Showing papers on "Coherent potential approximation published in 2003"
TL;DR: In this article, the Curie temperatures of the diluted magnetic semiconductors (Ga, Mn)As, Ga, Cr)As and Cr)N are evaluated from first principles.
Abstract: Curie temperatures of the diluted magnetic semiconductors (Ga, Mn)As, (Ga, Mn)N, (Ga, Cr)As and (Ga, Cr)N are evaluated from first principles. The electronic structure is calculated in the local spin density approximation by using the Korringa-Kohn-Rostoker method combined with the coherent potential approximation to describe the substitutional and spin disorder. From the total energy differences between the ferromagnetic state and the spin-glass state, realistic estimations of Curie temperatures are achieved by using a mapping on the Heisenberg model in the mean-field approximation. Effects of additional carrier doping treatments are also investigated. Very large Curie temperatures are obtained, lying above room temperature for (Ga, Mn)N, (Ga, Cr)As and (Ga, Cr)N. Upon hole doping the Curie temperature of (Ga, Mn)N further increases, while (Ga, Mn)As shows a plateau behavior.
287 citations
TL;DR: In this paper, a systematic study for the materials design of III-V and II-VI compound-based ferromagnetic diluted magnetic semiconductors is given based on ab initio calculations within the local spin density approximation.
Abstract: A systematic study for the materials design of III–V and II–VI compound-based ferromagnetic diluted magnetic semiconductors is given based on ab initio calculations within the local spin density approximation. The electronic structures of 3d-transition-metal-atom-doped GaN and Mn-doped InN, InP, InAs, InSb, GaN, GaP, GaAs, GaSb, AlN, AlP, AlAs and AlSb were calculated by the Korringa–Kohn–Rostoker method combined with the coherent potential approximation. It is found that the ferromagnetic ground states are readily achievable in V-, Cr- or Mn-doped GaN without any additional carrier doping treatments, and that InN is the most promising candidate for high-TC ferromagnet. A simple explanation of the systematic behavior of the magnetic states in III–V and II–VI compound-based diluted magnetic semiconductors is also given. It is also shown that V or Cr-doped ZnS, ZnSe, and ZnTe are ferromagnetic without p- or n-type doping treatment. However, Mn-, Fe-, Co- or Ni-doped ZnS, ZnSe and ZnTe are spin-glass states. V-, Cr-, Fe-, Co-, Ni-doped ZnO without any doping and Mn-doped ZnO with p-type hole doping all shows half-metallic transparent ferromagnetism.
122 citations
TL;DR: In this paper, structural and electron transport properties of Se-and Te-doped CoSb 3 skutterudites in relation to results of electronic structure calculations performed for this system were presented.
121 citations
TL;DR: In this article, the authors considered the low-frequency limit for propagation of sound waves in periodic elastic medium (phononic crystals) and derived exact analytical formulas for the speed of sound propagating in a three-dimensional periodic arrangement of liquid and gas or in a two-dimensional arrangement of solids.
Abstract: We consider the low-frequency limit (homogenization) for propagation of sound waves in periodic elastic medium (phononic crystals). Exact analytical formulas for the speed of sound propagating in a three-dimensional periodic arrangement of liquid and gas or in a two-dimensional arrangement of solids are derived. We apply our formulas to the well-known phenomenon of the drop of the speed of sound in mixtures. For air bubbles in water we obtain a perfect agreement with the recent results of coherent potential approximation obtained by Phys. Rev. Lett. 84, 6050 (2000)] if the filling of air bubbles is far from close packing. When air spheres almost touch each other, the approximation gives 10 times lower speed of sound than the exact theory does.
113 citations
TL;DR: In this paper, a systematic study for the materials design of III-V and II-VI compounds-based ferromagnetic diluted magnetic semiconductors is given based on ab initio calculations within the local spin density approximation.
78 citations
TL;DR: In this article, the Curie temperature in the diluted magnetic semiconductor (Ga12x2yMnxAsy) As alloys, where the compensation effect by As antisites is taken into account, was determined from first principles.
