Studies of magnetoactive materials
(materials with the colossal magnetoresistance, type II superconductors)
( Principal
investigators - A.L. Rakhmanov , K.I. Kugel )
Studies of thermomagnetic instabilities in superconductors: magnetic flux jumps, normal zone propagation, dendrite instability, and formation of spatial structures.
1. The thermomagnetic instability (flux jump) is often observed in type II superconductors with high current density. Such instability limits current-carrying capacity of technical superconductors and causes the propagation of nonlinear thermal waves (portions of non-superconducting phase) in superconductors. This field of research was addressed in ITAE during a number of years in connection with the applications of superconductivity. A comprehensive theory of the instabilities in superconductors was developed; it makes possible to describe the current-carrying capacity of superconducting wires under various conditions. The results of these studies are summarized in monographs, reviews and scientific papers.
Scaling
behavior of different high-Tc
superconductors during the transition to a non-superconducting state: dependence
of dimensionless temperature
q
and electrical field
e
on dimensionless time
t.
All the parameters involved to the dimensionless units are determined using the
experimental data. The plot is taken from
[7].
Main publications
1. R.G. Mints and A.L. Rakhmanov, "Critical state stability
in type II superconductors and
superconducting-normal metal composites", Reviews of Modern
Physics, 1981, v. 53, p. 551.
2. Р.Г. Минц, А.Л. Рахманов, "Неустойчивости в сверхпроводниках", Москва: Наука, 1984.
3. А.Вл. Гуревич, Р.Г. Минц, А.Л. Рахманов,
"Физика композитных сверхпроводников",
Москва: Наука (Главное издательство физико-математической
литературы), 1987.
4. A.V.
Gurevich, R.G.
Mints, and A.L. Rakhmanov, "The physics of
composite superconductors", Begell House Inc., New York, 1997.
5. A.A. Pukhov, V.N. Tsikhon, V.S.
Vysotsky, and A.L. Rakhmanov, "Acceleration of normal zone
propagation in
superconductors with changing current", Superconductivity:
Science and Technology, 1993, v. 7, p. 154.
6. N.A. Buznikov, A.A. Pukhov, and A.L. Rakhmanov, "Normal
zone acceleration: a new model to
describe quench process in superconductors with changing
current", Cryogenics, 1994, v. 34, p. 761.
7. V.S. Vysotsky, Yu.А.
Il’in, Т.
Kiss, A.L. Rakhmanov, and М.
Takeo, "Universal scaling
law for quench development in HTSC devices", Cryogenics,
2000, v. 40, p. 19.
8. V.S. Vysotsky, Yu.А.
Il’in, A.L. Rakhmanov, and M. Takeo, "Quench development analysis in HTSC coils
by
use of the universal scaling
theory", IEEE Transactions on Applied Superconductivity, 2001, v. 11, p. 1824.
2. It turned out that thermomagnetic instability manifests itself not only in technical superconductors but also in epitaxial thin films used in physical experiments. In particular, this instability underlies characteristic self-organization processes arising when magnetic flux enters MgB2 and Nb3Sn films – films, i.e. there appear spatial structures of magnetic flux such as "grass", "finger", and "dendrite" patterns. The criterion determining the formation of these structures was found and the numerical simulations were performed to study the evolution of instabilities at the initial stage of the magnetic flux penetration into the sample. The research in this field continues in close collaboration with team of Prof. Johansen in the University of Oslo.
Spatial patterns arising when magnetic flux penetrates
into
MgB2 superconducting films. Left panel: magnetic flux distribution
obtained in magnetooptical experiment; right panel: distributions of
magnetic and electrical fields found by the numerical simulation
[1].
Back to themes To the beginning
Electrodynamics of anisotropic high-Tc superconductors: macroturbulent instability, effects of commensurability of flux-line and crystal lattices, the effect of surfaces, planar and point defects on electromagnetic characteristics, mesoscopic-size superconductors.
1.
