2022 Abstracts Orbitronics

Sayantika BHOWAL

Electrical manipulation of the spin moments, e.g., in a spin Hall effect, is at the heart of the spintronic devices with the advantage of faster processing, higher information density, and low power consumption. Recently, an analogous orbital-degrees-driven effect, viz., the orbital Hall effect, has gained a lot of attention, in which an applied electric field generates a transverse orbital current. The fundamental nature of the orbital Hall effect, its large magnitude, and no dependence on the spin-orbit interaction drive the interest in this field. These also vastly increase the possible phase space of candidate materials for orbitronic applications, compared to spintronics, for encoding information. While the effect occurs for both inversion symmetric and asymmetric systems, the electrical manipulation of the orbital degrees becomes particularly interesting in systems with broken inversion symmetry where intrinsic orbital moments, crucial to the desired effects, are present in the Brillouin zone of the system even in presence of time-reversal symmetry. In my talk, I will discuss the origin of the orbital Hall effect1,2, its connection to the well-known “valley Hall effect”3, and “spin Hall effect”1,2, and the electric current induced orbital magnetization4 in the prototype two-dimensional systems with broken inversion symmetry, such as transition metal dichalcogenides and gapped graphene.

[1] S. Bhowal and S. Satpathy, Phys. Rev. B (Rapid) 101, 121112 (R) (2020)
[2] S. Bhowal and S. Satpathy, Phys. Rev. B 102, 035409 (2020)
[3] S. Bhowal and G. Vignale, Phys. Rev. B 103, 195309 (2021)
[4] S. Bhowal and S. Satpathy, Phys. Rev. B (Rapid) 102, 201403(R) (2020)

Luis Manuel CANONICO ARMAS

The orbital-Hall effect (OHE) refers to the transverse flow of orbital angular momentum due to a longitudinally applied electric field [1]. Most of the theoretical understanding of this phenomenon has been consolidated by studying three dimensional (3D) metallic systems with promising results [2,3,4]. Only recently, the OHE has acquired a consistent interest of the community interested in two dimensional (2D) materials. The interplay between the low-dimensionality and the particular geometry of the band structure of 2D systems allow the occurrence of orbital phenomena up to now absent in 3D materials, such as orbital Hall insulating phases [5].
In my talk, I will discuss the fundamentals of orbital angular momentum transport in 2D insulating systems. I will discuss the characterisation of the orbital Hall insulating phases in terms of the orbital Chern numbers [6]. Also, based on the reinterpretation of the valley Hall effect in terms of the orbital valley Hall effect [7], I will extend the analysis to discuss possible experimental signatures of orbital angular momentum transport in 2D systems and in particular, I will revisit the origin of non-local resistance signals in Gr/hBN heterostructures.

[1] Bernevig, B. A., Hughes, T. L., & Zhang, S. C. (2005). Orbitronics: The intrinsic orbital current in p-doped silicon. Physical Review Letters, 95(6), 066601.
[2] Kontani, H., Tanaka, T., Hirashima, D. S., Yamada, K., & Inoue, J. (2009). Giant orbital Hall effect in transition metals: Origin of large spin and anomalous Hall effects. Physical review letters, 102(1), 016601.
[3] Go, D., Jo, D., Kim, C., & Lee, H. W. (2018). Intrinsic spin and orbital Hall effects from orbital texture. Physical Review Letters, 121(8), 086602.
[4] Ding, S., Liang, Z., Go, D., Yun, C., Xue, M., Liu, Z., ... & Yang, J. (2022). Observation of the orbital Rashba-Edelstein magnetoresistance. Physical Review Letters, 128(6), 067201.
[5] Canonico, L. M., Cysne, T. P., Rappoport, T. G., & Muniz, R. B. (2020). Two-dimensional orbital Hall insulators. Physical Review B, 101(7), 075429.
[6] Cysne, T. P., Costa, M., Canonico, L. M., Nardelli, M. B., Muniz, R. B., & Rappoport, T. G. (2021). Disentangling orbital and valley Hall effects in bilayers of transition metal dichalcogenides. Physical Review Letters, 126(5), 056601.
[7] Bhowal, S., & Vignale, G. (2021). Orbital Hall effect as an alternative to valley Hall effect in gapped graphene. Physical Review B, 103(19), 195309.

