Exchange interaction and magnetoresistance in La₂/₃Ca₁/₃MnO₃ : experiment and models

The magnetization M(T) and electrical resistivity ρ(T) of a La₂/₃Ca₁/₃MnO₃ film have been studied in the temperature range 5 K⩽T⩽320 K in the magnetic field intervals 10 Oe⩽H⩽400 Oe and 0⩽H⩽50 kOe, respectively. It is found that the M(T)/M(0) value is larger than that predicted by the conventional m...

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Дата:	2002
Автори:	Beznosov, A.B., Belevtsev, B.I., Fertman, E.L., Desnenko, V.A., Naugle, D.G., Rathnayaka, K.D. D., Parasiris, A.
Формат:	Стаття
Мова:	English
Опубліковано:	Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2002
Назва видання:	Физика низких температур
Теми:	Сильно коррелированные системы и высокотемпературная сверхпроводимость
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Цитувати:	Exchange interaction and magnetoresistance in La₂/₃Ca₁/₃MnO₃ : experiment and models / A.B. Beznosov, B.I. Belevtsev, E.L. Fertman, V.A. Desnenko, D.G. Naugle, K.D. D. Rathnayaka, A.Parasiris // Физика низких температур. — 2002. — Т. 28, № 7. — С. 774-780. — Бібліогр.: 30 назв. — англ.

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spelling	nasplib_isofts_kiev_ua-123456789-1302292025-02-09T14:30:55Z Exchange interaction and magnetoresistance in La₂/₃Ca₁/₃MnO₃ : experiment and models Beznosov, A.B. Belevtsev, B.I. Fertman, E.L. Desnenko, V.A. Naugle, D.G. Rathnayaka, K.D. D. Parasiris, A. Сильно коррелированные системы и высокотемпературная сверхпроводимость The magnetization M(T) and electrical resistivity ρ(T) of a La₂/₃Ca₁/₃MnO₃ film have been studied in the temperature range 5 K⩽T⩽320 K in the magnetic field intervals 10 Oe⩽H⩽400 Oe and 0⩽H⩽50 kOe, respectively. It is found that the M(T)/M(0) value is larger than that predicted by the conventional molecular field model below the Curie point T=267 K, and that the ln ρ(T) dependence is close to linear in the temperature range 80 K<T<200 K (accordingly, ∂ ln ρ/∂T is constant in this region). A model of the electrical conductivity and magnetoresistivity of the system describing qualitatively the experimental results is proposed (the Δmτ model). The model includes a thermally activated (with characteristic energy Δ) mechanism of conductivity, dependence of the concentration and the effective mass (m) of the itinerant charge carriers on the magnetization, as well as scattering (with characteristic time τ) of the charge carriers by static breakings of the translational symmetry, thermal fluctuations of the magnetic order, and phonons. Authors are pleased to dedicate the paper to Academician V. V. Eremenko, whose multifaceted scientific interests and achievements in the physics of magnetic phenomena in the compounds of d and f elements are widely appreciated. 2002 Article Exchange interaction and magnetoresistance in La₂/₃Ca₁/₃MnO₃ : experiment and models / A.B. Beznosov, B.I. Belevtsev, E.L. Fertman, V.A. Desnenko, D.G. Naugle, K.D. D. Rathnayaka, A.Parasiris // Физика низких температур. — 2002. — Т. 28, № 7. — С. 774-780. — Бібліогр.: 30 назв. — англ. 0132-6414 PACS: 75.30.Vn, 72.80.Ga, 81.05.-t https://nasplib.isofts.kiev.ua/handle/123456789/130229 en Физика низких температур application/pdf Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
