Lanthanide f⁷ metalloxenes – a class of intrinsic 2D ferromagnets

Abstract

As the thickness of layered compounds approaches the monolayer limit, new electronic states and properties emerge. The sheer range of such properties is astounding but the list did not include intrinsic magnetism. Until recently. At the moment, several compounds do reveal intrinsic ferromagnetism at the 2D limit. However, they seem to be chemically and structurally unrelated, which is not conducive to a systematic search of new 2D magnets. Here, we demonstrate that lanthanide metalloxenes form a class of intrinsic 2D ferromagnets. Their stoichiometric layered structure LnX₂ is composed of a triangular lattice of lanthanide ions (Eu or Gd) coupled with a 2D Xene sheet, a honeycomb network formed by Si or Ge. The materials are synthesized by direct reaction between the elements, with varying thickness from the bulk down to 1 monolayer. The common pattern is transformation from 3D antiferromagnetism to 2D ferromagnetism as revealed by magnetization and electron transport measurements. This work sets a path for a rational synthesis of 2D magnets and study of their spin behaviors for spintronic applications.

---

New concepts

Traditional 2D materials are intrinsically non-magnetic. However, technological demand for robust and controllable magnetic order drives the search for atomically thin materials with intrinsic 2D ferromagnetism (FM). The first reports on intrinsic 2D FM in 3d-magnets whet the appetite for such materials but a coherent approach for their design/engineering is lacking: at the moment, the material landscape of 2D FMs is rather patchy – the compounds are chemically and structurally unrelated. We establish a systematic strategy to the development of an entire class of 2D FMs – lanthanide metalloxenes LnX₂. The central concept is LEGO-like design of layered materials by combination of matching building blocks – graphene-like honeycomb networks of silicene and germanene with 2D lanthanide layers. A distinctive feature of this class of materials is 4f-magnetism, thus widening significantly the number of potential 2D FMs. Evolution from 3D antiferromagnetism to 2D ferromagnetism makes the common pattern of LnX₂ magnetic behaviour. A remarkable advantage of the discovered materials is their seamless integration with the mature Si and Ge semiconductor technological platforms and compatibility with van der Waals heterostructures. The proposed conceptual approach may open new avenues for design of new 2D FM materials with extended functionality, for applications in spintronics and quantum computing.

1. Introduction

Recent decades have witnessed momentous progress in spintronics, owing much to extensive research in magnetic thin films and interfaces. Nowadays, however, the demand for ultra-compact spintronics pushes magnetic materials to the 2D limit. Magnetism in 2D systems is suppressed by strong spin fluctuations which, nevertheless, can be sustained by magnetocrystalline anisotropy and/or long-range interactions. The enhanced and tunable fluctuations open a wide range of opportunities for the search of new materials exhibiting quantum and topological phases as well as for their implementation in novel devices.^1,2 The traditional 2D materials are non-magnetic; magnetic states can be induced extrinsically by chemical functionalization and defects,³ engineering of edge states in nanoribbons⁴ or proximity to a ferromagnet (FM).^5,6

On the other hand, 2D atomic crystals containing regular patterns of magnetic ions provide a wider platform for studies of new phases and fundamental spin behaviors as well as designer van der Waals heterostructures. The intrinsic 2D FM has recently been discovered in atomically thin van der Waals materials Cr₂Ge₂Te₆⁷ and CrI₃.⁸ FM already in the bulk, they acquire new properties: the effective Curie temperature of a few monolayers (MLs) of Cr₂Ge₂Te₆ depends strongly on low magnetic fields,⁷ CrI₃ changes its magnetic state from FM in 1 ML to antiferromagnetic (AFM) in 2 ML and then back to FM in 3 ML samples.⁸ These discoveries triggered a surge in studies of 2D FM systems. Experimentally, the list of such materials at the ML level has been extended to include VSe₂,⁹ Fe₃GeTe₂,¹⁰ MnSe,¹¹ CrBr₃,¹² EuSi₂ and GdSi₂,¹³ hematene Fe₂O₃.¹⁴ Intrinsic 2D FMs exhibit a remarkable behavior in electron transport, optics, and magnetic state manipulations. Studies of 2D CrI₃ are especially prolific: they demonstrate giant tunneling magnetoresistance,^15,16 helical luminescence,¹⁷ control over magnetism with electric fields and electrostatic doping.^18–20 Strong gate-tunability of magnetism has been reported also in 2D Fe₃GeTe₂²¹ and Cr₂Ge₂Te₆.²²