High-Tc
superconductors (HTSC) have highly anisotropic of electromagnetic
characteristics. The anisotropy being a consequence of the crystal structure of
HTSC is additionally enhanced by planar defects characteristic of these
compounds, i.e. twinning planes, laminar structures, etc. The anisotropy leads
to a number of electrodynamic phenomena unusual for solids. One of the e most
spectacular effects is the so called macroturbulence of magnetic flux that
arises in the course of processes taking place in HTSC single crystals with the
orthorhombic structure. During the remagnetization, the interface between the
regions with different directions of magnetic flux becomes curved, there appear
characteristic non-steady-state flux structures such as "finger" patterns, and
then the vortex-type mixing of regions with different flux directions takes
place. Visually, the picture reminds a turbulent fluid flow. We were the first
to demonstrate the qualitative similarity between this effect and the turbulent
instability arising at tangential flow discontinuities in usual hydrodynamics.
The tangential discontinuity in the flow rates for Abrikosov vortices of
different signs occurs due to the anisotropy of superconductors. Our colleagues
from the University of Oslo, All-Russia Electric Engineering Institute, and the
Institute of Solid State physics of Russian Academy of Sciences performed an "experimentum crucis", which unambiguously demonstrated the appropriateness of this
interpretation.
Magnetooptical image of
the macroturbulent instability.
Increment of growth for the instability
versus wavevector of the perturbation.
Main publications
1.
L.M.
Fisher,
P.E.
Goa,
M.
Baziljevich,
T.H.
Johansen,
A.L.
Rakhmanov,
and
V.A.
Yampol'skii,
"Hydrodynamic
instability
of the flux-antiflux Interface in type-II superconductors", Physical Review
Letters, 2001, v. 87, 247005.
2.
А.Л.
Рахманов,
Л.М.
Фишер,
А.А.
Левченко,
В.А.
Ямпольский,
M. Baziljevich, T.H. Johansen,
"Нестабильность
фронта перемагничивания в сверхпроводниках с нелинейной анизотропной
вольт-амперной характеристикой",
Письма в ЖЭТФ, 2002, т. 76, с. 349.
3. А.Л. Рахманов, Л.М. Фишер,
В.А. Ямпольский,
M.
Baziljevich,
T.H.
Johansen,
"Неустойчивость
фронта перемагничивания в анизотропных сверхпроводниках",
ЖЭТФ, 2002, т. 95, с. 768.
4. L.M. Fisher, A. Bobyl, T.H.
Johansen, A.L. Rakhmanov, V.A. Yampol'skii,
A.V. Bondarenko,
M.A. Obolensky, "Anisotropic
origin of bending instability of the flux-antiflux interface
in type-II superconductors",
Physical Review Letters, 2004, v. 92, 037002.
5. L.M. Fisher, T.H. Johansen, A.L. Rakhmanov, A.A.
Levchenko, and V.A. Yampol'skii, "Macroturbulent
instability of the flux line
lattice in anisotropic superconductors", Physica C, 2004, v. 403, p. 230.
2.
The anisotropy of type-II superconductors caused by the
interaction of vortex structure with planar defects leads also to a number of
rather exotic electrodynamic effects. For example, in
BiCaCuO:Pb
single crystals, the interaction of vortices with the superstructure formed by
excess
Pb
atoms (i.e., laminar structure) leads to the violation of spatial parity when a
superconductor is magnetized in crossed fields
[1]. The interaction of the
lattice formed by Abrikosov vortices with the twin boundaries in
YBaCuO
single crystals leads to an anomalous magnetic field dependence (growth) of the
critical current density
Jc(B)
(peak effect). The peak in the
Jc(B)
function corresponds to an optimum ratio of the vortex-vortex coupling energy
and the energy characterizing the interaction of vortices with twin boundaries
[2].
The crystallographic anisotropy of HTSC compounds is related to
CuO
planes in the unit cell. The superconducting order parameter in the plane is
greater than between the planes. This is the fact verified by a number of direct
experiments. In particular,
YBaCuO
single crystals exhibit the effect of intrinsic pinning, i.e. a strong
interaction of flux lines with
CuO
planes. Naturally, the effect is most clearly pronounced in the case of
commensurability between the periods of the flux-line and crystal lattices.