language	English
topic	Сильно коррелированные системы и высокотемпературная сверхпроводимость Сильно коррелированные системы и высокотемпературная сверхпроводимость
spellingShingle	Сильно коррелированные системы и высокотемпературная сверхпроводимость Сильно коррелированные системы и высокотемпературная сверхпроводимость Beznosov, A.B. Belevtsev, B.I. Fertman, E.L. Desnenko, V.A. Naugle, D.G. Rathnayaka, K.D. D. Parasiris, A. Exchange interaction and magnetoresistance in La₂/₃Ca₁/₃MnO₃ : experiment and models Физика низких температур
description	The magnetization M(T) and electrical resistivity ρ(T) of a La₂/₃Ca₁/₃MnO₃ film have been studied in the temperature range 5 K⩽T⩽320 K in the magnetic field intervals 10 Oe⩽H⩽400 Oe and 0⩽H⩽50 kOe, respectively. It is found that the M(T)/M(0) value is larger than that predicted by the conventional molecular field model below the Curie point T=267 K, and that the ln ρ(T) dependence is close to linear in the temperature range 80 K<T<200 K (accordingly, ∂ ln ρ/∂T is constant in this region). A model of the electrical conductivity and magnetoresistivity of the system describing qualitatively the experimental results is proposed (the Δmτ model). The model includes a thermally activated (with characteristic energy Δ) mechanism of conductivity, dependence of the concentration and the effective mass (m) of the itinerant charge carriers on the magnetization, as well as scattering (with characteristic time τ) of the charge carriers by static breakings of the translational symmetry, thermal fluctuations of the magnetic order, and phonons.
format	Article
author	Beznosov, A.B. Belevtsev, B.I. Fertman, E.L. Desnenko, V.A. Naugle, D.G. Rathnayaka, K.D. D. Parasiris, A.
author_facet	Beznosov, A.B. Belevtsev, B.I. Fertman, E.L. Desnenko, V.A. Naugle, D.G. Rathnayaka, K.D. D. Parasiris, A.
author_sort	Beznosov, A.B.
title	Exchange interaction and magnetoresistance in La₂/₃Ca₁/₃MnO₃ : experiment and models
title_short	Exchange interaction and magnetoresistance in La₂/₃Ca₁/₃MnO₃ : experiment and models
title_full	Exchange interaction and magnetoresistance in La₂/₃Ca₁/₃MnO₃ : experiment and models
title_fullStr	Exchange interaction and magnetoresistance in La₂/₃Ca₁/₃MnO₃ : experiment and models
title_full_unstemmed	Exchange interaction and magnetoresistance in La₂/₃Ca₁/₃MnO₃ : experiment and models
title_sort	exchange interaction and magnetoresistance in la₂/₃ca₁/₃mno₃ : experiment and models
publisher	Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
publishDate	2002
topic_facet	Сильно коррелированные системы и высокотемпературная сверхпроводимость
url	https://nasplib.isofts.kiev.ua/handle/123456789/130229
citation_txt	Exchange interaction and magnetoresistance in La₂/₃Ca₁/₃MnO₃ : experiment and models / A.B. Beznosov, B.I. Belevtsev, E.L. Fertman, V.A. Desnenko, D.G. Naugle, K.D. D. Rathnayaka, A.Parasiris // Физика низких температур. — 2002. — Т. 28, № 7. — С. 774-780. — Бібліогр.: 30 назв. — англ.