Young-Gwan CHOI

The orbital angular momentum is a core ingredient of orbital magnetism, spin Hall effect, giant Rashba spin splitting, orbital Edelstein effect, and spin-orbit torque. However, its experimental detection is tricky. In particular, direct detection of the orbital Hall effect remains elusive despite its importance for electrical control of magnetic nanodevices. Here we report the direct observation of the orbital Hall effect in a light metal Ti1. The Kerr rotation by the accumulated orbital magnetic moment is measured at Ti surfaces, whose result agrees with theoretical calculations semi-quantitatively. As another evidence, we measured the orbital torque in the Ti/Co heterostructures, from which we determine the orbital Hall angle >0.31. Our experimental results confirm the orbital Hall effect in a light metal Ti and hint at opportunities in the emerging field of orbitronics.

[1] Choi et al., Observation of the orbital Hall effect in a light metal Ti, arXiv:2109.14847.

Tarik Pereira CYSNE

The orbital-Hall effect (OHE) refers to the creation of a transverse flow of orbital angular momentum (OAM) that is induced by a longitudinally applied electric field. This effect was predicted in p-doped silicon more than fifteen years ago. The theoretical development of the OHE was built in the context of three-dimensional (3D) metallic systems.
Only recently, the OHE acquired a consistent interest in the community of two-dimensional (2D) materials. The low dimensionality of the 2D materials and the geometry of its band structure allows the occurrence of orbital phenomena that are not present in most 3D systems. An example of these phenomena is the existence of orbital Hall insulating phases that can be indexed by an orbital Chern number [1]. The interest of the 2D-materials community by the OHE is also motivated, among other reasons, by the promise of the solution of old puzzles like the transport of OAM via valley Hall effect (VHE). In the conventional literature of 2D-materials, the transport of OAM was treated as a consequence of the VHE. This view successfully explained many experiments but it started to be questioned by an interpretation of the transport of OAM based on the OHE [1, 2]. In my talk, I will present some theoretical results that corroborate the idea of the OHE as a natural description of the transport of OAM in 2D materials. I will also extend the analysis to discuss possible experimental signatures of the OAM transport in 2D materials.

[1] T. P. Cysne, et al, Phys. Rev. Lett. 126, 056601 (2021), T. P. Cysne, et al, arxiv:2201.03491 (2022)
[2] S. Bhowal and G. Vignale, Phys. Rev. B 103, 195309 (2021)

Mathias KLÄUI

While so far the focus has been on spin currents, effects of orbital currents, i.e. the flow of the electrons with finite orbital angular momentum, can outperform conventional spin current effects. As shown, orbital currents can even play a pivotal role in generating spin currents thus leading to torques with unprecedented amplitude to manipulate magnetization. Experimentally, orbital currents for efficient manipulation of magnetization have only recently started to be explored. In order to generate orbital currents, materials with orbital Hall effects can be used that can be light metals and thus cheap, abundant and environmentally friendly.
In our work we studied spin orbit torques generated in TmIG/Pt/(Cu(O)x) heterostructures. We observed that the torques exerted on the TmIG are enhanced by a factor up to 16 if the CuOx is added on top of the Pt compared to the conventional TmIG/Pt stack [1]. Such an enhancement is extremely surprising if one considers only conventional spin-charge interconversion based on spin orbit coupling effects and given the low spin-orbit coupling of Cu and Cu(O)x one does not expect large torques. However the results can be naturally explained as Cu(O)x can generate large orbital currents that are then converted to spin currents in the Pt layer, which then manipulate the TmIG extremely efficiently. More recently we studied magnetoresistance effects in systems with layers that generate orbital currents. We found that the Orbital Rashba-Edelstein Magnetoresistance can be observed in Py/Cu(O)x, which is an orbital magnetoresistance effect related to the conventional spin Hall magnetoresistance [2]. In particular in this work, the length scale of the orbital to spin current conversion in Py could be identified as a key step to harnessing orbital currents efficiently even without a heavy metal based orbital to spin conversion layer [3].

