.33)MnO3 Tejas M. Tank* , Deepshikha Bhargava, S. P. Sanyal Solid State Physics Laboratory, Department of Physics, Barkatullah University, Bhopal – 462 026, India * E-mail: tejas.physics2020@gmail.com Abstract The study of perovskite manganites La0.67Sr0.33Mn1-xCrxO3 (0≤ x ≥0.10) has been carried out. The structure and magneto-transport properties of La0.67Sr0.33Mn1-xCrxO3 manganites are strongly dependent on the doping level x. Polycrystalline samples of La0.67Sr0.33Mn1-xCrxO3 (0≤ x ≥0.10) were prepared by solid state reaction method. The little difference between the ionic radii of Cr3+ and Mn3+ causes no change in the structure, the structure remains rhombohedral. The temperature dependence of the resistivity is measured from 5 – 400 K without and with magnetic field upto 5 T. The value of metal-insulator (M-I) transition temperature (TP) decreases when resistivity increases for all the samples while doping level x increases. The value of magnetoresistance (MR %) increases with increases Cr doping level for all samples. We have calculated energy band gap (Eg) for all samples and it is revealed that as per doping level increases Eg increases which is comparable with experimental data. So, the structure and magneto-transport behavior pretentious by Cr doping. Keywords: Colossal magnetoresistance, metal-insulator transition. PACS: 75.47.Gk; 71.30.+h; INTRODUCTION The physical properties of the hole doped manganites is one of the most studied topics in the last one and half decade due to the observation of ‘‘colossal’’ magnetoresistance (CMR) [1]. The basic magnetic and structural properties of R1-xAxMnO3 (R: rare earth, A: Ca, Ba, Sr) were widely studied in the past. Both end members – LaMnO3 and AMnO3 – of La1-xAxMnO3 (A = Ca, Sr, Pb, Ba, etc) are antiferromagnetic insulators, but, doped compounds (0.2 < x < 0.4) exhibit metal-insulator transition in concomitant with the ferromagnetic- paramagnetic transition. The extraordinary electronic and magnetic properties of colossal magnetoresistance (CMR) materials R1−xAxMn1−yByO3 (where R is a trivalent rare earth and A is a divalent alkali earth, B is transition metal) have attracted considerable attention during the past decade. In these perovskite compounds, interplay between magnetism, charge ordering, and electronic transport have been studied in detail [2]. In manganites Mn ions play a crucial role in shaping the magnetic properties. Effects of Mn site substitution with different elements such as Fe, Ni, Co etc. on the TC and other physical properties have been reported by some workers [3]. We report here a thorough study on the effects of the replacement of Mn by Cr in the colossal magnetoresistive La0.67Sr0.33MnO3. Replacing trivalent Cr ion with Mn ion provides us a system to understand weakened double-exchange (DE) interaction (Mn3+ - O- Cr3+ ) and the effect of co-doping of electrons on the system with a network of Mn3+ - O- Cr3+ and Mn4+ - O- Cr4+ . In this paper, we report the results of structural and transport properties and also energy band gap calculation on La0.67Sr0.33Mn1-xCrxO3 (0≤ x ≥0.10) compounds. This made it possible to determine change in the electrical transport near the metal- insulator transition in this compound. EXPERIMENTAL Polycrystalline samples of La0.67Sr0.33MnO3 (LSMO), La0.67Sr0.33Mn0.95Cr0.05O3 (LSMCO-5) and La0.67Sr0.33Mn0.90Cr0.10O3 (LSMCO-10) were synthesized by the solid state reaction method. Stoichiometric mixture of respective oxide powders was ground and reacted at 1100 ºC for 24 h in air. The samples were reground, pressed into pellets, heated again and sintered at 1300 ºC for 24 h. The structure and phase purity of samples were confirmed by Powder X-ray diffraction using Cu Kα radiation at room temperature. The temperature dependence of the resistivity was measured from 5 – 400 K without and with applied magnetic field upto 5 T. The magnetic field dependence magnetoresistance carried out at various temperatures. RESULTS AND DISCUSSION Figure 1 shows the XRD patterns of La0.67Sr0.33Mn1-xCrxO3 with x=0, 0.05 and 0.10. The XRD analysis indicates that all samples are single phase with perovskite rhombohedral structure and lattice cell parameters and unit cell volume are tabulated in Table 1. No impurity phase is observed in the XRD patterns, which suggest that the doped Cr substitute mainly for Mn. The similarity between the crystal structures of pure and Cr-doped samples imply that the doped Cr3+ ion does not change the crystalline structure of pure LSMO, which may mainly result from the similar ionic size of Mn3+ and Cr3+ and the structure remains rhombohedral.