series	Физика низких температур
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first_indexed	2025-11-26T21:29:20Z
last_indexed	2025-11-26T21:29:20Z
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fulltext	Fizika Nizkikh Temperatur, 2002, v. 28, No. 7, p. 774– 780 Exchange interaction and magnetoresistance in La2/3Ca1/3MnO3 : experiment and models A. B. Beznosov, B. I. Belevtsev, E. L. Fertman, and V. A. Desnenko B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine, 47 Lenin Ave., Kharkov 61103, Ukraine E-mail: beznosov@ilt.kharkov.ua D. G. Naugle, K. D. D. Rathnayaka, and A. Parasiris Department of Physics, Texas A & M University, College Station, TX 77843, USA Received March 5, 2002 The magnetization M(T) and electrical resistivity �(T) of a La Ca MnO2 1 3 33 film have been studied in the temperature range 5 K � T � 320 K in the magnetic field intervals 10 Oe � H � 400 Oe and 0 � H � 50 kOe, respectively. It is found that the M(T)/M(0) value is larger than that predicted by the conventional molecular field model below the Curie point T = 267 K, and that the ln �(T) dependence is close to linear in the temperature range 80 K < T < 200 K (accordingly, � ln �/�T is constant in this region). A model of the electri- cal conductivity and magnetoresistivity of the system describing qualitatively the experimen- tal results is proposed (the �m� model). The model includes a thermally activated (with cha- racteristic energy �) mechanism of conductivity, dependence of the concentration and the effective mass (m) of the itinerant charge carriers on the magnetization, as well as scattering (with characteristic time �) of the charge carriers by static breakings of the translational sym- metry, thermal fluctuations of the magnetic order, and phonons. PACS: 75.30.Vn, 72.80.Ga, 81.05.–t 1. Introduction Complex oxides containing manganese ions Mn3+ and Mn4+ have been attracting much atten- tion in physics and technology in the last 10 years due to the «colossal magnetoresistance (CMR) ef- fect» discovered in them: the electrical resistance of the compounds decreases substantially (in orders of magnitude) when an external magnetic field is ap- plied to a sample in the vicinity of the Curie tem- perature (see reviews [1–6]). The nature of this phenomenon is being studied intensively; the main directions of the research are outlined in the above-mentioned reviews. We note here also the following original papers, references to which will be made below [7–14]. The key point in an understanding of the CMR mechanisms is elucidating of the nature of changes of the electrical resistance on passage through the Curie point, first of all in the absence of the exter- nal magnetic field. The present work is devoted to an experimental study of the problem as well as to a theoretical modeling of the phenomenon. The dependences of the magnetization and elec- trical conductivity of a La2/3Ca1/3MnO3 film on the temperature and magnetic field are studied ex- perimentally and analyzed. A model of the electri- cal conductivity and magnetoresistive behavior is proposed (�m� model). The model includes a ther- mally activated (with the characteristic energy �) mechanism of conductivity, dependence of the con- centration and effective mass (m) of the itinerant charge carriers on the magnetization, as well as scattering (with the characteristic time �) of those carriers by static breakings of translational symme- try, thermal fluctuations of the magnetic order, and phonons. © A. B. Beznosov, B. I. Belevtsev, E. L. Fertman, V. A. Desnenko, D. G. Naugle, K. D. D. Rathnayaka, and A. Parasiris, 2002 2. The �m� model of conductivity The proposed effective model of conductivity is based on the concept of thermal excitation of the charge carriers from localized states to itinerant states. We do not specify here the type of charge carriers, but for simplicity, without any loss in ge- nerality, we call them electrons. In this picture, above the Curie point the charge carriers are loca- lized, so that their motion between the crystal sites can only be of the thermally activated kind. At the same time they appear to be nearly free in the ferromagnetically ordered state. Thus their activa- tion energy has to be dependent on the magnetic or- der parameter. 