{
  "id": "2311.03435",
  "version": "v1",
  "published": "2023-11-06T19:00:01.000Z",
  "updated": "2023-11-06T19:00:01.000Z",
  "title": "Signatures of hidden octupolar order from nonlinear Hall effects",
  "authors": [
    "Sopheak Sorn",
    "Adarsh S. Patri"
  ],
  "comment": "5+5 pages, 4+5 figures; the two authors contributed equally to this work",
  "categories": [
    "cond-mat.mes-hall",
    "cond-mat.str-el"
  ],
  "abstract": "Detecting symmetry-breaking hidden orders with conventional probes has been a long-standing challenge in the field of magnetism. Higher-rank multipolar ordering $-$ anisotropic charge and magnetization distributions arising from a combination of spin-orbit coupling and crystalline environments $-$ is a quintessential example of such hidden orders, where new protocols of direct detection remain highly desirable. In this work, we propose non-linear Hall effects as a novel probe for multipolar ordering in metallic systems. Taking inspiration from the family of Pr-based heavy-fermion compounds, Pr(Ti,V)$_2$Al$_{20}$, we formulate a minimal cubic-lattice model of conduction electrons coupled to a ferro-octupolar order parameter. The time-reversal-breaking order leads to a band structure that supports strong quadrupolar moments of the Berry curvature (BC). Using a semi-classical Boltzmann formalism in conjunction with a symmetry analysis, we demonstrate that the BC quadrupoles produce a third harmonic generation of the Hall voltage $[V_H(3 \\omega)]$ measurable in an AC Hall experiment. Properties of the Hall response such as its anisotropy, its dissipationlessness, and its dependence on the order parameter are also examined. Our work encourages a new realm of investigation of multipolar ordering from non-linear transport experiments.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-06T19:00:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonlinear hall effects",
      "hidden octupolar order",
      "detection remain highly desirable",
      "hidden orders",
      "multipolar ordering"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}