Condensed-matter physics

Magnetism in flatland

A pair of two-dimensional materials have been shown to exhibit ferromagnetism — the familiar type of magnetism found in iron bar magnets. Such materials could have applications from sensing to data storage. See Letters p.265 & p.270

Ferromagnetism is perhaps the oldest known phenomenon of purely quantum-mechanical origin. It refers to the alignment of magnetic moments (spins) in certain materials that results in uniform, permanent magnetization, such as that seen in iron. An approach to studying truly two-dimensional ferromagnets has been lacking, but on pages 265 and 270, respectively, Gong et al.1 and Huang et al.2 report an advance in this direction. Using a high-sensitivity microscopy technique, the authors remarkably observe ferromagnetic behaviour in atomically thin layers of two magnetic materials: chromium germanium telluride (Cr2Ge2Te6) and chromium triiodide (CrI3).

The study of low-dimensional ferromagnets, comprised of spins arranged on 1D or 2D lattices, was motivated in the 1970s by a broad interest in understanding how the number of spatial dimensions affects phase transitions and associated phenomena3,4. Experimentalists initially used 3D crystalline magnetic materials to approximate 2D spin lattices. In these crystals, the interactions between the spins in a given plane of the crystal lattice are much stronger than those between spins on different planes5. Later, epitaxial synthesis techniques — in which materials are grown over the top of a substrate in a layer-by-layer fashion — extended these adventures in magnetic 'flatland' closer to ideal 2D systems6. Such techniques allowed ultrathin magnetic films to be studied, but these films had unavoidable imperfections. A generalized method for creating truly 2D ferromagnets has until now not been demonstrated.

Since the discovery7 of graphene in 2004, there has been a vast exploration of flatland using ultrathin films exfoliated (removed) from van der Waals crystals — crystals held together by short-range van der Waals forces8. Although many phenomena associated with the quantum behaviour of electrons have been observed using this approach9, the ferromagnetic ordering of spins in a single atomic layer has been particularly elusive, requiring a technique of much greater sensitivity than that provided by conventional magnetometers. To achieve the necessary level of sensitivity, Gong et al. and Huang et al. use a method called polar magneto-optical Kerr effect microscopy to determine the spatial extent of ferromagnetic order in their materials. This technique uses the rotation of linearly polarized light to spatially map out the direction and magnitude of spins, with micrometre spatial resolution10,11.

In their 3D crystalline form, CrI3 and Cr2Ge2Te6 have similar properties. First, they display ferromagnetic order at temperatures below 61 kelvin1,2 (known as their Curie temperature). Second, they have a distinct magnetic anisotropy12,13 — their response to a magnetic field depends strongly on the direction of the field. And finally, they are soft ferromagnets, meaning that the spins of the chromium atoms are readily aligned when a magnetic field is applied in a specific direction, but they do not remain aligned when the field is removed. However, the authors show that the properties of these materials differ when the layers approach the 2D limit.

Huang and colleagues demonstrate that ferromagnetic order remains intact in CrI3 even in a single layer of the material (albeit with a suppressed Curie temperature of 45 K). Unlike the case of the 3D crystals, the authors show that a single layer of CrI3 has a substantial remnant magnetization in the absence of a magnetic field, directed perpendicular to the plane of the lattice. The magnetic system is therefore well described by the 2D Ising model3, in which spins are constrained to lie perpendicular to the plane (Fig. 1a). Remarkably, Huang et al. find that the nature of the ferromagnetic order in CrI3 is highly sensitive to the number of layers in the system. In a bilayer, the remnant magnetization present in a single layer is suppressed — consistent with the two layers having oppositely oriented spins (an antiferromagnet). Conversely, in a trilayer, this cancellation is lost and the net magnetization is recovered.

Figure 1: The Ising and Heisenberg models.

a, Two-dimensional magnetic systems consist of magnetic moments (spins) arranged on a lattice. Huang et al.2 show that atomically thin layers of chromium triiodide (CrI3) are well described by the Ising model3, in which spins are constrained to lie perpendicular to the plane of the lattice: either into the plane (black) or out of the plane (red). b, Conversely, Gong et al.1 find that the properties of ultrathin layers of chromium germanium telluride (Cr2Ge2Te6) are consistent with the Heisenberg model4, in which spins are free to point in any spatial direction. The two groups demonstrate that, below a critical temperature called the Curie temperature, both CrI3 and Cr2Ge2Te6 exhibit ferromagnetism, whereby all the spins point in the same direction.

Gong and colleagues show that, in strong contrast to CrI3, ultrathin layers of Cr2Ge2Te6 have a highly suppressed Curie temperature in the 2D limit (for example, about 30 K for a bilayer). Consistent with the Mermin–Wagner theorem4, the authors demonstrate that ferromagnetic order is not present in a single layer of Cr2Ge2Te6 — at least down to the lowest temperature studied (4.7 K). Furthermore, Cr2Ge2Te6 always remains a soft ferromagnet that has an extremely weak remnant magnetization perpendicular to the plane of the lattice. By comparing their results with theory, the authors show that the magnetic behaviour of Cr2Ge2Te6 in both the 2D and 3D regimes is well described by the Heisenberg model4, in which spins are free to point in any direction (Fig. 1b). The reduction in the material's Curie temperature with decreasing number of layers can be explained by the thermal excitation of vibrations called spin waves, whose energy distribution is intimately connected to the number of spatial dimensions.

The experiments reported in these papers demonstrate that ultrathin exfoliated layers of CrI3 and Cr2Ge2Te6 provide realizations of 2D Ising and Heisenberg ferromagnets, respectively, as envisaged by theory half a century ago3,4. However, one might wonder what scientific delights this new generation of truly 2D ferromagnetic materials might bring to the sophisticated palate of the contemporary condensed-matter physicist. After all, extensive previous measurements5,6 of quasi-2D crystals and ultrathin epitaxial films have shown that these materials act as excellent approximations of 2D magnets. But rather than hark back to the well-understood physics of yore, these exfoliated 2D ferromagnets perhaps demand a fresh, contemporary perspective on low-dimensional magnetism.

For instance, one might imagine using these materials as building blocks to create new magnetic textures by systematically stacking Ising and Heisenberg ferromagnets into hybrid multilayers, or by draping them over curved nano-substrates to create spins that have exotic quantum-mechanical phases (Berry phases). The promise of incorporating these 2D ferromagnets into spin-based electronics and information technologies also beckons, but achieving this goal will require overcoming the extremely high bar of robust magnetic ordering at temperatures of technological relevance. Nevertheless, the opportunities and challenges of this relatively unexplored region of magnetic flatland are many, and will undoubtedly lead to surprises.Footnote 1


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Correspondence to Nitin Samarth.

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Samarth, N. Magnetism in flatland. Nature 546, 216–217 (2017).

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