[1] S. Ding et al., Phys. Rev. Lett. 125, 177201 (2020)
[2] S. Ding et al., arxiv:2105.04495; Phys. Rev. Lett. (in press 2021)
[3] D. Go, MK et al., Perspectives Review in EPL 135, 37001 (2021)

Srijani MALLIK

The two-dimensional electron gas (2DEG) at the interface between SrTiO3 (STO) and LaAlO3[1], displays a wide array of functionalities such as high electronic mobility, low temperature superconductivity[2] and tunable Rashba spin-orbit coupling (SOC)[3]. Among these, the Rashba SOC enables gate tunable highly efficient spin – charge interconversion which paves the path towards spin-orbitronics[4]. We have already demonstrated such effect and correlated it with band structure for STO based 2DEGs[4]. We have shown that the spin – charge conversion process is amplified by enhanced Rashba-like splitting due to orbital mixing and in the vicinity of avoided band crossings with topologically non-trivial order[4]. Further, theoretical calculation predicts that the orbital Edelstein effect exceeds the spin Edelstein effect by more than one order of magnitude in this system[5].
Similar to STO, KTaO3 (KTO) is a quantum paraelectric material that in the bulk can be turned into a metal by minute electron doping, leading to high-mobility transport[6]. Due to the presence of Ta (5d element), it is expected the Rashba SOC in KTO 2DEGs should be larger than in STO 2DEGs. In this work, 2DEGs are generated by the simple deposition of Al metal on KTO single crystals and transport measurements are performed to explore the 2DEG properties. Further, the samples are characterized by angle-resolved photoemission spectroscopy to probe the band structure, and by spin-pumping experiments to study the inverse Edelstein effect. Their spin–charge conversion efficiency is then related to the 2DEG electronic structure and compared with that of STO-based interfaces[7]. In addition, superconductivity has been observed very recently in (111) and (110) oriented KTO samples which adds further functionalities to the system. We will conclude by giving perspectives towards the implementation of KTO 2DEGs into spin-orbitronic and pure orbitronic devices.

[1] A. Ohtomo et al. Nature 2004, 427, 423
[2] N. Reyren et al. Science 2007, 317, 1196
[3] A. D. Caviglia et al. Phys. Rev. Lett. 2010, 104, 126803
[4] D. C. Vaz et al. Nature Materials 2019, 18, 1187
[5] A. Johansson et al. Phys. Rev. Research 2021, 3, 013275
[6] S. H. Wemple Phys. Rev. 1965, 137, A1575
[7] L. M. Vicente-Arche et al. Adv. Mater. 2021, 2102102

Kyung-Jin LEE

The orbital Hall effect [1] describes the generation of the orbital current flowing in a perpendicular direction to an external electric field, analogous to the spin Hall effect. As the orbital current carries the angular momentum as the spin current does, injection of the orbital current into a ferromagnet can result in torque on the magnetization [2], which provides a way to detect the orbital Hall effect. With this motivation, we examine the current-induced spin-orbit torques in various ferromagnet/heavy metal bilayers by theory and experiment [3]. Analysis of the magnetic torque reveals the presence of the contribution from the orbital Hall effect in the heavy metal, which competes with the contribution from the spin Hall effect. In particular, we find that the net torque in Ni/Ta bilayers is opposite in sign to the spin Hall theory prediction but instead consistent with the orbital Hall theory, which unambiguously confirms the orbital torque generated by the orbital Hall effect. Our finding opens a possibility of utilizing the orbital current for spintronic device applications, and it will invigorate researches on spin-orbit-coupled phenomena based on orbital engineering.

