Polar Phase of an Egg-Yolk Particle in a Rotating Magnetic Field
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 B0/Ba<1/√2, 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→0. Numerical phase diagrams show that increasing κ tilts the bistable band to higher fields at higher frequencies and extends stable precession above B0/Ba=1/√2, 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.
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BibTeX
@misc{treize2026polar,
title = {{Polar Phase of an Egg-Yolk Particle in a Rotating Magnetic Field}},
author = {Roberts Treize and Janis Cimurs},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37008},
eprint = {2609.37008},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37008},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Polar Phase of an Egg-Yolk Particle in a Rotating Magnetic Field
AU - Roberts Treize
AU - Janis Cimurs
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37008
UR - https://arxiv.org/abs/2609.37008
AB - 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/√2, 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→0. 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/√2, 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.
ER -