The material landscape of 2D FMs seems to be rather patchy, i.e. largely formed by compounds which are chemically and structurally unrelated. Discoveries of entire classes of 2D FM compounds may provide insights into the role of the chemical composition, leading to coherent strategies for a systematic search/design of new materials. Among the established 2D FMs, CrI₃⁸ and CrBr₃¹² are chemically similar and may form a nucleus of a class despite differences in the atomic structure of their parent 3D compounds.²³ However, extension of this class is not obvious: 2D CrX₃ inherit their FM state from the bulk but FM is lacking among other layered transition metal (TM) halides.²³ A promising approach is to derive 2D intrinsic FMs from van der Waals AFMs.²⁴ Indeed, a number of layered AFM systems, such as TM halides, are composed of FM MLs,²³ predicted to be a source of 2D FM materials.²⁵ Another proposal to extend the above class is to half-substitute Cr for W.²⁶ MLs of MnNX and CrCX (X = Cl, Br, I; C = S, Se, Te) are predicted to be a family of high-T_c FM semiconductors.²⁷

A nucleus of a class of 2D FM materials can be recognized in lanthanide (Ln) disilicides GdSi₂ and EuSi₂¹³ – 2D FMs emerging from the AFM bulk. The FM state in LnSi₂ is not limited to 1 ML. The magnetic properties of EuSi₂ and GdSi₂ are quite similar.¹³ The similarity extends to electron transport which is strongly layer-controlled:²⁸ the temperature dependence of the resistivity R(T) evolves from metallic Kondo-like log T for 4 ML to 1/T for 2 ML to semiconducting exp(Δ/T) for 1 ML; 1 ML LnSi₂ demonstrate colossal negative magnetoresistance with an exponential dependence R(B).

Potential extensions of the LnSi₂ class follow from their structure which is composed of two coupled layers – formed by Ln and Si, respectively. The metal atoms arrange in a 2D triangular net as many other compounds of the same stoichiometry such as TM dihalides.²³ Geometrical frustration of this lattice is expected for AFM interactions, a potential reason for the observed FM/AFM interplay.¹³ On the other hand, Si forms a lattice of silicene,²⁹ the Si analogue of graphene established as a prospective material for electronics.³⁰ Silicene is a member of the class of buckled 2D Xenes;³¹ buckling being a crucial factor determining their electronic and chemical properties.^32,33 One can imagine that lanthanide metalloxenes LnX₂ are the type of materials where 2D FM can be searched and found. Variations in the lanthanide ingredient of LnX₂ are partially covered by probing Eu(II) and Gd(III);¹³ however, the study can be extended because silicides of Ln from Gd to Tm are isostructural.³⁴

Here, we replace silicene with germanene,³⁵ another 2D Xene. We synthesize films of EuGe₂ and GdGe₂, study their atomic structure, magnetic and transport properties. In particular, we track evolution of the magnetic state in LnGe₂ with the film thickness; the materials exhibit 2D FM emerging from the AFM bulk. Thus, we establish lanthanide metalloxenes as a versatile class of intrinsic 2D FMs.

2. Results and discussion

2.1. MBE synthesis of LnGe₂

Our aim is to synthesize LnGe₂ compounds combining layers of lanthanide Ln and germanene. The use of free-standing germanene is not an option because it requires stabilization by the surface of a substrate.^36–39 Different MGe₂ compounds with the germanene sublattice are known; it is likely that they host Dirac cone states, in analogy with their silicene counterparts.⁴⁰ However, their main line of exploration is covalent functionalization via topotactic transformation^35,41 producing germanane GeH⁴² and its derivatives. It has recently been recognized that the simple atomic structure of the Zintl phase 1T-EuGe₂ (Fig. 1a) transforms into the GeH polytype with the simplest stacking motif.⁴³

Fig. 1 (a) A ball-and-stick model of EuGe₂ formed by Eu and germanene layers. (b) RHEED image of 2 ML EuGe₂ along the [11̄0] azimuth of the Ge substrate. (c) θ–2θ X-ray diffraction scan for bulk EuGe₂ (34 nm) on Ge(111); asterisk denotes peaks from the Ge substrate. (d) RHEED image of 2 ML GdGe₂ along the [11̄0] azimuth of the Ge substrate.

