Double Exchange Hamiltonian Research Articles

Quantum phase transition in quarter-filled nanoclusters of manganite induced by element substitution at B site

In the present paper, we study the effect of element substitution for quarter-filled nanoclusters of perovskite manganite by introducing Jahn-Teller type of perturbation interaction to the double-exchange Hamiltonian. Using the unrestricted real-space Hartree-Fock approximation method we find that, the Jahn-Teller electron-phonon interaction plays the central role in producing the phase transition from ferromagnetic phase to CE type antiferromagnetic phase. Not only the Jahn-Teller interaction benefits antiferromagnetic correlation, it also increases the charge density order parameter. These theoretical results provide a guidance to predict the properties and modify the composition of particles of perovskite manganite under nano-scale.

Competition between double exchange and purely magnetic Heisenberg models in mixed valence systems: Application to half-doped manganites

A truncated Hubbard model is developed for the description of the electronic structure of odd-electron TM-L-TM units (TM=transition metal and L=ligand). The model variationally treats both the double exchange and purely magnetic Heisenberg configurations. This Hubbard model can either be mapped on a purely magnetic Heisenber model in which the bridging oxygen is also magnetic or on a double exchange model owing to the hybridization of the magnetic and ligand or bitals. The purely magnetic Heisenberg model is analytically solved in the general case of two metals (having n magnetic orbitals) bridged by a magnetic oxygen. The comparison of the analytical expressions of the Heisenberg energies to those of the double exchange model reveals that the two model spectra are identical except for one state which does not belong to the model space of the double exchange Hamiltonian. Consequently, the fitting of the model spectra to accurate ab initio spectra does not discriminate between the physically different models. These concepts are illustrated for the Mn-O-Mn unit (or Zener polaron) found in the half-doped manganite Pr(0.6)Ca(0.4)MnO3. It is shown that in the present case the projections of the ab initio ground state wave function onto both model spaces are almost identical provided that one uses properly localized orbitals, proving that the magnetic description of the Zener polaron and the double exchange viewpoint of the electronic structure are equally valid.

The Double Exchange Phenomenon Revisited: The [Re2OCl10]3− Compound

Correlated ab initio calculations have been performed on the [Re2OCl10]3− anion. The calculated spectrum does not respect the intervals given by the usually accepted double exchange Hamiltonian. Surprisingly enough the ground-state happens to be of intermediate spin multiplicity (i.e. a quartet) at any level of correlation treatment. A model that combines the Anderson and Hasegawa method and the usually used double exchange one rationalizes the spectrum calculated both by a configuration interaction restricted to the open shell molecular orbitals and at a more correlated level of calculation. An alternative analysis of the double exchange phenomenon, based on a molecular orbital language, is presented. The specific effects of the electronic correlation brought by extended active space and by a difference dedicated configuration interaction are also analyzed.

Effect of Lattice Distortion on Charge Order inManganites at Doping x = 0.5

In the present paper, we continue our investigationon the antiferromagnetic origin of the charge orderobserved in the half-doped manganese.By introducing a Su–Schrieffer–Heeger (SSH) type of perturbationinteraction to the double-exchange Hamiltonian, we calculateagain its ground-state phase diagram at filling x = 0.5by the unrestricted real-space Hartree–Fock approximation method.We find that, as the SSH electron-phonon interaction increases,the charge order parameter decreases to zero rapidly but the CE-typeantiferromagnetic order becomes more stable. In other words,the charge order is much more fragilethan the CE-type or the Neel-type antiferromagnetic ordersunder the electron-phonon perturbation.These results support the proposed theory in the recent publicationsthat the charge order in these systems is inducedby the antiferromagnetic correlations.

Some Fermi Surface Properties of Double-Exchange Interaction Systems

We study the photoemission spectrum of the double-exchange (DE) interaction systems. The DE Hamiltonian can be transformed into a simple form consisting of fermions and Schwinger bosons. We apply the gauge-field model and calculate the Green's function of the gauge field, fermions, and bosons. The imaginary part of the Green's function of an electron has an asymmetrical peak with strong temperature dependence. This can explain why the shape of the angle-resolved photoemission spectra of manganites near the Fermi surface is very different from that of Fermi liquid. We also show why the position of the Fermi surface is not sensitive to temperature.

