1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
//! Orbitronics Module
//!
//! This module implements orbital angular momentum (OAM) transport phenomena,
//! a rapidly growing field in condensed matter physics that studies how orbital
//! currents can be generated, manipulated, and converted to achieve functionality
//! beyond conventional spin-based spintronics.
//!
//! ## Overview
//!
//! Orbitronics exploits the orbital angular momentum of electrons (as opposed to
//! their spin) for information processing and magnetization control. The key
//! insight is that orbital currents can be generated even in light metals with
//! weak spin-orbit coupling (SOC), through the Orbital Hall Effect (OHE).
//!
//! ## Key Physics
//!
//! ### Orbital Hall Effect (OHE)
//! Analogous to the Spin Hall Effect, the OHE generates transverse orbital
//! angular momentum current from longitudinal charge current. Crucially, the
//! OHE does not require strong SOC and can be giant in light 3d transition
//! metals like Cr and Ti.
//!
//! ### Orbital-to-Spin Conversion
//! At interfaces with materials possessing strong SOC (e.g., Pt, Bi), orbital
//! currents can be efficiently converted to spin currents, enabling
//! magnetization manipulation.
//!
//! ### Orbital Torques
//! Orbital currents can exert torques on ferromagnetic layers, providing an
//! alternative pathway to spin-orbit torques for current-driven magnetization
//! switching.
//!
//! ### Orbital Rashba Effect
//! At interfaces lacking inversion symmetry, orbital angular momentum splits
//! in momentum space, leading to the orbital Edelstein effect.
//!
//! ## Modules
//!
//! - [`orbital_hall`]: Orbital Hall Effect, material database, orbital-to-spin conversion
//! - [`orbital_torque`]: Orbital torques, orbital Rashba effect, switching efficiency
//!
//! ## References
//!
//! - H. Kontani et al., "Giant Orbital Hall Effect in Transition Metals",
//! Phys. Rev. Lett. 102, 016601 (2009)
//! - D. Go et al., "Intrinsic Spin and Orbital Hall Effects from Orbital Texture",
//! Phys. Rev. Lett. 121, 086602 (2018)
//! - D. Go and H.-W. Lee, "Orbital torque: Torque generation by orbital
//! current injection", Phys. Rev. Research 2, 013177 (2020)
//! - S. Lee et al., "Efficient conversion of orbital Hall current to spin
//! current for spin-orbit torque switching", Commun. Phys. 4, 234 (2021)
// Re-exports for convenient access
pub use ;
pub use ;