For our purposes EuGe₂ is an ideal candidate because its magnetism comes from Eu(II) with a half-filled f-shell which ensures a high spin moment and a vanishing orbital moment. The same applies to Gd(III) in GdGe₂. Thus, magnetism in Eu- and Gd-based metalloxenes is expected to be more pronounced (in both AFM bulk and FM monolayers) than in other Ln-metalloxenes – a decisive factor for the selection of materials for magnetization measurements at such a featherweight level. Another reason for the use of Eu and Gd compounds is that they cover major differences in lanthanide metalloxenes – divalent vs. trivalent ions; buckled vs. flat 2D-Xene layers. Also, magnetic properties of both LnGe₂ can be directly compared with their Si-based counterparts.¹³

Bulk EuGe₂ is extensively studied⁴⁴ and established as a phase prototype. It is synthesized by heating elemental Eu and Ge in a crucible.^43,44 To get nanoscale films we carry out the same reaction

Eu + 2Ge = EuGe₂

but employ the MBE technique allowing for controlled growth of epitaxial layers of different thickness. MBE has demonstrated its merits in synthesis of various metalloxenes including previously unknown trigonal polymorphs of SrSi₂ and EuSi₂.^13,45,46 The synthesis of 1T-EuGe₂ is actually easier than that of 1T-EuSi₂ because the former is thermodynamically stable while the latter has a tendency to re-crystallize into a more stable tetragonal EuSi₂.⁴⁷ The source of Ge in the MBE synthesis is the Ge substrate – its surface comes into contact with a flow of Eu atoms. As the film grows, the supply of Ge to the surface is ensured by the effective vacancy mechanism. We employ Ge(111) because this face of the substrate is lattice matched with germanene. The MBE synthesis is carried out at 290 °C – a temperature optimized according to RHEED images. Note that the growth of bulk samples requires a significantly higher temperature (exceeding 1000 °C).^43,44 The MBE synthesis of GdGe₂ is similar to that of EuGe₂ but the optimal temperature is somewhat higher (400 °C). It is likely that the GdGe₂ stoichiometry is idealized – similar to GdSi₂ a flat Xene layer supports a significant number of vacancies.¹³ For both EuGe₂ and GdGe₂ we synthesized a number of films differing by the number of MLs – from the bulk down to 1 ML. All the films are covered with SiO_x which makes ex situ studies possible without risking partial oxidation of the films – the latter may affect the number of MLs and hinder interpretation of the results.

2.2. Atomic structure of LnGe₂ films

The atomic structure of the films is studied with a number of techniques. RHEED is very helpful in control of the surface state of the film in the growth chamber. Fig. 1b demonstrates a typical RHEED image for 2 ML EuGe₂ which is characterized by well-developed streaks. The streaks appear in RHEED images of EuGe₂ films of different thickness from 1 ML to the bulk (Fig. S1, ESI†) but the distance between them changes. This shift corresponds to a slight increase of the lateral lattice parameter a with the number of MLs, reaching 0.412(3) nm, close to the bulk value 0.41035(1) nm.⁴⁴ The parameter c in thick EuGe₂ films is determined from the θ–2θ XRD scan (Fig. 1c). The extracted c = 0.49804(4) nm agrees well with the bulk value 0.49972(3) nm.⁴⁴ Only (000n) reflexes from EuGe₂ and peaks from the Ge substrate show up certifying the absence of unwanted phases. The synthesis does not result in other Eu–Ge compounds (such as Eu₂Ge, Eu₅Ge₃, EuGe, or Eu₃Ge₅) because of the presence of virtually unlimited source of Ge (the substrate).

A similar picture is observed for GdGe₂. Fig. 1d shows the RHEED image for 2 ML GdGe₂; the evolution of RHEED from 1 ML to the bulk is illustrated by Fig. S1, ESI.† Ultrathin films are smooth but the roughness increases significantly in thick GdGe₂ films. The parameters a = 0.401(3) nm (according to RHEED) and c = 0.4193(2) nm (according to XRD) in thick films of GdGe₂ are smaller than those in EuGe₂. The most significant difference is in the c parameter which arises from the flat vs. buckled structure of the germanene sublattice in the two compounds.

The structure of the films is further confirmed employing scanning transmission electron microscopy (STEM) in the HAADF mode. Fig. 2a presents a top view of bulk EuGe₂ which comprises the triangular sublattice of Eu (brighter dots) and the honeycomb structure of germanene (dimmer dots). The side views on bulk EuGe₂ (Fig. 2b) and GdGe₂ (Fig. 2c) look different because the Ge layer is buckled in EuGe₂ but flat in GdGe₂. However, the situation with GdGe₂ is more nuanced: the surface Ge layer in 1 ML GdGe₂ (Fig. 2d) and 2 ML GdGe₂ (Fig. 2e) is buckled as in both Gd silicide³⁴ and a few ML EuGe₂ (Fig. S2, ESI†). This buckling is probably a reason for ∼4% larger c parameter in 2 ML GdGe₂ than that in the bulk. The termination of the films with a germanene layer may be employed for engineering of van der Waals ferromagnetic heterostructures⁴⁸ and/or integration of 2D materials with the technological Ge platform. A major type of defects in the LnGe₂ films comes from terraces present on the surface of the Ge substrate; they cause atomic steps in the films as illustrated by Fig. S3, ESI.† The lattice parameters in thick films determined by electron microscopy are in agreement with the data of RHEED and XRD. In particular, in EuGe₂a = 0.411(4) nm and c = 0.500(4) nm while in GdGe₂a = 0.401(3) nm and c = 0.424(3) nm.