Abstract: We have determined from first principles the Curie temperature in the diluted magnetic semiconductor (Ga12x2yMnxAsy) As alloys, where the compensation effect by As antisites is taken into account. The disorder due to random positions of Mn impurities and As antisites is taken into account in the framework of the coherent potential approximation. We demonstrate that a simple mean-field approximation~MFA! already gets Tc accurately. In particular, it is shown that the calculated Tc in the random-phase approximation and Monte Carlo simulations differ only weakly from the MFA values. The reason is that a proper treatment of the disorder beyond the virtual-crystal approximation leads, in this doped material, to a flat magnon dispersion in a large part of the Brillouin zone.
64 citations
TL;DR: The Korringa-Kohn-Rostocker nonlocal coherent-potential approximation (KKR-NLCPA) as mentioned in this paper was proposed for describing the electronic structure of disordered systems.
Abstract: We introduce the Korringa-Kohn-Rostocker nonlocal coherent-potential approximation (KKR-NLCPA) for describing the electronic structure of disordered systems The KKR-NLCPA systematically provides a hierarchy of improvements upon the widely used KKR-CPA approach and includes nonlocal correlations in the disorder configurations by means of a self-consistently embedded cluster The KKR-NLCPA method satisfies all of the requirements for a successful cluster generalization of the KKR-CPA; it remains fully causal, becomes exact in the limit of large cluster sizes, reduces to the KKR-CPA for a single-site cluster, is straightforward to implement numerically, and enables the effects of short-range order upon the electronic structure to be investigated In particular, it is suitable for combination with electronic density-functional theory to give an ab initio description of disordered systems Future applications to charge correlation and lattice displacement effects in alloys, and spin fluctuations in magnets amongst others, are very promising We illustrate the method by application to a simple one-dimensional model
60 citations
TL;DR: In this article, a selfconsistent method for electronic structure calculations of correlated systems was proposed, which combines the local spin-density approximation (LSDA) and the dynamical mean field theory (DMFT).
Abstract: We propose a self-consistent method for electronic structure calculations of correlated systems, which combines the local spin-density approximation (LSDA) and the dynamical mean field theory (DMFT). The LSDA part is based on the exact muffin-tin orbital approach, meanwhile the DMFT uses a perturbation scheme that includes the T matrix with fluctuation exchange approximation. The current LSDA+DMFT implementation fulfills both self-energy and charge self-consistency requirements. We present results on the electronic structure calculations for bulk 3d transition metals (Cr, Fe, and Ni) and for Fe/Cr magnetic multilayers. The latter demonstrates the importance of the correlation effects for the properties of magnetic heterostructures.
50 citations
TL;DR: In this article, the Lanczos method is used to compute the spectral function of the Holstein polaron in one and two dimensions, and the results agree well with previous calculations within the many-body coherent potential approximation.
Abstract: Cluster perturbation theory in combination with the Lanczos method is used to compute the one-electron spectral function of the Holstein polaron in one and two dimensions. It is shown that the method allows reliable calculations using relatively small clusters, and at the same time significantly reduces finite-size effects. Results are compared with exact data and the relation to existing work is discussed. We also use a strong-coupling perturbation theory---equivalent to the Hubbard I approximation---to calculate the spectral function of the quarter-filled Holstein model of spinless fermions, starting from the exact atomic-limit Green function. The results agree well with previous calculations within the many-body coherent potential approximation.
41 citations
TL;DR: In this article, the authors make a theoretical study of the quantum oscillations of the tunneling magnetoresistance (TMR) as a function of the spacer layer thickness and calculate the TMR ratio for disordered tunneling junctions containing a spacer at which quantum well states are formed.
Abstract: We make a theoretical study of the quantum oscillations of the tunneling magnetoresistance (TMR) as a function of the spacer layer thickness. Such oscillations were recently observed in tunneling junctions with a nonmagnetic metallic spacer at the barrier-electrode interface. We calculate the TMR ratio for disordered tunneling junctions containing a spacer at which quantum well states are formed. A single-orbital tight-binding model, the linear response theory, and the coherent potential approximation are used for the calculation. As a function of the spacer thickness, calculated TMR ratio shows damped oscillation around zero with a single period given by the Fermi wave vector of the spacer, which is consistent with observed results. It is shown that momentum selection due to the insulating barrier and conduction via quantum well states in the spacer, mediated by diffusive scattering caused by disorder, are essential features required to explain the observed oscillation in the TMR ratio. We further show that calculated results can be reproduced by the stationary phase approximation, which implies that obtained results hold qualitatively in more realistic band models.
