Mean-field theory of charge ordering and phase transitions in the colossal-magnetoresistive manganites

Abstract

Abstract. We study phase transitions in the colossal-magnetoresistive manganites by using a mean-field theory both at zero and non-zero temperatures. Our Hamiltonian includes doubleexchange, superexchange, and Hubbard terms with on-site and nearest-neighbour Coulomb interaction, with the parameters estimated from earlier density-functional calculations. The phase diagrams show magnetic and charge-ordered (or charge-disordered) phases as a result of the competition between the double-exchange, superexchange, and Hubbard terms, the relative effects of which are sensitively dependent on parameters such as doping, bandwidth, and temperature. In accord with the experimental observations, several important features are reproduced from our model, namely, (i) a phase transition from an insulating, charge-ordered antiferromagnetic to a metallic, charge-disordered ferromagnetic state near dopant concentration x = 1/2, (ii) the reduction of the transition temperature T AF→F by the application of a magnetic field, (iii) melting of the charge order by a magnetic field, and (iv) phase coexistence for certain values of temperature and doping. An important feature, not reproduced in our model, is the antiferromagnetism in the electron-doped systems, e.g., La 1−x Ca x MnO 3 over the entire range of 0.5 x 1, and we suggest that a multi-band model which includes the unoccupied t 2g orbitals might be an important ingredient for describing this feature.

Energy spectrum analysis and finite temperature properties of the Falicov-Kimball model with Hund coupling at half filling

“…A theoretical description of this issue is often done on a basis of the double exchange model ͑DEM͒, also referred to as the ferromagnetic Kondo lattice model or s-d model. [3][4][5][6] Here we choose an alternative approach based on the Falicov-Kimball model ͑FKM͒ supplemented with the Hund coupling that was proposed in Ref. 7.…”

Inhomogeneous phases in a double-exchange magnet with long range Coulomb interactions

“…Band theory calculations 9,29 suggest that typical values of the hopping amplitude t in the CMR manganates lie between 0.3 eV and 0.5 eV. The value of J can be roughly estimated from the experimentally observed Néel temperatures in the fully doped or undoped (with no conduction e g electrons or with no holes) case 3,4 , T N ∼ 100 − 200K, corresponding to J ∼ 5 − 10meV.…”

“…The logics behind this simplification is summarized, e.g., in Ref. 9: it is assumed that the mechanism for phase separation (charge ordering) is the competition between ferro-and antiferromagnetism in the presence of a long-range Coulomb repulsion [all contained in Eq. (1)].…”

“…The manganates physics involves several degrees of freedom of substantially different nature, including localized core spins S i of Mn ions, fermionic degrees of freedom associated with conduction e g -electrons, lattice distortions, etc. In such systems, the presence of competing interactions (such as FM and AFM) often gives rise to phase separation 6,7,8,9 , whereby areas of different phases are stabilized in a structurally and stoichiometrically homogeneous sample. In the case of the manganates, it has even been suggested 7,10 that phase separation into insulating paramagnetic and metallic FM phases may explain the resistivity peak observed near the Curie temperature.…”

“…Once x is tuned away from the optimal CMR doping region, the homogeneous FM metallic state no longer corresponds to the energy minimum. Instead, energy can be gained by changing the magnetic ordering, carrier density, bandstructure, and/or orbital state in part of the system, making the sample inhomogeneous 6,7,8,9,16,17 . The surface tension between different phases 16,18 then competes against the long-range interactions present in the system in the form of electrostatic forces 6,16,19,20 or long-range crystal strain fields 21,22 .…”