Fig. 2 HAADF-STEM electron microscopy images. (a) Top view of bulk EuGe₂ (34 nm). (b) Cross-section of bulk EuGe₂. (c) Cross-section of bulk GdGe₂. (d) Cross-section of 1 ML GdGe₂ on Ge(111). (e) Cross-section of 2 ML GdGe₂ on Ge(111). Images (b–e) are along the [11̄0] zone axis of the Ge substrate.

2.3. Magnetism of 3D and 2D LnGe₂

Magnetism is the focal point of this study. To demonstrate that the LnGe₂ compounds join LnSi₂¹³ in forming a class of 2D FMs, it is sufficient to study a few ML films. However, much insight is gained by tracking changes in the magnetic structure and properties on the way from bulk to 1 ML. Fig. 3 presents temperature dependence of the AFM magnetic susceptibility in bulk films of EuGe₂ and GdGe₂. The measurements are carried out in two magnetic fields – directed out-of-plane (Ge[111]) and in-plane (Ge[112̄], the choice of in-plane direction is arbitrary because we do not detect any in-plane magnetic anisotropy). The dependences manifest a textbook 3D AFM in both materials. The Néel temperatures T_N of EuGe₂ and GdGe₂ are ∼48 K and ∼38 K, respectively. The pattern observed for different magnetic field directions certifies that the AFM moments prefer the in-plane orientation, as in LnSi₂.¹³ The two LnGe₂ compounds seem to be quite similar in terms of magnetism. However, we observe a striking difference between the Curie–Weiss fits of the magnetic susceptibility in the paramagnetic state. While the effective moments in both LnGe₂ are consistent with the 4f⁷ states of the Ln ions, the Curie–Weiss temperatures differ: in GdGe₂θ_CW ≈ −80 K (not far from expectations for such an AFM compound) but in EuGe₂θ_CW ≈ 0 K. This can be a consequence of competing interactions within the geometrically frustrated triangular lattice of Eu ions. Incidentally, bulk EuGe₂ demonstrates a positive θ_CW ≈ 13 K suggesting weak FM coupling between the Eu moments.⁴⁴ Thus, at least EuGe₂ seems to be a promising candidate for the search of 2D FM.

Fig. 3 Temperature dependence of the AFM magnetic susceptibility in (a) bulk EuGe₂ (34 nm, 1 kOe) and (b) bulk GdGe₂ (94 nm, 10 kOe) measured in magnetic fields along directions Ge[111] (green) and Ge[112̄] of the substrate.

We consider EuGe₂ films with a small number of MLs. Temperature dependence of the magnetic moment in 1 ML EuGe₂ (Fig. 4a) certifies the emergence of 2D FM: not only the magnetic moment exhibits characteristic evolution but also the effective Curie temperature T_C* is controlled by low magnetic fields. The latter property is a hallmark of 2D FM, observed in Cr₂Ge₂Te₆⁷ and LnSi₂.¹³ FM is not limited to 1 ML samples. Fig. S4, ESI† provides data on FM in 2 ML, 4 ML and 9 ML EuGe₂. One can notice that the dependence of T_C* on low magnetic fields tends to disappear as the number of MLs increases. This fact is best illustrated by normalized temperature dependence curves M(T)/M(2 K) (Fig. S5, ESI†): a set of curves for different magnetic fields (as well as the remnant moment) in 1 ML EuGe₂ merges into a single curve in 9 ML thick film.

Fig. 4 Magnetism of 2D EuGe₂. (a) Temperature dependence of the FM moment in 1 ML EuGe₂ in (in-plane) magnetic fields 10 Oe (red), 20 Oe (turquoise), 35 Oe (black), 100 Oe (purple), 200 Oe (green), 500 Oe (orange), 2000 Oe (blue). (b) Temperature dependence of the FM moment in 4 ML EuGe₂ measured in magnetic fields 100 Oe along the directions Ge[111] (green) and Ge[112̄] (red) of the substrate. (c) In-plane magnetic field dependence of the magnetic moment in 2 ML EuGe₂ at 2 K. (d) Temperature dependence of magnetic moment in an in-plane magnetic field of 100 Oe in 2 ML EuGe₂ (red) and 2 ML SrGe₂ (green).