32 citations
TL;DR: In this paper, the effect of magnetic moment disorder and compositional disorder on the stability of Pu 3 Al, Pu 3 Ga and Pu 3 In compounds was investigated using density functional theory (DFT).
TL;DR: In this article, the authors consider electron transport in magnetic multilayers and consider how electron transport is affected by disorder at the interface between two layers, and show that the fraction of electrons scattered diffusely depends on the angle of incidence as well as the energy and the degree of interfacial disorder.
Abstract: We consider electron transport in magnetic multilayers. In particular, we consider how electron transport is affected by disorder at the interface between two layers. Standard semiclassical approaches characterize diffusive scattering at interfaces with a specularity constant S such that S is the fraction of electrons that are specularly scattered. S is typically considered to be the same for the reflected and transmitted electron beams. Here we show for two models of interfacial disorder that (a) S is not a constant, but depends on the angle of incidence as well as the energy and the degree of interfacial disorder, and (b) S is different for reflected and transmitted electrons. The two different models that we consider are (1) random point scatterers at a planar interface between layers in a free electron approximation and (2) random substitutional disorder of atoms on atomic layers near the interface. The latter model is treated within the coherent potential approximation using the layer Korringa-Kohn-Rostoker method. The fraction of electrons scattered diffusely $[1\ensuremath{-}S({\mathbf{k}}_{\ensuremath{\Vert}})]$ is shown to have the same dependence on ${\mathbf{k}}_{\ensuremath{\Vert}}$ (i.e., angle of incidence) in the free electron limit of model (2) as in model (1). Model (2) provides a realistic description of interfacial scattering that can be readily evaluated for technologically important systems such as Co-Cu.
TL;DR: In this paper, a general approach for the description of correlated hopping in infinite dimensions, which is based on an expansion over electron hopping around the atomic limit, is developed, keeping the dynamical mean-field theory local ideology and allowing one to calculate the thermodynamical functions.
Abstract: A general approach for the description of correlated hopping in infinite dimensions, which is based on an expansion over electron hopping around the atomic limit, is developed. Such an approach keeps the dynamical mean-field theory local ideology and allows one to calculate the thermodynamical functions. A grand-canonical potential functional and a $\ensuremath{\Phi}$-derivable theory that does not introduce the self-energy is proposed. As limiting cases the Falicov-Kimball model with correlated hopping and the model with broken bonds (``diluted'' conductor) are investigated, and the connection with the Blackman-Esterling-Berk coherent potential approximation approach in the theory of the binary alloy with off-diagonal disorder is considered.
TL;DR: In this article, the chemical trends of transition metal-doped chalcopyrite diluted magnetic semiconductors were calculated by using the Korringa-Kohn-Rostoker Green's function method and the coherent potential approximation combined with the local density approximation.
TL;DR: In this article, the authors used the Kubo-Greenwood formula in combination with the fully relativistic spin-polarized screened Korringa-Kohn-Rostoker method and the Coherent Potential Approximation to calculate the residual resistivity and the anisotropic magnetoresistance of bulk Ni-rich alloys.
Abstract: By using the Kubo-Greenwood formula in combination with the fully relativistic spin-polarized Screened Korringa-Kohn-Rostoker method and the Coherent Potential Approximation we calculated the residual resistivity and the anisotropic magnetoresistance of bulk ${\mathrm{Ni}}_{1\ensuremath{-}c}{\mathrm{Fe}}_{c}$ alloys in the Ni-rich regime. While the calculated residual resistivities are typically 30--40% smaller than the measured values, for the anisotropic magnetoresistance ratios we obtained an excellent agreement between theory and experiment. Varying the angle between the directions of the magnetization and of the current we found a functional dependence of the resistivity consistent with the formula proposed originally by D\"oring.
TL;DR: In this article, the authors applied the dynamical coherent potential approximation to a simple model, and systematically studied the carrier states in A 1 x Mn x B -type diluted magnetic semiconductors (DMS's).
Abstract: Applying the dynamical coherent potential approximation to a simple model, we have systematically studied the carrier states in A 1- x Mn x B -type diluted magnetic semiconductors (DMS's). The model calculation was performed for three typical cases of DMS's: cases with strong and moderate exchange interactions in the absence of nonmagnetic potential, and a case with strong attractive nonmagnetic potential in addition to moderate exchange interaction. When the exchange interaction is sufficiently strong, magnetic impurity bands split from the host band. Carriers in the magnetic impurity band mainly stay at magnetic sites, and coupling between the carrier spin and the localized spin is very strong. The hopping of the carriers among the magnetic sites causes ferromagnetism through a double-exchange (DE)-like mechanism. We have investigated the conditions for the operation of DE-like mechanism in DMS's. The result reveals that the nonmagnetic attractive potential at the magnetic site assists the formation of ...
