Abstract
The Mermin-Wagner theorem states that long-range magnetic order does not exist in one- (1D) or two-dimensional (2D) isotropic magnets with short-ranged interactions. Here we show that in finite-size 2D van der Waals magnets typically found in lab setups (within millimetres), short-range interactions can be large enough to allow the stabilisation of magnetic order at finite temperatures without any magnetic anisotropy. We demonstrate that magnetic ordering can be created in 2D flakes independent of the lattice symmetry due to the intrinsic nature of the spin exchange interactions and finite-size effects. Surprisingly we find that the crossover temperature, where the intrinsic magnetisation changes from superparamagnetic to a completely disordered paramagnetic regime, is weakly dependent on the system length, requiring giant sizes (e.g., of the order of the observable universe ~ 1026 m) to observe the vanishing of the magnetic order as expected from the Mermin-Wagner theorem. Our findings indicate exchange interactions as the main ingredient for 2D magnetism.
| Original language | English |
|---|---|
| Article number | 6917 |
| Number of pages | 8 |
| Journal | Nature Communications |
| Volume | 13 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 14 Nov 2022 |
Bibliographical note
Funding Information:We thank David Mermin, Mikhail Katsnelson, and Bertrand Halperin for valuable discussions. L.R. gratefully acknowledges funding by the National Research, Development and Innovation Office of Hungary via Project No. K131938 and by the Young Scholar Fund at the University of Konstanz. U.A. gratefully acknowledges funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)-Project-ID 328545488-TRR 227, Project No. A08; and grants PID2021-122980OB-C55 and RYC-2020-030605-I funded by MCIN/AEI/10.13039/501100011033 and by “ERDF A way of making Europe” and “ESF Investing in your future”. E.J.G.S. acknowledges computational resources through CIRRUS Tier-2 HPC Service (ec131 Cirrus Project) at EPCC funded by the University of Edinburgh and EPSRC (EP/P020267/1); ARCHER UK National Supercomputing Service ( http://www.archer.ac.uk ) via Project d429. E.J.G.S. acknowledges the Spanish Ministry of Science’s grant program “Europa-Excelencia” under grant number EUR2020-112238, the EPSRC Early Career Fellowship (EP/T021578/1), and the University of Edinburgh for funding support. K.S.N. is supported by the Ministry of Education, Singapore, under its Research Centre of Excellence award to the Institute for Functional Intelligent Materials (I-FIM, project No. EDUNC-33-18-279-V12) and by the Royal Society (UK, grant number RSRP\R\190000). For the purpose of open access, the authors have applied a Creative Commons Attribution (CC BY) licence to any Author Accepted Manuscript version arising from this submission.
Publisher Copyright:
© 2022, The Author(s).