  • 2. Advances in Physics Theories and Applications www.iiste.org ISSN 2224-719X (Paper) ISSN 2225-0638 (Online) Vol.19, 2013 - Selected from International Conference on Recent Trends in Applied Sciences with Engineering Applications 131 TABLE 1. Lattice Parameters and Unit Cell Volume for La0.67Sr0.33Mn1-xCrxO3 samples. Sample Code Lattice Parameters ( Å ) Unit Cell Volume (Å)3 a (Å) b (Å) c (Å) LSMO 5.4797 5.4797 13.4040 402.483 LSMCO-5 5.4767 5.4767 13.3749 401.169 LSMCO-10 5.4741 5.4741 13.3600 400.342 FIGURE 1: X-ray diffraction patterns for La0.67Sr0.33Mn1-xCrxO3 with x=0, 0.05 and 0.10 samples. Figure 2 demonstrates the temperature dependence of resistivity under 0 T, 1 T, 3 T and 5 T magnetic fields. When Mn is partly substituted by Cr, the system displays a complicated and interesting transport behavior. With increasing Cr content, the M–I transition near TP shifts to lower temperature; meanwhile an additional bump grows up subsequent to it. The coexistence of two bumps of CMR results in CMR remains in a broad temperature range from the lowest (T2) to above room temperature (T1). The double-peaked feature of ρ-T curve has been also observed in high doping level (y ≥ 0.07) La0.67A0.33Mn1-yByO3 [4]. In the absence of a magnetic field LSMCO shows Tmin in the vicinity of 60 K. Assorted possible causes for the low-temperature resistivity minimum in the LSMCO sample are considered. These include the grain boundary, phase-separation, and electron-electron localization [5]. To confirm these reasons, work is under process by using theoretical model. The value of metal-insulator (M-I) transition temperature (TP) decreases when resistivity increases for all the samples while doping level x increases. The resistivity and TP are listed in Table-2. TABLE 2. Metal-Insulator Transition Temperature and Resistivity for La0.67Sr0.33Mn1-xCrxO3 samples. Sample Code M-I Transition (TP) K Resistivity (ρ) Ω*cm LSMO 373 0.0356 LSMCO-5 351 (T1) 289 (T2) 0.0450 0.0419 LSMCO-10 327 (T1) 0.0548 257 (T2) 0.0506
  • 3. Advances in Physics Theories and Applications www.iiste.org ISSN 2224-719X (Paper) ISSN 2225-0638 (Online) Vol.19, 2013 - Selected from International Conference on Recent Trends in Applied Sciences with Engineering Applications 132 FIGURE 2. Temperature dependence of resistivity of La0.67Sr0.33 Mn1-xCrxO3 with and without magnetic fields. Therefore, it should be ascribed to the crucial role of Cr. It suggests that Cr element substitution on Mn site can be a potent way in tuning CMR response. This suggests that it originates from the same mechanism based on the DE between Mn ions as in undoped La0.67Sr0.33MnO3. As we mentioned that, there is a possibility of DE through Mn3+ –O–Cr3+ due to the identical electronic configuration between Cr3+ and Mn4+ . The present results of CMR behavior in La0.67Sr0.33Mn1-xCrxO3 could be supporting evidence to this view. We have calculated energy bandgap (Eg) of for all samples and it is revealed that as per doping level increases Eg increases which is comparable with experimental data as well as due to the interruption of well known phenomena of exchange between Mn3+ and Mn4+ while as the magnetic field increases Eg decreases for each samples which is theoretically provide evidenced of CMR [6] and Eg values for each samples tabulated in Table 2. One can see that Cr doping is inefficiency in lowering TP, which imply that there might exist FM interaction between Mn3+ and Cr3+ . Considering those electrical properties, we assume that a FM interaction between Cr3+ and Mn3+ is similar to the traditional Mn3+ -O-Mn4+ DE process. Because of the different effect of the crystal field over Mn4+ and Cr3+ , this cause an energetic difference between eg orbital levels of Mn3+ and Cr3+ , which becomes strong enough to result in that electronic exchange between them that is not equivalent to that between Mn3+ and Mn4+ . Hence, the DE interaction between Mn3+ and Cr3+ is similar to the DE interaction between Mn3+ and Mn4+ but the former is weaker than the latter.
