12/20/2023 0 Comments Crossover symmetry h.i.i.t system![]() ![]() Such a symmetry is very common in several vdW materials holding magnetic properties and interfaces 3, 28, such as Cr 2Ge 2Te 6 (CGT) or CrI 3 in which 2D magnetic ordering was first discovered 29, 30. 1a) to model the magnetic ordering process for a large flake of 1000 × 1000 nm 2. The intrinsic magnetisation is 〈 ∣ m ∣〉 ≈ 1 in the short-range-ordered regime and converges to zero when the spins become completely disordered 6, 26, 27.įor simplicity we first consider a 2D honeycomb lattice (Fig. With recent advances in computational power and parallelisation scalability, it is possible to directly model magnetic ordering processes and dynamics of 2D materials on the micrometre length-scale accessible experimentally. Nevertheless, it is unclear which kind of spin ordering can be foreseen in thin vdW layered compounds when finite-size effects and exchange interactions play together. It is known that thermal fluctuations will affect the emergence of spontaneous magnetisation at low dimensionality. 1a), in light of the Mermin-Wagner theorem. An intriguing question on this long-range limit is how we can understand real-life materials, which routinely have a finite size L (Fig. ![]() ![]() Previous numerical studies and the scaling analysis of 2D Heisenberg magnets 19, 20, 21, 22 have established that although only short-range order is observable at finite temperature, the spin correlation length can be larger than the system size below some finite crossover temperature. The long-range order characterising infinite systems only becomes distinguishable from short-range order describing the local alignment of the spins if the system size exceeds the correlation length at a given temperature 18. Previous reports 8, 9, 10, 11, 12, 13, 14, 15, 16, 17 have discussed at different levels of theoretical and experimental approaches the limitations and the potential ways to overcome the Mermin-Wagner theorem, which provides a historical evolution of the common concepts used in the field of 2D magnetism. However, the common understanding is that the theorem also excludes the alignment of spins in samples studied experimentally which are a few micrometres in size 6, 7, suggesting that such systems are indistinguishable from infinite. Importantly, the theorem only excludes long-range magnetic order at finite temperature in the thermodynamic limit 5, i.e., for infinite system sizes. As it was initially pointed out by Hohenberg 4 for a superfluid or a superconductor, and extended by Mermin and Wagner 5 for spins on a lattice, long-range order should be suppressed at finite temperatures in the 2D regime, when only short-range isotropic interactions exist. Indeed, the magnetic stability of vdW layers has been one of the central limitations for finding suitable candidates, given that strong thermal fluctuations are able to rule out any magnetism. The discovery of magnetically stable 2D vdW materials could allow for the development of spintronic devices with unprecedented power efficiency and computing capabilities that would, in principle, address some of these challenges 3. To keep up with this trend, smaller and increasingly energy-efficient devices must be developed, which require the study of compounds not yet explored in data-storage technologies. The demand for computational power is increasing exponentially, following the amount of data generated across different devices, applications and cloud platforms 1, 2. ![]() Our findings indicate exchange interactions as the main ingredient for 2D magnetism. 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 ~ 10 26 m) to observe the vanishing of the magnetic order as expected from the Mermin-Wagner theorem. 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. 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. 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. ![]()
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