2.1. Activation energy Analysis of the results of our present measure- ments of the electrical resistivity and magnetization of the La2/3Ca1/3MnO3 film (see Secs. 5, 6) has shown that the dependence of the activation energy � on the ferromagnetic order parameter of the sys- tem � = M(T, H)/M0 in a vicinity of the Curie point TC is close to linear (here M is the magnetiza- tion, T is the temperature, H is the magnetic field, and M0 is the magnetization at T=0). On the other hand, the conductivity must be of the nonactivated kind at T = 0 (the experiment gives a finite value of the corresponding electrical resistivity of the sys- tem �). Thus we choose the simplest dependence �(�) satisfying the above mentioned requirements, in the form � �� 0 1 � , (1) where �0 is the activation energy in the para- magnetic region and will be determined in the model by fitting to the experimental data. Expression (1) gives for the concentration of the electrons in the «conduction band» the value � � n n T 0 10 e � � , (2) where n0 is the concentration of the conduction electrons in the completely ordered system (� = 1). Note that a dependence of the form in Eq. (2) was established for the concentration of the con- duction electrons of EuO in Ref. 8. 2.2. Effective mass of charge carriers The hopping integral of the electrons in the «conduction band» depends on the mutual orienta- tion of the local spins of nearest magnetic ions [5], so that their effective mass m* also depends on � � m m* * �0 2 1 � . (3) Here m0 * is the effective mass of the perfect crystal (� = 1) and will be considered further as a fitting parameter of the model. The expression (3) has been obtained by the av- eraging of the hopping integral over the crystal with a subseqnent transition to the effective mass representation in a model of magnetization in which the local quantization axes for the itinerant electrons (i.e., the directions of the local magnetic moments considered as classical vectors) are de- flected from the easy magnetization axis by the same polar angle at every Mn site, and the azimuth angles are randomly distributed uniformly in the interval (0,2 ). 2.3. Transport relaxation time The electrical resistivity of the system is calcu- lated in the model by the Drude formula � � m e n * 2 , (4) where e is the electron charge, m* and n are determined by Eqs. (1)–(3), and the transport relaxation time � is defined by the sum � � � � � � 1 1 1 1 st ph m . (5) Here �st, �ph and �m are the characteristic times for the scattering by the static breakings of the trans- lational symmetry of the system (this is principally because of the random distribution of the La and Ca ions in the crystal), phonons, and fluctuations of the local magnetic moments, respectively. Taking into account Eqs. (1), (2), (4), and (5), and using the theoretical approaches from Refs. 15–17, we write the expression for the electri- cal resistivity of the system in the form � � � � � �e st ph 2 3 � T m( ) . (6) Here the resistivity �st , caused by the static brea- kings of the crystal-lattice translational symmetry, is given by � �� st � � � � � � �0 22 1 , (7) where Eq. (3) and the theory of Ref. 15 have been taken into account. The resistivity �ph , caused by the electron–pho- non scattering, is evaluated by the Bloch-Grüneisen formula [16] Fizika Nizkikh Temperatur, 2002, v. 28, No. 7 775 Exchange interaction and magnetoresistance in La2/3Ca1/3MnO3 � �� ph e e � � �� 4 1 1 5 5 0 D D x x TT x dx D � � , (8) where the Debye temperature �D is taken equal to 440 K (by our estimate made using the sound velocity from Ref. 18), which is in accordance with other estimates [6,19]. The resistivity �m caused by the electron scatter- ing on the disordered local spins is evaluated using the Kasuya expression [17], modified for the pre- sent case by replacing the constant effective mass by a function of magnetization [Eq. (3)]: � � � � �m m S S S � � � � � � � �� 2 1 1 2 2( ) . (9) Note that as one can see from Eqs. (6), (7), and (9), all