Indeed, in
YBaCuO, this commensurability manifests itself in
characteristic oscillations of certain components of magnetic susceptibility
tensor. We gave a theoretical interpretation of this effect taking into account
the interplay between the interactions of vortices with planar (CuO
planes) and point defects. It was shown that an unusual crossover between
quasi-2D and 3D modulation of the Abrikosov vortex lattice takes place, which
resembles the corresponding transition in liquid crystals
[3-5]. The possibility
of the melting of a 3D vortex structure with the formation of a 2D one was
demonstrated for superconductors with a very high anisotropy. This effect was
observed for
BiCaCuO:Pb
single crystals in crossed fields using the magnetooptical technique
[6, 7].
.
Main publications
1. L.S. Uspenskaya, A.B.
Kulakov, and A.L. Rakhmanov, "Anisotropic flux creep in
Bi2212:Pb single crystal in crossed magnetic fields", Physica
C, 2004, v. 402, 136.
2. И.Ф.
Волошин,
А.В.
Калинов,
К.И.
Кугель,
А.Л.
Рахманов,
Л.М.
Фишер,
"Пиннинг на границах двойникования
и пик-эффект в высокотемпературных сверхпроводниках YBCO",
ЖЭТФ, 1997, т. 111, с. 2158.
3. A.A. Zhukov, H. Kupfer, G.K. Perkins, A.D. Caplin, T. Wolf, K.I. Kugel, A.L.
Rakhmanov,
M.G. Mikheev, V.I. Voronkova, M. Klaser, and H.
Wuhl, "Commensurability oscillations and smectic
vortex phase transition in
YBa2Cu3Oy
single crystals", Physical Review B, 1999, v. 59, p. 11213.
4. А.А.
Жуков,
К.И.
Кугель,
А.Л.
Рахманов,
М.Г.
Михеев,
В.И.
Воронкова,
Х.
Кюпфер,
Г.К.
Перкинс,
А.Д.
Каплин,
Т.
Вольф,
"Осцилляции соизмеримости и новый фазовый
переход в монокристаллах
YBa2Cu3Oy",
Письма в ЖЭТФ, 1999, т. 69, с. 832.
5. К.I.
Kugel, А.А.
Zhukov, and A.L. Rakhmanov, "Commensurability effects in
superconductors with bulk and
intrinsic pinning", Physica C, 2000, v. 334, p. 203.
6. Л.С. Успенская, А.Б. Кулаков, А.Л. Рахманов,
"Фазовый переход в
системе
вихрей в монокристалле
Bi2212:Pb",
Письма в ЖЭТФ, 2002, т. 76, с. 214.
7. L.S. Uspenskaya, A.B. Kulakov, and A.L. Rakhmanov, "Strong three-dimensional
correlations
in the vortex system for
Bi0.7Pb0.3O2.2Sr2CaCu2O8",
Physical Review B, 2003, v. 68, 014532.
3. The interaction
vortices with the surface determines in many respects the features of
magnetization in superconductors. In a certain sense, the surface of a
superconductor could be considered as a planar defect. Corresponding theoretical
methods were extended by us to the case of the boundary of a superconductor with
vacuum and normal metal. As a result, we developed a variational approach to
calculations of magnetic structure in type-II superconductors (the structure of
separate vortex and magnetic flux distribution) with a due account of surface
effects
[1]. For the first time, the explicit expression
for the magnetization of superconductors valid for the whole range of between
the first and second critical magnetic fields,
Hc1<Hext<Hc2
[2].
Magnetization of superconductors versus magnetic field:
theory (solid line) and experiment for
YBaCuO
(triangles)
and
NdCeCuO
(circles) single crystals [2].
The developed variational approach was used to describe properties of
mesoscopic-size superconductors
[3] and superconductors with
regular arrays of mesoscopic-size defects [4].