The direction of the FM moments in 2D EuGe₂ is determined from temperature dependence of the magnetic moment in magnetic fields of different orientation: according to Fig. 4b the FM moments are in-plane, as in LnSi₂.¹³ In this case, the 2D FM is likely to be sustained by a combination of high magnetic anisotropy and dipolar interactions, suppressing thermal fluctuations of the local moments.⁴⁹ The appearance of the FM state is accompanied by divergence of field-cooled (FC) and zero-field-cooled (ZFC) temperature dependences of magnetic moments (Fig. S6a, ESI†). M(H) curves in the FM state of 2 ML EuGe₂ have the characteristic form with a sizable hysteresis loop (Fig. 4c). However, hysteresis disappears in 1 ML EuGe₂ (Fig. S7, ESI†), probably due to difficulties of forming magnetic domains in the 2D limit. To demonstrate that the magnetism is not an artefact of the substrate or measurement procedure, we synthesized a few ML films of SrGe₂ – a compound isomorphous to EuGe₂, with close lattice parameters, albeit free of local magnetic moments. The comparison of 2 ML EuGe₂ and 2 ML SrGe₂ (Fig. 4d) certifies that the observed FM is an intrinsic property of EuGe₂.

Ultrathin films of GdGe₂ also demonstrate FM signals, as illustrated by temperature dependence of the magnetic moment of 2 ML GdGe₂ (Fig. 5a). Lower (and therefore noisier) magnetization signals in 1 ML GdGe₂ are demonstrated in Fig. S8, ESI.† As in other LnX₂, the effective Curie temperature T_C* is controlled by low magnetic fields. Another feature common with other 2D LnX₂ compounds is that the FM moments prefer the in-plane orientation (Fig. 5b). As expected, the FM state in GdGe₂ results in divergence of FC and ZFC curves (Fig. S6b, ESI†) as well as hysteresis in magnetic field dependence of magnetization (Fig. 5c). M(H) measurements for GdGe₂ films of intermediate thickness suggest a negative shift of the FM hysteresis loop (Fig. 5d). The exchange bias seems not very much surprising for a system with the thickness-dependent AFM-to-FM transition. The exchange bias field diminishes as the film approaches the 2D limit: ∼470 Oe in 9 ML GdGe₂ and ∼300 Oe in 6 ML GdGe₂, both at 2 K.

Fig. 5 Magnetism of 2D GdGe₂. (a) Temperature dependence of the FM moment in 2 ML GdGe₂ in (in-plane) magnetic fields 10 Oe (red), 50 Oe (black), 100 Oe (purple), 200 Oe (green), 500 Oe (orange), 2000 Oe (blue). (b) Temperature dependence of the FM moment in 2 ML GdGe₂ measured in magnetic fields 100 Oe along the directions Ge[111] (green) and Ge[112̄] (red) of the substrate. (c) In-plane magnetic field dependence of the magnetic moment in 2 ML GdGe₂ at 2 K. (d) In-plane magnetic field dependence of the magnetic moment in 9 ML GdGe₂ at 2 K.

2D EuSi₂ and GdSi₂ exhibit quantitatively similar magnetic properties, in particular the FM moments are slightly less than 1 μ_B per formula unit at saturation.¹³ We expected the same situation for EuGe₂ and GdGe₂. The saturation moment M_S of the film can be normalized either to surface area S or formula unit. Dependence of M_S/S on the number of MLs in EuGe₂ (Fig. S9a, ESI†) certifies the emerging character of the FM: it increases strongly as the film thins down. On the other hand, in GdGe₂ the analogous dependence is not monotonic (Fig. S10a, ESI†): it looks like some mechanism suppressing FM in ultrathin films is still in play. In EuGe₂, the saturation moment reaches almost 3 μ_B per formula unit (for 1 ML, Fig. S9b, ESI†). Such a high value can only be explained by magnetic ordering of Eu ion moments (DFT calculations show that Ge orbitals in EuGe₂ are magnetically inactive⁴⁴). In contrast, the saturation moment in GdGe₂ is an order of magnitude smaller than that in EuGe₂ (Fig. S10b, ESI†). An explanation of this difference would probably require a detailed theoretical analysis of the electronic and magnetic structures of these strongly correlated materials, which is out of scope of the present experimental study.

2.4. Electron transport in LnGe₂ films

The magnetization measurements are supported by those of lateral electron transport. Temperature dependences of resistance of thick films of EuGe₂ (Fig. 6a) and GdGe₂ (Fig. 6b) demonstrate pronounced features at the corresponding Néel temperatures – 48 K and 38 K. Below T_N, the resistance drops due to suppressed scattering in magnetically ordered systems. Both compounds are metals; thus, they belong to the so-called metallic Zintl phases. The metallic character of EuGe₂ is in agreement with electronic structure calculations.⁴⁴

Fig. 6 (a) Temperature dependence of sheet resistance R in bulk EuGe₂ (34 nm, blue) and its temperature derivative dR/dT (red). (b) Temperature dependence of sheet resistance R in bulk GdGe₂ (94 nm, blue) and its temperature derivative dR/dT (red). (c) Magnetic field dependence of sheet resistance in 2 ML GdGe₂ at 2 K. (d) Anomalous Hall effect in 2 ML GdGe₂ at 2 K.

