[Paper Review] Orbital Pumping by Magnetization Dynamics in Ferromagnets

Dongwook Go, Kazuya Ando+4 more|arXiv (Cornell University)|Sep 26, 2023

Magnetic Properties of Alloys4 citations

TL;DR

This paper proposes that magnetization dynamics in ferromagnets can generate non-equilibrium orbital angular momentum (orbital pumping) via spin-orbit coupling, analogous to spin pumping. First-principles calculations show orbital pumping is 5–15% of spin pumping, strongest in Ni and weakest in Fe, explaining experimental observations of significant orbital pumping in Ti/Ni but suppression in Ti/Fe bilayers.

ABSTRACT

We show that dynamics of the magnetization in ferromagnets can pump the orbital angular momentum, which we denote by orbital pumping. This is the reciprocal phenomenon to the orbital torque that induces magnetization dynamics by the orbital angular momentum in non-equilibrium. The orbital pumping is analogous to the spin pumping established in spintronics but requires the spin-orbit coupling for the orbital angular momentum to interact with the magnetization. We develop a formalism that describes the generation of the orbital angular momentum by magnetization dynamics within the adiabatic perturbation theory. Based on this, we perform first-principles calculation of the orbital pumping in prototypical $3d$ ferromagnets, Fe, Co, and Ni. The results show that the ratio between the orbital pumping and the spin pumping ranges from 5 to 15 percents, being smallest in Fe and largest in Ni. This implies that ferromagnetic Ni is a good candidate for measuring the orbital pumping. Implications of our results on experiments are also discussed.

Motivation & Objective

• To establish the theoretical framework for orbital pumping as the reciprocal of orbital torque in ferromagnets.
• To quantify the magnitude of orbital pumping relative to spin pumping in 3d ferromagnets (Fe, Co, Ni) using first-principles methods.
• To explain the experimental discrepancy in orbital pumping between Ti/Ni and Ti/Fe bilayers, where Ni shows strong signal but Fe shows near-complete suppression.
• To explore the role of spin-orbit coupling and electronic structure in enabling orbital pumping, particularly in systems with varying d-shell filling.
• To provide a theoretical basis for future experiments detecting orbital angular momentum generation via inverse orbital Hall effect or related phenomena.

Proposed method

• Formalism based on adiabatic perturbation theory to describe orbital angular momentum generation by magnetization dynamics.
• Derivation of a Green’s function expression for the linear response of orbital angular momentum to magnetization precession.
• Use of first-principles density functional theory (DFT) with spin-orbit coupling to compute orbital pumping tensor components in Fe, Co, and Ni.
• Calculation of response functions χαβL as a function of energy broadening (Γ) to assess robustness and intrinsic behavior.
• Analysis of the dependence of orbital pumping on d-electron filling and Hund’s rule behavior, comparing Fe (d6), Co (d7), and Ni (d8).
• Comparison of theoretical predictions with experimental data from Hayashi et al. on Ti/Ni and Ti/Fe bilayers, focusing on DC component of orbital pumping.

Experimental results

Research questions

• RQ1 Can magnetization dynamics in ferromagnets generate non-equilibrium orbital angular momentum, and if so, what is the underlying mechanism?
• RQ2 How does the magnitude of orbital pumping compare to spin pumping in 3d ferromagnets like Fe, Co, and Ni?
• RQ3 Why is orbital pumping observed in Ti/Ni bilayers but nearly absent in Ti/Fe bilayers, despite theoretical predictions?
• RQ4 How does spin-orbit coupling mediate the coupling between magnetization dynamics and orbital angular momentum?
• RQ5 What role does the d-shell electron filling and Hund’s rule behavior play in determining the strength of orbital pumping?

Key findings

• Orbital pumping arises as a reciprocal effect to orbital torque, requiring spin-orbit coupling for the interaction between orbital angular momentum and magnetization.
• The ratio of orbital pumping to spin pumping ranges from 5% in Fe to 15% in Ni, indicating a strong Hund’s rule-like dependence on d-electron filling.
• First-principles calculations confirm that Ni exhibits the strongest orbital pumping, making it the most promising candidate for experimental detection.
• The experimental suppression of orbital pumping in Ti/Fe bilayers cannot be explained by bulk Fe properties alone, suggesting interfacial transmission effects dominate.
• Energy broadening (Γ) dependence shows that orbital pumping is more sensitive to scattering than spin pumping due to the smaller energy scale of spin-orbit coupling.
• Theoretical predictions align with recent experiments on the inverse orbital Hall effect and orbital Seebeck effect, supporting the feasibility of OAM-based phenomena in ferromagnetic heterostructures.