three scattering times in Eq. (5) have the same dependence on n (� � n–1/3), �st and �m have the same dependence on m* � �( )*� st m m �1 . Exponential dependences of the electrical resis- tivity, compatible with Eq. (6) (i.e., with the ar- gument of the exponential function being linearly dependent on magnetization), were observed expe- rimentally in Refs. 7–9. Other forms of the �(�) dependence were proposed in Refs. 7, 11–14. On our opinion, these last do not have as good agree- ment with the known experimental data (see Refs. 1–6) and with those obtained in this work. 3. The modified molecular field model for magnetization The local spin S in Eq. (9) was put equal to 2, and the reduced magnetization � = M/M0 was esti- mated in the modified molecular field model. This model differs from the conventional form (see, for example, [20]) by the additional fitting parameters a and h. They formally take into account the effect of spontaneous magnetization on the interatomic exchange parameter and the effect of the short- range order on the charge-carrier scattering above the Curie temperature. The latter is substantial in the case of a short mean free path of the carriers, because they are localized in the absence of mag- netic order, as is evidenced by the change of charac- ter of the conductivity from metallic to semicon- ductive when going from the ferromagnetic to the paramagnetic state of the oxide. The ferromagnetic order parameter in the model is defined by the following equation: � � � � � � � �� B h T S S T a TS C3 1 1 2 . (10) Here BS(x) is the Brillouin function for spin S = 2, TC is the Curie temperature, h is a fictive magnetic field modeling the effect of short-range magnetic order above TC , and a is a magnetoelastic para- meter describing the magnetostrictive shift of TC [21]. Note that the value S = 2 for the local spin used in the model corresponds to the spin of the Mn3+ ion but not to the spin S = 3/2 of the Mn4+ ion, which must actually be regarded as the local spin. This is done just because it gives a better fit (com- pared to S = 3/2) of the experimental data in the low-temperature region, where molecular field the- ory, used in the model over the whole temperature range for simplicity, is not valid a priori. Thus, such a substitution can be made without any funda- mental significance. In the most important region, in the vicinity of TC , the value S = 3/2 gives the better result in the conventional molecular field model and therefore requires a weaker correction for agreement with the experimental data. 4. Nature of the activation energy � As one can see from Sec. 7, this simple model (it will be referred to below as the �m� model) gives a temperature dependence of the electrical resistivity of the given oxide quite close to the experimental one. Here, however, a detailed microscopic picture of the phenomenon (i.e., mainly the nature of the activation energy �) is not considered. Moreover, we do not discuss here the values of all the fitting parameters (they are physically quite reasonable) and their exact origin. Obviously, behavior of the conductivity similar to that in the �m� model can be obtained in a different way, but we suppose that this model is the simplest which takes into account the most important factors that can influence the magnetoresistive effect in doped manganites. The activation energy � in the model can reflect an effect of localization of the charge carriers [22] when the magnitude of the fluctuations of their ex- change energies exceeds some critical value, at least for the majority of them at T � TC . Apparently, a starting point for constructing a model of conduc- tivity in manganites can be the concept of double exchange [23–25]. In reality the picture of the phe- nomenon appears to be more complex. The role of the charge carriers be played by magnetic polarons, which are being formed due to the interactions bet- ween the quasilocal charge carriers and magnetic 776 Fizika Nizkikh Temperatur, 2002, v. 28, No. 7 A. B. Beznosov et al. moments of the surrounding lattice sites, and due to deformations of the atomic structure over dis- tances of the order of the first coordination sphere (see the general discussion in Refs. 22, 26, and 27 and the manganite-specific one in Refs. 2, 6, and 28). Note that the origin of the local lattice defor- mations can be of an exchange–relativistic nature [29]. There is no necessity, however, to make more precise the character of the charge carriers in the original �m� model. 