Quadrupolar Singlet Ground State of Praseodymium in a Modulated Pyrochlore

TL;DR

This study reveals that Pr in a pyrochlore structure exhibits a quadrupolar singlet ground state due to disorder-induced splitting, with magnetic properties influenced by structural complexity and alloying effects.

Contribution

It demonstrates the lifting of Pr doublet degeneracy to a quadrupolar singlet ground state caused by structural disorder in a pyrochlore, expanding understanding of non-Kramers ion behavior.

Findings

Pr has a quadrupolar singlet ground state due to disorder.

Bi alloying increases inhomogeneous crystal field splitting.

No Pr sublattice magnetic order observed down to 100 mK.

Abstract

The complex structure and magnetism of Pr$_{2-x}$Bi$_x$Ru$_2$O$_7$ was investigated by neutron scattering and EXAFS. Pr has an approximate doublet ground-state and the first excited state is a singlet. This overall crystal field level scheme is similar to metallic Pr$_2$Ir$_2$O$_7$, which is also reported here. While the B-site (Ru) is well ordered throughout, this is not the case for the A-site (Pr/Bi). A distribution of the Pr-O2 bond length indicates the Pr environment is not uniform even for $x=0$. The Bi environment is highly disordered ostensibly due to the 6s lone pairs on Bi$^{3+}$. Correspondingly we find the non-Kramers doublet ground state degeneracy otherwise anticipated for Pr in the pyrochlore structure is lifted so as to produce a quadrupolar singlet ground state with a spatially varying energy gap. For $x=0$, below T$_N$, the Ru sublattice orders antiferromagnetically, with propagation vector \textbf{k}= (0,0,0), as for Y$_2$Ru$_2$O$_7$. No ordering associated with the Pr sublattice is observed down to 100 mK. The low energy magnetic response of Pr$_{2-x}$Bi$_x$Ru$_2$O$_7$ features a broad spectrum of magnetic excitations associated with inhomogeneous splitting of the Pr quasi-doublet ground state. For $x=0$ ($x=0.97$) the spectrum is temperature dependent (independent). It appears disorder associated with Bi alloying enhances the inhomogeneous Pr crystal field level splitting so that inter-site interactions become irrelevant for $x=0.97$. The structural complexity for the A-site may be reflected in the hysteretic uniform magnetization of B-site ruthenium in the N\'{e}el phase.