Double Exchange Model for Magnetic Hexaborides

A microscopic theory for rare-earth ferromagnetic hexaborides, such as Eu1-xCaxB6, is proposed on the basis of the double-exchange Hamiltonian. In these systems, the reduced carrier concentrations place the Fermi level near the mobility edge, introduced in the spectral density by the disordered spin background. We show that the transport properties such as the Hall effect, magnetoresistance, frequency dependent conductivity, and dc resistivity can be quantitatively described within the model. We also make specific predictions for the behavior of the Curie temperature T(C) as a function of the plasma frequency omega(p).

Double exchange in a pair of transition metal ions with unquenched orbital angular momenta

The solution of the double exchange problem is proposed for the mixed valence systems containing orbitally degenerate metal ions. The energy levels for a face-shared bioctahedral dimer are found as the functions of two hopping integrals t a and t e implied by the trigonal overall symmetry. The symmetry properties of the double exchange Hamiltonian are discussed in the context of the strong magnetic anisotropy arising from the orbital interactions.

Considerations on the quantum double-exchange Hamiltonian

Schwinger bosons allow for an advantageous representation of quantum double exchange. We review this subject, comment on previous results, and address the transition to the semiclassical limit. We derive an effective fermionic Hamiltonian for the spin-dependent hopping of holes interacting with a background of local spins, which is used in a related publication within a two-phase description of colossal magnetoresistant manganites.

First-order transitions in double exchange materials

It is shown that the double-exchange Hamiltonian, with weak antiferromagnetic interactions, has a rich variety of first-order transitions between phases with different electronic densities and/or magnetizations. For band fillings in the range 0.3⩽ x⩽0.5, and at finite temperatures, a discontinuous transition between phases with similar electronic densities but different magnetizations takes place.

Discontinuous transitions in double-exchange materials

It is shown that the double-exchange Hamiltonian, with weak antiferromagnetic interactions, has a rich variety of first-order transitions between phases with different electronic densities and/or magnetizations. The paramagnetic-ferromagnetic transition moves towards lower temperatures, and becomes discontinuous as the relative strength of the double-exchange mechanism and antiferromagnetic coupling is changed. This trend is consistent with the observed differences between compounds with the same nominal doping, such as ${\mathrm{La}}_{2/3}{\mathrm{Sr}}_{1/3}{\mathrm{MnO}}_{3}$ and ${\mathrm{La}}_{2/3}{\mathrm{Ca}}_{1/3}{\mathrm{MnO}}_{3}.$ Our results suggest that, in the low doping regime, a simple magnetic mechanism suffices to explain the main features of the phase diagram.

Variational mean-field approach to the double-exchange model

It has been recently shown that the double exchange Hamiltonian, with weak antiferromagnetic interactions, has a richer variety of first and second order transitions than previously anticipated, and that such transitions are consistent with the magnetic properties of manganites. Here we present a thorough discussion of the variational Mean Field approach that leads to the these results. We also show that the effect of the Berry phase turns out to be crucial to produce first order Paramagnetic-Ferromagnetic transitions near half filling with transition temperatures compatible with the experimental situation. The computation relies on two crucial facts: the use of a Mean Field ansatz that retains the complexity of a system of electrons with off-diagonal disorder, not fully taken into account by the Mean Field techniques, and the small but significant antiferromagnetic superexchange interaction between the localized spins.

The Charged and the Spin-Excitation Gaps in the Double-Exchange Model: a Rigorous Result**The project supported by National Natural Science Foundation of China under Grant No. 19874004

We extend a previous result of ours [G.S. Tian, Phys. Rev. B58 (1998) 76121 on the charged gap and the spin-excitation gap of the half-filled Kondo lattice model to the doubleexchange model. In our original approach, this model cannot be dealt with since its localized spins have a large spin number S=3/2. By following a construction argument due to Zener and rewriting the double-exchange Hamiltonian, we are able to overcome this difficulty and re-establish the same relation for this model.