5. Experimental The La1–xCaxMnO3 (x � 1/3) film (about 1500 Å thick) was grown by pulsed laser deposition on a LaAlO3 substrate. A KrF excimer laser operating at 248 nm was used to ablate the target material, with a nominal composition La2/3Ca1/3MnO3 . The tar- get was prepared by the conventional solid-state re- action method starting from high-purity powders of La2O3 , CaCO3 , and MnCO3 . An x-ray study of the target has shown that it is homogeneous in com- position and does not contain a residue of the start- ing chemical components. The film obtained was tested by the x-ray diffraction method and on an atomic force microscope. The resistance as a func- tion of temperature (in the range 5–320 K) and magnetic field (up to 50 kOe) was measured by a standard four-point probe technique. The magneto- resistance �(T, H) = [�(T, H) – �(T, 0)]/�(T, 0) was measured in a transverse geometry (with the field perpendicular to the film plane). The magne- tization was measured by a SQUID magnetometer in the field range 10 Oe � H � 400 Oe in a longitu- dinal geometry (with the field parallel to the film plane). 6. Results of experiment Figures 1–7 present the following characteristics obtained for the La2/3Ca1/3MnO3 film studied: the square of the reduced magnetization (M(T)/M(0))2 in the Curie-point region, the re- duced magnetization M(T)/M(0) at magnetic fi- eld H = 10 Oe, the magnetization M(H) at tempe- ratures of 10, 20, 40, and 60 K, the electrical resistivity �(T), the electrical resistivity in a loga- rithmic scale, the logarithmic temperature derivati- ve of the resistivity � ln �/�T, and the magne- toresistance �(T,H) in magnetic field H = 50 kOe. An extrapolation to � = 0 of the linear part of the dependence �2(T) (Fig. 1) gave a value of TC equal to 267 K. The sharp growth of the magnetiza- tion below TC seen in Fig. 2 confirms the high ho- mogeneity of the film. The magnetic field depen- dence of the magnetization is found to be nonlinear in the temperature and magnetic field ranges stu- died (Fig. 3). At T = 10 K the magnetization M is Fizika Nizkikh Temperatur, 2002, v. 28, No. 7 777 Exchange interaction and magnetoresistance in La2/3Ca1/3MnO3 Fig. 1. Square of the reduced magnetization (M(T)/M(0))2 of the La Ca MnO2 1 3 33 film in a mag- netic field H = 10 Oe in the Curie-point region (�); the solid line determines the Curie point TC ; the dashed and dotted lines show the expected dependences in the conventional molecular field model for spins S = 2 and S = 3/2, respectively. Fig. 2. Temperature dependence of the reduced magne- tization M(T)/M(0) of the La Ca MnO2 1 3 33 film in a magnetic field H = 10 Oe applied in the film surface plane: experiment (�) and calculations (solid line) in the modified molecular field model; the dashed line shows the M(T)/M(0) dependence in the conventional molecular field model (the Brillouin curve) for spin S = 2. equal to 86 G at H = 10 Oe, and it obeys the equa- tion M G H[ ] . � � 85 3 75 10 2 [Oe] in the range 100–400 Oe. The magnetic moment per Mn atom is equal to 0.61 �B at H = 400 Oe. This shows that the magnetization is far from saturation in the field range under study. As one can see from Fig. 4, the �(T) behavior has a semiconductive character above TC . Below TC the resistivity decreases sharply, falling to � = 90.6 �� cm at T = 5 K. As is evident from Fig. 5, the dependence �(T) in a logarithmic scale (i.e., lg �(T)) is close to linear in the range 80 K � T � 200 K. The nearly constant value of the logarithmic derivative of �(T) seen in Fig. 6 also confirms the exponential temperature dependence of �(T) in this temperature range. The temperature dependence of the � at H = 50 kOe presented in Fig. 7 is of the usual type 778 Fizika Nizkikh Temperatur, 2002, v. 28, No. 7 