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# Topologically protected magnetoelectric switching in a multiferroic

## Abstract

Electric control of magnetism and magnetic control of ferroelectricity can improve the energy efficiency of magnetic memory and data-processing devices1. However, the necessary magnetoelectric switching is hard to achieve, and requires more than just a coupling between the spin and the charge degrees of freedom2,3,4,5. Here we show that an application and subsequent removal of a magnetic field reverses the electric polarization of the multiferroic GdMn2O5, thus requiring two cycles to bring the system back to the original configuration. During this unusual hysteresis loop, four states with different magnetic configurations are visited by the system, with one half of all spins undergoing unidirectional full-circle rotation in increments of about 90 degrees. Therefore, GdMn2O5 acts as a magnetic crankshaft that converts the back-and-forth variations of the magnetic field into a circular spin motion. This peculiar four-state magnetoelectric switching emerges as a topologically protected boundary between different two-state switching regimes. Our findings establish a paradigm of topologically protected switching phenomena in ferroic materials.

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## Data availability

The data that support the findings of this study are available at https://doi.org/10.5281/zenodo.5817751.

## Code availability

The code of the model used to produce the fits is available on GitHub at https://github.com/louisponet/GdMn2O5_paper.

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## Acknowledgements

This work was supported by the Austrian Science Funds (I 2816-N27 and P 32404-N27). The work at Rutgers University was supported by the DOE under grant number DOE: DE-FG02-07ER46382. M.M. acknowledges Vrije FOM-programma ‘Skyrmionics’.

## Author information

Authors

### Contributions

Andrei Pimenov initiated the project; Andrei Pimenov, S.A., M.M. and S.-W.C, supervised the project; A.S. and T.K. designed the experiment; X.W. grew the samples; Anna Pimenov, T.K. and J.W. characterized the samples using various techniques; J.W. and T.K. conducted the experiments and analysed the data; L.P., S.A. and M.M. developed the theory; L.P., S.A., Andrei Pimenov and M.M. wrote the manuscript with the feedback from all authors.

### Corresponding author

Correspondence to S. Artyukhin.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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### Peer review information

Nature thanks Hena Das and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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## Extended data figures and tables

### Extended Data Fig. 1 Magic-angle region.

The panels demonstrate the influence of selected model parameters on the magic-angle region. In each panel only the parameter labelled on the vertical axis is varied, whereas the others are kept at the values reported in the text of this section, and used for Fig. 3 of the main text. All parameters are reported in units of meV. The blue regions signify the low-angle switching regime, while the red denotes the high angle switching regime. The white boundary region is where the double loop switching regime occurs, characterized by a winding number of 1, and is topologically protected by the neighbouring regimes.

### Extended Data Fig. 2 Switching with modified model parameters.

ac Evolution of electric polarization $${P}_{b}$$ during the magnetic field sweep cycle for various magnetic field orientations. In each panel, the changes of the curve colour from red to blue indicate the progression of the sweep cycle. The four-state switching is seen for the field at the magic orientation. The insets indicate the corresponding switching paths and winding numbers. d– Trajectories (in white) of AFM order parameter orientations $$({\varphi }_{{{\rm{L}}}_{1}},{\varphi }_{{{\rm{L}}}_{2}})$$ through the field sweep cycles in different regimes. The colour map shows the energy landscape at an intermediate field $${H}^{* }$$.

### Extended Data Fig. 3 Simplified single chain model.

The crankshaft behaviour can be reproduced within the model that only involves the single AFM chain (purple ions), coupled to Gd ions $${{\bf{S}}}_{3}$$ and $${{\bf{S}}}_{6}$$ (indicated by the dashed rectangle).

### Extended Data Fig. 4 Mechanism of the spin reorientation transition.

a Exchange interactions between Gd ions and neighbouring AFM Mn chains (v1,2). Easy axes for L1,2 coincide with the longer zigzag segments; for Gd – with blue lines indicating v1 exchange. b Field dependence of energy contributions: magnetodipolar interactions, Gd–Mn exchange, Zeeman energy of Gd spins and energy of antiferromagnetically ordered Mn spins, for the field pointing at 10° to the a axis. c Spin configuration in state 2 and in the states, corresponding to the saddle points at the barriers toward the neighbouring minima at $$H={H}^{* }$$ (states and colour coding for spins is indicated in the inset). The numbers in blue show the field projections of magnetization difference of Gd and Mn ions in the saddle-point states. The difference of magnetization components along the field in two saddle-point states results in the asymmetric barrier evolution when the field is varied.

### Extended Data Fig. 5 The spin configurations corresponding to the four states.

Gd ions are shown in green while Mn ions are in purple. The blue lines indicate the AFM zigzag chains.

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Reprints and Permissions

Ponet, L., Artyukhin, S., Kain, T. et al. Topologically protected magnetoelectric switching in a multiferroic. Nature 607, 81–85 (2022). https://doi.org/10.1038/s41586-022-04851-6

• Accepted:

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• DOI: https://doi.org/10.1038/s41586-022-04851-6

• ### Topology turns the crank on a magnetoelectric switch

• Wei Ren
• Laurent Bellaiche

Nature (2022)