Main publications
1. В.В. Погосов, К.И. Кугель, А.Л. Рахманов,
"Намагниченность сверхпроводников второго
рода в интервале полей Hc1
≤ H
≤
Hc2. Вариационный метод", ЖЭТФ, 2000, т.
118, с. 676.
2. W.V. Pogosov, K.I. Kugel, A.L. Rakhmanov, and E.H. Brandt,
"Approximate Ginzburg-Landau solution
for the regular flux-line lattice. Circular cell method",
Physical Review B, 2001, v. 64, 064517.
3. W.V. Pogosov, A.L. Rakhmanov, and E.A. Shapoval,
"Vortex state in mesoscopic
cylinders. Variational approach",
Physica C, 2001,
v. 356, p. 225.
4.
W.V. Pogosov, A.L. Rakhmanov, and V.V. Moschalkov,
"Vortex lattice in the presence
of a tunable periodic pinning potential", Physical Review B, 2003,
v. 67, p. 014532.
Back to themes To the beginning
Intrinsic Josephson effect in layered high-Tc superconductors, plasma modes, emission of THz range radiation by "fast" vortices - Cherenkov and transition radiation, photonic crystals in the mixed state.
The terahertz frequency range (3х1011 ÷ 3х1013 Hz) of electromagnetic radiation lies between microwave and infrared ranges. It is hardly accessible for existing electronic and optical devices. However this frequency range is very important for different applications: in medicine, geophysics, astronomy, etc. The high-Tc superconductors with high anisotropy (BiCaCuO single crystals and films) are currently considered as very for promising materials for applications in this frequency range. Numerous experiments clearly demonstrate that such superconductors can be treated as layered superconductor-dielectric structures of where electromagnetic waves in the terahertz range can propagate and be generated.
In collaboration with the group of Prof. F. Nori team from RIKEN Institute (Japan), we are engaged in the studies of intense electromagnetic radiation in layered superconductors (or artificial superconductor-dielectric structures) at frequencies of the order of several terahertz. As possible mechanisms of this radiation, we consider the analogs of the Cherenkov and transition radiation. We derived an appropriate "non-local relativistic" equations of motion for ultrafast Josephson vortices in the layered medium with a singled-out weakened junction. Analytical formulas for this kind of radiation were derived and the numerical calculations were performed [1]. We also demonstrated the possibility of a pronounced magnetic field effect on transmission and reflection of the terahertz radiation in these layered structures [2]. In particular, the interaction of electromagnetic radiation with the lattice of Josephson vortices can give rise to the formation of photonic crystals.
Left panel:
the distribution of the "Cherenkov" radiation generated by a fast Josephson
vortex.
Right panel:
the formula the "Cherenkov" radiation and the "band" structure of the photonic
crystal.
1. S. Saveliev, F. Nori, A.L. Rakhmanov, and V.A. Yampol'skii,
"Cherenkov radiation of a Josephson vortex
in
layered superconductors", NATO Advanced Research Workshop,
Abstracts, p. 63, Yalta, September, 2004.
2.
S. Savel’ev, A.L. Rakhmanov, and F. Nori, "Using
Josephson vortex lattices to control terahertz
radiation: tunable
transparency and terahertz photonic crystals",
Physical Review
Letters, 2005, v. 94,
157004.
Back to themes To the beginning
Electronic characteristics of magnetic oxides: the Kugel-Khomskii model and phase separation, formation of stripe structures, giant isotope effect in manganites. Phase diagrams of materials with the colossal magnetoresistance: studies based on the Kondo-lattice type model with impurities, two-band model and redistribution of charge carriers between itinerant and localized states. Electron transport in the phase-separated magnetic oxides: conductivity, magnetoresistance, magnetic susceptibility, noise spectrum.
Inhomogeneous materials with nanosize inhomogeneities are being studied for several decades. In the recent years they attract a special attention. First of all, it is due to the discovery of the colossal magnetoresistance effect in manganites (the nature of which is believed to be closely related to inhomogeneous structures). There is also a significant increase in the research activity in the field of artificial magnetic nanocomposites for different applications. The wealth of publications including a lot of reviews is related not only to the possible technical applications of artificial and natural nanocomposites, but also with the fact that they are very promising objects for the studies in the physics of strongly correlated electron systems. Of particular interest is the interaction of spin, charge, degrees of freedom in manganites, cobaltites, and other magnetic oxides, as well as a very rich phase diagram characteristic of these compounds.
