Transport properties and Kohler's rule in $R$$_x$Lu$_{1-x}$B$_{12}$ solid solutions with $x$ $\leq$ 0.03: do charge stripes really exist in metallic dodecaborides?

TL;DR

This study investigates the transport properties of $R$$_x$Lu$_{1-x}$B$_{12}$ solid solutions, confirming Kohler's rule applicability and suggesting charge-transport anisotropy arises from electron-phonon interactions and Fermi surface effects, not charge stripes.

Contribution

It provides experimental evidence that charge stripes do not significantly influence transport in these compounds, contrasting previous hypotheses of stripe formation.

Findings

Kohler's rule holds across a wide temperature range.

Charge-transport anisotropy is linked to electron-phonon scattering and Fermi surface topology.

No evidence of dynamic charge stripes affecting scattering channels.

Abstract

Nonmagnetic metal LuB$_{12}$ is known to exhibit considerable transport anisotropy, which was explained in literature by different mechanisms including possible formation of dynamic charge stripes below the point $\sim$ 150K. Here we study transport properties of solid solutions based on LuB$_{12}$ host compound with general formula $R$$_x$Lu$_{1-x}$B$_{12}$ ($R$$-$Dy, Er, Tm, Yb, Lu) and with $x$ $\leq$ 0.03. The experiment has been performed on single crystals of high quality in the temperature range 1.8 $-$ 300K in magnetic fields up to 82kOe. The application of several models to the analysis of zero-field resistivity is discussed. A phenomenological description of large positive quadratic component of transverse magnetoresistance $\Delta$$\rho$/$\rho$($H$) = $\mu_D^2$$H^2$, which dominates for all compounds under investigation, allows to estimate drift mobility exponential changes $\mu_D$ $\sim$ $T^{-\alpha}$ with the index $\alpha$ $\approx$ 0.95 $-$ 1.46. In order to check the existence of additional channel of scattering, caused by probable presence of dynamic charge stripes, we performed the study of the anisotropy of magnetoresistance in Dy$_{0.01}$Lu$_{0.99}$B$_{12}$ and Tm$_{0.03}$Lu$_{0.97}$B$_{12}$ compositions including the measurements of the field scans with different current and field geometries. The data obtained allow us to confirm the fulfillment of semi-empirical Kohler's rule in a wide interval of temperatures 30 $-$ 240K regardless of the orientation of current and magnetic field. This result was attributed as a proof of the absence of additional channel of scattering caused by stripes. We argue, that charge-transport anisotropy is originated in $R$$_x$Lu$_{1-x}$B$_{12}$ due to the anisotropy of electron-phonon scattering on the one hand and the effects of Fermi surface (FS) topology (at low temperatures) on the other.