Peculiarities of the volume magnetostriction in La₁₋xSrxMnO₃ in the Curie point region

The parallel λ∥ and perpendicular λ⊥ magnetostriction (with respect to the applied magnetic field) and the thermal expansion Δl/l are studied on La1−xSrxMnO₃ single crystals with x=0.1, 0.15, and 0.3. For the conducting sample with x=0.3 and the semiconducting sample with x=0.15 the volume magnetost...

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Published in:Физика низких температур
Date:2001
Main Authors: Koroleva, L.I., Abramovich, A.I., Demin, R.V., Michurin, A.V.
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Language:English
Published: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2001
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Cite this:Peculiarities of the volume magnetostriction in La₁₋xSrxMnO₃ in the Curie point region / L.I. Koroleva, A.I. Abramovich, R.V. Demin, A.V. Michurin // Физика низких температур. — 2001. — Т. 27, № 4. — С. 398-402. — Бібліогр.: 15 назв. — англ.

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spelling Koroleva, L.I.
Abramovich, A.I.
Demin, R.V.
Michurin, A.V.
2018-02-04T16:44:17Z
2018-02-04T16:44:17Z
2001
Peculiarities of the volume magnetostriction in La₁₋xSrxMnO₃ in the Curie point region / L.I. Koroleva, A.I. Abramovich, R.V. Demin, A.V. Michurin // Физика низких температур. — 2001. — Т. 27, № 4. — С. 398-402. — Бібліогр.: 15 назв. — англ.
0132-6414
PACS: 75.80.+q, 75.30.Kz, 75.40.-s, 74.72.-h
https://nasplib.isofts.kiev.ua/handle/123456789/130017
The parallel λ∥ and perpendicular λ⊥ magnetostriction (with respect to the applied magnetic field) and the thermal expansion Δl/l are studied on La1−xSrxMnO₃ single crystals with x=0.1, 0.15, and 0.3. For the conducting sample with x=0.3 and the semiconducting sample with x=0.15 the volume magnetostriction (ω=λ∥+2λ⊥) is negative and the |ω|(T) curves go through a maximum at the Curie point TC. At T>TC its Δl/l temperature dependence is stronger than linear. For the semiconducting sample with x=0.1, ω is negative at T<TC and |ω|→0 at T∼TC. Its Δl/l is linear at T<=TC. The behavior of ω and Δl/l are explained by a magnetic two-phase state, due to strong s−d exchange.
This paper was supported by grants from INTAS, #97-0253, NATO #HTECH LG 972942, and the Russian Basic Investigations Foundation #00-15- 96695, #00-02-17810. We are grateful by A.M. Balbashov for preparation of the samples and their analysis.
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
Физика низких температур
Специальный выпуск Низкотемпеpатуpная магнитостpикция магнетиков и свеpхпpоводников Под редакцией В. В. Еременко и В. А. Сиренко
Peculiarities of the volume magnetostriction in La₁₋xSrxMnO₃ in the Curie point region
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Peculiarities of the volume magnetostriction in La₁₋xSrxMnO₃ in the Curie point region
spellingShingle Peculiarities of the volume magnetostriction in La₁₋xSrxMnO₃ in the Curie point region
Koroleva, L.I.
Abramovich, A.I.
Demin, R.V.
Michurin, A.V.
Специальный выпуск Низкотемпеpатуpная магнитостpикция магнетиков и свеpхпpоводников Под редакцией В. В. Еременко и В. А. Сиренко
title_short Peculiarities of the volume magnetostriction in La₁₋xSrxMnO₃ in the Curie point region
title_full Peculiarities of the volume magnetostriction in La₁₋xSrxMnO₃ in the Curie point region
title_fullStr Peculiarities of the volume magnetostriction in La₁₋xSrxMnO₃ in the Curie point region
title_full_unstemmed Peculiarities of the volume magnetostriction in La₁₋xSrxMnO₃ in the Curie point region
title_sort peculiarities of the volume magnetostriction in la₁₋xsrxmno₃ in the curie point region
author Koroleva, L.I.
