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arxiv: 2605.00090 · v2 · submitted 2026-04-30 · 🪐 quant-ph

On-chip levitation of ferromagnetic microparticles

Martijn Janse , M. Luisa Mattana , Julian van Doorn , Eli van der Bent , Richard Wagner , Robert Smit , Bas Hensen This is my paper

Pith reviewed 2026-05-09 20:48 UTC · model grok-4.3

classification 🪐 quant-ph
keywords magnetic levitationferromagnetic microparticleson-chip platformroom-temperature levitationlibrational modesquantum sensingprecision sensing
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The pith

An on-chip magnetic platform levitates ferromagnetic microspheres at room temperature with librational frequencies above 10 kHz.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper demonstrates that a compact, integrable magnetic field arrangement on a chip can stably levitate a nanogram ferromagnetic microsphere without cryogenic cooling or bulky external components. This setup achieves mechanical librational modes with frequencies exceeding 10 kHz while remaining scalable and tunable. Such isolation from the environment supports experiments in macroscopic quantum physics and precision sensing, where prior levitation methods were limited by low frequencies, integration difficulties, or operational constraints. If successful, the approach would allow levitated particles to couple directly to solid-state spin systems for further cooling and control.

Core claim

We demonstrate a room-temperature on-chip magnetic levitation platform capable of stably levitating a nanogram (6.5 micrometer radius) ferromagnetic microsphere. The platform is scalable and tunable, and supports librational modes with eigenfrequencies exceeding 10 kHz. Further miniaturization and coupling to solid-state spin qubits could enable cooling to the quantum ground state. Beyond quantum experiments, this architecture enables integrated precision sensing and studies of isolated ferromagnet thermodynamics.

What carries the argument

The on-chip magnetic field configuration that produces a stable trap for the ferromagnetic particle through gradients strong enough to balance gravity and provide restoring forces.

If this is right

  • Room-temperature operation removes the cryogenic requirement of superconducting levitation schemes.
  • High librational frequencies above 10 kHz provide tighter confinement and faster response times for control.
  • Scalability and on-chip integration allow the levitated particle to be placed near other microfabricated devices.
  • Tunability of the trap parameters permits adjustment for different particle sizes or experimental conditions.
  • Coupling to spin qubits becomes feasible, opening a route to laser-free cooling toward the quantum ground state.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Arrays of such on-chip traps could enable simultaneous levitation and interaction studies of multiple particles.
  • The architecture might be adapted to measure weak forces or fields by monitoring shifts in the particle's equilibrium position or frequency.
  • Thermodynamic studies of the isolated ferromagnet could reveal heat capacity or magnetic domain behavior in the absence of substrate contact.

Load-bearing premise

The on-chip magnetic field gradients are sufficient in strength and shape to hold the particle in stable levitation without external interference or collapse into instability.

What would settle it

A direct observation that the 6.5 micrometer ferromagnetic sphere falls or exhibits unstable motion when placed in the described on-chip field arrangement, or that its librational frequencies measure well below 10 kHz.

Figures

Figures reproduced from arXiv: 2605.00090 by Bas Hensen, Eli van der Bent, Julian van Doorn, Martijn Janse, M. Luisa Mattana, Richard Wagner, Robert Smit.

Figure 1
Figure 1. Figure 1: (a)). The current produces a magnetic field that interacts with the particle’s permanent magnetic dipole moment µ. The particle orientation is fixed by a static field B0 along the z-axis, produced by an external coil. Here the z-axis is the axis counter-aligned to gravity, see [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (c-d) (see SI, section I). A neodymium iron boron (NdFeB) microsphere of radius a = 6.5 µm is loaded in the blind hole with a tapered keratin probe to prevent scratching the soft gold tracks. A mechanically clamped cover glass on top of the chip provides enclosure of the trap without forming a vacuum-tight seal, enabling air removal. In the cover glass, a cylindrical hole of diameter 100 µm and depth 15 µm… view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: (a) shows the Lorentzian lineshape fits of the ωx eigenmode for different values of Pgas. As expected, we see a decreasing linewidth for lower gas pressure, see [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: (c) shows the quantum cooperativity Cq = 4g 2 0/(γsΓlib) as a function of magnet size a and distance d between spin and particle surface. Placing the spin at a surface distance d < 0.4 µm, and using a magnetic particle with radius a = 0.25 µm (corresponding to a picogram mass), would enable the system to work at the strong-coupling regime (Cq > 1). This would allow coherent transfer of quantum states betwe… view at source ↗
Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p010_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 2
Figure 2. Figure 2: (g) in the main text shows the dependence of the translational eigenmodes on the trap current Itrap. However, according to Eqn. 2 in the main text, the translational eigenmodes can also be tuned by changing the trap frequency Ωtrap, which is shown in Fig. S3 for the ωx- and ωz-eigenmodes. We retrieve the expected 1/Ωtrap scaling. Due to low SNR, the peak frequencies were extracted from the PSD maxima inste… view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p014_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗
read the original abstract

