Session Z24: Recent Advances in Orbitronics

Optical observation of the orbital Hall effect in a light metal Ti, Mn, and Cu

Orbitronics aims for control of the orbital current in non-magnetic materials. Among various techniques to measure orbital, the optical method employing the magneto-optical Kerr effect has the advantages of high sensitivity and vector-and-time resolution. I will present the magneto-optical observation of the orbital Hall effect in a light metal Ti. The Kerr rotation by the orbital magnetic moment accumulated at Ti surfaces due to the orbital Hall current is measured, whose result agrees with theoretical calculations quantitatively and is supported by the orbital torque measurement in Ti-based magnetic heterostructures. In addition, I will present the optical detection of the orbital Hall effect in other light metals of Mn and Cu. The direct detection of orbital accumulation on the surfaces of light metals provides important information for orbital generation, transport, and relaxation.   

On the reciprocal relation between the direct and inverse orbital Hall effects

The reciprocal relation is a fundamental manifestation of the fluctuation-dissipation theorem for near-equilibrium transport phenomena. In orbitronics, the orbital Hall effect plays a pivotal role as it can be used to generate orbital currents. Its reciprocal counterpart, the inverse orbital Hall effect refers to a generation of charge current by gradient of orbital-dependent chemical potential, namely “orbital voltage”, which can serve as a mechanism to electrically detect orbital currents in orbitronic devices. In recent years, the orbital-to-charge conversion has been experimentally detected [1-5]. However, the theoretical description of the reciprocity between the direct and inverse orbital Hall effects is far from trivial because orbital currents are ill-defined and the orbital angular momentum is not conserved. We show that the reciprocal relation between charge and orbital transport can be rigorously established by adopting the definition of “proper” current proposed by Shi et al. [6], in which the non-conserving effect is considered. Based on the implementation in our first-principles codes, we present a detailed analysis of the direct and inverse orbital Hall effects in Pt(111) and W(110) thin films, prototypical systems used in experiments. We demonstrate that the reciprocal relation is exactly satisfied for the “total” responses. However, we find interesting features in “local” responses, especially near the surface, where the direct and inverse effects can significantly deviate from each other. We find its origin in the orbital Rashba coupling at the surface, in which the angular momentum transfer between the lattice and orbital degrees of freedom is strongly pronounced. We believe this explains the large inverse orbital Rashba-Edelstein effect measured in a recent THz spectroscopy experiment [1]. We discuss further implications of our finding and its relevance in various experimental setups.

[1] T. Seifert, D. Go et al. Nat. Nanotechnol. 18, 1132 (2023)

[2] P. Wang et al. npj Quantum Mater. 8, 28 (2023). 

[3] Y. Xu et al. arXiv:2208.01866 (2022).

[4] A. E. Hamdi et al. Nat. Phys. (2023). https://doi.org/10.1038/s41567-023-02121-4

[5] H. Hayashi and K. Ando, arXiv:2304.05266 (2023).

[6] J. Shi et al. Phys. Rev. Lett. 96, 076604 (2006).

[7] D. Go et al. Manuscript in Preparation.   

Orbital Rashba effects and light-induced Orbital Current in Teraherz Emission Experiments.

Orbitronics is based on the use of orbital currents as information carriers. These may be generated by the application of an electric field, and inversely, by reciprocity, they could be converted back to charge or even spin currents. In this presentation,  I will start my presentation by describing experiments showing the strong enhancement of the current-induced torques on the Co layer of a Pt/Co bilayer by the addition of an Al layer on Co (Al protected from oxidation). The enhancement is predominant for the FL torque, up to factor of 9. The interpretation [2] comes from ab-initio calculations showing large Co orbital moments in the interfacial Co layer with a helical texture similar to the spin texture on the surface of topological insulators. The calculation of the resulting torques leads to a good agreement between the calculated and enhanced experimental torques.