Abramovich, A.I.
Demin, R.V.
Michurin, A.V.
author_facet Koroleva, L.I.
Abramovich, A.I.
Demin, R.V.
Michurin, A.V.
topic Специальный выпуск Низкотемпеpатуpная магнитостpикция магнетиков и свеpхпpоводников Под редакцией В. В. Еременко и В. А. Сиренко
topic_facet Специальный выпуск Низкотемпеpатуpная магнитостpикция магнетиков и свеpхпpоводников Под редакцией В. В. Еременко и В. А. Сиренко
publishDate 2001
language English
container_title Физика низких температур
publisher Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
format Article
description The parallel λ∥ and perpendicular λ⊥ magnetostriction (with respect to the applied magnetic field) and the thermal expansion Δl/l are studied on La1−xSrxMnO₃ single crystals with x=0.1, 0.15, and 0.3. For the conducting sample with x=0.3 and the semiconducting sample with x=0.15 the volume magnetostriction (ω=λ∥+2λ⊥) is negative and the |ω|(T) curves go through a maximum at the Curie point TC. At T>TC its Δl/l temperature dependence is stronger than linear. For the semiconducting sample with x=0.1, ω is negative at T<TC and |ω|→0 at T∼TC. Its Δl/l is linear at T<=TC. The behavior of ω and Δl/l are explained by a magnetic two-phase state, due to strong s−d exchange.
issn 0132-6414
url https://nasplib.isofts.kiev.ua/handle/123456789/130017
citation_txt Peculiarities of the volume magnetostriction in La₁₋xSrxMnO₃ in the Curie point region / L.I. Koroleva, A.I. Abramovich, R.V. Demin, A.V. Michurin // Физика низких температур. — 2001. — Т. 27, № 4. — С. 398-402. — Бібліогр.: 15 назв. — англ.
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AT abramovichai peculiaritiesofthevolumemagnetostrictioninla1xsrxmno3inthecuriepointregion
AT deminrv peculiaritiesofthevolumemagnetostrictioninla1xsrxmno3inthecuriepointregion
AT michurinav peculiaritiesofthevolumemagnetostrictioninla1xsrxmno3inthecuriepointregion
first_indexed 2025-11-27T08:36:32Z
last_indexed 2025-11-27T08:36:32Z
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fulltext Fizika Nizkikh Temperatur, 2001, v. 27, No. 4, p. 398–402 Kor oleva L. I., Ab ra movich A . I., Demin R. V., a nd Mich urin A . V.Peculiar it ie s o f the volum e mag net ostr ic tion in La1– xSr xMnO3 in th e Cu rie point r eg io nKoro le va L. I. , Ab ram ovich A. I. , De min R. V., an d Michu rin A. V .Pe culiarities of t he volume m ag neto strict io n in La 1–xSrxMnO3 in the Cur ie point r egion Peculiarities of the volume magnetostriction in La1–xSrxMnO3 in the Curie point region L. I. Koroleva, A. I. Abramovich, R. V. Demin, and A. V. Michurin M. V. Lomonosov Moscow State University, Vorobyevy Gory, Moscow 119899, Russia E-mail: koroleva@ofef343.phys.msu.su Received September 25, 2000 The parallel λ|| and perpendicular λ⊥ magnetostriction with respect to the applied magnetic field and the thermal expansion ∆l/l are studied on La1−xSrxMnO3 single crystals with x = 0.1, 0.15, and 0.3. For the conducting sample with x = 0.3 and the semiconducting sample with x = 0.15 the volume magneto- striction (ω = λ|| + 2λ⊥) is negative and the |ω|(T) curves go through a maximum at the Curie point T C . At T > TC its ∆l/l temperature dependence is stronger than the linear one. For the semiconducting sample with x = 0.1 ω is negative at T < TC and |ω| → 0 at T ∼ TC . Its ∆l/l is linear at T ≥ TC . The behavior of ω and ∆l/l are explained by a magnetic two-phase state, due to strong s–d exchange. PACS: 75.80.+q, 75.30.Kz, 75.40.–s, 74.72.