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Crystal time-reversal symmetry breaking and spin splitting in collinear antiferromagnets

Libor Šmejkal

Relativistic bandstructure of solids generates functionalities of modern quantum, topological and spintronics materials1. Common collinear antiferromagnets exhibit Kramers spin degenerate bands2 and for many decades were believed to be excluded from spin splitting physics. Our recent prediction of crystal time-reversal symmetry breaking by anisotropic magnetization densities due to the collinear antiferromagnetism combined with nonmagnetic atoms3 changes this perspective. Unlike the conventional spin-orbit interaction induced spin splitting, our antiferromagnetic spin splitting is of exchange origin, can reach giant eV values, and can preserve spin quantum number.
In this talk, we will discuss the basic properties of this new type of antiferromagnetic spin splitting, its local magnetic symmetry origin and symmetry criteria for its emergence and we will catalogue broad class of material candidates. Furthermore, we will show that this antiferromagnetic spin splitting generates a crystal Hall effect controllable via rearrangement of nonmagnetic atoms3. Finally, we will present an experimental discovery of crystal Hall effect in ruthenium dioxide antiferromagnet4.

[1] Šmejkal, L., Mokrousov, Y., Yan, B. & MacDonald, A. H. Topological antiferromagnetic spintronics. Nat. Phys. 14, 242 (2018).
[2] Šmejkal, L., Železný, J., Sinova, J. & Jungwirth, T. Electric Control of Dirac Quasiparticles by Spin-Orbit Torque in an Antiferromagnet. Phys. Rev. Lett. 118, 106402 (2017), arXiv (2016)
[3] Šmejkal, L., González-Hernández, R., Jungwirth, T. & Sinova, J. Crystal time-reversal symmetry breaking and spontaneous Hall effect in collinear antiferromagnets. Sci. Adv. 6, eaaz8809 (2020), arXiv (2019)
[4] Feng, Z., Zhou, X., Šmejkal, L. et al. Observation of the Crystal Hall Effect in a Collinear Antiferromagnet. arXiv (2020)

Optical spectroscopy of 2-dimensional antiferromagnetic materials

Hyeonsik Cheong

Magnetism in low dimensional systems is a fascinating topic for the fundamental physics as well as for possible applications in future spintronic devices. Although ferromagnetic 2-dimensional (2D) materials are attracting the most interest, antiferromagnetic 2D materials are equally interesting for the rich physics they reveal. However, antiferromagnetic ordering is much more difficult to investigate because the lack of net magnetization hinders easy detection of antiferromagnetic ordering. Neutron scattering, which is a powerful tool to detect antiferromagnetic order in bulk materials, cannot be used for atomically thin samples due to the small sample volume. Raman spectroscopy has proven to be a powerful tool to detect antiferromagnetic ordering by monitoring magnetically induced changes in the Raman spectrum. In this talk, I will review recent achievements in the study of antiferromagnetism in 2 dimensions using Raman spectroscopy. FePS3 exhibits an Ising-type antiferromagnetic ordering down to the monolayer limit, in good agreement with the Onsager solution for 2-dimensional order-disorder transition. The transition temperature remains almost independent of the thickness from bulk to the monolayer limit, indicating that the weak interlayer interaction has little effect on the antiferromagnetic ordering. On the other hand, NiPS3, which shows an XXZ-type antiferromagnetic ordering in bulk, exhibits antiferromagnetic ordering down to 2 layers with a slight decrease in the transition temperature, but the magnetic ordering is suppressed in the monolayer limit. A Heisenberg-type antiferromagnet MnPS3 also exhibits ordering down to 2 layers with a small decrease in the transition temperature. Furthermore, a recent discovery of a peculiar excitonic transition that exhibit a dramatic decrease of the linewidth below the transition temperature will be reported.

