TRANSPORT PROPERTIES IN A SIMPLIFIED DOUBLE-EXCHANGE MODEL

TRANSPORT PROPERTIES IN A SIMPLIFIED DOUBLE-EXCHANGE MODEL

The interesting phenomena in the family of doped manganese oxides T_1−xD_xMnO₃ have been recently renewed.¹-⁴ As doping x and temperature T are varied, these manganites show a rich variety of phases.¹-⁴ Particularly interesting is the dop-ing region 0.1 < x < 0.3, where the compounds undergo a transition from either insulating or very high resistance metallic,paramagnetic (PM) phase at high tem-peratures to a ferromagnetic (FM) phase at low temperatures. Near the transition point, the resistivity of the compounds changes by orders of magnitude. The appli-cation of a strong magnetic field substantially reduces this effect, thus giving rise to a very large negative magnetoresistance.¹-⁴ Although the physical mechanism which is responsible for the behavior has recently been the subject of much discussion and controversy,¹-⁴ the double-exchange (DE) mechanism^5,6 still provides a well-established starting point.¹ -⁴ The DE model was proposed by Zener⁵ who considered the explicit movement of electrons from the Mn³⁺ ion to Mn⁴⁺ ion. There are two simultaneous motions involving electrons moving from the oxygen atom to the Mn⁴⁺ ions and other electrons from the Mn³⁺ to the oxygen atom. In the DE process the motion of the itinerant electron favors the ferromagnetic ordering of the local spins and, vice versa, the presence of ferromagnetic order facilitates the motion of the itinerant electron. Hence, only the z-component part of the Hund interaction between the local spins and the itinerant electron spin plays an essential role in the DE. In this paper we study the transport properties by a simplified DE (SDE) model where only the z-component part of the Hund in-teraction is incorporated. The SDE model has been studied by several authors.^7,8 However, the question on whether the SDE model could reproduce qualitatively the transport properties of the manganites is still open. In this paper the transport quantities such as the electronic resistivity, the thermal conductivity and the thermal power are calculated by using the dynamical mean-field theory (DMFT).⁹ The DMFT has been extensively used for investigating strongly correlated electron systems. It is based on the fact that the self-energy depends only on the frequency in the infinite-dimension limit. Using the DMFT these transport quantities can be expressed by the spectral function. We find that the SDE model captures the main features of the transport properties of the manganites. These results indicate that the DE process in the manganites can be studied by the SDE model which is much simpler than the full version of the DE model and hence simplifies calculations very much. This provides a starting point to the various variations of the DE mechanism such as randomness, charge or orbital ordering.

The paper is organized as follows. In Sec. 2 we present the SDE model and the background for calculating the resistivity, the thermal conductivity and the thermal power. In Sec. 3 we provide the application DMFT for the SDE model. Numerical result and discussions are presented in Sec. 4. Finally, Sec. 5 concludes the paper.

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