Unveiling hidden multipolar orders with magnetostriction.
Nat Commun 2019;
10:4092. [PMID:
31501429 PMCID:
PMC6733943 DOI:
10.1038/s41467-019-11913-3]
[Citation(s) in RCA: 24] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2019] [Accepted: 08/12/2019] [Indexed: 11/28/2022] Open
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 \documentclass[12pt]{minimal}
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\begin{document}$${\cal{O}}_{20,22}$$\end{document}O20,22 and octupole \documentclass[12pt]{minimal}
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\begin{document}$${\cal{T}}_{xyz}$$\end{document}Txyz. 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.
Higher-order multipolar phases are unusual states that can form in correlated materials and are difficult to observe as they do not directly couple to conventional probes. Patri et al. theoretically show that angle-dependent magnetostriction measurements can probe quadrupolar and octupolar ordering.
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