Conductance as a function of temperature in the double-exchange model

We have used the Kubo formula to calculate the temperature dependence of the electrical conductance of the double exchange Hamiltonian. We average the conductance over an statistical ensemble of clusters, which are obtained by performing Monte Carlo simulations on the classical spin orientation of the double exchange Hamiltonian. We find that for electron concentrations bigger than 0.1, the system is metallic at all temperatures. In particular it is not observed any change in the temperature dependence of the resistivity near the magnetical critical temperature. The calculated resistivity near $T_c$ is around ten times smaller than the experimental value. We conclude that the double exchange model is not able to explain the metal to insulator transition which experimentally occurs at temperatures near the magnetic critical temperature.

Monte Carlo simulations for the magnetic phase diagram of the double-exchange Hamiltonian

We have used Monte Carlo simulation techniques to obtain the magnetic phase diagram of the double exchange Hamiltonian. We have found that the Berry's phase of the hopping amplitude has a negligible effect in the value of the magnetic critical temperature. To avoid finite size problems in our simulations we have also developed an approximated expression for the double exchange energy. This allows us to obtain the critical temperature for the ferromagnetic to paramagnetic transition more accurately. In our calculations we do not observe any strange behavior in the kinetic energy, chemical potential or electron density of states near the magnetic critical temperature. Therefore, we conclude that other effects, not included in the double exchange Hamiltonian, are needed to understand the metal-insulator transition which occurs in the manganites.

Magnetic dynamics in colossal magnetoresistive perovskite manganites

We have measured the spinwave dispersion throughout the Brillouin zone of the doubleexchange ferromagnet La0.7Pb0.3MnO3 by using inelastic neutron scattering. An unexpectedly simple Heisenberg Hamiltonian with solely a nearestneighbour coupling accounts for the entire dispersion relation. The value of the Curie temperature Tc calculated from the derived coupling constant agrees with the experimental value to within 15%. The results, including damping of the zone boundary spin waves near Tc, can be fully understood in the framework of the doubleexchange Hamiltonian. In the paramagnetic phase of the twodimensional analogue La1.2Sr1.8Mn2O7, we have observed longlived antiferromagnetic clusters coexisting with ferromagnetic fluctuations. This effect must be included in theories that attempt to explain giant magnetoresistance in manganites, at least in two dimensions.

Charge localization in disordered colossal-magnetoresistance manganites

The metallic or insulating nature of the paramagnetic phase of the colossal-magnetoresistance manganites is investigated via a double exchange Hamiltonian with diagonal disorder. Mobility edge trajectory is determined with the transfer matrix method. Density of states calculations indicate that random hopping alone is not sufficient to induce Anderson localization at the Fermi level with 20-30% doping. We argue that the metal-insulator transtion is likely due to the formation of localized polarons from nonuniform extended states as the effective band width is reduced by random hoppings and electron-electron interactions.

Spin waves and other magnetic fluctuations in giant magnetoresistive perovskite manganites

We have used inelastic neutron scattering to measure the spin wave dispersion througout the Brillouin zone of the double exchange ferromagnet La 0.7Pb 0.3MnO 3. The dispersion is well described by that for the double exchange Hamiltonian. The Curie temperature calculated for a local moment ferromagnet with the observed dispersion agrees with experiment within 15%. In the paramagnetic phase of the two-dimensional analogue La 1.2Sr 1.8Mn 2O 7, we have observed long-lived antiferromagnetic cluster coexisting with ferromagnetic fluctuations. This effect must be included in theories that attempt to explain giant magnetoresistance in manganites, at least in two dimensions.

Electronic Hamiltonian for transition-metal oxide compounds.

An effective electronic Hamiltonian for transition metal oxide compounds is presented. For Mn-oxides, the Hamiltonian contains spin-2 ``spins'' and spin-3/2 ``holes'' as degrees of freedom. The model is constructed from the Kondo-lattice Hamiltonian for mobile $e_g$ electrons and localized $t_{2g}$ spins, in the limit of a large Hund's coupling. The effective electron bond hopping amplitude fluctuates in sign as the total spin of the bond changes. In the large spin limit, the hopping amplitude for electrons aligned with the core ions is complex and a Berry phase is accumulated when these electrons move in loops. The new model is compared with the standard double exchange Hamiltonian. Both have ferromagnetic ground states at finite hole density and low temperatures, but their critical temperatures could be substantially different due to the frustration effects induced by the Berry phase.