It would be interesting to study temperature dependences of the resistivity in a few ML LnGe₂ films, in analogy with LnSi₂.²⁸ However, as the film thins down it expectedly becomes progressively insulating. As a result, the Ge substrate shunts current away from the ultrathin LnGe₂ film. Nevertheless, the measurements are still possible at the lowest temperatures as the carriers in the substrate essentially freeze out. Fig. 6c demonstrates negative magnetoresistance in 2 ML GdGe₂ at 2 K. It may indicate the emerging FM state, especially taking into account the typical positive magnetoresistance in the thick films of GdGe₂. Fig. 6d illustrates magnetic field dependence of the anomalous Hall effect in the same film at 2 K – the behavior expected for a ferromagnet. Similar properties – negative magnetoresistance and anomalous Hall effect – are detected in ultrathin EuGe₂ films (Fig. S11, ESI†).

3. Conclusions

In this paper, we address the general problem of finding a class of 2D FM materials. More specifically, we would like to establish whether lanthanide metalloxenes form such a class. This problem is still far too general. So, we follow a heuristic proposed by George Pólya in his classic How to Solve It: “If you can't solve a problem, then there is an easier problem you can solve: find it”. Thus, we consider changes in EuX₂ and GdX₂ brought up by replacement of silicene with germanene. We succeeded in synthesis and characterization of EuGe₂ and GdGe₂ structures ranging from the bulk down to 1 ML. This study establishes a small but likely to be extendable class of materials LnX₂ (Ln = Eu or Gd, X = Si or Ge) which (i) share the same structural motif based on a triangular lattice of magnetic lanthanide ions; (ii) evolve from a paradigmatic 3D AFM to a 2D FM as soon as their thickness goes down. This result provides an excellent occasion to advocate for the use of lanthanide compounds in the rapidly growing field of functional 2D materials. The other intrinsic 2D FMs are based on 3d TMs; suggestions of new such systems do not go beyond “materials with 4d/5d elements”¹ thus missing the whole range of opportunities provided by lanthanide magnets, not least in relation to spin–orbit coupling, strong correlations and local character of 4f-electrons. We envisage that the discovery of a class of lanthanide magnets would play an important role in finding new magnetic materials and spintronic applications, studies of fundamental spin systems.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work is supported by NRC “Kurchatov Institute”, the Russian Foundation for Basic Research [grant 19-07-00249] (magnetization measurements), and the Russian Science Foundation [grant 19-19-00009] (transport measurements). The measurements have been carried out using equipment of the resource centers of electrophysical, laboratory X-ray and electron microscopy techniques in NRC “Kurchatov Institute”.