[1] H. Kontani et al., Phys. Rev. Lett. 102, 016601 (2009)
[2] D. Go and H.-W. Lee, Phys. Rev. Research 2, 013177 (2020)
[3] D. Lee et al., Nat. Commun. 12, 6710 (2021)

Jieun LEE

Berry curvature is a physical quantity intrinsic in some periodic crystals which can give rise to many interesting physical phenomena in solid-state materials. Two-dimensional transition metal dichalcogenides such as MoS2 have non-trivial Berry curvatures at the edges of the conduction band at K and K’ valleys. This feature leads to many interesting valley-dependent phenomena such as the valley optical selection rule and the valley Hall effect. In this talk, we show that by further applying strain to monolayer MoS2 and breaking the 3-fold rotational symmetry of the crystal, the dipole moment of the Berry curvature emerges, giving rise to new quantum geometric phenomena. In particular, by applying an electric field in the direction parallel to the Berry curvature dipole, we found the generation of the valley orbital magnetization on monolayer MoS2 through an optical detection scheme using the scanning Kerr rotation microscopy. By fabricating a flexible monolayer MoS2 transistor with tunable strain, we measured the valley orbital magnetization that depends on the magnitude and direction of strain, which is in excellent agreement with the Berry curvature dipole effect. The dependence of the valley magnetization on the electric field, crystal orientation and carrier doping will also be discussed. Our results show that the Berry curvature dipole acts as an effective magnetic field in current-carrying systems, providing a novel route to generate magnetization in 2D crystals.

Hyun-Woo LEE

Orbital dynamics in time-reversal-symmetric centrosymmetric systems is examined theoretically. Contrary to common belief, we demonstrate that many aspects of orbital dynamics are qualitatively different from spin dynamics because the algebraic properties of the orbital and spin angular momentum operators are different. This difference generates interesting orbital responses, which do not have spin counterparts. For instance, the orbital angular momentum expectation values may oscillate even without breaking neither the time-reversal nor the inversion symmetry. Our quantum Boltzmann approach reproduces the previous result on the orbital Hall effect and reveals additional orbital dynamics phenomena, whose detection schemes are discussed briefly. Our work will be useful for the experimental differentiation of the orbital dynamics from the spin dynamics.

Aurélien MANCHON

Orbitronics, based on the generation and manipulation of orbital angular momentum, offers interesting perspectives for the conception of alternative microelectronic components. Nonetheless, before any workable device can be realized, efficient means to generate, propagate and detect orbital information must be identified. In this presentation, I will discuss two methods to generate orbital angular momentum out of equilibrium: the orbital Rashba effect and the orbital Hall effect. The former generates nonequilibrium orbital densities whereas the latter unlocks flows of charge-neutral orbital momentum. I will discuss these two mechanisms in different classes of materials, using toy model [1,3] and realistic calculations [2]. In particular, I will demonstrate that the nonequilibrium orbital momentum not only arises from intra-atomic contribution, but also possess an inter-atomic contribution that can be substantial. I will then discuss numerical simulations of both contributions in selected materials of highest interest for experimental realization, using Wannier interpolation of realistic band structures obtained from ab initio calculations. I will show that inter-atomic contribution tends to dominate over the intra-atomic one in the vicinity of the gap of narrow-gap semiconductors (SnTe, PbTe), whereas intra-atomic contribution dominates in large-gap semiconductors (MoS2) as well as in transition metals (V and Pt). These results open appealing perspectives for the realization of efficient sources of orbital angular momentum currents for electrically controlled orbitronics devices.

[1] Manchon et al. Physical Review B 101, 174423 (2020)
[2] Pezo et al., arXiv:2201.05807 (2021)
[3] Caruana et al., unpublished