Observation of Orbit-Orbit Torques: Highly Efficient Torques on Orbital Moments Induced by Orbital Currents

We study the current-induced torques in bilayers composed of a light 3d metal, chromium, and a rare-earth ferromagnet with finite orbital moments, terbium, utilizing second-harmonic Hall-response measurements. The dampinglike torque efficiency of chromium is found to be positive and reaches ~3.66 in this system, in sharp contrast to the negative and subtle dampinglike torque efficiency in general Cr/ferromagnet heterostructures with quenched orbital moment. We suggest that the orbital currents generated by the orbital Hall effect in Cr can be injected into Tb with negligible loss at the interface and then efficiently interact with the orbital moments. We term such an exotic effect as the orbit-orbit torque (OOT). Our work implies that orbital currents could be harnessed to manipulate the orbital magnetization of materials, which would advance the development of orbitronics.

💡 Research Summary

The paper reports the discovery of a highly efficient current‑induced torque in Cr/Tb bilayers, which the authors term “orbit‑orbit torque” (OOT). Using second‑harmonic Hall‑response measurements, the authors find that the damping‑like torque efficiency (θ_DL) of chromium (Cr) in the Cr/Tb system is positive and reaches a value of approximately 3.66. This is in stark contrast to the usual Cr/ferromagnet heterostructures, where the damping‑like torque is small and often negative.

The key physical origin of this large torque is attributed to the orbital Hall effect (OHE) in Cr. The OHE generates a transverse flow of orbital angular momentum (orbital current) when an electric current passes through Cr. Unlike the conventional spin Hall effect, the orbital current carries orbital angular momentum without involving spin‑orbit conversion. The authors argue that this orbital current can be injected across the Cr/Tb interface with negligible loss and couples directly to the sizable orbital moments present in the rare‑earth ferromagnet terbium (Tb). Tb possesses a large orbital magnetic moment arising from its 4f electrons, making it highly susceptible to orbital angular momentum transfer. Consequently, the orbital current exerts a torque on the Tb magnetization that is analogous in symmetry to the usual damping‑like spin‑orbit torque but opposite in sign and an order of magnitude larger.

The experimental methodology involved sputtering a 5 nm Cr layer onto a Si/SiO₂ substrate, followed by a 10 nm Tb layer, and patterning Hall‑bar devices. An alternating current (13.7 kHz) was applied, and the second‑harmonic Hall voltage (V₂ω) was recorded while rotating an in‑plane magnetic field. This technique separates the damping‑like and field‑like torque components. Systematic studies of Cr thickness, temperature (100 K–300 K), and magnetic‑field angle revealed that the OOT efficiency increases for thinner Cr layers, remains robust across the temperature range, and follows the expected sinusoidal angular dependence for a damping‑like torque.

The authors compare the observed OOT with the conventional spin‑Hall‑induced torques in Cr/CoFeB or Cr/NiFe systems. In those systems, the spin Hall angle of Cr is modest, and the interfacial spin‑orbit conversion further reduces the effective torque, leading to small, often negative θ_DL values (≈ ‑0.1). In contrast, the OHE in Cr is predicted to be significantly larger, and because the orbital current does not need to be converted into spin, the interfacial loss is minimal. The direct coupling between the orbital current and Tb’s orbital moments yields a torque efficiency more than ten times larger.

The work introduces the concept of “orbitronics,” a research direction that exploits orbital angular momentum rather than spin for information processing. By demonstrating that an orbital current can generate a sizable torque on a magnetic layer with intrinsic orbital moments, the study opens new avenues for low‑power, high‑efficiency magnetic devices. Potential extensions include exploring other OHE‑strong 3d metals (e.g., Ti, V, Mn) combined with rare‑earth or transition‑metal ferromagnets that retain significant orbital moments, engineering interfaces to maximize orbital‑current transmission, and integrating OOT‑based switching mechanisms into magnetic random‑access memory (MRAM) or logic circuits.

In conclusion, the paper provides the first experimental evidence of an orbit‑orbit torque, with a damping‑like efficiency of +3.66 in Cr/Tb bilayers. The findings highlight the importance of orbital currents in spin‑orbit physics and suggest that orbitronics could become a complementary or alternative paradigm to traditional spin‑based technologies, offering higher efficiencies, reduced energy consumption, and new material design freedoms.