The phase separation phenomena and the formation of inhomogeneous states are characteristic for many strongly correlated electron systems where the potential energy of interactions among electrons exceeds their kinetic energy. In particular, they were widely discussed for high-Tc superconductors and heavy fermion materials. Note that one of the first most spectacular examples of such kind was the formation of ferromagnetic (FM) droplets (magnetic polarons or ferrons) in antiferromagnetic (AFM) semiconductors alt low doping levels as well as FM spin polarons in the paramagnetic state. Another similar example is the formation of a string (the linear trace formed by frustrated spins) arising when a hole moves in an AFM insulator. These examples correspond to the case of so called electron phase separation caused by self-trapping of charge carriers, which change their local environment. It is favorable for these regions to be as far apart as possible to minimize the Coulomb energy. In addition to such a small-scale phase separation, in manganites, as well as in other compounds exhibiting first order transitions (e.g., between FM and AFM phases), there also arises the phase separation of another type related to rather wide region where different phases coexist. An example of such larger scale phase separation is the formation of rather large FM droplets with the size of the order of 100 ÷ 1000 Å inside the AFM matrix. Note also that an important feature of manganites is the strong coupling of electron and lattice subsystems. This is related to the Jahn-Teller nature of Mn3+ ions and thus any phase separation gives rise to the elastic distortions of the crystal lattice, which can be observed in experiment. Another characteristic feature of manganites is the charge ordering, i.e. a possible regular arrangement of Mn3+ and Mn4+ ions. Actually, an additional lattice period arises and we have a superstructure. In addition to the formation of such superstructure, the charge ordering can also lead to a nontrivial spin and orbital ordering. An example of this ordering is a well-known CE magnetic structure in manganites like Pr0.5C0.5MnO3, where the charge ordering is accompanied by the formation of the zigzag type magnetic chains. The interaction of spin, charge, and orbital degrees of freedom can also lead to the formation of stripe structures instead of droplets at high content of the alkaline earth element. In manganites in contrast to high-Tc superconductors, these structures are not dynamical but static owing to the strong electron-lattice interactions, and can be observed by the electron diffraction and the low-angle neutron scattering. The phase separation also produces a significant effect on the transport characteristics of magnetic materials, such as electrical conductivity, magnetoresistance, and noise spectrum.
In ITAE, there is a long-term experience in the studies of electron, magnetic, and crystal structures of the magnetic oxides, in particular, manganites. The results of earlier studies were summarized in the review article [1]. In the recent years, the following results were obtained. It was shown that the characteristic features of the interplay between spin, orbital, and charge degrees of freedom lead to an unusual elementary excitation spectrum and to the tendency toward the phase separation [3]. The quantum description of the magnetic structure and the phase separation was given for the systems like manganites and it was shown that the uniform canted magnetic structure is unstable in the wide range of doping levels [7]. The instability of uniform charge ordering toward the formation of the local metallic regions at the antiferromagnetic charge ordered insulating background was demonstrated for doping levels near 0.5 [9]. The features of the phase separation in the layered magnetic systems were analyzed [7]. The mechanism underlying the formation of the stripe structures was suggested for manganites at high doping levels; it is possibly related to elastic interactions between the Jahn-Teller centers [8, 15]. The conductivity, magnetoresistance, and noise spectrum were calculated for manganites at doping levels far from the percolation threshold corresponding to metal-insulator transition based on the droplet model of the phase separation [6, 10-12, 17]. The detailed comparison of the theory and experiment allowed us to reveal the main characteristics of the inhomogeneous state [13, 14, 19]. The theoretical description of the phase separation was performed on the basis of the generalized Kondo-lattice model taking into account the Coulomb repulsion of electrons at neighboring centers. The model was analyzed using the Green function technique and variational methods. It was demonstrated that such an approach gives qualitatively correct description of the main features of the phase diagram of manganites [17, 19]. The magnetic structure and the phase diagram were found for one-dimensional chains of magnetic ions, modeling the situation typical of manganites [20, 21]. The theoretical results were successfully applied to the interpretation of the giant isotope effect and the kinetics of the phase separation in manganites [2, 4, 18]. The results and the methods of the studies of the phase separation in manganites and the related compounds were summarized in review articles [7, 10, 16].
