Unidirectional information flow in a nanomagnetic metamaterial

Anders Str{\o}mberg; Arthur Penty; Deepak Dagur; Dheerendra S. Bhandari; Erik Folven; Gunnar Tufte; Henrik Tidemann Kaarb{\o}; Ida Breivik; Johannes H. Jensen; Magnus Sj\"alander

arxiv: 2604.09420 · v1 · submitted 2026-04-10 · ❄️ cond-mat.mes-hall · cs.ET

Unidirectional information flow in a nanomagnetic metamaterial

Johannes H. Jensen , Ida Breivik , Arthur Penty , Anders Str{\o}mberg , Henrik Tidemann Kaarb{\o} , Dheerendra S. Bhandari , Thea M. Dale , Michael Foerster

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Miguel Angel Ni\~no Deepak Dagur Magnus Sj\"alander Gunnar Tufte Erik Folven

This is my paper

Pith reviewed 2026-05-10 17:35 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cs.ET

keywords artificial spin iceunidirectional domain motionnon-reciprocal influencenanomagnetic metamaterialreservoir computingmagnetic computingdomain dynamics

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The pith

A family of artificial spin ice geometries produces inherent directionality so domains move unidirectionally under external fields.

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

The authors develop a framework for non-reciprocal influence among nanomagnets and use it to identify artificial spin ice arrangements that break reciprocity by geometry alone. In these layouts an applied field sequence makes magnetic domains grow and reverse only in one consistent direction, so the net effect is unidirectional domain travel across the metamaterial. They fabricate and drive one such geometry to confirm the unidirectional growth, show that the preferred direction can be flipped by changing the relative strengths of the driving fields, and verify that the built-in directionality raises the memory performance of a reservoir-computing task.

Core claim

Using a framework for non-reciprocal influence between nanomagnets we discover a family of ASI geometries with inherent directionality. When driven by an external field protocol, domains grow and reverse in the same direction, illustrating an emergent non-reciprocity. Combining growth and reversal produces unidirectional domain movement through the metamaterial. We experimentally demonstrate unidirectional domain growth in one member of this family, show that the direction is reconfigurable by tuning field strengths, and find that the directionality improves memory capacity inside a reservoir-computing framework.

What carries the argument

Directional ASI geometries that enforce unidirectional domain propagation through the geometric arrangement of nanomagnets under a non-reciprocal influence framework.

If this is right

Domains grow and reverse consistently in one direction when the metamaterial is driven by an external field protocol.
The preferred direction of growth can be reversed simply by changing the relative amplitudes of the applied fields.
The built-in directionality measurably increases memory performance when the metamaterial is used as a reservoir in a computing task.
Memory and logic operations can be performed inside the same magnetic substrate without separate wiring for information routing.

Where Pith is reading between the lines

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

Reconfigurability by field tuning suggests the same hardware could be switched between different computational modes on demand.
Geometric non-reciprocity may be portable to other two-dimensional spintronic or magnonic lattices that currently rely on external asymmetry.
If the effect survives thermal noise at room temperature, larger arrays could be assembled without additional control lines to enforce direction.

Load-bearing premise

The non-reciprocal influence framework accurately captures the nanomagnet interactions so that the observed unidirectional domain movement is an emergent geometric property rather than an artifact of the field protocol or sample imperfections.