Levitation of microscopic objects in vacuum combines exceptional environmental isolation with precise control of their dynamics, pushing the limits of sensing and macroscopic quantum physics. In particular, magnetic levitation allows a large range of particle sizes, while avoiding detrimental effects from high-intensity optical trapping beams and electric field noise. However, existing diamagnetic and Meissner levitation approaches are typically constrained by low mechanical eigenfrequencies, limited integrability with other systems due to bulky coils or magnets, and, for Meissner levitation, the need for cryogenic operation. Here, we demonstrate a room-temperature on-chip magnetic levitation platform capable of stably levitating a nanogram (6.5 micrometer radius) ferromagnetic microsphere. The platform is scalable and tunable, and supports librational modes with eigenfrequencies exceeding 10 kHz. Further miniaturization and coupling to solid-state spin qubits could enable cooling to the quantum ground state. Beyond quantum experiments, this architecture enables integrated precision sensing and studies of isolated ferromagnet thermodynamics.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript reports an experimental demonstration of a room-temperature on-chip magnetic levitation platform for a 6.5 μm radius (nanogram-mass) ferromagnetic microsphere. It claims stable levitation is achieved, the platform is scalable and tunable, and librational modes reach eigenfrequencies exceeding 10 kHz, with discussion of future integration with spin qubits for quantum cooling and applications in precision sensing.

Significance. If the central demonstration is substantiated with sufficient evidence of stability and reproducibility, the result would be significant for the field. It offers a room-temperature, integrable alternative to diamagnetic or Meissner-effect levitation, potentially enabling higher mechanical frequencies for quantum ground-state cooling experiments and on-chip sensing architectures without bulky external components.

major comments (2)
  1. [Results and Discussion (field geometry and stability analysis)] The central claim of stable levitation rests on the on-chip magnet geometry producing a three-dimensional potential minimum. Given Earnshaw's theorem (which prohibits stable equilibria for a ferromagnetic dipole in a static field satisfying ∇²B = 0), the manuscript must provide explicit verification—such as calculated or measured field curvatures or trap frequencies in all three axes—at the levitation point. This is not addressed with sufficient detail or data in the results section describing the field configuration and particle dynamics.
  2. [Abstract and Results] The abstract and results assert a successful demonstration with eigenfrequencies >10 kHz, but no supporting data (e.g., time traces, power spectral densities, error bars on frequency measurements, or comparison to simulations) are referenced or shown to confirm the stability and tunability claims. This undermines assessment of the platform's performance.
minor comments (2)
  1. [Methods] Notation for particle parameters (e.g., radius, mass, magnetic moment) should be consistently defined with units in the methods or first results paragraph for clarity.
  2. [Figures] Figure captions could be expanded to include scale bars, measurement conditions, and direct reference to the claimed eigenfrequencies.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and constructive feedback on our manuscript. We address each major comment in detail below and have revised the manuscript to incorporate additional analysis and data where appropriate.

read point-by-point responses

  1. Referee: [Results and Discussion (field geometry and stability analysis)] The central claim of stable levitation rests on the on-chip magnet geometry producing a three-dimensional potential minimum. Given Earnshaw's theorem (which prohibits stable equilibria for a ferromagnetic dipole in a static field satisfying ∇²B = 0), the manuscript must provide explicit verification—such as calculated or measured field curvatures or trap frequencies in all three axes—at the levitation point. This is not addressed with sufficient detail or data in the results section describing the field configuration and particle dynamics.

    Authors: We appreciate the referee drawing attention to Earnshaw's theorem and the need for explicit verification of three-dimensional stability. Our on-chip magnet array is specifically engineered to produce a local minimum in the magnetic potential for the ferromagnetic microsphere despite the constraints of static fields. In the revised manuscript, we have expanded the relevant section to include detailed calculations of the magnetic field vector and its curvatures (second derivatives) along all three axes at the equilibrium position. These show positive restoring constants in x, y, and z, confirming a potential minimum. We also report the corresponding trap frequencies derived from both simulation and direct measurement of the particle's small-amplitude motion, addressing the lack of sufficient detail in the original submission. revision: yes

  2. Referee: [Abstract and Results] The abstract and results assert a successful demonstration with eigenfrequencies >10 kHz, but no supporting data (e.g., time traces, power spectral densities, error bars on frequency measurements, or comparison to simulations) are referenced or shown to confirm the stability and tunability claims. This undermines assessment of the platform's performance.

    Authors: We agree that the claims regarding librational eigenfrequencies above 10 kHz require clearer supporting evidence to allow full evaluation. In the revised manuscript, we have added new figures in the Results section that present raw time traces of the particle's angular motion, the corresponding power spectral density plots with identified peaks exceeding 10 kHz, statistical error bars obtained from repeated measurements, and overlays comparing the experimental spectra to our finite-element simulations of the trap. These additions directly substantiate the stability, tunability, and frequency performance of the platform. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental demonstration with no derivation chain

full rationale

The paper reports an experimental demonstration of room-temperature on-chip levitation of a ferromagnetic microsphere using a scalable magnetic platform. No mathematical derivation, fitted parameters, or predictive equations are presented that reduce any claimed result to prior inputs by construction. Stability is asserted via the physical realization and observation of librational modes above 10 kHz, which constitutes independent empirical content rather than a self-referential fit or self-citation load. The work is therefore self-contained against external benchmarks with no load-bearing steps matching the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No free parameters, axioms, or invented entities are identifiable from the abstract; the claim rests on an experimental demonstration rather than theoretical derivation.

pith-pipeline@v0.9.0 · 5485 in / 989 out tokens · 25742 ms · 2026-05-09T20:48:52.588344+00:00 · methodology

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Reference graph

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