Research articlesA model study of tunneling conductance spectra of ferromagnetically ordered manganites
Introduction
Doped rare-earth manganites having chemical composition (R: Trivalent rare-earth ion and M: divalent alkaline earth ion) are of cubic perovskite structures which undergo distortions at low temperatures. The colossal magnetoresistive (CMR) property [1] and complex crystal phases with various magnetic, electronic and structural orders provide intensive research interest for their study [2], [3]. In the strongly correlated manganite systems, the physics is mainly due to the competition between the localization of charges due to lattice degrees of freedom and Coulomb interaction and delocalization of charges due to their kinetic energies. The core magnetic moments are aligned ferromagnetically (FM) with a metallic ground state if charges are delocalized whereas antiferromagnetic (AFM) alignment of core magnetic moments along with an insulating ground state is observed if localization of charges is dominating. In the insulating phase, the local lattice distortion of the near cubic symmetry as well as charge and orbital ordered states are associated. A strong competition between these two phases may be observed by varying different external parameters like concentration of chemical doping, lattice strain and magnetic field. The ordering of and ions is traditionally assumed to be the cause of charge ordering, but till now the origin of orbital and charge order state is not clear. The charge disproportion of Mn ions is observed to be much smaller than 1. Presence of two types of cations, x concentration of one type of cation and concentration of the other type, forms a stripe phase. Commensurate states are observed for doping concentrations . With as the reciprocal lattice vector, the charge modulation wave vector is written as . Despite of the competition, ferromagnetic metallic and charge order insulating phases co-exist in manganites.
The co-existence of the ferromagnetic (FM) metallic (M) and the charge ordered (CO) insulating (I) state is experimentally observed in the study of specific heat measurement of single crystal [4], magnetization and specific heat study of [5] and magnetocaloric effect of [6]. The metal–insulator (MI) transition near shows that there must be a change in electron density of states (DOS) near the Fermi level at this temperature. The transport properties of the material is decided by the electron DOS. The electronic phase separation is observed in manganites due to the presence of both electron rich ferromagnetic metallic phase and electron deficient charge ordered insulating phase. Low conductivity implies depletion of DOS at Fermi level. The presence of an insulating phase in a ferromagnetic metallic background near has been observed using scanning tunneling microscopy (STS) [7]. The angle resolved photo-emission spectroscopy (ARPES) measurements show the existence of a pseudo gap (PG) at the chemical potential () [8]. The depletion in DOS appearing in the paramagnetic (PM) phase in the tunneling spectroscopic measurements does not disappear completely on cooling down to the FM phase [9]. Tunneling conductance measurements always show the presence of either a small gap or a pseudo gap near the Fermi level in manganite systems.
Soon after the discovery of CMR property, Zener [10] has proposed a double-exchange (DE) interaction between the magnetic spins. He has suggested that this mechanism is responsible for ferromagnetism in the mixed valent perovskite manganites. Anderson and Hasegawa [11] have studied the DE mechanism using a semi-classical model, where they have considered core spin of each Mn ion classically, but the mobile electron quantum mechanically. They have found that the effective transfer integral is directly proportional to , where is the classical angle between the core spins. The DE model is further developed by de Gennes [12]. He has treated the effect of DE in the presence of AFM background and has predicted that, at low doping level, an AFM super-exchange interaction competes with the ferromagnetic DE interaction which leads to a spin-canted state. Further, de Gennes has considered localization and self-trapping of charge carriers, which gives rise to local distortion of spin lattice i.e. the concept of the magnetic polaron. Goodenough [13] has studied the magnetic lattice, the crystallographic lattice, the electrical resistivity, and the Curie temperature as functions of the fraction of ions present in manganites using the semi-covalent bond approach and elastic energy considerations. A semi-covalent bond arises due to overlapping of spin-polarized sp orbitals of Mn ions with occupied orbitals of oxygen. Searle and Wang [14] have interpreted the magnetoresistivity with the help of a model study based on a strongly spin-polarized conduction band. They have interpreted the resistivity and magnetoresistance data obtained from 77 K to 700 K. Kubo and Ohata [15] have considered a fully quantum mechanical approach employing mean-field theory for metallic double-exchange ferromagnets. They have calculated a magnetic phase diagram, resistivity and the magnetoresistance. Their results show a ferro- to paramagnetic transition at , accompanied by a change in the temperature dependence of resistivity, and diverging magnetoresistance at . Further, Furukawa [16] has proposed an unconventional one-magnon scattering process in manganites using the dynamical mean-field theory and found that the low temperature resistivity follows power law. Millis et al. [17] have calculated resistivity in dynamical mean-field theory of DE model and found that the resistivity is several orders of magnitude smaller than the observed value. Though DE model can explain the observed CMR property of manganites qualitatively, it can not explain it quantitatively. They have proposed that some extra mechanism like electron–phonon coupling due to Jahn–Teller (JT) distortion, which leads to localization of conduction band electrons as small polarons, is required along with DE mechanism. Within a 2-D DE model in the presence of AFM and JT phonons, the coexistence of FM-CO-OO, CE-CO-OO phase was observed in the DOS studies [18]. Though, generally, CO phase is associated with antiferromagnetism, it is observed that, for lower values of electron–phonon coupling, the CO state coexists with ferromagnetism. The octahedra are strongly distorted because of the strong electron–phonon coupling and the system becomes insulator due to localization of charges, whereas for weak electron–phonon interaction, a less number of charges are localized due to slight distortion of the octahedra and this leads to a metallic phase. The transport and optical properties of CMR manganites in a DE model, in the presence of JT distortion and disorder is studied by Majumdar and coworkers in the limit (J: Hund’s coupling constant) using classical Monte-Carlo simulation [19], [20]. A non-zero DOS at near the Fermi level indicates the presence of metallic phase [19]. Also the competition between FMM, CO and OO-CE phase was studied by them through the study of electron DOS [21]. Dagotto and co-workers have addressed the spin-charge-orbital orderings in manganites by using mean-field and Monte-Carlo simulation techniques beyond the mean-field approach [2], [22]. They have attempted to explain the phase separation techniques in Mn-oxides by using nano-scale clusters. They have shown that the inhomogeneities lead to the colossal magnetoresistance (CMR) effects in manganites. Model calculations using Monte-Carlo technique and computation of the DOS for manganites with Jahn–Teller (JT) phonons show unexpectedly robust PG at phase transition region [23]. The PG is formed due to the presence of FM metallic clusters in an orbitally ordered (OO) insulating background. Depletion of DOS and PG formation are also observed in the Monte-Carlo simulation in the FM-CE phase [24] and in the study of partial density of states using dynamical mean-field theory (DMFT) [25]. A pseudo-gap is observed in the chemical potential dependent DOS [26], in the model study of manganese oxides consisting of JT interaction.