Spin-orbit torques based on topological spin texture and magnon

Hyunsoo Yang

Layered topological materials such as topological insulators (TIs) and Weyl semimetals are a new class of quantum matters with large spin-orbit coupling, and probing the spin texture of these materials is of importance for functional devices. We reveal spin textures of such materials using the bilinear magneto-electric resistance (BMR), which depends on the relative orientation of the current with respect to crystallographic axes [1,2]. We also visualize current-induced spin accumulation in topological insulators using photocurrent mapping [3]. Topological surface states (TSS) dominated spin orbit torques are identified in Bi2Se3 [4], and magnetization switching at room temperature using Bi2Se3 as a spin current source is demonstrated [5]. Nevertheless, the resistive nature of TIs can cause serious current shunting issues, leading to a large power consumption. In order to tackle this issue, we propose two approaches.
Weyl semimetals have a larger conductivity compared to TIs and they can generate a strong spin current from their bulk states. The Td-phase Weyl semimetal WTe2 can be produced with high quality, simplifying interfacial studies and facilitating device applications. Utilizing the magneto-optical Kerr microscopy, we show the current-driven magnetization switching in WTe2/NiFe with a low current density and a low power [6].
The current shunting issue can be also overcome by the magnon-mediated spin torque, in which the angular momentum is carried by precessing spins rather than moving electrons. Magnon-torque-driven magnetization switching is demonstrated in the Bi2Se3/NiO/Py devices at room temperature [7]. By injecting the electric current to an adjacent Bi2Se3 layer, spin currents were converted to magnon torques through an antiferromagnetic insulator NiO. The presence of magnon torque is evident for larger values of the NiO-thickness where magnons are the only spin-angular-momentum carriers. The demonstration reveals that the magnon torque is sufficient to control the magnetization, which is comparable with previously observed electrical spin torque ratios of TIs [5].
Looking towards the future, we hope that these studies will spark more works on harnessing spin currents from topological materials and revealing interesting spin textures at topological material/magnet interfaces. All magnon-driven magnetization switching without involving electrical parts could be achieved in the near future. The results will invigorate magnon-based memory and logic devices, which is relevant to the energy-efficient control of spin devices.

[1] P. He et al., Nat. Phys. 14, 495 (2018)
[2] P. He et al., Nat. Comm. 10, 1290 (2019)
[3] Y. Liu et al., Nat. Comm. 9, 2492 (2018)
[4] Y. Wang et al., Phys. Rev. Lett. 114, 257202 (2015)
[5] Y. Wang et al., Nat. Comm. 8, 1364 (2017)
[6] S. Shi et al., Nat. Nano. 14, 945 (2019)
[7] Y. Wang et al., Science 366, 1125 (2019)

Intrinsic 2D-XY ferromagnetism in a van der Waals monolayer

Amilcar Bedoya-Pinto

Long before the recent fascination with two-dimensional materials, the critical behaviour and universality scaling of phase transitions in low-dimensional systems has been a topic of great interest. Recent experiments on layered magnetic systems show that a sizable out-of-plane magnetic anisotropy is able to stabilize 2D long-range ferromagnetic order, as demonstrated in CrI3, CrBr3, Fe3GeTe2 and Cr2Ge2Te6 [1], while a spontaneous magnetic ordering has remained elusive for an in-plane 2D magnetic system in the monolayer limit. Here, we construct a nearly ideal easy-plane system, a CrCl3 monolayer grown on Graphene/6H-SiC (0001), which exhibits ferromagnetic ordering as unambiguously determined by element-specific X-ray magnetic dichroism [2]. Hysteretic behaviour of the field-dependent magnetization is sustained up to a temperature of 10 K, and angular dependent measurements evidence a clear in-plane easy axis, unlike all other van der Waals monolayer magnets reported to date. The origin of the easy-plane anisotropy is discussed in terms of a non-zero orbital moment and a trigonal distortion of the CrCl3 unit cell. Moreover, the analysis of the critical exponents of the temperature-dependent magnetization show a scaling behaviour that is characteristic of a 2D-XY system. These observations suggest the first realization of a finite-size Berezinskii-Kosterlitz-Thouless (BKT) phase transition in a quasi-freestanding monolayer magnet with a XY universality class; accessible through the bottom-up growth of a van der Waals layer with an in-plane hexagonal crystal symmetry and negligible substrate interaction.