Possible types of stripe structures in the basal
plane of
La1-xCaxMnO3
manganite at
x=2/3:
(a)
separate stripes;
(b)
bistripes with different orbitals at
Mn3+
ions;
(c)
bistripes with similar orbitals at
Mn3+
ions.
Blue circles:
Mn3+
ions, red
"figures-of-eight" denote the electron density distribution corresponding to
d orbitals at
Mn3+
ions [15].
Temperature dependence of magnetoresistance for
phase separated manganites of different composition:
circles, squares, and other symbols denote experimental
data, the red solid line corresponds to the predicted
behavior of magnetoresistance (MR
~T-5)
[13].
The phase diagram for an antiferromagnetic chain with
donor impurities, where the formation of magnetic
polarons (ferrons) of different length is possible.
J
is the exchange integral for spins in the chain,
V
is the electron-impurity coupling constant,
n
is the number of lattice sites within a ferron.
Solid line is the "melting line" for ferrons, the dot-dash
line is the depinning line, above which the ferron comes
off the impurity (retaining its magnetic structure)
[21].
Main publications
1. К.И. Кугель, Д.И. Хомский, "Эффект
Яна-Теллера и магнетизм:
соединения переходных металлов",
УФН, 1982, т. 136, № 4, c. 621-664.
2. N.A. Babushkina, L.M. Belova,
O.Yu. Gorbenko, A.R. Kaul, A.A. Bosak, V.I. Ozhogin,
K.I. Kugel, "Metal-insulator transition induced by oxygen isotope exchange in
magnetoresistive perovskite manganites", Nature, 1998, v. 391, no.
6663, pp. 159-161.
3. J. van den Brink, W.
Stekelenburg, D.I. Khomskii, G.A. Sawatzky, K.I. Kugel, "Elementary
excitations in the coupled spin-orbital model", Phys. Rev. B, 1998, v. 58, no.
16, pp. 10276-10282.
4. И.Ф. Волошин, А.В. Калинов, С.Е. Савельев, Л.М. Фишер, Н.А. Бабушкина,
Л.М. Белова, Д.И. Хомский, К.И. Кугель, "Фазовое
расслоение в La-Pr манганитах
и его эволюция в магнитном поле",
Письма в ЖЭТФ, 2000, т. 71, вып. 3, с. 157-163.
5.
N.A.Babushkina,
A.N.
Taldenkov,
L.M.
Belova,
E.A.
Chistotina,
O.Yu.
Gorbenko,
A.R.
Kaul,
K.I.
Kugel,
and D.I.
Khomskii,
"Partial
16O
®
18O isotope substitution and
phase separation in
(La0.25Pr0.75)0.7Ca0.3MnO3
manganite",
Phys.
Rev. B, 2000, v. 62, no. 10, pp.
R6081-R6084.
6. A.L. Rakhmanov, K.I. Kugel, Ya.M. Blanter, M.Yu. Kagan, "Resistivity and 1/f
noise in non-metallic
phase separated manganites", Phys. Rev.
B, 2001,
v. 63,
no. 17,
174424, 6 pages.
7. М.Ю. Каган, К.И. Кугель, "Неоднородные зарядовые
состояния и фазовое
расслоение в манганитах", УФН,
2001, т. 171, № 6, с. 577-596.
8. D.I. Khomskii, K.I. Kugel, "Why
stripes? Spontaneous formation of inhomogeneous
structures due to elastic interactions", Europhys. Lett.,
2001, v.
55, no. 2, pp. 208-213.