Rout and coworkers have considered a model Hamiltonian consisting of Jahn–Teller (JT) distortion in the itinerant electron band, Heisenberg spin interaction among the core electrons besides the hybridization between electron band and the core electron states. They have considered ferromagnetic order in the core states by considering the Heisenberg interaction in the Ising limit. They have applied this microscopic model Hamiltonian to study the effect of JT interaction and the magnetic-nonmagnetic phase transition on the temperature dependent magnetic spin susceptibility and resistivity [27], [28], [29]. They have observed high resistivity just above the Curie temperature and below the lattice distortion temperature in the pure JT distorted phase. This insulating phase explains the CMR effect near Curie temperature and it separates the low temperature FM metallic (FMM) phase and high temperature paramagnetic metallic (PMM) phase. They have further improved this model by considering a more realistic DE model [15] instead of hybridization in the presence of charge density wave (CDW) formed due to the CO phase, as an extra-mechanism. They have applied this model calculation to investigate the temperature dependent magnetization, magnetic spin susceptibility, velocity of sound and Raman spectra for manganite systems [30], [31], [32], [33], [34]. They have observed a very strong interplay between FMM order and charge ordered insulating (COI) phases. The susceptibility and Raman spectra explains the evolution of the FM magnetic and CO excitation peaks. In another model, the same authors have considered JT interaction as an extra mechanism instead of CDW interaction and investigated the effect of temperature and magnetic field dependent resistivity to explain qualitatively the CMR effect observed near the Curie temperature separating the low temperature FMM phase and high temperature PMM phase [35], [36]. Recently Panda et al. have theoretically studied the interplay of the temperature dependent charge, spin and lattice degrees of freedom considering both CDW and JT interactions as extra mechanisms besides the usual DE model [37]. More recently, Panda et al. have presented a microscopic theoretical study of the interplay of antiferromagnetic (AFM) order and charge ordering in manganites which reveals the presence of pseudo-gap (PG) near the Fermi level [38]. It is observed that the depletion of the charge carriers near the Fermi level is associated with the formation of the CO state.
In the present communication, we report a microscopic model taking into account of the charge and spin degrees of freedom in the presence of Kubo-Ohata type DE interaction [15] to investigate theoretically the metal–insulator (MI) transition and the probable reason for CMR behavior in manganites near Curie temperature. Here we calculate the tunneling conductance and the temperature dependent specific heat of manganites to explain the strong interplay between the charge and spin degrees of freedom in manganites leading to the CMR effect near Curie temperature. The rest of the work is organized as follows. The model Hamiltonian and calculation of gap parameters are explained in Section 2. The results obtained are discussed in Section 3 and finally conclusion in Section 4.
Section snippets
Formalism
The ion in octahedron of the manganite system plays an important role in describing the CMR effect. The ion consists of three fold degenerate orbitals having three electrons and one excess electron in the upper two fold degenerate orbital. On the other hand, the orbitals of ions are empty. According to strong Hund’s coupling the electron spins of the Mn ion forms the localized spin of magnitude equal to . The electrons of ions form the band.
Results and discussion
The ferromagnetic magnetization () of the core spins and the CDW gap () given in Eqs. (9), (11) respectively are involved functions and hence they are solved self-consistently. Before numerical computation the physical parameters involved in the calculation are made dimensionless with respect to the width of conduction band (W) for convenience. Here we have taken the conduction band width , which is nearly equal to 10,000 K. The dimensionless parameters are the DE coupling , the
Conclusion
We have presented here the interplay between charge ordering and ferromagnetic ordering through Kubo-Ohata type [15] double exchange spin interactions. The charge gap and the ferromagnetic magnetizations are calculated by Green’s function technique and are solved self-consistently. The temperature dependent charge and spin orderings exhibit strong interplay between them. Particularly the charge ordering and its transition temperatures are strongly modified, when the magnetic ordering exists
Acknowledgment
The authors would like to gracefully acknowledge the research facilities of the Institute of Physics, Bhubaneswar, available to them.
References (59)
- et al.
Physica B
(2009) - et al.
Int. J. Mod. Phys. B
(2006) - et al.
Indian J. Phys.
(2009) - et al.
J. Phys.: Condens. Matter
(2009) Rep. Prog. Phys.
(2006)Nanoscale Phase Separation and Colossal Magnetoresistance
(2002)- et al.
Phys. Today
(2003) - et al.
Phys. Rev. Lett.
(1999) - et al.
Phys. Rev. B
(2002) - et al.
J. Appl. Phys.
(2012)