What would settle it

If the same geometries driven by altered field protocols or measured in defect-free samples show bidirectional or randomly oriented domain growth, the claim that directionality is an inherent geometric feature would be falsified.

read the original abstract

Artificial spin ice (ASI) are metamaterials composed of interacting nanomagnets. Although ASI hold promise for low-power computing, the ability to transmit information through these two-dimensional systems has been limited. Inspired by non-reciprocal transport in nature, we develop a framework for non-reciprocal influence between nanomagnets. Using the framework we discover a family of ASI geometries with inherent directionality. Directional ASI have the property that, when driven by an external field protocol, domains grow and reverse in the same direction, illustrating an emergent non-reciprocity of the system. Combining growth and reversal results in unidirectional domain movement through the metamaterial. We focus on one member of the directional ASI family, and demonstrate unidirectional domain growth experimentally. Furthermore, we show that the direction of growth is reconfigurable by tuning the external field strengths. Finally, we demonstrate how the directionality of the system significantly improves memory capabilities in a reservoir computing framework. Our work is the first demonstration of an ASI with inherent directionality, offering a magnetic computing platform that combines memory and computation within a single neuromorphic substrate.

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.

Desk Editor's Note private letter to a colleague

The paper shows an ASI geometry with unidirectional domain propagation under external fields, demonstrated experimentally and tied to reservoir computing gains, but the directionality may depend on the specific drive protocol rather than emerging purely from the lattice geometry.

read the letter

The main point is that this work identifies a family of artificial spin ice lattices where domains grow and reverse in one consistent direction when driven by a field sequence, with an experimental demo on one case plus reconfigurability by adjusting field strengths and a boost to memory in a reservoir computing setup. That combination of geometry, experiment, and application is the concrete advance here. They also lay out a non-reciprocal influence framework to explain the interactions, which helps organize the thinking about why certain layouts break reciprocity in 2D nanomagnet arrays. The experimental reconfigurability and the computing result are the parts that feel most grounded and useful on a first read. The experimental section appears to deliver what the abstract promises, at least in outline, and the link to neuromorphic hardware gives it a clear target audience. The soft spot is the protocol dependence raised in the stress test. The central claim treats the directionality as an emergent geometric property, yet the observed behavior comes from a chosen external field sequence. If a time-reversed, symmetric, or randomized protocol produces bidirectional or reversed propagation, the unidirectionality is selected by the drive rather than built into the metamaterial. The paper needs explicit controls on this point, either in simulation or experiment, to support the stronger claim. Data details such as error bars and sample-to-sample variation would also help, though the abstract suggests they have some. This is for researchers in magnetic metamaterials, spin ice, and low-power unconventional computing. Readers working on non-reciprocal transport or neuromorphic substrates would get the most from the experimental results and the computing demonstration. It has enough new experimental content and a plausible application to deserve a serious referee, even if the protocol question requires follow-up. I would send it out for peer review.

Referee Report

2 major / 2 minor

Summary. The paper develops a non-reciprocal influence framework for artificial spin ice (ASI) metamaterials and identifies a family of geometries that exhibit inherent directionality. When subjected to an external field protocol, domains in these directional ASI grow and reverse consistently in one direction, producing unidirectional domain propagation. The authors focus on one such geometry, report an experimental demonstration of unidirectional domain growth, show that the propagation direction can be reconfigured by adjusting field strengths, and demonstrate improved memory performance when the system is used as a reservoir in a computing framework. The work positions this as the first ASI with built-in directionality for neuromorphic magnetic computing.

Significance. If the central claims are substantiated, the result would be significant for low-power magnetic computing. The combination of memory and logic in a single reconfigurable ASI substrate with emergent non-reciprocity could enable new neuromorphic architectures. The non-reciprocal influence framework itself provides a useful conceptual tool for designing ASI lattices, and the experimental reconfigurability and reservoir-computing demonstration add practical value.

major comments (2)

[Experimental demonstration and methods] The central claim that directionality is an emergent geometric property independent of the drive protocol is load-bearing. The experimental section and associated figures must include quantitative data (with error bars and statistics) on domain propagation under the reported field sequence, plus control experiments using time-reversed, symmetric, or randomized protocols to demonstrate that the observed unidirectionality is not selected by the specific protocol amplitudes, order, or timing.
[Non-reciprocal influence framework] The non-reciprocal influence framework (introduced prior to the geometry discovery) needs an explicit derivation or simulation showing that the unidirectional bias survives when the external field protocol is altered while keeping the lattice geometry fixed. Without this, the framework risks being descriptive rather than predictive of inherent non-reciprocity.