TL;DR: In this paper, first principles of transport properties of disordered alloys based on the Kubo-Greenwood formalism and the spin-polarized Korringa-Kohn-Rostoker coherent potential approximation are presented.
Abstract: First-principles calculations of transport properties of disordered alloys based on the Kubo-Greenwood formalism and the spin-polarized Korringa-Kohn-Rostoker coherent potential approximation are presented. Application to the fcc alloy systems NixCr12x and NixCu12x yields results for the residual resistivity, anomalous magnetoresistance, and the magnetic moments that are in very satisfying agreement with experiment. In particular, the different sign for the resistance anisotropy in Ni xCr12x and NixCu12x and the concentration of the onset of magnetism could be reproduced. Scalar-relativistic calculations were performed on the basis of the two-current model in order to assess the importance of relativistic effects in these systems.
TL;DR: In this article, a spin-polarized Korringa-Kohn-Rostoker method is combined with a real-space formulation of the Kubo-Greenwood equation to describe electrical transport properties of nanostructures.
Abstract: We propose a method suitable to describe electrical transport properties of nanostructures. In this approach a Green's function embedding technique based on the fully relativistic spin-polarized Korringa-Kohn-Rostoker method and the coherent potential approximation is combined with a real-space formulation of the Kubo-Greenwood equation. We present calculations for the Ag(100) surface, Ag bulk, two types of CuPt bulk alloys in the ``large cluster'' limit as well as finite Fe and Co chains embedded into the surface layer of Ag(100) in order to illustrate the reliability and applicability of this approach.
TL;DR: In this paper, an incorporation of the LDA+U formalism into the spin-polarized relativistic Korringa-Kohn-Rostoker (SPR-KKR) method of band-structure calculations is presented.
TL;DR: In this paper, the effect of localization of the 5f electrons in δ-Pu has been investigated using a full-potential linear muffin-tin orbitals (FPLMTO) method and the Korringa-Kohn-Rostocker method within Green's function formalism.
Abstract: First-principles methods are employed to study the effect of localization of the 5f electrons in δ-Pu. First, a full-potential linear muffin–tin orbitals (FPLMTO) method was applied to a model system, , where Puloc are Pu atoms with localized (nonbonding) 5f electrons and Puit atoms with itinerant (bonding) 5f electrons. Within the FPLMTO, this system was treated as an ordered compound, either in the Cu3Au or the CuAu structure to model δ-Pu which crystallize in a face-centred-cubic structure. A more realistic alloy treatment of our model system was provided by the Korringa–Kohn–Rostocker method within Green's function formalism in which compositional disorder is treated by means of the coherent potential approximation. With these two approaches best agreement with the experimental lattice constant for δ-Pu were achieved for a 67–68% fraction of itinerant (Puit) atoms. This corresponds to a little less than four itinerant 5f electrons/atom in δ-Pu which agrees well with some proposed theoretical models, but disagree with at least an other theoretical suggestion. We show that a good lattice constant (by construction), good bulk modulus, and full mechanical stability for δ-Pu follows from our model. The main problem with the present approach and some other presented models, trying to capture localization in δ-Pu, is that the contribution to the total energy from the localized 5f electrons cannot be calculated accurately and therefore one parameter (usually the lattice constant) needs to be fitted to experiment.
TL;DR: In this article, the formation energy and resistivity for domain walls in permalloy (fcc-Ni 8 5 Fe 1 5 ) were determined using the fully relativistic spin-polarized screened Korringa-Kohn-Rostoker method for layered systems.
Abstract: To determine the formation energy and resistivity for domain walls in permalloy (fcc-Ni 8 5 Fe 1 5 ) we use the fully relativistic spin-polarized screened Korringa-Kohn-Rostoker method for layered systems and the corresponding Kubo-Greenwood equation in the context of the (inhomogeneous) coherent potential approximation. We find that the difference in formation energy between 90° and 180° domains becomes very small if the domain wall width increases. Furthermore, we show that regardless of the configuration within a domain wall the in-plane components of the resistivity are larger than in a single domain and, in particular, that the anisotropic magnetoresistance ratio within the domain wall vanishes.