–h Introduction At present the perovskite Mn oxides R1−xAxMnO3 (R = La, Pr, Y, Nd, Sm and other rare-earth ele- ments; A = Ca, Sr and Ba) are intensively studied. These investigations are described in a great number of papers and reviews [1–4]. The interest in these materials is associated with a colossal magnetore- sistance near room temperature which has been observed at certain doping levels. Unfortunately, there is no common point of view on the physical processes leading to colossal magnetoresistance in manganites. Attempts have been made to relate this observed colossal magnetoresistance to the Zener double exchange, to the polaron effect caused by a very strong electron–phonon coupling stemming from a Jahn–Teller splitting of the Mn3+ ions, and to the charge ordering. However, the calculations performed in Refs. 5, 6 have shown that double exchange alone cannot account for the very large resistivity of the T > TC phase or for the sharp drop in resistivity just below TC . In addition, the calcu- lated resistivity has a too weak doping dependence and incorrect behavior for T > TC or in a field. Millis and co-workers [6,7] proposed to combine the physics of dynamic Jahn–Teller and double-ex- change effects to explain the anomalies of the elec- trical resistivity ρ and colossal magnetoresistance in these compounds. However, this hypothesis cannot explain the fact that the temperatures of the metal– semiconductor transition and of the region of maxi- mum colossal magnetoresistance are focused in the immediate vicinity of the Curie point. In this paper we propose another mechanism for the explanation of anomalies of the electrical resis- tivity, colossal magnetoresistance, volume magne- tostriction, and thermal expansion of La1−xSrxMnO3 compounds in the TC region. Namely, we believe that the magnetic phase separation that is charac- teristic for magnetic semiconductors [8] is respon- sible for these features. Experimental procedure We studied the parallel λ|| and perpendicular λ⊥ magnetostriction with respect to the applied mag- netic field, the thermal expansion ∆l/l, the mag- netization, and the paramagnetic susceptibility of La1−xSrxMnO3 single crystals. Single crystals were grown by the method of floating-zone method by Balbashov and have a rhombohedral structure (the sample with x = 0.3) or an orthorhombic structure (the samples with x = 0.1 and 0.15). The magnetization measure- ments, carried out with the aid of a vibrating magnetometer, showed that the magnetization reaches saturation at a magnetic field H < 0.2 T. The Curie points were determined by the Belov– Arrot method and practically coincide with the published data [9]. The temperature dependence of © L. I. Koroleva, A. I. Abramovich, R. V. Demin, and A. V. Michurin, 2001 the paramagnetic susceptibility, measured by the Faraday balance method, is described by the Curie– Weiss law. The strain gauge technique was used for study of the magnetostriction and thermal expan- sion. The magnetostriction was measured in a dc magnetic field up to H ≤ 1 T and for the sample with x = 0.15 up to H = 12 T in the laboratory of M. R. Ibarra (University of Zaragoza, Spain). The accuracy of the ∆l/l measurements was better than 4⋅10−6. Results and discussion By way of example, Fig. 1 shows the isotherms of the parallel and perpendicular magnetostriction with respect to the applied magnetic field at some selected temperatures for the sample with x = 0.3. From the experimental λ||(H) and λ⊥(H) curves the isotherms of the anisotropic magnetostriction λt = = λ|| − λ⊥ and volume magnetostriction ω = λ|| + 2λ⊥ were constructed. Their temperature dependence for the sample with x = 0.3 at H = 0.9 T is shown in Fig. 2. On increase in temperature the anisotropic magnetostriction decreases continuously to zero in the TC region, as can be seen in Fig. 2. The λt(T) curves, measured in magnetic fields above 0.2 T, practically coincide with the λt(T) curve shown in Fig. 2. It should be pointed out that the λt value is large in the low-temperature region, e.g., λt ≅ 10−4 at 90 K (H = 1 T) and λt ≅ 10−3 at 4.2 K (H = 3 T). As illustrated in Fig. 2, the volume magnetostric- tion is positive at T < 280 K; however, it becomes negative at T > 280 K and its magnitude reaches a maximum in the vicinity of TC = 371 K. On further heating |ω| vanishes rapidly. The