  • 4. Advances in Physics Theories and Applications www.iiste.org ISSN 2224-719X (Paper) ISSN 2225-0638 (Online) Vol.19, 2013 - Selected from International Conference on Recent Trends in Applied Sciences with Engineering Applications 133 FIGURE 3: The Temperature vs. MR % for La0.67Sr0.33Mn1-xCrxO3 at various magnetic fields. Sample Magnetoresistance 1T 3T 5T MR% T (K) MR% T (K) MR% T (K) LSMO LSMCO-5 LSMCO-10 8 9 11 371 354 327 10 12 13 372 353 327 17 18 20 372 354 327 TABLE 3. Temperature dependent MR % at 1, 3 and 5 T magnetic fields for La0.67Sr0.33Mn1-xCrxO3 samples. The samples show a significant change in resistance with the applied magnetic field. In other words, they bear varying amount of MR. We show in Fig. 3, the variation of MR value with applied magnetic field at different temperatures. It is clear from Fig. 3 that the prominent MR at very low temperature, the low-field (< 1 T) MR for Cr doped samples of about 32 % may be attributed to the intergranular spin polarized tunneling (SPT) of carriers [7]. Thus, it is noted that, at low temperatures, the grain boundary has a significant contribution to the electrical resistivity of the bulk sample. This is usually observed in polycrystalline samples and may result from the grain boundary effect. MR value increases gradually with magnetic field for all samples. CONCLUSION In conclusion, Cr doping at Mn site weakened double-exchange interaction is reflected in the progressive decrease in metal-insulator transition (TP) and transport and magneto transport properties in manganite and FM interaction between Cr3+ and Mn3+ is similar to the traditional Mn3+ -O-Mn4+ DE process. ACKNOWLEDGEMENTS The Authors are thankful to Dr. R. Rawat, Dr. V. Ganesan and Dr. M. Gupta of UGC-DAE CSR, Indore for help in experimental work and to UGC, New Delhi through the research project (No. F. No. 37-90/2009 (SR)) and Special Assistance Programme (SAP). Tejas M. Tank would like to acknowledge UGC-SAP, New Delhi, India for award of UGC (SAP) – JRF.
  • 5. Advances in Physics Theories and Applications www.iiste.org ISSN 2224-719X (Paper) ISSN 2225-0638 (Online) Vol.19, 2013 - Selected from International Conference on Recent Trends in Applied Sciences with Engineering Applications 134 REFERENCES 1. C. N. R. Rao and B. Raveau, Colossal Magnetoresistance, Charge Ordering and Related Properties and Manganese Oxides, first ed., World Scientific, Singapore (1998). 2. N. Gayatri, A. K. Raychaudhuri, S. K. Tiwary, R. Gundakaram, A. Arulraj and C. N. R. Rao, Phys. Rev. B 56, 1345 (1997). 3. B Raveau, Phil. Trans. R. Society A 366, 83 (2008). 4. N. Paunović, Z. V. Popović, A. Cantarero, F. Sapina, Science of Sintering 40, 55 (2008). 5. B. L. Altshuler and A. G. Aronov, in Electron-Electron Interaction in Disordered Systems, edited by A. L. Efros and M. Pollak, North Holland, Amsterdam (1985). 6. M.F.Thorpe, Physics of Manganites, edited by T. Kalpan and S. Mahanti, New York (2002). 7. H. Y. Hwang, S. W. Cheong and B. Batlogg, Phys. Rev. Letter 77, 2041 (1996).
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