PHYSICAL REVIEW B, VOLUME 65, 094407
Low-temperature resistivity minima in colossal magnetoresistive La0.7Ca0.3MnO3 thin films D. Kumar and J. Sankar Center for Advanced Materials and Smart Structures, Department of Mechanical Engineering, North Carolina State University, Raleigh, North Carolina 27695
J. Narayan Department of Materials Science and Engineering, North Carolina State University, Raleigh, North Carolina 27695
Rajiv K. Singh Department of Materials Science and Engineering, University of Florida, Gainesville, Florida 32611
A. K. Majumdar* Department of Physics, University of Florida, Gainesville, Florida 32611 and Physics Department, Indian Institute of Technology, Kanpur 208016, Uttar Pradesh, India 共Received 8 December 2000; revised manuscript received 21 March 2001; published 5 February 2002兲 The low-temperature magnetoresistance of La0.7Ca0.3MnO3 共LCMO兲 thin films has been investigated using a four-probe dc technique with a 5 T superconducting magnet. Thin film samples of LCMO were prepared in situ using a pulsed laser deposition technique. The results obtained from the high-resolution low-temperature 共5–50 K兲 measurements, carried out on various samples differing widely in their resistivities, have shown distinct minima at T m in the resistivity versus temperature plots for all fields. The depth of the resistance minima was found to increase with an increase in applied magnetic field H, while T m versus H curves showed maxima at around 2 T. We have fitted the resistivity versus temperature data for all H to an expression that contains three terms, namely, residual resistivity, inelastic scattering, and electron-electron (e-e) interaction and Kondo effects. We conclude that the e-e interaction effect is the dominant mechanism for the negative temperature coefficient of resistivity of these colossal magnetoresistance 共CMR兲 materials at low temperatures. DOI: 10.1103/PhysRevB.65.094407
PACS number共s兲: 72.15.Gd, 72.15.Qm, 72.15.Rn
I. INTRODUCTION
Colossal magnetoresistance 共CMR兲 in rare-earth manganese perovskites has attracted a lot of attention because of its rich physics and its possible applications in magnetic recording and in magnetoresistive sensors. Specifically, the complete phase diagram of La1⫺x Cax MnO3 was established by Schiffer et al.1 They found transitions from a hightemperature paramagnetic insulating phase to a lowertemperature ferromagnetic metallic phase 共or antiferromagnetic insulating phase depending on the calcium doping兲. The transition is associated with a large drop in electrical resistivity. Application of a magnetic field gives rise to a large 共colossal兲 magnetoresistance defined by
MR共 % 兲 ⫽
共 H 兲⫺共 0 兲 ⫻100, 共 0 兲
共1兲
where (H) is the resistivity in a field H and (0) is that in zero field. For x⫽0.25, a negative MR of 80% was observed at around 240 K. Chahara et al.2 obtained a negative CMR of 53% in La0.75Ca0.25MnOx thin films. Subsequently, Jin et al.3 were able to get a CMR as high as 92.86% even at room temperature (99.92% at 77 K兲 in a single-phase singlecrystalline thin film of La0.67Ca0.33MnOx . The ‘‘doubleexchange’’ model of Zener and a strong electron-phonon interaction arising from the Jahn-Teller splitting of Mn d levels 0163-1829/2002/65共9兲/094407共6兲/$20.00
explain most of the electrical and magnetic properties of these manganites. Singh et al.4 observed a minimum in (T) in Pr0.67Ca0.33MnO3 thin films at around 15 K for H⫽4 T and Petrov et al.4 observed the same in granular La0.7Ca0.3MnO3 共LCMO兲 at around 25 K for H⫽0 as well as for 5 T. But no quantitative analysis of the temperature dependence around the low-temperature minimum was done. An excellent review of CMR is given by Ramirez.5 Very recently, Tiwari and Rajeev6 extensively studied the electrical resistance of bulk CMR oxides La0.7A0.3MnO3 (A ⫽Ca, Sr, Ba) and observed resistance minima below 30 K. They were explained in terms of electron-electron (e-e) interaction and inelastic scattering of electrons. These materials have a resistivity of (10–40) m⍀ cm which is higher than the Mott’s maximum metallic resistivity (⯝10 m⍀ cm in this system兲, justifying the interpretation in terms of the e-e interaction. However, the latter6 study was restricted to zero-magnetic-field observations. The resistivity minimum was first observed at very low temperatures in crystalline noble-metal alloys with magnetic impurity 共e.g., Mn, Cr兲 concentration much less than 1 at. %. This is now known as the Kondo effect.7 In later years such minima have been found at higher temperatures in structurally disordered metallic glasses8 共both magnetic and nonmagnetic兲 as well as in compositionally disordered concentrated crystalline metallic alloys9 like Fe-rich Fe100⫺x Nix Cr20 (14⭐x⭐30), Ni-rich Ni100⫺x⫺y Fex Cry (8⭐x⭐17.5, 8⭐y ⭐21), Cu100⫺x Mnx (36⭐x⭐83), etc. These minima are
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FIG. 1. Electrical resistivity ( ) vs temperature 共T兲 plots at H ⫽0 and 5 T for sample 1. On the right is plotted the negative magnetoresistance MR (%) vs T. The solid lines are just guides to the eye.