ω(T) dependence in some selected magnetic field is shown in the insert in Fig. 2. As will be seen from Fig. 3, the behavior of ω for the sample with x = 0.15 is rather like the one for the sample with x = 0.3. For the sample with x = 0.15 the anisotropic magnetostriction λt is positive and its value decreases continuously to zero in the Curie point region, too (TC = 268 K). The temperature dependence of the thermal expansion ∆l/l in the TC region is stronger than linear for the samples with x = 0.15 and 0.3. This is apparent from Fig. 4, which shows the ∆l/l(T) dependence for the sample with x = 0.3. It is well known that this dependence is nearly linear for dia- and para- magnetic systems. Fig. 1. The isotherms of the perpendicular (curves 1–4) and parallel (curves 5–7) magnetostriction λ at different tempera- tures T, K: 361 (1), 97 (2), 349 (3), 375 (4), 300 (5), 188 (6), and 96 (7) for the single crystal La0.7Sr0.3MnO3 . Fig. 2. Temperature dependence of the anisotropic magneto- striction λt and volume magnetostriction ω in the magnetic field of 0.9 T for the single crystal La0.7Sr0.3MnO3 . Insert: tempera- ture dependence of ω in the TC region in some selected magnetic fields for this sample. Fig. 3. Temperature dependence of the volume magnetostriction ω in some selected magnetic fields for the single crystal La0.85Sr0.15MnO3 . Peculiarities of the volume magnetostriction in La1–xSrxMnO3 in the Curie point region Fizika Nizkikh Temperatur, 2001, v. 27, No. 4 399 The positive anisotropic magnetostriction λt of the sample with x = 0.1 decreases continuously to zero in the TC region (TC = 162 K), as in the samples with x = 0.15 and 0.3. However the beha- vior of volume magnetostrictriction ω of the sample with x = 0.1 differs from that of the samples with x = 0.15 and 0.3. Figure 5 shows the temperature dependence of ω at some selected magnetic fields for a La0.9Sr0.1MnO3 single crystal. Notice that the volume magnetostriction of the sample with x = 0.1 is negative. With increasing temperature the values of |ω| decrease continuously to zero in the TC region, as can be seen in Fig. 5. As mentioned above, the ω(T) curves have a minimum in the TC region for the single crystals La0.7Sr0.3MnO3 (Fig. 2) and La0.85Sr0.15MnO3 (Fig. 3). Figure 5 shows that the ω(T) curves have no such minimum for the sample with x = 0.1. Their temperature dependence of the thermal expansion ∆l/l is nearly linear at T ≥ TC as well as at T ≤ TC , and no surplus ther- mal expansion occurs at T ≥ TC for this sample. According to data [9,10] for these compositions, the electrical resistivity ρ of the metallic type is observed at T < TC , and ρ increases abruptly in the TC region for the sample with x = 0.3; for the samples with x = 0.1 and 0.15 a semiconducting type of conductivity is observed. The transition from the semiconducting to the metallic type of conductivity takes place at x ∼ 0.17 in the La1−xSrxMnO3 system. Ibarra et al. [11] observed a similar behavior of the volume magnetostriction and thermal expansion of a La0.4Y0.07Ca0.33MnO3 ceramic sample. In their opinion, the anomalies of the thermal expansion and the volume magnetostriction are due to the forma- tion of a small polaron at T ≥ TC . As discussed in the Introduction, this hypothesis fails to explain the fact that the polaron formation occurs only in the vicinity of the Curie point. Anomalies of the volume magnetostriction, ther- mal expansion, and electrical resistivity, listed above, may be attributed to the existence of a magnetic two-phase state (MTPS) in this crystal [8]. As is well known, in magnetic semiconductors the charge carrier energy is minimal when the total ordering in the crystal is ferromagnetic. However, in nongenerate antiferromagnetic semiconductors the carrier concentration is small, so they are not able to modify the state of the entire crystal. None- theless, these electrons may cause