TL;DR: In this article, it has been shown that the free energy of the Falicov-Kimball model and the dynamical mean field theory solution are numerically equal to each other.
Abstract: Falicov and Kimball proposed a real-axis form for the free energy of the Falicov-Kimball model that was modified for the coherent potential approximation by Plischke. Brandt and Mielsch proposed an imaginary-axis form for the free energy of the dynamical mean field theory solution of the Falicov-Kimball model. It has long been known that these two formulas are numerically equal to each other; an explicit derivation showing this equivalence is presented here.
TL;DR: In this paper, the authors analyzed the itinerant model for ferromagnetism with both single-site and two-site electron correlations, and used the coherent potential approximation technique (CPA) with two self-energies.
Abstract: We will analyze the itinerant model for ferromagnetism with both single-site and two-site electron correlations. We will include band degeneration into the model. This will allow us to consider the on-site exchange interactions in the Hamiltonian. The modified Hartree–Fock approximation for the two-site interactions will be used. This approximation will give the relative one spin band broadening with respect to the other, in addition to the shift in position of majority and minority spin bands. Next, we will use the coherent potential approximation technique (CPA) with two self-energies. One will describe the on-site correlation and the second one the inter-site correlation. We will separate from these self-energies, the linear terms arising from Hartree–Fock approximation which will be applied to both; the on-site and inter-site interactions. These terms will contribute to the effective molecular field and the remaining ones (non-linear) will contribute to the correlation factors. The Green function technique and CPA decoupling will allow for the change in the shape of spin bands, which has been described by the correlation factors and which will decrease the kinetic energy of the system. The gain in kinetic energy due to the on-site and inter-site correlation factors will drive the ferromagnetism and significantly reduce the effective Hartree field necessary to create this ordering.
TL;DR: In this article, the authors studied the dynamics of a single Frenkel exciton in a disordered molecular chain and derived asymptotic formulas relating the absorption linewidth and the exciton coherence length to the strength of disorder.
Abstract: We study the dynamics of a single Frenkel exciton in a disordered molecular chain. The coherent-potential approximation is applied to the situation where the single-molecule excitation energies as well as the transition dipole moments, both their absolute values and orientations, are random. Such a model is believed to be relevant for the description of the linear optical properties of one-dimensional J aggregates. We calculate the exciton density of states, the linear absorption spectra, and the exciton coherence length which reveals itself in the linear optics. A detailed analysis of the low-disorder limit of the theory is presented. In particular, we derive asymptotic formulas relating the absorption linewidth and the exciton coherence length to the strength of disorder. Such expressions account simultaneously for all the above types of disorders and reduce to well-established form when no disorder in the transition dipoles is present. The theory is applied to the case of purely orientational disorder and is shown to agree well with exact numerical diagonalization.
TL;DR: In this article, the role of the interfaces in the magnetoresistance of a spin-polarized screened Korringa-Kohn-Rostoker (KKR) system is investigated.
Abstract: By using the fully relativistic spin-polarized screened Korringa-Kohn-Rostoker method and the corresponding Kubo-Greenwood equation resistivities and the giant magnetoresistance are evaluated for Fe/Au/Fe/Au spin valves assuming both bcc-like Fe and fcc-Au leads. The theoretically obtained values for a spacer thickness of 7 monolayers of Au are in a rather good agreement with the corresponding experimental data. These data, in particular the temperature dependence of the resistivities reported in here, are analyzed with respect to the experimental setup and related to the theoretical models assumed. Since in the theoretical calculations interdiffused interfaces are taken into account by means of the inhomogeneous coherent potential approximation, the role of the interfaces in the magnetoresistance of this system can be discussed rigorously.
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TL;DR: In this article, the problem of an electromagnetic wave scattered from a random medium layer with rough boundaries is formulated using integral equations which involve two kinds of Green functions, one describing the wave scattered by the random medium and the rough boundaries, and the second one which corresponds to the unperturbed Green functions describes the scattering by an homogeneous layer with the rough boundary.
