The emergence of a large helical orbital texture due to the formation of the surface states at the metallic Co/Al interfaces originating from the orbital Edelstein effect and giving rise to a nonequilibrium orbital accumulation is revealed to produce large current-induced torques, providing an essential theoretical background for the experimental observations. Spin-orbit coupling is found to produce smaller contributions with a higher-order winding of the orbital moments.

In-plane orbital textures at the interfacial Co layer in the Brillouin zone calculated for 12Co(0001)/12Al(111) and 12Co(0001)/12Cu(111) heterostructures. Arrows for the Co/Cu interface are magnified by a factor of 2 for clarity

Search for efficient ways to control the magnetization in magnetic materials has been one of the central activities in the field of spintronics, which exploits the intrinsic spin of an electron with a focus on providing novel functionalities in electronic devices. In this regard, spin-orbit coupling (SOC) has brought a progressive venue to achieving high-efficiency electrical control of magnetization via spin-orbit torques (SOT), which historically relied on two cornerstone mechanisms, i.e. spin Hall (SHE) and spin Rashba-Edelstein (REE) effects. In recent years, there has been a lot of evidence that SHE and REE may not be the only principal ways to generate SOTs. It was shown that one can realize electrical generation of the transverse orbital currents via orbital Hall effect (OHE) and/or can produce a substantial orbital accumulation under applied electric fields due to the orbital Edelstein effect (OEE). Recent experiments by S. Krishnia et al. [Nano Lett. 23, 6785 (2023)] reported an unprecedentedly large enhancement of torques upon inserting thin Al layer in Co/Pt heterostructure that suggested the presence of a Rashba-like interaction at the metallic Co/Al interface.

In order to uncover the physical mechanisms responsible for these experimental observations, first-principles calculations combined with Wannier interpolation of the electronic structure were carried out for Co(0001)/Al(111) and Co(0001)/Cu(111) heterostructures comprising between 6 and 12 monolayers of each element. Drastic changes in electronic and magnetic properties at the Co/Al and Co/Cu interfaces are revealed by calculating the orbital and spin profiles in reciprocal space, L(k) and S(k), respectively. Both are found to exhibit a 3-fold rotational texture in agreement with the C3v symmetry of the constructed heterostructures. More strikingly, peculiar hybridization between the surface states at the Co/Al interface turns out to give rise to an exceptionally large chiral orbital texture with an in-plane helical locking at the interfacial Co layer due to the so-called orbital Rashba effect, as opposed to the Co/Cu interface where the in-plane orbital texture is much less pronounced (see Figure). The in-plane orbital texture at the Co/Al interface is preserved without SOC, as opposed to the transverse spin texture, which is identically zero in the absence of relativistic effects that found to produce much smaller contributions with a higher-order winding of the orbital moments.

These results unveil that the orbital texture gives rise to a nonequilibrium orbital accumulation producing large current-induced torques, thus providing an essential theoretical background for the experimental data and advancing the use of orbital transport phenomena in all-metallic magnetic systems with light elements.

Team: Theory & simulation

Collaboration: Univ. of Osaka (Japan), Laboratoire Albert Fert, CNRS, Thales, Univ. Paris-Saclay (France)

Funding: PEPR SPIN ANR-22-EXSP -0009 “SPINTHEORY”, ANR-20-CE30-0022-02 “ORION”, EU Horizon 2020 “OBELIX”

Further reading: Large Chiral Orbital Texture and Orbital Edelstein Effect in Co/Al Heterostructure, S. A. Nikolaev✉, M. Chshiev, F. Ibrahim, S. Krishnia, N. Sebe, J.-M. George, V. Cros, H. Jaffres and Albert Fert, Nano Lett. 24, 13465 (2024), hal-04747758

Contact at Spintec: Mairbek CHSHIEV