local changes in the magnetic ordering, creating ferromagnetic mic- roregions, which provide a gain in the s–d exchange energy, and stabilize them by autolocalization in- side them. At a not-too-high density of the charge carriers an insulating MTPS is realized in the crys- tal: ferromagnetic small droplets, in which the charge carriers are localized, are embedded in the insulating host. On increase in the carrier density, ferromagnetic droplets begin to make contact with each other. Thus, percolation of the electron liquid occurs and another MTPS is formed: the insulating antiferromagnetic microregions are embedded in a conducting ferromagnetic host. This is a conducting MTPS. Yanase and Kasuya showed [12] that inside a ferromagnetic part of crystal the lattice constants are reduced. The reason is that in a ferromagnetic part of crystal the spacing between an impurity ion and its nearest magnetic ion is shortened to screen the new charge distribution and to lower the energy of the ferromagnetic part of crystal by increasing the overlap between the valence electron shells of the impurity and the d shells of the nearest mag- netic ions. La0.7Sr0.3MnO3 is a heavily doped antiferromag- netic semiconductor LaMnO3 , in which a conduct- ing MTPS is realized. The MTPS is destroyed at T ≥ TC and so an extra contribution in ∆l/l arises. An applied magnetic field induces magnetization Fig. 4. Temperature dependence of the thermal expansion ∆l/l for the single crystal La0.7Sr0.3MnO3 . Fig. 5. Temperature dependence of the volume magnetostriction in some selected magnetic fields for the single crystal La0.9Sr0.1MnO3 . L. I. Koroleva, A. I. Abramovich, R. V. Demin, and A. V. Michurin 400 Fizika Nizkikh Temperatur, 2001, v. 27, No. 4 near impurities at T > TC , since its action is en- hanced by the s–d exchange. One produces MTPS and the lattice compression inherent in it. The sharp increase in the negative volume magnetostriction at the TC region (Fig. 2) can be explained by this effect. However, the above-mentioned process of MTPS restoration by a field takes place only in a limited temperature interval at T ≥ TC . Because of this the ω(T) curves have a sharp minimum in the TC region, and |ω| quickly falls upon further in- crease in temperature. The MTPS in the sample with x = 0.3 is confirmed by the fact that the value of its spontaneous magnetization at 4.2 K is less than the value expected in the case of a total ferromagnetic ordering. Namely, the former is equal to 95% of the latter (our data agree with those found in Refs. 9, 10) and a value of 84% is obtained by neutron experiments [13]. This indicates that the ratio between the volumes of the ferromagnetic and antiferromagnetic portions of the crystal is ∼ 90/10. In this case the TC value is determined by the ferromagnetic portion of the crystal only. It is well known that the paramagnetic Curie point Θ is determined by the sum of the exchange interactions realized in the crystal. The contribution from the antiferromagnetic microregions to the total ex- change lowers the Θ value and, therefore, TC = 371 K exceeds Θ = 364 K in the sample with x = 0.3 (in ferromagnetic ordering TC ≤ Θ is normally ob- served). It should be remarked that the volume magneto- striction of the sample with x = 0.1 is negative (Fig. 5). By this we mean that the sample shrinks in an applied magnetic field. It is known [9] that this sample is a p-type semiconductor. There is a small maximum of the electrical resistivity ρ and a nega- tive colossal magnetoresistance in the TC region for this crystal [9,10]. Thus ρ and the magnetoresist- ance anomalies are attributable to an insulating MTPS [8]. If an insulating MTPS is present in this sample, the negative ω denotes that the radii of the ferromagnetic droplets are increased by a magnetic field. This is characteristic of an insulating MTPS [8]. At the same time, the ferromagnetic