Unveiling hidden multipolar orders with magnetostriction

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 $${\cal{O}}_{20,22}$$ O 20 , 22 and octupole $${\cal{T}}_{xyz}$$ T x y z . 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.

Many-Body Physics of Single and Double Spin-Flip Excitations in NiO

“…Since the final states of XAS act as the intermediate states of RIXS, the final states of RIXS are strongly affected by them. Therefore, the transition probability to spin-triplet final states (e.g., 3 T 2g ) is large compared to spin-singlet final states (e.g., 1 A 1g ) in RIXS, for incident photon energies around MP, while the opposite is true at SP as shown in Fig. 1(b).…”

“…As we delve into more and more complex materials we find that the existing order parameters are coupled to each other and hence not easily separable. Many states also exist, whose order parameters completely evade characterization by conventional measurement techniques and hence dubbed as "hidden" [1][2][3][4]. Dynamical behavior of spin-dipolar excitations associated with long-range magnetic order for example, can be probed using inelastic neutron scattering (INS).…”

Unconventional Superconductivity arising from Multipolar Kondo Interactions

“…Conduction electron mediating RKKY-like interactions permit the development of spontaneous ferro-and antiferro-multipolar orderings. In this work, we focus on the possible development of ferro-like order of both quadrupolar and octupolar moments described by the coarse-grained Landau order parameters [65],…”

“…1. smaller than the octupolar mass (m O ∼ (T −T O )) to reflect the fact that the proposed octupolar ordering temperature T O is lower than the quadrupolar ordering temperature T Q [65]; here T is the temperature, which is taken to be above T Q,O in the paramagnetic phase. The choices of the other phenomenological values a 0,1,2 > 0 were chosen to ensure that the multipolar action is non-singular, thus permitting the Gaussian fluctuations to be integrated out.…”

Thermal and field-induced transitions in ferroquadrupolar Kondo systems

“…From this viewpoint, we expect multispin interactions to also emerge naturally in Kondo materials if we view the large-to-small FS transition as an orbital-selective Mott transition of the f electrons [42,43]. The impact of such couplings has only recently been investigated in multipolar Kondo systems [44][45][46][47], although there has been some suggestive previous work in dipolar Kondo materials [48,49]. Given this, we ask the following questions.…”