Extremely Large Magnetoresistance and Anisotropic Transport in Multipolar Kondo System PrTi${}_2$Al${}_{20}$

Abstract

Multipolar Kondo systems offer unprecedented opportunities for designing astonishing quantum phases and functionalities beyond spin-only descriptions. A model material platform of this kind is the cubic heavy-fermion system Pr$T{r}_2$Al${}_{20}$ ($Tr=$ Ti, V), which hosts a nonmagnetic crystal-electric-field (CEF) ground state and substantial Kondo entanglement of the local quadrupolar and octopolar moments with the conduction electron sea. Here, we explore magnetoresistance (MR) and Hall effect of PrTi${}_2$Al${}_{20}$ that develops ferroquadrupolar (FQ) order below $T_Q\sim 2$ K and compare its behavior with that of the non-4$f$ analog, LaTi${}_2$Al${}_{20}$. In the FQ ordered phase, PrTi${}_2$Al${}_{20}$ displays extremely large magnetoresistance (XMR) of $\sim 10^3\%$. The unsaturated, quasi-linear field ($B$) dependence of the XMR violates the conventional Kohler's scaling and defies description based on carrier compensation alone. By comparing the MR and the Hall effect observed in PrTi${}_2$Al${}_{20}$ and LaTi${}_2$Al${}_{20}$, we conclude that the open-orbit topology on the electron-type Fermi surface (FS) sheet is key for the observed XMR. The low-temperature MR and the Hall resistivity in PrTi${}_2$Al${}_{20}$ display pronounced anisotropy in the [111] and [001] magnetic fields, which is absent in LaTi${}_2$Al${}_{20}$, suggesting that the transport anisotropy ties in with the anisotropic magnetic-field response of the quadrupolar order parameter.