phase in an insulating MTPS sample occupies as little as a few per cent of the sample volume [8]. Therefore the volume of the ferromagnetic part is small in the sample with x = 0.1, and the anomalies of ω and ∆l/l are not detected at the TC region. In the conducting MTPS sample with x = 0.3 the ferro- magnetic phase occupies ∼ 90% of the sample volu- me, and the destruction of MTPS in the TC region may have a marked effect on ω and ∆l/l. The sample with x = 0.15 is situated on the boundary between the semiconducting and metallic states [9]. Therefore the volume of its ferromagnetic phase is larger than in the sample with x = 0.1, and the anomalies of ω and ∆l/l at T ∼ TC are observed in this sample. In connection with the aforesaid we may be make the following supposition. It is well known that the crystal volume per manganese ion is higher in the orthorhombic than in the rhombohedral structure of this system. Recently it has been found that in the semiconducting compound with x = 0.17 of the system considered, a transition from the orthorhom- bic to the rhombohedral phase occurs in an applied magnetic field at T ≤ TC [14,15]. This can be ex- plained by the increase of the volume of the ferro- magnetic phase in an applied magnetic field, accom- panied by the lattice compression. It is known that the compounds of this system with x ≤ 0.17 have the orthorhombic structure and the semiconductive type of conductivity, while the compounds with 0.175 ≤ x ≤ 0.6 have the rhom- bohedral structure and the metallic type of conduc- tivity [9,10]. On this basis it is reasonable to expect that the transition from the semiconductive ortho- rhombic phase to the metallic rhombohedral phase in this system is caused by the transition from the insulating MTPS to the conducting MTPS, which is accompanied by lattice compression of the ferro- magnetic phase, occupied the nearly all volume of crystal. Summary It has been found that for La1−xSrxMnO3 single crystals with x = 0.15 and 0.3 the volume magneto- striction ω is negative, the |ω|(T) curves go through a maximum at the Curie point TC , and the tem- perature dependence of the thermal expansion ∆l/l(T) at T > TC is stronger than linear. For the sample with x = 0.1 ω is negative at T < TC , |ω| → 0 at T ∼ TC , and ∆l/l(T) is linear at T ≥ TC . The behavior of ω, ∆l/l, ρ, and the colossal magne- toresistance are explained by a magnetic two-phase state, due to strong s–d exchange. In antiferromagnetic semiconductors the charge carriers self-trap near impurities and produce ferro- magnetic microregions because of energy gain in respect to the s–d exchange [8]. At a not-too-high density of the charge carriers an insulating MTPS is realized in the crystal: ferromagnetic small droplets, in which the charge carriers are localized, are em- bedded in an insulating host. On increase in the carrier density, percolation of the electron liquid occurs and a conducting MTPS is formed: the insulating antiferromafnetic microregions are em- Peculiarities of the volume magnetostriction in La1–xSrxMnO3 in the Curie point region Fizika Nizkikh Temperatur, 2001, v. 27, No. 4 401 bedded in a conducting ferromagnetic host. Yanase and Kasuya showed [12] that inside a ferromagnetic part of the crystal the lattice constants are reduced. La1−xSrxMnO3 is a doped antiferromagnetic se- miconductor LaMnO3 . Let us suppose that a con- ducting MTPS is realized in the sample with x = 0.3. MTPS in this case is destroyed at T ≥ TC , and thus an extra contribution to ∆l/l arises. An applied magnetic field induces magnetization near impu- rities at T > TC , since its action is enhanced by the s–d exchange. A field produces MTPS and the corresponding lattice compression. It follows that ω is negative in the TC region and that a minimum on the ω(T) curves is observed at this region. The sharp increase in the electrical resistivity in the TC region is