[Paper Review] Macroscopic Magnetic Monopoles in a 3D-Printed Mechano-Magnet

Hamilton A. Teixeira, Maria F. Bernardo+4 more|arXiv (Cornell University)|Dec 11, 2021

Theoretical and Computational Physics8 references4 citations

TL;DR

This paper demonstrates the first experimental realization of macroscopic magnetic monopoles in a 3D-printed mechanical system composed of pivoting dipoles on adjustable-height rotors. By tuning rotor height to achieve degeneracy in a square lattice, the system exhibits free magnetic monopole dynamics under external magnetic fields, replicating nanoscale spin ice behavior at the macroscale with measurable coercive fields near 10 Oe.

ABSTRACT

The notion of magnetic monopoles has puzzled physicists since the introduction of Maxwell's Equations and famously Dirac had hypothesized them in the context of quantum mechanics. While they have proved experimentally elusive as elementary particles, the concept has come to describe excitations or topological defects in various material systems, from liquid crystals, to Hall systems, skyrmion lattices, and Bose-Einstein condensate. Perhaps the most versatile manifestation of magnetic monopoles as quasiparticles in matter has been in so-called spin ice materials. There, they represent violations of the ice rule, carry a magnetic charge, and can move freely unbound. Spin ice emergent magnetic monopoles appear at the atomic scale in rare earth pyrochlores or at the nano-scale in artificial spin ices systems. Here we demonstrate for the first time that the notion of magnetic monopoles can be transported at the macroscopic scale. We have built a mechano-magnet realized via 3D-printing, that consists of mechanical rotors on which macroscopic magnets can pivot. By controlling the relative height of the rotors we can achieve different regimes for magnetic monopoles, including the free monopole state. We then explore their driven dynamics under field. In the future, integration of our proof of principle in an elastic matrix can lead to novel macroscopic mechano-magnetic materials, to explore unusual piezomagnetism and magnetostriction, with applications to actuators and soft-robotics.

Motivation & Objective

• To realize macroscopic magnetic monopoles in a controllable, mechanical system using 3D-printed rotors with adjustable heights.
• To replicate the three distinct magnetic regimes—antiferromagnetic, ferromagnetic, and degenerate square ice—observed in nanoscale spin ice at the macroscale.
• To explore driven dynamics of magnetic monopoles under external magnetic fields in a classical, macroscopic system.
• To establish a platform for studying monopole avalanches, topological dynamics, and athermal relaxation in a mechanically constrained system.
• To open pathways for novel macroscopic magneto-mechanical materials with unusual piezomagnetism and magnetostriction for soft robotics and actuators.

Proposed method

• Design and 3D-printing of mechanical rotors with pivoting neodymium magnets, where rotor height is varied in 5mm increments to control magnetic interactions.
• Assembly of 84 rotors into a square lattice geometry, embedded within a Helmholtz coil to apply controlled, time-varying magnetic fields.
• Implementation of a demagnetization protocol with a sinusoidal, time-decreasing magnetic field envelope to drive system reversal and observe monopole dynamics.
• Use of vertex configuration classification (T1, T2, T3) to identify ice-rule compliance (T1, T2) and monopole-creating violations (T3), with T3 vertices carrying ±2 magnetic charge.
• Experimental measurement of magnetization reversal and monopole population dynamics under field cycling, compared with simulated trajectories using a sinusoidal annealing protocol.
• Application of the degeneracy condition via height offset (h2) to achieve a topologically constrained, disordered ground state resembling artificial spin ice.

Experimental results

Research questions

• RQ1 Can macroscopic magnetic monopoles be engineered and observed in a 3D-printed mechanical system with tunable magnetic interactions?
• RQ2 How do different magnetic regimes—ferromagnetic, antiferromagnetic, and degenerate square ice—manifest in a macroscopic, classical system with pivoting dipoles?
• RQ3 What is the role of field-driven dynamics in monopole creation, separation, and annihilation in a macroscale analog of spin ice?
• RQ4 Can fast cascade transitions and avalanche-like dynamics, known in nanoscale systems, be observed in a macroscopic mechanical analog?
• RQ5 To what extent can athermal, driven systems mimic thermal ensembles in the absence of thermal fluctuations?

Key findings

• The system successfully realizes three distinct magnetic regimes—ferromagnetic, antiferromagnetic, and degenerate square ice—by adjusting rotor height, with the degenerate case showing free monopole dynamics.
• A coercive field of approximately 10 Oe was measured in the degenerate (h2) case, where monopole populations peak near this field strength during magnetization reversal.
• In the degenerate regime, the magnetization reversal exhibits a primary drop around 10 Oe due to ballistic monopole motion, followed by a secondary transition around 20 Oe as T1 vertices convert to T3 and T2 configurations.
• The experimental magnetization profiles and vertex statistics show qualitative agreement with simulated trajectories under sinusoidal annealing, validating the model's predictive power.
• Fast cascade transitions that reabsorb monopole pairs were observed both experimentally and in simulations, suggesting potential for self-organized criticality and punctuated equilibria.
• The system demonstrates that topological phenomena such as magnetic monopoles and constrained disorder can be realized in classical, macroscopic mechanical systems, enabling new platforms for studying magneto-mechanical effects.