Unveiling hidden multipolar orders with magnetostriction

Adarsh S Patri,Satoru Nakatsuji,Akito Sakai,Sungbin Lee,Yong Baek Kim,Arun Paramekanti

doi:10.1038/s41467-019-11913-3

Abstract

Broken symmetries in solids involving higher order multipolar degrees of freedom are historically referred to as “hidden orders” due to the formidable task of detecting them with conventional probes. In this work, we theoretically propose that magnetostriction provides a powerful and novel tool to directly detect higher-order multipolar symmetry breaking—such as the elusive octupolar order—by examining scaling behaviour of length change with respect to an applied magnetic field h. Employing a symmetry-based Landau theory, we focus on the family of Pr-based cage compounds with strongly correlated f-electrons, Pr(Ti,V,Ir)2(Al,Zn)20, whose low energy degrees of freedom are purely higher-order multipoles: quadrupoles {cal{O}}_{20,22} and octupole {cal{T}}_{xyz}. We demonstrate that a magnetic field along the [111] direction induces a distinct linear-in-h length change below the octupolar ordering temperature. The resulting “magnetostriction coefficient” is directly proportional to the octupolar order parameter, thus providing clear access to such subtle order parameters.

Highlights

Broken symmetries in solids involving higher order multipolar degrees of freedom are historically referred to as “hidden orders” due to the formidable task of detecting them with conventional probes
The nature of the quadrupolar ordering in these cage compounds has been indirectly examined with a few techniques40,41 such as ultrasound experiments42–45, as well as NMR measurements
For other magnetic field directions, we predict the signature of quadrupolar ordering as a constant plus quadratic-in-h scaling behaviour in the length change; the scaling behaviour explicitly involves the FQ order, the antiferro-quadrupolar ordering (AFQ) order parameter can be inferred from the FQ, as it scales as the square root of the FQ order parameter

Summary

Introduction

Broken symmetries in solids involving higher order multipolar degrees of freedom are historically referred to as “hidden orders” due to the formidable task of detecting them with conventional probes. Studying the mysterious ordering patterns of higher order multipoles is often rendered challenging since they typically coexist with conventional dipolar moments Examples of such symmetry breaking which are of great interest include spin-nematic order in spin S ≥ 1 quantum magnets, quadrupolar charge order in transition metal oxides, and higher multipolar order in actinide dioxides, such as NpO219, and f-electron heavy fermion materials, such as URu2Si221–29 and UBe1330–32. The nature of the quadrupolar ordering in these cage compounds has been indirectly examined with a few techniques such as ultrasound experiments (indicating softening of elastic modulus at quadrupolar ordering temperature, TQ), as well as NMR measurements (where the magnetic field-induced dipole moment is strongly dependent on the underlying quadrupolar phase). Some of us (A.S. and S.N., unpublished) have begun experiments to study angle-dependent magnetostriction, the change in sample length induced by a magnetic field which can point along various crystalline directions, in a wide class of materials with multipolar degrees of freedom

Methods

Results

Conclusion