A. B. Beznosov et al. Fig. 3. Magnetization M(H) vs magnetic field H applied in the surface plane of the La Ca MnO2 1 3 33 film at temperatures of 10 K (�), 20 K (�), 40 K (�), and 60 K (�). Fig. 4. Electrical resistivity of the La Ca MnO2 1 3 33 film vs temperature (�); the solid and dashed lines represent calculations in the �m� model for magnetic fields of 0 and 50 kOe, respectively. Fig. 5. Electrical resistivity of the La Ca MnO2 1 3 33 film vs temperature in logarithmic scale (�); the solid and dashed lines represent calculations in the �m� model for magnetic fields of 0 and 50 kOe, respectively. Fig. 6. The logarithmic temperature derivative of the electrical resistivity of the La Ca MnO2 1 3 33 film vs tem- perature (�); solid line represents the �m� model cal- culations. for CMR manganites of fairly good crystal quality. It should be noted here that at the field 5 kOe the � value was positive practically in the whole tem- perature range studied. 7. Comparison of the model and experimental data The magnetization of the film, as one can see from Figs. 1 and 2, is substantially higher than that predicted by the conventional molecular field model (h = 0, a = 0 in Eq. (10)): the coefficient b in the formula �2 = b (1 – T/TC ), which is valid in some neigborhood just below the Curie tempera- ture, turned out to be about three times larger than the theoretical value (see Fig. 1). Possible reasons for this are a peculiarity of the double exchange [7] and an enhancement of the effective interatomic ex- change interaction by the magnetoelastic coupling. The last has been taken into account in the modi- fied molecular field model by the factor (1–a�2) (in accordance with Ref. 21), which gives practi- cally complete coincidence with the experimental data just below TC (Fig. 2), in contrast to the re- sults of Ref. 7, where the model curve increases faster than the experimental curve on lowering of the temperature. Using Eqs. (1)–(10) and the experimental data on the magnetization and electrical resistivity, we obtained the following model parameters giving the best fit to the experimental data on resistivity pre- sented in Fig. 4: �0 = 555 K, �0 = 90.6 �� cm, �D = 400 �� cm, �m� = 29.7 �� cm, h = 1 K (this corresponds to a fictitious «short-range-order field» of about 3725 Oe), a = 0.26. The model tempe- rature dependence �mod(T) calculated with these parameters practically coincides with the experi- mental data for �(T) (see Fig. 4). The model tem- perature dependences lg �mod(T) and � ln �mod/�T also agree well with the experiment in the main temperature region (see Figs. 5, 6). The numerical analysis has shown that the nearly linear in T region of the lg �(T) dependence, which can be seen clearly (Fig. 5) in the range 80 K < T < 200 K, as well as the nearly constant value of the �ln�/�T derivative in the same tem- perature interval (see Fig. 6), are caused by the compensation of the bending «up» of the �/T curve in the Eq. (6) by the bending «down» of the curve lg [�st(T) + �ph (T) + �m(T)]. The first can be seen from the approximation �(T) = g – pT – qT2 – rT3 – ... , where g, p, q and r are constants, which gives immediately the bending «up» curve: �/T = �0 [1 – �(T)]/T = = �0 [– (g – 1)/T + p + qT + rT2 + … ] . The second is caused by the �ph(T) contribution (the contribution from �m(T) is small in the tem- perature range under consideration, and the �st value changes weakly there). The character of the temperature dependence of the model magnetoresistive effect �mod(T, H) = = [�mod (h, T, H) – �mod(h, T, 0)]/�mod(h, T, 0) also corresponds rather well to the experiment at high magnetic fields (Fig. 7), though the accuracy in this case is somewhat lower: the maximal value at H = 50 kOe is –0.65 at T = 274 K in the experi- ment, whereas the model gives –0.63 at 273 K. A somewhat unexpected finding is the experi- mental observation of a positive magnetoresistive effect with a maximum near TC at low fields (H = 5 kOe). In the framework of the �m� model this can imply an increase of the activation energy � and an enhancement of the electron scattering. One of the possible reasons may be the