Unveiling hidden multipolar orders with magnetostriction

Abstract

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 $${\cal{O}}_{20,22}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mi>O</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>20</mml:mn> <mml:mo>,</mml:mo> <mml:mn>22</mml:mn> </mml:mrow> </mml:msub> </mml:math> and octupole $${\cal{T}}_{xyz}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mrow> <mml:mi>T</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>x</mml:mi> <mml:mi>y</mml:mi> <mml:mi>z</mml:mi> </mml:mrow> </mml:msub> </mml:math> . 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.