Figure 1. (a) Schematic crystal structure of CrCl3/Graphene/6H-SiC layers in top view and cross-section configurations. (b) Atom resolved image of the CrCl3 lattice featuring a moiré pattern, which corresponds to a 23.8° rotation between the hexagonal unit cell of CrCl3 and graphene.(c) XMCD hysteresis loops taken in grazing (in-plane) and normal (out-of-plane) incidence, evidencing a weak anisotropy favouring an in-plane easy axis. (d) Modified Arrott-Plots for the temperature-and field dependent XMCD data. A consistent set of critical exponents is inferred (β=0.235, γ= 2.2), matching with the predictions of the 2DXY model.

References
[1] K. S. Burch, D. Mandrus, J. G. Park, Nature. 563, 47–52 (2018)
[2] A. Bedoya-Pinto et al., arXiV https://arxiv.org/abs/2006.07605 (2020)

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Intrinsic magnetic topological states in MnBi2Te4

Jing Wang

Here, we predict the tetradymite-type compound MnBi2Te4 and its related materials host topologically nontrivial magnetic states. The magnetic ground state of MnBi2Te4 is an antiferromagetic topological insulator state with a large topologically non-trivial energy gap (0.2 eV). It presents the axion state, which has gapped bulk and surface states, and the quantized topological magnetoelectric effect. It has several advantages over the previous proposals on realizing the topological magnetoelectric effect. The intrinsic magnetic and band inversion further lead to quantum anomalous Hall effect in odd layer MnBi2Te4 thin film with combined inversion and time-reversal symmetry breaking, which has been recently observed in experiments. The high quality intrinsic MnBi2Te4 together with other magnetic/superconducting 2D materials provides fertile ground for exploring exotic topological quantum phenomena.

We further show the Moire superlattice of twisted bilayer MnBi2Te4 exhibits highly tunable Chern bands with Chern number up to 3. We show that a twist angle of 1 degree turns the highest valence band into a flat band with Chern number ±1, that is isolated from all other bands in both ferromagnetic and antiferromagnetic phases. This result provides a promising platform for realizing time-reversal breaking correlated topological phases, such as fractional Chern insulator and p+ip topological superconductor.

ARPES studies of candidate van der Waals ferromagnets

Phil King

Control over materials thickness down to the single-atom scale has emerged as a powerful tuning parameter for manipulating not only the single-particle band structures of solids, but increasingly also their interacting electronic states and phases. Recently, magnetism has emerged as the new frontier in the area of 2d materials. Here, I will show how direct measurement of the electronic structure using angle-resolved photoemission (ARPES) can lead to valuable insight not only on the question of whether a 2d material does in fact exhibit long-range magnetic order, but also on the microscopic mechanisms of the magnetic ordering when it occurs. First, I will consider the example of epitaxial monolayers of VSe2.1 Our ARPES measurements, combined with x-ray magnetic circular dichroism (XMCD), demonstrate that a putative magnetic order is prevented from occurring by the formation of a robust charge density wave,2 which gaps the complete Fermi surface thus removing a Stonor-like channel for ferromagnetism. The instability can be expected to be nearby in phase space, however, and we show how ferromagnetism can be induced via proximity coupling with a ferromagnetic  Fe layer.3 Second, I will show ARPES results from bulk Cr2Ge2Te6, which is an established van der Waals ferromagnet,4 where long-range order has been shown to persist to the bilayer thickness.5 From ARPES, we identify atomic- and orbital-specific band shifts upon cooling through TC. From these, together with XMCD, we identify the states created by a covalent bond between the Te 5p and the Cr eg orbitals as the primary driver of the ferromagnetic ordering in this system, while it is the Cr t2g states that carry the majority of the spin moment. This reflects a rather direct observation of how 90° superexchange leads to ferromagnetism, and demonstrates how an experimental band-structure perspective can give important insight even in a “local moment" magnetic system.

