Breaking through the Mermin-Wagner limit in 2D van der Waals magnets

Abstract The Mermin-Wagner theorem~\cite{Mermin1966} states that long-range {magnetic} order does not exist in one- or two-dimensional (2D) isotropic magnets with short-ranged interactions. The theorem has been a milestone on magnetism and has been driving the research of recently discovered 2D van der waals (vdW) magnetic materials\cite{gong_discovery_2017,firstCrI3} from fundamentals up to potential applications\cite{Genome22}. In such systems, the existence of magnetic ordering is typically attributed to the presence of a significant magnetic anisotropy, which is known to introduce a spin-wave gap and circumvent the core assumption of the theorem\cite{Bogolyubov,Mermin1966,Hohenberg}. Here we show that in finite-size 2D vdW magnets typically found in lab setups ({\it e.g.,} within millimetres), short-range interactions can be large enough to allow the stabilisation of magnetic order at finite temperatures without any magnetic anisotropy for practical implementations. We demonstrate that magnetic ordering can be created in flakes of 2D materials despite of the lattice symmetry due to the intrinsic nature of the spin exchange interactions and finite-size effects in two-dimensions. 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 ({\it e.g.,} of the order of the observable universe $\sim$10$^{26}$ m) to be reconcilable with the Mermin-Wagner theorem for zero magnetic ordering at finite temperatures. Our findings indicate exchange interactions as the main driving force behind the stabilisation of short-range order in 2D magnetism and broaden the horizons of possibilities for exploration of compounds with low anisotropy at an atomically thin level.