explained in terms of weak localization and electron-electron (e-e) interactions10 in three dimensions. The electrical resistivity of any of the above alloys is typically 0.2 m⍀ cm and one finds that quantum interference effects do take place irrespective of the nature of disorder, viz., structural or compositional. These resistivity minima do not disappear with the application of magnetic fields 共unlike the Kondo effect兲 and their interpretation in terms of electron-electron interactions is independent of the magnetic state of the material. The motivation behind the present work is to study the temperature dependence of the electrical resistivity of thin films of La0.7Ca0.3MnO3 , specially at low temperatures 共5–50 K兲 and in magnetic fields up to 5 T. This should throw new light on the behavior of resistivity minima in the presence of magnetic fields. These low-temperature minima are to be distinguished from the high-temperature minima associated with the charge ordering transition at around 150–200 K in La1⫺x Srx MnO3 (x⫽0.12 and 0.15兲.11
II. EXPERIMENTAL DETAILS
The bulk sample of nominal composition La0.7Ca0.3MnO3 was prepared by the ceramic method. The required quantities of respective oxide or carbonate powders were mixed and sintered at 1400 °C for 24 hr in oxygen ambient. The films of these materials were grown in situ using a pulsed laser deposition system. A detailed description of the system is mentioned elsewhere.12 In brief, a 248 nm KrF pulsed laser with a repetition rate of 5 Hz, energy per pulse of 400 mJ, and a
FIG. 2. Resistivity ( ) vs T plots at H⫽0, 1, 2, 3, 4, and 5 T for sample 1. All curves show a distinct minimum between 13 and 30 K. The solid lines are the best fits to Eq. 共3兲 which includes lattice and e-e interaction terms.
rectangular laser spot of area 1.2 cm⫻0.2 cm was used. The substrate temperature during film deposition was varied. The films deposited were characterized using x-ray diffraction, x-ray photoelectron spectroscopy, high-resolution transmission electron microscopy, atomic force microscopy 共AFM兲, and Rutherford backscattering spectroscopy 共RBS兲, and the results are reported elsewhere.12,13 The films were found to be of very-high-quality single-phase material. The thickness of the film was measured using a profilometer. LCMO films with different resistivities were fabricated by changing the deposition temperature keeping other deposition parameters unchanged. One set of LCMO films was deposited at 750 °C and another set was deposited at 800 °C. The resistivity of LCMO film deposited at 800 °C 共called sample 1兲 was 0.08 ⍀ cm, while the resistivity of LCMO film deposited at 750 °C 共called sample 2兲 was 0.2 ⍀ cm, both at 300 K. The thickness of both films was ⯝1000 Å. The temperature dependence of the resistance of the films was measured in zero as well as in some applied magnetic fields using the standard four-probe technique and a magnetic field provided by a Quantum Design superconducting quantum interference device 共SQUID兲 magnetometer. Both the transport current and applied field were in the film plane with the current parallel to the field.
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correction to the electrical conductivity is given by10
共 T 兲 ⫽ 共 0 兲 ⫹BT 1/2,
FIG. 3. T min and the depth of the minima are plotted against magnetic field H for samples 1 and 2. T min is higher for sample 2 which also has a higher electrical resistivity. The solid lines are just guides to the eye.