9. M.Yu. Kagan, K.I. Kugel, D.I. Khomskii, "Phase separation in
systems
with charge ordering",
ЖЭТФ,
2001, т.
120, вып.
2(8), с.
470-481.
10. M.Yu. Kagan, K.I. Kugel, D.I. Khomskii, A.L. Rakhmanov, "Inhomogeneous
charge states
and electronic transport in manganites" (review article),
ФНТ, 2001,
т. 27, №
8, с. 815-825.
11. А.О. Сбойчаков, А.Л. Рахманов, К.И. Кугель, М.Ю. Каган, И.В.
Бродский, "Туннельное
магнитосопротивление
фазово-расслоенных манганитов", ЖЭТФ,
2002, т. 122,
вып. 4(10),
с. 869-878.
12. A.O. Sboychakov, A.L.
Rakhmanov, K.I. Kugel, M.Yu. Kagan, I.V. Brodsky, "Tunnelling magnetoresistance
and
1/f noise in phase-separated manganites", J. Phys.: Condens.
Matter, 2003, v. 15, no. 10, pp. 1705-1717.
13. Н.А. Бабушкина, Е.А. Чистотина, К.И. Кугель, А.Л. Рахманов, О.Ю. Горбенко,
А.Р. Кауль, "Высокотемпературные
свойства манганитов: проявление
неоднородности парамагнитной фазы?", ФТТ, 2003, т. 45, №
3, стр. 480-484.
14. N.A.
Babushkina, E.A. Chistotina, O.Yu. Gorbenko, A.R. Kaul, D.I. Khomskii, and K.I.
Kugel, "Modification of the ground
state in Sm-Sr manganites by oxygen isotope substitution",
Phys.
Rev.
B, 2003, v. 67, no. 10,
100410(R), 4 pages.
15. D.I. Khomskii, K.I. Kugel,
"Elastic interactions and superstructures in manganites and
other Jahn-Teller systems", Physical Review B, 2003, v. 67,
no. 13, 134401, 9 pages.
16. М.Ю. Каган, А.В. Клапцов, И.В. Бродский, К.И. Кугель, А.О. Сбойчаков, А.Л.
Рахманов, "Мелкомасштабное
фазовое расслоение и электронный
транспорт в манганитах", УФН, 2003, т. 173, № 8, с. 877-883.
17. M.Yu. Kagan, A.V. Klaptsov,
I.V. Brodsky, K.I. Kugel, A.O. Sboychakov, A.L. Rakhmanov, "Nanoscale
phase separation in manganites", J.
Phys.
A:
Math. and General, 2003, v. 36, no. 35, pp. 9155–9163.
18.
L.M. Fisher, A.V. Kalinov, I.F.
Voloshin, N.A. Babushkina, D.I. Khomskii, K.I. Kugel,
"Phase separation and isotope effect in the ferromagnetic
insulating state of the
Pr1–xCaxMnO3
system (0.2 < x < 0.33)", Phys. Rev.
B, 2003,
v. 68,
no. 17, 174403, 8
pages.
19. К.И. Кугель, А.Л. Рахманов, А.О. Сбойчаков, М.Ю. Каган, И.В. Бродский,
А.В. Клапцов,
"Характеристики фазово-расслоенного
состояния манганитов и их связь с транспортными
и магнитными свойствами", ЖЭТФ,
2004, т. 125,
вып. 3,
с. 648-658.
20. I. González, J. Castro, D.
Baldomir, A.O. Sboychakov, A.L. Rakhmanov, K.I. Kugel, "Magnetic polarons
in a doped one-dimensional antiferromagnetic chain", Phys.
Rev. B, 2004, v. 69, no. 22, 224410, 5 pages.
21. A.O.
Sboychakov, A.L. Rakhmanov, K.I. Kugel, I. González, J. Castro, D. Baldomir,
"Evolution
with temperature of the magnetic polaron state in an antiferromagnetic
chain with impurities",
Phys. Rev. B, 2005,
v.
72,
no.
1,
8
pages.