Notes and references

1. K. S. Burch, D. Mandrus and J.-G. Park, Nature, 2018, 563, 47.
2. C. Gong and X. Zhang, Science, 2019, 363, eaav4450.
3. H. González-Herrero, J. M. Gómez-Rodríguez, P. Mallet, M. Moaied, J. J. Palacios, C. Salgado, M. M. Ugeda, J.-Y. Veuillen, F. Yndurain and I. Brihuega, Science, 2016, 352, 437.
4. M. Slota, A. Keerthi, W. K. Myers, E. Tretyakov, M. Baumgarten, A. Ardavan, H. Sadeghi, C. J. Lambert, A. Narita, K. Müllen and L. Bogani, Nature, 2018, 557, 691.
5. F. Katmis, V. Lauter, F. S. Nogueira, B. A. Assaf, M. E. Jamer, P. Wei, B. Satpati, J. W. Freeland, I. Eremin, D. Heiman, P. Jarillo-Herrero and J. S. Moodera, Nature, 2016, 533, 513.
6. D. V. Averyanov, I. S. Sokolov, A. M. Tokmachev, O. E. Parfenov, I. A. Karateev, A. N. Taldenkov and V. G. Storchak, ACS Appl. Mater. Interfaces, 2018, 10, 20767.
7. C. Gong, L. Li, Z. Li, H. Ji, A. Stern, Y. Xia, T. Cao, W. Bao, C. Wang, Y. Wang, Z. Q. Qiu, R. J. Cava, S. G. Louie, J. Xia and X. Zhang, Nature, 2017, 546, 265.
8. B. Huang, G. Clark, E. Navarro-Moratalla, D. R. Klein, R. Cheng, K. L. Seyler, D. Zhong, E. Schmidgall, M. A. McGuire, D. H. Cobden, W. Yao, D. Xiao, P. Jarillo-Herrero and X. Xu, Nature, 2017, 546, 270.
9. M. Bonilla, S. Kolekar, Y. Ma, H. C. Diaz, V. Kalappattil, R. Das, T. Eggers, H. R. Gutierrez, M.-H. Phan and M. Batzill, Nat. Nanotechnol., 2018, 13, 289.
10. Z. Fei, B. Huang, P. Malinowski, W. Wang, T. Song, J. Sanchez, W. Yao, D. Xiao, X. Zhu, A. F. May, W. Wu, D. H. Cobden, J.-H. Chu and X. Xu, Nat. Mater., 2018, 17, 778.
11. D. J. O’Hara, T. Zhu, A. H. Trout, A. S. Ahmed, Y. K. Luo, C. H. Lee, M. R. Brenner, S. Rajan, J. A. Gupta, D. W. McComb and R. K. Kawakami, Nano Lett., 2018, 18, 3125.
12. D. Ghazaryan, M. T. Greenaway, Z. Wang, V. H. Guarochico-Moreira, I. J. Vera-Marun, J. Yin, Y. Liao, S. V. Morozov, O. Kristanovski, A. I. Lichtenstein, M. I. Katsnelson, F. Withers, A. Mishchenko, L. Eaves, A. K. Geim, K. S. Novoselov and A. Misra, Nat. Electron., 2018, 1, 344.
13. A. M. Tokmachev, D. V. Averyanov, O. E. Parfenov, A. N. Taldenkov, I. A. Karateev, I. S. Sokolov, O. A. Kondratev and V. G. Storchak, Nat. Commun., 2018, 9, 1672.
14. A. P. Balan, S. Radhakrishnan, C. F. Woellner, S. K. Sinha, L. Deng, C. de los Reyes, B. M. Rao, M. Paulose, R. Neupane, A. Apte, V. Kochat, R. Vajtai, A. R. Harutyunyan, C.-W. Chu, G. Costin, D. S. Galvao, A. A. Martí, P. A. van Aken, O. K. Varghese, C. S. Tiwary, A. M. M. R. Iyer and P. M. Ajayan, Nat. Nanotechnol., 2018, 13, 602.
15. T. Song, X. Cai, M. W.-Y. Tu, X. Zhang, B. Huang, N. P. Wilson, K. L. Seyler, L. Zhu, T. Taniguchi, K. Watanabe, M. A. McGuire, D. H. Cobden, D. Xiao, W. Yao and X. Xu, Science, 2018, 360, 1214.
16. D. R. Klein, D. MacNeill, J. L. Lado, D. Soriano, E. Navarro-Moratalla, K. Watanabe, T. Taniguchi, S. Manni, P. Canfield, J. Fernández-Rossier and P. Jarillo-Herrero, Science, 2018, 360, 1218.
17. K. L. Seyler, D. Zhong, D. R. Klein, S. Gao, X. Zhang, B. Huang, E. Navarro-Moratalla, L. Yang, D. H. Cobden, M. A. McGuire, W. Yao, D. Xiao, P. Jarillo-Herrero and X. Xu, Nat. Phys., 2018, 14, 277.
18. S. Jiang, J. Shan and K. F. Mak, Nat. Mater., 2018, 17, 406.
19. B. Huang, G. Clark, D. R. Klein, D. MacNeill, E. Navarro-Moratalla, K. L. Seyler, N. Wilson, M. A. McGuire, D. H. Cobden, D. Xiao, W. Yao, P. Jarillo-Herrero and X. Xu, Nat. Nanotechnol., 2018, 13, 544.
20. S. Jiang, L. Li, Z. Wang, K. F. Mak and J. Shan, Nat. Nanotechnol., 2018, 13, 549.