where (0) is the residual conductivity contributed by the temperature-independent scattering processes and B is proportional to the diffusion constant. Measurements on amorphous7 and concentrated crystalline8 alloys have shown a near-universal value of B⫽6 (⍀ cm K1/2) ⫺1 . In these LCMO films ⬎10 m⍀ cm at 5 K and so electron localization is quite plausible at low temperatures. However, inelastic scattering, which increases monotonically with temperature, competes with the e-e interaction 关which decreases with temperature as given in Eq. 共2兲兴 and gives rise to the resistivity minimum. Assuming all the temperaturedependent scattering processes, like electron-phonon, electron-magnon, and electron-electron, are adequately described by a single power law (AT n ), one could write
共 T 兲⫽
III. RESULTS AND DISCUSSION
Figure 1 shows the resistivity ( ) versus temperature 共T兲 plots at H⫽0 and 5 T for sample 1 from 10 K to 300 K. Here (T) at H⫽0 shows a peak at 220 K which separates the high-temperature paramagnetic insulating phase from the low-temperature ferromagnetic metallic phase. At H⫽5 T, (T) drops down considerably and the peak shifts to a higher temperature of 260 K. The negative MR兵 关 (5 T) ⫺ (0) 兴 / (0) 其 is also plotted against T in Fig. 1. It has a maximum of 76% at a lower temperature of 190 K, a feature rather commonly observed in LCMO films.3 Much closer (T) data were taken at low temperatures (⬍50 K) since our main interest lies in studying the resistivity minima. Figure 2 shows vs T for sample 1 at H⫽0, 1, 2, 3, 4, and 5 T. All of them have a minimum at T min as shown in Fig. 3 (T min vs H), which also includes plots for the depth of minima versus H. The upturn of (T) in Fig. 2 below T min could be due to factors like the Kondo effect or the electron-electron (e-e) interaction. Let us first consider the latter effect. Here one encounters the phase coherence of two electrons, both becoming localized through elastic impurity scattering. The
1
共 0 兲 ⫹BT 1/2
⫹AT n ,
H 共T兲
(0) (⍀ cm) ⫺1
B (⍀ cm K1/2) ⫺1
A (10⫺6 ⍀ cm/Kn )
n
2 (10⫺6 )
0.05 0.1 1 2 3 4 5
111.0 110.9 121.9 128.7 128.5 128.5 132.5
2.2 2.3 4.2 6.3 10.8 16.9 21.0
1.04 0.93 0.02 0.01 0.08 0.54 1.36
1.89 1.90 2.75 2.93 2.45 2.00 1.79
0.80 0.80 0.13 0.46 3.16 4.1 2.6
2⫽
冉 冊兺冋 1 N
i⫽1 n
i ⫺ifit兲2 共raw
共ifit兲2
共3兲
after assuming Mathiessen’s rule. The (T) data for all H, shown in Fig. 2, are fitted to Eq. 共3兲. Excellent fits are obtained as shown by the solid lines in Fig. 2. The coefficients of the fits are given in Table I along with values of the normalized 2 . A typical value of 2 ⫽10⫺6 共Table I兲 compares favorably with the experimental resolution of 0.5⫻10⫺3 in ⌬ / . The fits are found to be better at lower fields. Data were also taken down to 2 K and up to 30 K for H⫽0.05 and 0.1 T as shown in Fig. 4 for sample 1. Here the fits are even better. It should be noted that in Fig. 4 the resistivity axis is highly magnified and so the deviation of the best-fitted curves from the data seems to be large. The best-fitted coefficients (0), B, A, and n are plotted against H in Fig. 5 for sample 1. The coefficient B increases monotonically with H from 2 to 21 (⍀ cm K1/2) ⫺1 . Tiwari and Rajeev6 found B⫽0.7 (⍀ cm K1/2) ⫺1 at H⫽0 compared to 2.2 (⍀ cm K1/2) ⫺1 of the present work. A nearuniversal value of B⫽6 (⍀ cm K1/2) ⫺1 has been found at zero field in many crystalline and amorphous alloys8,9 of moderate resistivity (0.2 m⍀ cm). The increase of B with H
TABLE I. Magnetic field, coefficients of the fit to Eq. 共3兲, and the normalizeda 2 for sample 1.
a
共2兲
册
.