 

This work was performed in close collaboration with M.D. Watson, A. Rajan, K. Underwood, J. Feng, D. Biswas, D. Burn, T. Hesjedal, G. van der Laan, M. Ciomaga Hatnean, G. Balakrishnan, G. Vinai, G. Panaccione and colleagues from the Universities of St Andrews, Oxford, Warwick, Diamond, and Elettra.

 

1 Rajan et al., Phys. Rev. Materials 4 (2020) 014003

2 Feng et al., Nano Lett. 18 (2018) 4493

3 Vinai et al., Phys. Rev. B 101 (2020) 035404

4 Carteaux et al., J. Phys. Condens. Mat. 7 (1995) 69

5 Gong et al., Nature 546 (2017) 265

6 Watson et al., Phys. Rev. B 101 (2020) 205125

Thin layers of CrBr3 and CrI3: reconaissance ventures into 2D magnetism

Maciej Koperski

The magnetism of chromium has been investigated for almost a century now, providing substantial knowledge about its electronic configuration. Extensive research has been conducted regarding the physics of valence electrons from d-shell, which is fundamentally important for understanding the mechanisms of magnetic ordering. Interestingly, chromium atom, exhibiting a stable electronic configuration exempting from Hund’s rules, has half-filled 3d shell, which leads to manifestation of robust magnetic effects in a variety of structures. Recently, attention has been refocused on chromium trihalides (CrCl3, CrBr3 and CrI3), which constitute a group of electrically insulating layered materials displaying magnetic ordering at low temperatures, as established by inspection of bulk crystals carried out few decades ago. The progress of mechanical exfoliation techniques, performed in a controlled argon atmosphere, enables now isolation of thin layers (down to monolayers) and their incorporation in van der Waals heterostructures.
Initial reports demonstrated layer-dependent ferromagnetic and anti-ferromagnetic order below Curie temperature using Kerr rotation measurements as magnetization probe. These appealing findings motivate further study to uncover the underlying microscopic mechanisms. One possible path to learn about the electronic structure and characteristics of electronic states via optical methods involves investigations of emission and absorption processes. Here, we present detailed optical studies of exfoliated films of CrBr3 and CrI3 to demonstrate that the emergent interband luminescence has molecular-like character (most likely due to formation of Frenkel-type excitons) and the details of the structure of emission resonances can be explained by Franck-Condon principle involving multiple phonon modes. The photoluminescence studies unveil unambiguous signatures of coupling between the magnetic moments of Cr3+ ions with band carriers, offering insight into fundamental properties of these novel magnetic structures and opening up new routes for potential applications of 2D systems.

Emergent properties of 2D magnets and their heterostructures explored by MBE

Masaki Nakano

 

Bottom-up molecular-beam epitaxy (MBE) provides a complementary approach to top-down mechanical exfoliation in 2D materials research. A great success lies in the application of MBE-grown large-area monolayer films to ARPES and STM/STS studies, unveiling emergent monolayer properties of various 2D materials. Considering the research history of semiconductors and oxides, however, one of the biggest advantages of MBE-based approach should be to create novel material systems unachievable by bulk-based approach and examine their transport phenomena, although such examples are very much limited presumably due to difficulties in making high-enough quality samples.

 

We have recently developed a fundamental route to layer-by-layer epitaxial growth of a wide variety of 2D materials and their heterostructures on insulating substrates by MBE [1-7], opening a door for exploration of emergent transport phenomena of 2D materials arising at the monolayer limit and at the interface between dissimilar materials even based on hardly-cleavable, chemically-unstable, and/or thermodynamically-metastable compounds. In this presentation, I will introduce our recent achievements in particular on the MBE-grown 2D magnets and their heterostructures, including observation of the emergent itinerant 2D ferromagnetism with intrinsic spin polarization in hardly-cleavable compound that are missing in its bulk counterpart [4], as well as control of its magnetic properties by the magnetic proximity effect across the van der Waals interface [7].