In a second part, we will demonstrate that orbital currents can also be generated by femtosecond light pulses and optical absorption on thin Ni films. In multilayers associating Ni with oxides and nonmagnetic metals such as Cu, we detect the generated orbital currents by their conversion into charge currents varying in time in the subpicosecond scale and thus resulting in a terahertz emission as provided by oscillating dipoles. We show that the orbital currents extraordinarily predominate the light-induced spin currents in Ni-based systems, whereas, unlike, only spin currents can be detected with CoFeB-based similar systems and heterostructures. In addition, the analysis of the time delays of the terahertz pulses leads to relevant information on the group velocity and subsequent propagation of orbital carriers. Our finding of light-induced orbital currents and our observation of their conversion into charge currents opens new avenues in orbitronics, including the development of novel type of orbitronic terahertz devices   

Giant Orbital Hall Effect and Orbital-to-Spin Conversion in 3d, 5d and 4f Metallic Heterostructures

Recent theories have shown that an electric field can induce a transverse flow of orbital angular momenta in elemental metals, even if crystal field and band structure effects completely quench the orbital magnetism at equilibrium [1-3]. In particular, electric currents in 3d elements can generate a substantial non-equilibrium orbital accumulation that is comparable to or even larger than the spin accumulation caused by the spin Hall effect and the Rashba-Edelstein effect in the 5d elements [4,5]. The generation of orbital currents plays a pivotal role in inducing spin-orbit torques in ferromagnets [6-9], which opens new avenues for the realization of spintronic devices for memory and logic applications [10]. In this talk I will discuss the emergence of strong orbital Hall in 3d metals, focusing on the crucial role of orbital-to-spin conversion in the generation of spin-orbit torques [9] and orbital magnetoresistance [11,12]. I will further show how the inclusion of rare-earths as spacer layers or as alloyed species can be used to boost the orbital-to-spin conversion and the torque efficiency in magnetic heterostructures and discuss recent results involving the orbital Rashba-Edelstein effect.

 

References

[1] T. Gao et al., Phys. Rev. Lett. 121, 17202 (2018).

[2] D. Go et al., Phys. Rev. Research 2, 033401 (2020); Phys. Rev. Res. 2, 013177 (2020).

[3] L. Salemi and P. M. Oppeneer, Phys. Rev. Mater.6, 095001 (2022).

[4] Y.-G. Choi et al., Nature 619, 52 (2023).

[5] C. Stamm et al., Phys. Rev. Lett. 119, 087203 (2017).

[6]  D. Lee et al., Nat. Comm. 12, 6710 (2021).

[7]  J. Kim et al., Phys. Rev. B 103, L020407 (2021).

[8]  S. Ding et al., Phys. Rev. Lett. 128 (2022) 067201.

[9]  G. Sala and P. Gambardella, Phys. Rev. Res. 4 033037 (2022).

[10] A Manchon et al., Rev. Mod. Phys. 91, 035004 (2019). 

[11] S. Ding et al., Phys. Rev. Res. 4, L032041 (2022).

[12] G. Sala et al., Phys. Rev. Lett. 131, 156703 (2023).   

Orbital Hall effect in two-dimensional materials

I will explore orbital effects in two-dimensional (2D) materials and the potential implications they hold. A central theme of my presentation will be the orbital Hall effect (OHE), a phenomenon closely related to the spin Hall effect (SHE). The OHE, much like the SHE, gives rise to a transverse flow of angular momentum due to a longitudinally applied electric field. However, what sets it apart is its distinct origin, emerging from the interplay between orbital attributes and crystal symmetries, free from reliance on spin-orbit coupling.

I will discuss various aspects of the OHE within the realm of 2D materials. Specifically, I will showcase how monolayers and bilayers of transition metal dichalcogenides (TMDs) display the OHE phenomenon, in their insulating phase [1]. These TMDs, when cut along precise orientations, host conductive edge states that traverse the bulk energy gap. This unique characteristic facilitates the transport of orbital angular momentum [2].

Furthermore, I will explore the emergence of the orbital Edelstein effect in 2D materials with lower symmetry [3], shedding light on its implications. The outcomes of our research offer the prospect of utilizing 2D materials for injecting orbital currents and facilitating orbital torque transfer, potentially surpassing the capabilities of their spin-based counterparts. 

[1] Tarik P. Cysne, Marcio Costa, Luis M. Canonico, M. Buongiorno Nardelli, R. B. Muniz, Tatiana G. Rappoport , Phys. Rev. Lett. 126, 056601(2021). 

[2] Marcio Costa, Bruno Focassio, Tarik P. Cysne, Luis M. Canonico, Gabriel R. Schleder, Roberto B. Muniz, Adalberto Fazzio, Tatiana G. Rappoport, Phys. Rev. Lett. 130, 116204 (2023). 

[3] Tarik P. Cysne, Marcio Costa, M. Buongiorno Nardelli, R. B. Muniz, Tatiana G. Rappoport, arXiv:2307.03866.