Hexadecapolar Kondo effect in URu$_2$Si$_2$?

TL;DR

This paper models the coupling of hexadecapolar modes to conduction electrons in tetragonal systems, relating it to the two-channel Kondo model, and discusses potential realization in URu$_2$Si$_2$ with experimental agreement.

Contribution

It introduces a theoretical model for hexadecapolar Kondo effect in tetragonal symmetry and connects it to the two-channel Kondo model, applicable to URu$_2$Si$_2$.

Findings

Good agreement with susceptibility measurements

Good agreement with specific heat measurements

Identification of crystal field splitting as relevant factor

Abstract

We derive the coupling of a localized hexadecapolar mode to conduction electrons in tetragonal symmetry. The derivation can be easily adapted to arbitrary multipoles in arbitrary environment. We relate our model to the two-channel Kondo (2CK) model and show that for an $f^2$-configuration, a relevant crystal field splitting in addition to the 2CK interaction is intrinsic to tetragonal symmetry. We discuss possible realizations of a hexadecapolar Kondo effect in URu$_2$Si$_2$. Solving our model we find good agreement with susceptibility and specific heat measurements in Th$_{1-x}$U$_x$Ru$_2$Si$_2$ ($x\ll1$).