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FIG. 5. The best-fitted parameters (0), B, A, and n 关see Eq. 共3兲 for definition兴 are plotted against H of sample 1. The solid lines are just guides to the eye.
where (0) is the residual conductivity and C is a constant of proportionality. Putting together the inelastic scattering term as in Eq. 共3兲 one gets
共 T 兲⫽ FIG. 4. Resistivity ( ) vs T plots at H⫽0.05 and 0.1 T for sample 1. The solid lines are the best fits to Eq. 共3兲. Note the expanded axis showing apparently deeper minima and higher deviation of the best-fitted lines from the data.
is understandable in view of the increase in the depth of minima at higher fields as shown in Fig. 3. Consequently B increases with the depth of minima. However, the e-e interaction should give rise to a small positive magnetoresistance.10 But the large negative MR in these materials overshadows the positive magnetoresistance due to the e-e interaction. The inelastic scattering temperature exponent n varies from 1.8 to 2.9. Tiwari and Rajeev6 found n⫽2.4 at H⫽0 compared to n⫽1.9 of ours. Schiffer et al.1 obtained n⫽2.5 in La0.75Ca0.25MnO3 below T c /2. Neither the maximum of n at H⫽2 T nor the corresponding minimum in A is understood. (0) increases slowly with H. We have tried to isolate the e-phonon and e-magnon terms by fitting (T) to a Bloch-Gruneissen kind of integral for e-phonon scattering along with a T 2 term for the electronmagnon scattering. Very good fits were obtained but the parameters were randomly varying over a wide range and no meaningful conclusions could be drawn from them. As stated before Eq. 共2兲, the other plausible reason for the occurrence of the resistance minimum is the Kondo effect in dilute crystalline alloys. Below T min , the conductivity decreases with decreasing temperature as
共 T 兲 ⫽ 共 0 兲 ⫹C ln T,
共4兲
1 ⫹AT n , 共 0 兲 ⫹C ln T
共5兲
where C ln T is the additional conductivity term due to the Kondo effect, if it is present. The value of 2 is higher by a factor of 6 when compared to the fit to Eq. 共3兲 which has instead an e-e interaction term. The deviation of the raw data from the best-fitted data ( raw ⫺ f itted ) as a function of temperature is plotted in Fig. 6 for sample 1 at H⫽1 and 2 T for
FIG. 6. The deviation in of the raw data from the best-fitted data ( raw ⫺ f itted ) is plotted as a function of temperature for sample 1 at magnetic fields of 1 and 2 T. Lines and symbols are used for fits with the lattice and the e-e interaction terms 关see Eq. 共3兲兴 while only lines represent fits with the lattice and the Kondo effect terms 关see Eq. 共5兲兴. The solid lines are just guides to the eye.
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FIG. 8. Same as in Fig. 6 except now for sample 2. Here H ⫽1 and 5 T. These fits are much better than those in Fig. 6.
FIG. 7. Same as in Fig. 2 except now for sample 2. Here H ⫽0, 1, 3, and 5 T.
both fits, i.e., e-e interaction 关Eq. 共3兲兴 and Kondo effect 关Eq. 共5兲兴. Clearly, the e-e interaction theory fits the present data better at both fields. We have done a very similar analysis with the data of sample 2 where we have measured (T) at H⫽0, 1, 3, and 5 T. This sample has a much higher resistivity 关 (T min ,H ⫽0)⬇200 m⍀ cm for sample 2 and 10 m⍀ cm for sample 1兴. However, the conclusion of the analysis is very much the same as in the case of sample 1. The data as well as the best-fitted curves are shown in Fig. 7. The coefficients of the fit to Eq. 共3兲 are given in Table II. The coefficient B increases almost linearly with H from 0.4 to 6.0 (⍀ cm K1/2) ⫺1 . Here, too, the depth of minima and hence B increase with magnetic field as shown in Fig. 3. Sample 2 having a higher resistivity 共dirty兲 than sample 1 is more prone to e-e interactions. This shows up in the higher values of the depth of minima and T min 共Fig. 3兲.