21. Y. Deng, Y. Yu, Y. Song, J. Zhang, N. Z. Wang, Z. Sun, Y. Yi, Y. Z. Wu, S. Wu, J. Zhu, J. Wang, X. H. Chen and Y. Zhang, Nature, 2018, 563, 94.
22. Z. Wang, T. Zhang, M. Ding, B. Dong, Y. Li, M. Chen, X. Li, J. Huang, H. Wang, X. Zhao, Y. Li, D. Li, C. Jia, L. Sun, H. Guo, Y. Ye, D. Sun, Y. Chen, T. Yang, J. Zhang, S. Ono, Z. Han and Z. Zhang, Nat. Nanotechnol., 2018, 13, 554.
23. M. A. McGuire, Crystals, 2017, 7, 121.
24. N. Miao, B. Xu, L. Zhu, J. Zhou and Z. Sun, J. Am. Chem. Soc., 2018, 140, 2417.
25. V. V. Kulish and W. Huang, J. Mater. Chem. C, 2017, 5, 8734.
26. C. Huang, J. Feng, F. Wu, D. Ahmed, B. Huang, H. Xiang, K. Deng and E. Kan, J. Am. Chem. Soc., 2018, 140, 11519.
27. C. Wang, X. Zhou, L. Zhou, N.-H. Tong, Z.-Y. Lu and W. Ji, Sci. Bull., 2019, 64, 293.
28. O. E. Parfenov, A. M. Tokmachev, D. V. Averyanov, I. A. Karateev, I. S. Sokolov, A. N. Taldenkov and V. G. Storchak, Mater. Today, 2019 DOI:10.1016/j.mattod.2019.03.017.
29. A. Molle, C. Grazianetti, L. Tao, D. Taneja, Md. H. Alam and D. Akinwande, Chem. Soc. Rev., 2018, 47, 6370.
30. L. Tao, E. Cinquanta, D. Chiappe, C. Grazianetti, M. Fanciulli, M. Dubey, A. Molle and D. Akinwande, Nat. Nanotechnol., 2015, 10, 227.
31. A. Molle, J. Goldberger, M. Houssa, Y. Xu, S.-C. Zhang and D. Akinwande, Nat. Mater., 2017, 16, 163.
32. D. Jose and A. Datta, Acc. Chem. Res., 2014, 47, 593.
33. A. Nijamudheen, R. Bhattacharjee, S. Choudhury and A. Datta, J. Phys. Chem. C, 2015, 119, 3802.
34. S. Sanna, C. Dues, W. G. Schmidt, F. Timmer, J. Wollschläger, M. Franz, S. Appelfeller and M. Dähne, Phys. Rev. B, 2016, 93, 195407.
35. N. Liu, G. Bo, Y. Liu, X. Xu, Y. Du and S. X. Dou, Small, 2019, 15, 1805147.
36. M. E. Dávila, L. Xian, S. Cahangirov, A. Rubio and G. Le Lay, New J. Phys., 2014, 16, 095002.
37. M. E. Dávila and G. Le Lay, Sci. Rep., 2016, 6, 20714.
38. J. Zhuang, N. Gao, Z. Li, X. Xu, J. Wang, J. Zhao, S. X. Dou and Y. Du, ACS Nano, 2017, 11, 3553.
39. J. Yuhara, H. Shimazu, K. Ito, A. Ohta, M. Araidai, M. Kurosawa, M. Nakatake and G. Le Lay, ACS Nano, 2018, 12, 11632.
40. E. Noguchi, K. Sugawara, R. Yaokawa, T. Hitosugi, H. Nakano and T. Takahashi, Adv. Mater., 2015, 27, 856.
41. W. L. B. Huey and J. E. Goldberger, Chem. Soc. Rev., 2018, 47, 6201.
42. E. Bianco, S. Butler, S. Jiang, O. D. Restrepo, W. Windl and J. E. Goldberger, ACS Nano, 2013, 7, 4414.
43. N. D. Cultrara, Y. Wang, M. Q. Arguilla, M. R. Scudder, S. Jiang, W. Windl, S. Bobev and J. E. Goldberger, Chem. Mater., 2018, 30, 1335.
44. S. Bobev, E. D. Bauer, J. D. Thompson, J. L. Sarrao, G. J. Miller, B. Eck and R. Dronskowski, J. Solid State Chem., 2004, 177, 3545.
45. A. M. Tokmachev, D. V. Averyanov, I. A. Karateev, O. E. Parfenov, A. L. Vasiliev, S. N. Yakunin and V. G. Storchak, Nanoscale, 2016, 8, 16229.
46. A. M. Tokmachev, D. V. Averyanov, I. A. Karateev, O. E. Parfenov, O. A. Kondratev, A. N. Taldenkov and V. G. Storchak, Adv. Funct. Mater., 2017, 27, 1606603.
47. D. V. Averyanov, A. M. Tokmachev, C. G. Karateeva, I. A. Karateev, E. F. Lobanovich, G. V. Prutskov, O. E. Parfenov, A. N. Taldenkov, A. L. Vasiliev and V. G. Storchak, Sci. Rep., 2016, 6, 25980.
48. D. Zhong, K. L. Seyler, X. Linpeng, R. Cheng, N. Sivadas, B. Huang, E. Schmidgall, T. Taniguchi, K. Watanabe, M. A. McGuire, W. Yao, D. Xiao, K.-M. Fu and X. Xu, Sci. Adv., 2017, 3, e1603113.
49. P. Bruno, Phys. Rev. B: Condens. Matter Mater. Phys., 1991, 43, 6015.

---

Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c9mh00444k

---