Abstract: The problem of an electromagnetic wave scattered from a random medium layer with rough boundaries is formulated using integral equations which involve two kinds of Green functions. The first one describes the wave scattered by the random medium and the rough boundaries, and the second one which corresponds to the unperturbed Green functions describes the scattering by an homogeneous layer with the rough boundaries. As these equations are formally similar to classical equations used in scattering theory by an infinite random medium, we will be able to apply standard procedures to calculate the coherent field. We will use the coherent potential approximation where the correlations between the particles will be taken into account under the quasi-crystalline approximation.
01 Mar 2003
TL;DR: The low-frequency limit (homogenization) for propagation of sound waves in periodic elastic medium (phononic crystals) is considered and exact analytical formulas for the speed of sound propagating in a three-dimensional periodic arrangement of liquid and gas or in a two-dimensional arrangement of solids are derived.
Abstract: We consider the low-frequency limit (homogenization) for propagation of sound waves in periodic elastic medium (phononic crystals). Exact analytical formulas for the speed of sound propagating in a three-dimensional periodic arrangement of liquid and gas or in a two-dimensional arrangement of solids are derived. We apply our formulas to the well-known phenomenon of the drop of the speed of sound in mixtures. For air bubbles in water we obtain a perfect agreement with the recent results of coherent potential approximation obtained by Phys. Rev. Lett. 84, 6050 (2000)] if the filling of air bubbles is far from close packing. When air spheres almost touch each other, the approximation gives 10 times lower speed of sound than the exact theory does.
TL;DR: In this paper, the magnetic Compton profiles of ordered and disordered Fe3Pt alloys were calculated using linear muffin-tin orbital and KKR methods, the latter incorporating the coherent potential approximation to describe the substitutional disorder, the electronic band structure and measurable quantities such as the Fermi surface topology.
Abstract: The electronic structure of invar alloys (i.e. materials in which the near absence of thermal expansion is observed) has been the focus of much study, owing both to the technological applications of these materials and interest in the fundamental mechanism that is responsible for the effect. Here, calculations of the magnetic Compton profiles are presented for ordered and disordered Fe3Pt alloys. Using linear muffin-tin orbital and KKR methods, the latter incorporating the coherent potential approximation to describe the substitutional disorder, the electronic band structure and measurable quantities such as the Fermi surface topology are presented.
TL;DR: In this paper, the magnetic and electronic structure of two different Ni-H materials, the first one being synthesized under a few bar hydrogen pressure and the second one being stabilized under ultra high pressure, were analyzed.
TL;DR: In this article, the coherent potential approximation (CPA) is applied to the problem of off-diagonal disorder caused by random spin orientations in the paramagnetic (PM) state of the double-exchange (DE) model.
Abstract: The coherent potential approximation (CPA) is applied to the problem of off-diagonal disorder caused by random spin orientations in the paramagnetic (PM) state of the double-exchange (DE) model. The CPA calculations are supplemented by the variational mean-field approach for the Curie temperature ${(T}_{C}).$ Our formulation of CPA is essentially nonlocal and based on the perturbation theory expansion for the T matrix with respect to fluctuations of interatomic hopping parameters near the ``mean values'' specified by matrix elements of the self-energy for the effective medium, so that in the first order it becomes equivalent to the DE theory by de Gennes. The second-order effects, considered in the present work, are not negligible and lead to substantial reduction of ${T}_{C}$ in the one-orbital case. Even more dramatic changes are expected for the degenerate DE model, where each site of the cubic lattice is represented by two ${e}_{g}$ orbitals, which also specify the form of interatomic hoppings. Particularly, the existence of two Van Hove singularities in the spectrum of the degenerate model lead to the branching of CPA solutions, when Green's function and the self-energy become multivalued functions in certain regions of the complex plane. Different solutions can be classified by some nonlocal parameter of interatomic orbital polarization ${\mathcal{O}}_{\mathrm{NL}},$ and the multivalued behavior itself has many similarities with the phenomenon of metamagnetism with respect to ${\mathcal{O}}_{\mathrm{NL}}.$ This changes the traditional concept of the DE physics dramatically. Particularly, we predict the transition to the two-phase state (with different values of the order parameter ${\mathcal{O}}_{\mathrm{NL}})$ in the PM region below a certain temperature ${T}_{P}.$ It is followed by two consecutive magnetic transitions, which go separately in two different phases. Our scenario naturally explains the phase coexistence and the appearance of several magnetic transition points, which are frequently observed in perovskite manganites.