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Transport theory of pyrochlore conductors

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Pyrochlore conductors Ln2Ir2O7 (Ln=rare earth) give valuable opportunities to study the effect of geometrical frustration on itinerant electrons. These compounds have double-pyrochlore structure, where Ln and Ir ions are located on different pyrochlore sublattices interpenetrating with each other. The Ir 5d electrons form a conduction band, while the Ln 4f electrons form localized moments, i.e. these compounds can be considered as systems, where itinerant electrons interact with localized moments under strong geometrical frustration.

In this talk, we focus on the compounds (Ln=Pr, Nd), in which the Ln 4f localized moments develop substantial spin ice correlation; an emergent magnetic state where most of the tetrahedral units are occupied by “2-in 2-out” spin configuration. Indeed, the interplay between the conduction electrons and spin ice seems to explain anomalous transport phenomena observed in these compounds, such as non-monotonic magnetic field dependence of Hall conductivity [1] and low-temperature resistivity upturn [2].

To address these issues, we adopt a spin-ice-type Ising Kondo lattice model on a pyrochlore lattice, and solve this model by applying the cluster dynamical mean-field theory and the perturbation expansion in terms of the spin-electron coupling. As a result, we found that (i) the resistivity shows a minimum at a characteristic temperature below which spin ice correlation sets in [3]. Moreover, (ii) the non-monotonic Hall response can be understood as topological Hall effect due to the scattering from the spatially extended spin scalar chirality incorporated in spin ice manifold [4]. These results give unified understanding to the thermodynamic and transport properties of Ln2Ir2O7 (Ln=Pr, Nd), and give new insights into the role of geometrical frustration in itinerant systems.

This work has been done in collaboration with H. Ishizuka, Y. Motome and R. Moessner.

[1] Y. Machida et al., Phys. Rev. Lett. 98, 057203 (2007).

[2] S. Nakatsuji et al., Phys. Rev. Lett. 96, 087204 (2006).

[3] M. Udagawa, H. Ishizuka and Y. Motome, Phys. Rev. Lett. 108, 066406 (2012).

[4] M. Udagawa and R. Moessner, Phys. Rev. Lett., 111, 036602 (2013).

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