characteristic of a conducting MTPS [8]. There are two mechanisms through which the impurity–magnetic interaction influences the resistance: the scattering of charge carriers, which reduces their mobility; the formation of band tails, consisting of the localized states. The decrease of the mobility of the charge carriers and their partial localization in band tails are most prominent in the TC region. Imposition of a magnetic field on the sample increases the charge carrier mobility and excites the charge carriers from the band tails; this is the cause of the colossal magnetoresistance. If an insulating MTPS is present in the sample with x = 0.1, the negative ω indicates that the ferromagnetic droplet radii increase with applied magnetic field; this is typical for an insulating MTPS [8]. But the ferromagnetic phase in an insu- lating MTPS sample occupies only a few percent of the sample volume [8]. Therefore the volume of ferromagnetic part is small in the sample with x = = 0.1, so that the anomalies of ω and ∆l/l are not detected near TC . There is a small maximum of ρ and a colossal magnetoresistance in the TC region for this semiconducting crystal [9,10]. Thus ρ and the magnetoresistance anomalies can be attributed to an insulating MTPS, too [8]. One can explain the colossal magnetoresistance by the increase of the ferromagnetic droplet radii in the magnetic field, which facilitates electron tunneling between ferromagnetic droplets. Moreover the magnetic mo- ments of the ferromagnetic droplets are aligned along with the external field, and that also facili- tates the tunneling. Ultimately the field tends to destroy the ferromagnetic droplets. Thus the mag- netic field increases the electron energy inside the droplets and in doing so it facilitates their transi- tion to a delocalized state. The sample with x = 0.15 has conductivity of the semiconducting type, but it is situated near the boundary between the semiconducting and metallic states [9]. Therefore the volume of its ferromagnetic phase is larger than in the sample with x = 0.1, and the anomalies of ω and ∆l/l at T ∼ TC are observed in this sample. The anomalies of ρ and the colossal magnetoresistance in the TC region for the sample with x = 0.15 are explained as well as for the sample with x = 0.1. Acknowledgments This paper was supported by grants from INTAS, #97-0253, NATO #HTECH LG 972942, and the Russian Basic Investigations Foundation #00-15- 96695, #00-02-17810. We are grateful by A.M. Balbashov for preparation of the samples and their analysis. 1. E. L. Nagaev, Sov. Phys. Usp. 166, 833 (1996). 2. A. P. Ramirez, J. Phys.: Condens. Matter 9, 7 (1997). 3. Y. Tokura and Y. Tomioka, J. Magn. Magn. Mater. 200, 1 (1999). 4. A. Moreo, S. Yunoki, and E. Dagotto, Cond-mat/9901057 8 Jan (1999). 5. A. J. Millis, P. B. Littlewood, and B. I. Shraiman, Phys. Rev. Lett. 74, 5144 (1995). 6. A. J. Millis, B. I. Shraiman, and R. Mueller, Phys. Rev. Lett. 77, 175 (1996). 7. A. J. Millis, Phys. Rev. B53, 8434 (1996). 8. E. L. Nagaev, Physics of Magnetic Semiconductors, Mir, Moscow (1983). 9. A. Urushibara, Y. Moritomo, T. Arima, A. Asamutsu, G. Kido, and Y. Tokura, Phys. Rev. B51, 14103 (1995). 10. H. Y. Hwang, S.-W. Cheong, N. P. Ong, and B. Battlogg, Phys. Rev. Lett. 77, 2041 (1996). 11. M. R. Ibarra, P. A. Algarabel, C. Marquina, J. Blasco, and J. Garcia, Phys. Rev. Lett. 75, 3541 (1995). 12. A. Yanase and T. Kasuya, J. Phys. Soc. Jpn. 25, 1025 (1968). 13. P. G. Radaelli, G. Iannone, M. Marezio, H. Y. Hwang, S.-W. Cheong, J. D. Jorgensen, and D. N. Argyriou, Phys. Rev. B56, 8265 (1997). 14. A. Asamutsu, Y. Moritomo, Y. Tomioka, T. Arima, and Y. Tokura, Nature 373, 407 (1995). 15. K. V. Kamenev, G. J. McIntyre, D. McK Paul, M. R. Lees, and G. Balakrishnan, Phys. Rev. B57, R6775 (1998). L. I. Koroleva, A. I. Abramovich, R. V. Demin, and A. V. Michurin 402 Fizika Nizkikh Temperatur, 2001, v. 27, No. 4