 

Reference:

[1] M. Nakano et al., Nano Lett. 17, 5595 (2017).

[2] Y. Wang et al., Appl. Phys. Lett. 113, 073101 (2018).

[3] Y. Kashiwabara et al., Adv. Funct. Mater. 29, 1900354 (2019).

[4] M. Nakano et al., Nano Lett. 19, 8806 (2019).

[5] Y. Tanaka et al., Nano Lett. 20, 1725 (2020).

[6] H. Matsuoka et al., Rhys. Rev. Research 2, 012064(R) (2020).

[7] H. Matsuoka et al., submitted.

Proximity induced spin-orbit coupling and magnetism in graphene

Alexey Kaverzin

With a reference to our experimental observations I will discuss how proximity effects modify the spin transport phenomena in graphene when it is placed in the vicinity of other layered materials. For example, the combination of graphene and TMDs results in the presence of large spin-orbit interaction imprinted from TMD into graphene with the emergence of spin manipulation mechanisms including conversion between spin and charge currents. I will highlight our recent results obtained on a van der Waals heterostructure of graphene and anti-ferromagnetic material CrSBr. The presence of CrSBr introduces a large exchange interaction in graphene such that its conductivity becomes spin polarised with the polarisation of approximately 14%. This implies that spin current is generated in graphene on CrSBr with efficiency close to that of the conventional ferromagnetic materials. Overall, we experimentally demonstrate the functionality of various building blocks that can be used for assembly of spin-based devices made out of layered materials only.

Electrostatic Control of Magnetism in Van Der Waals Ferromagnets

Ivan Verzhbitskiy

Control of magnetism via electric fields is a long-standing exciting challenge of fundamental significance for future spintronic devices. Recent discovery of two-dimensional magnetism in van der Waals systems such as CrI3, Fe3GeTe2, and Cr2Ge2Te6 (CGT) highlights their unique potential as a platform to probe the interplay between charge and magnetic ordering [1]. Here, we report the first observation of carrier-induced ferromagnetic order in heavily doped thin crystals of CGT [2]. Upon degenerate electron doping, the CGT transistor exhibits clear hysteresis in the magnetoresistance (MR), which is a distinctive signature of ferromagnetism. Surprisingly, the hysteresis persists up to 200 K, which is in contrast to undoped CGT whose Curie temperature is only 61 K. We demonstrate that the Curie temperature can be modulated over 140 K by altering the electron density. Further, we find the magnetic easy-axis of doped CGT to lie within the plane of the crystal. This is in stark contrast to the out-of-plane magnetic easy-axis of the pristine CGT. We attribute these changes to emergence of the double-exchange interaction mediated by free carriers. This mechanism dominates over superexchange interaction, which is responsible for the ferromagnetic order in undoped CGT. Our calculations show that the magnetic anisotropy energy changes sign in degenerate doping limit, in agreement with our experimental observations. Our findings reveal a unique role of the electric field in tailoring the magnetic anisotropy and leading exchange interaction in semiconducting 2D ferromagnets.

[1] Gibertini, M.; Koperski, M.; Morpurgo, A. F. & Novoselov, K. S. Magnetic 2D materials and heterostructures. Nat. Nanotechnol. 14, 408–419 (2019).

[2] Verzhbitskiy, I.; Kurebayashi, H.; Cheng, H.; Zhou, J.; Khan, S.; Feng, Y. P. & Eda, G. Controlling the magnetic anisotropy in Cr2Ge2Te6 by electrostatic gating. Nat. Electron. (2020), DOI:https://doi.org/10.1038/s41928-020-0427-7