Figure 8 shows the deviation 共as in Fig. 6兲 versus T for sample 2 for both fits at H⫽1 and 5 T. Here, the values of 2 for the e-e interaction fits are about an order of magnitude smaller than those for the Kondo effect fits. We have no doubt that the present data strongly suggest e-e interactions as the dominant mechanism for the resistivity minima in these CMR oxides. For both samples, we find the same trend of variation of T min with H; both exhibit a broad maximum at around 2 T. We believe that T min is the temperature beyond which the increase in due to inelastic scattering overtakes the decrease in due to the e-e interaction effect. The decrease in due to the e-e interaction is essentially due to the increase of the coefficient B with the field and, hence, T min moves to higher temperatures at higher fields. However, the reason for the subsequent slow decrease of T min at higher fields is not at all clear. IV. CONCLUSIONS
Thin films of La0.7Ca0.3MnO3 were grown by pulsed laser ablation. Two samples deposited at different temperatures had resistivities of 80 and 200 m⍀ cm at 300 K. Both show resistivity minima at low temperatures (⬍40 K) over a range of field as wide as 0⭐H⭐5 T. The (T) data up to 50 K were fitted to expressions containing the residual reistivity, inelastic scattering term, and electron-electron interaction and Kondo effects 共the term causing an initial decrease in with increasing temperature giving rise to a minimum兲. Unequivocal evidence established that the most dominant
TABLE II. Magnetic field, coefficients of the fit to Eq. 共3兲, and the normalized 2 for sample 2. H 共T兲
(0) (⍀ cm) ⫺1
B (⍀ cm/K1/2) ⫺1
A (10⫺6 ⍀ cm/Kn )
n
2 (10⫺6 )
0 1 3 5
3.36 4.8 3.0 0.7
0.36 1.14 3.0 6.0
0.34 0.000 06 0.002 0.83
1.87 3.82 2.89 1.36
3.1 2.8 74 14
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contribution to the resistivity minima in these CMR materials comes from the e-e interaction term. The large values of electrical resistivity in these oxides justify the observation of quantum interference effects in their electrical transport. The associated positive magnetoresistance, which normally arises from the e-e interaction effect, is overshadowed by the negative CMR. To conclude, resistivity minima in mangnites in the presence of magnetic fields have been analyzed here quantitatively in terms of electron-electron interaction effects.
*Author to whom correspondence should be addressed. Electronic address:
[email protected] 1 P. Schiffer, A.P. Ramirez, W. Bao, and S-W. Cheong, Phys. Rev. Lett. 75, 3336 共1995兲. 2 Ken-ichi Chahara, Toshiyuki Ohno, Masahiro Kesai, and Yuzoo Kozono, Appl. Phys. Lett. 63, 1990 共1993兲. 3 S. Jin, T.H. Tiefel, M. McCormack, R.A. Fastnacht, R. Ramesh, and L.H. Chen, Science 264, 413 共1994兲. 4 S.K. Singh, S.B. Palmer, D. M. Paul, and M.R. Lees, Appl. Phys. Lett. 69, 263 共1996兲; D.K. Petrov, L. Krusin-Elbaum, J.Z. Sun, C. Feild, and P.R. Duncombe, ibid. 75, 995 共1999兲. 5 A.P. Ramirez, J. Phys.: Condens. Matter 9, 8171 共1997兲. 6 A. Tiwari and K.P. Rajeev, Solid State Commun. 111, 33 共1999兲. 7 J. Kondo, Prog. Theor. Phys. 32, 37 共1964兲. 8 R.W. Cochrane and J.O. Strom-Olsen, Phys. Rev. B 29, 1088
ACKNOWLEDGMENTS
One of us 共A.K.M.兲 acknowledges the Physics Department, University of Florida, Gainesville for local hospitality and experimental facilities. Financial support from the DOD/ AFOSR MURI 共Grant No. F49620-96-1-0026兲, NSF, and DOE are gratefully acknowledged. We thank Debashish Chowdhury, Ram Shanker Patel, and Rajiv Bhat for carefully going through the manuscript and suggesting important changes.
共1984兲; A. Das and A.K. Majumdar, ibid. 43, 6042 共1991兲; T.K. Nath and A.K. Majumdar, ibid. 55, 5554 共1997兲. 9 S. Banerjee and A.K. Raychaudhuri, Phys. Rev. B 50, 8195 共1994兲; S. Chakraborty and A.K. Majumdar, ibid. 53, 6235 共1996兲; J. Magn. Magn. Mater 186, 357 共1998兲. 10 B.L. Altshuler and A.G. Aronov, in Electron-Electron Interactions in Disordered Systems, edited by A.L. Efros and M. Pollak 共North-Holland, Amsterdam, 1985兲; P.A. Lee and T.V. Ramakrishan, Rev. Mod. Phys. 57, 287 共1985兲. 11 J.-S. Zhou, J.B. Goodenough, A. Asamitsu, and Y. Tokura, Phys. Rev. Lett. 79, 3234 共1997兲. 12 D. Kumar, R.K. Singh, and C.B. Lee, Phys. Rev. B 56, 13 666 共1997兲. 13 S.V. Pietambaram, D. Kumar, R.K. Singh, C.B. Lee, and V.S. Kaushik, J. Appl. Phys. 86, 3317 共1999兲.
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