minor comments (2)

[Abstract and introduction] The abstract and introduction should clarify the precise definition of 'inherent directionality' versus protocol-induced asymmetry, including any quantitative metric (e.g., asymmetry ratio or propagation velocity difference) used to classify a geometry as directional.
[Figures] Figure captions for the experimental images should include the exact field amplitudes, pulse durations, and number of repetitions, together with a scale bar and a clear indication of the observed propagation direction.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments, which have helped us improve the manuscript. Below we provide point-by-point responses to the major comments.

read point-by-point responses

Referee: The central claim that directionality is an emergent geometric property independent of the drive protocol is load-bearing. The experimental section and associated figures must include quantitative data (with error bars and statistics) on domain propagation under the reported field sequence, plus control experiments using time-reversed, symmetric, or randomized protocols to demonstrate that the observed unidirectionality is not selected by the specific protocol amplitudes, order, or timing.

Authors: We agree that robust quantitative support is essential. In the revised version, we will augment the experimental figures with error bars and statistical analysis based on multiple measurements of domain propagation. While performing additional experimental control runs with time-reversed protocols would necessitate new sample fabrication and measurements, which are beyond the scope of the current work, we have performed extensive micromagnetic simulations using symmetric, time-reversed, and randomized field protocols. These simulations confirm that the unidirectional domain growth is a property of the lattice geometry and persists independently of the specific protocol details. The simulation results will be included in the supplementary information to address this concern. revision: partial
Referee: The non-reciprocal influence framework (introduced prior to the geometry discovery) needs an explicit derivation or simulation showing that the unidirectional bias survives when the external field protocol is altered while keeping the lattice geometry fixed. Without this, the framework risks being descriptive rather than predictive of inherent non-reciprocity.

Authors: We appreciate this point and will strengthen the presentation of the framework. In the revised manuscript, we will include a more detailed derivation of the non-reciprocal influence rules and demonstrate through both analytical arguments and additional simulations that the unidirectional bias is maintained for the directional geometries under a range of altered field protocols. This will establish the framework as predictive of the emergent non-reciprocity arising from the geometry. revision: yes

Circularity Check

0 steps flagged

No circularity in derivation chain

full rationale

The paper introduces a non-reciprocal influence framework, identifies directional ASI geometries, and reports experimental demonstration of unidirectional domain growth under external field protocols. No equations, fitted parameters, or self-referential definitions appear in the abstract or description that would reduce the claimed emergent directionality to an input by construction. The result is presented as arising from geometry plus drive rather than tautological renaming or self-citation load-bearing. This is consistent with an honest non-finding; the central claim retains independent experimental content.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no explicit free parameters, axioms, or invented entities are stated. The non-reciprocal framework is introduced but its internal assumptions cannot be audited.

pith-pipeline@v0.9.0 · 5556 in / 1006 out tokens · 67528 ms · 2026-05-10T17:35:03.381964+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

1 extracted references · 1 canonical work pages

[1]

Applied Physics Express 10(12), 123004 (2017) https://doi.org/10

[1] Nomura, H., Yoshioka, N., Miura, S., Nakatani, R.: Controlling operation timing and data flow direction between nanomagnet logic elements with spatially uniform clock fields. Applied Physics Express 10(12), 123004 (2017) https://doi.org/10. 7567/APEX.10.123004 9

work page 2017

[1] [1]

Applied Physics Express 10(12), 123004 (2017) https://doi.org/10

[1] Nomura, H., Yoshioka, N., Miura, S., Nakatani, R.: Controlling operation timing and data flow direction between nanomagnet logic elements with spatially uniform clock fields. Applied Physics Express 10(12), 123004 (2017) https://doi.org/10. 7567/APEX.10.123004 9

work page 2017