presence of an antiferromagnetic component in the magnetic structure of the system at low fields (see Refs. 14, 27, 30). In this case an increase of magnetization under the influence of the magnetic field should be accompanied by a reduction of the order parameter of the antiferromagnetic component and by a corre- sponding increase in the activation energy and elec- tron scattering. Fizika Nizkikh Temperatur, 2002, v. 28, No. 7 779 Exchange interaction and magnetoresistance in La2/3Ca1/3MnO3 Fig. 7. Magnetoresistance [�(H) – �(0)]/�(0) of the La Ca MnO2 1 3 33 film vs temperature in a magnetic field of 50 kOe (�); the dotted, solid, and dashed lines represent the �m� model calculations for magnetic fields of 5, 50, and 500 kOe, respectively. A detailed discussion of this effect is beyond the scope of this paper. In general, however, the cha- racter of the behavior of the model magnetoresis- tive effect �mod(H) in the interval 0 < H < 75 kOe at Ò = 273 K is quite consistent with the experi- ment. 8. Conclusion 1. The magnetization M(T) and the electrical re- sistivity �(T) of a 150-nm thick La Ca MnO2 1 3 33 film have been studied in the temperature range 5 K � T � 320 K in the magnetic field intervals 10 Oe � H � 400 Oe and 0 � H � 50 kOe, respec- tively. It is found, that the M(T)/M(0) value is larger than that predicted by the conventio- nal molecular field model below the Curie point TC = 267 K, and that the lg �(T) dependence is close to linear (lg �(T) = A+BT) in the temperature range 80 K < T < 200 K (accordingly � ln �/�T is constant in this region). 2. A model of the electrical conductivity and magnetoresistivity of the system describing qualita- tively the experimental results is proposed (the �m� model). The model includes a thermally acti- vated (with characteristic energy �) mechanism of conductivity, dependence of the concentration and the effective mass (m) of the itinerant charge carri- ers on the magnetization, as well as scattering (with character time �) of the charge carriers by static breakings of the translational symmetry, thermal fluctuations of the magnetic order, and phonons. Acknowledgment Authors are pleased to dedicate the paper to Academician V. V. Eremenko, whose multifaceted scientific interests and achievements in the physics of magnetic phenomena in the compounds of d and f elements are widely appreciated. 1. E. L. Nagaev, Phys. Usp. 39, 781 (1996). 2. J. M. D. Coey, M. Viret, and S. von Molnar, Adv. Phys. 48, 167 (1999). 3. N. Furukawa, in: Physics of Manganites, T. A. Kaplan and S.D. Mahanti (eds.), Kluwer Academic, New York (1999), p.1. 4. V. M. Loktev and Yu. G. Pogorelov, Fiz. Nizk. Temp. 26, 231 (2000) [Low Temp. Phys. 26, 171 (2000)]. 5. E. Dagotto, T. Hotta, and A. Moreo, Phys. Rep. 344, 1 (2001). 6. M. Salamon and M. Jaime, Rev. Mod. Phys. 73, 583 (2001). 7. C. W. Searle and S. T. Wang, Can. J. Phys. 48, 2023 (1970). 8. T. Penney, M. W. Shafer, and J. B. Torrance, Phys. Rev. B5, 3669 (1972). 9. M. F. Hundley, M. Hawley, R. H. Heffner, Q. X. Jia, J. J. Neumeier, J. Tesmer, J. D. Thompson, and X. D. Wu, Appl. Phys. Lett. 67, 860 (1995). 10. J. Z. Sun, L. Krusin-Elbaum, S. S. Parkin, and G. Xiao, Appl. Phys. Lett. 67, 2726 (1995). 11. I. Esaki, P. J. Stiles, and S. von Molnar, Phys. Rev. Lett. 19, 852 (1967). 12. N. Furukawa, J. Phys. Soc. Jpn. 64, 3164 (1995). 13. M. Viret, L. Ranno, and J. M. D. Coey, Phys. Rev. B55, 8067 (1997-I). 14. J. Inoue and S. Maekawa, Phys. Rev. Lett. 74, 3407 (1995). 15. A. J. Dekker, J. Appl. Phys. 36, 906 (1965). 16. F. J. Blatt, Physics of Electronic Conduction in Solids, McGraw-Hill Book Company (1968). 17. T. Kasuya, Progr. Theor. Phys. 16, 58 (1956). 18. H. Fujishiro, T. Fukase, M. Ikebe, and T. 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Beznosov, E. L. Fertman, P. P. Pal-Val, and V. P. Popov, Adv. Cryogenic Eng. 46, 413 (2000). 30. J. Jiang, J. Dong, and D. Y. Xing, Phys. Rev. B55, 8973 (1997-II). 780 Fizika Nizkikh Temperatur, 2002, v. 28, No. 7 A. B. Beznosov et al.

Exchange interaction and magnetoresistance in La₂/₃Ca₁/₃MnO₃ : experiment and models

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