{
  "abstract": "The orbit selected by a magnetic particle in a viscous liquid under a rotating field is commonly described in the instantaneous Stoner--Wohlfarth limit, in which the magnetic moment always occupies a minimum of the anisotropy energy. In this limit, precession out of the field plane exists only for reduced fields $B_0/B_a<1/\\sqrt2$, and stronger fields admit only planar synchronous rotation or libration. We study a macroscopic egg-yolk particle, a printed shell containing two freely rotating permanent magnets in fluid-filled cavities, driven by a compensated rotating field and tracked optically. In addition to synchronous rotation, precession, and libration, the particle exhibits a polar phase: above the instantaneous bound and at high frequency, the shell axis leaves the field plane and locks onto a narrow cone about the rotation axis. We extend the model by a finite viscous friction between the magnets and the shell. The extension introduces a single dimensionless parameter, the ratio $κ$ of inner to outer rotational friction, and reduces to the instantaneous theory as $κ\\to0$. Numerical phase diagrams show that increasing $κ$ tilts the bistable band to higher fields at higher frequencies and extends stable precession above $B_0/B_a=1/\\sqrt2$, whereas for large $κ$ planar libration returns at high frequency. With a calibrated anisotropy field, relaxation rate, and $κ$ of order unity, the model reproduces the terminal state of all measured records and their tilt angles, including the polar cone. In the model the polar state is maintained by a steady rotation of the magnets relative to the shell, driven by the field and anisotropy torques and dissipated by the inner friction; it therefore exists only for intermediate $κ$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37008",
  "author_total": 2,
  "authors": [
    {
      "name": "Roberts Treize"
    },
    {
      "name": "Janis Cimurs"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bykde24hbgbny.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37008",
  "fulltext_url": null,
  "id": "bykde24hbgbny",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37008",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.soft"
    ],
    [
      "openalex",
      "2204|Characterization and Applications of Magnetic Nanoparticles"
    ]
  ],
  "openalex": "W7214946279",
  "pdf_url": "https://arxiv.org/pdf/2609.37008",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bykde24hbgbny.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:31Z",
      "native_id": "2609.37008",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37008"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.soft",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Polar Phase of an Egg-Yolk Particle in a Rotating Magnetic Field",
  "title_text": "Polar Phase of an Egg-Yolk Particle in a Rotating Magnetic Field",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:31Z",
  "url": "https://research.draconitic.com/paper/bykde24hbgbny",
  "venue": "arXiv",
  "versions": []
}