Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Quantum Geometric Origin of Orbital Magnetization

Xiao-Bin Qiang, Tianyu Liu, Hai-Zhou Lu, X. C. Xie

TL;DR

The paper addresses how magnetization can be understood from quantum geometry by linking equilibrium and kinetic magnetization to Berry curvature and quantum metric within a single-particle framework. It develops a geometric foundation for orbital magnetization and decomposes kinetic magnetization into extrinsic and intrinsic contributions for both spin and orbital sectors, connecting theory to Edelstein-type phenomena observed experimentally and outlining nonlinear avenues. The work provides a unified, geometry-based perspective with implications for spintronics and orbitronics, guiding future experimental and theoretical explorations. Overall, it reframes magnetization as a direct manifestation of the geometric structure of electronic states, with practical relevance to material design and interpretation of magneto-electric responses.

Abstract

The exploration of the Riemannian structure of the Hilbert space has led to the concept of quantum geometry, comprising geometric quantities exemplified by Berry curvature and quantum metric. While this framework has profoundly advanced the understanding of various electronic phenomena, its potential for illuminating magnetic phenomena has remained less explored. In this Perspective, we highlight how quantum geometry paves a new way for understanding magnetization within a single-particle framework. We first elucidate the geometric origin of equilibrium magnetization in the modern theory of magnetization, then discuss the role of quantum geometry in kinetic magnetization, and finally outline promising future directions at the frontier of quantum geometric magnetization.

Quantum Geometric Origin of Orbital Magnetization

TL;DR

The paper addresses how magnetization can be understood from quantum geometry by linking equilibrium and kinetic magnetization to Berry curvature and quantum metric within a single-particle framework. It develops a geometric foundation for orbital magnetization and decomposes kinetic magnetization into extrinsic and intrinsic contributions for both spin and orbital sectors, connecting theory to Edelstein-type phenomena observed experimentally and outlining nonlinear avenues. The work provides a unified, geometry-based perspective with implications for spintronics and orbitronics, guiding future experimental and theoretical explorations. Overall, it reframes magnetization as a direct manifestation of the geometric structure of electronic states, with practical relevance to material design and interpretation of magneto-electric responses.

Abstract

The exploration of the Riemannian structure of the Hilbert space has led to the concept of quantum geometry, comprising geometric quantities exemplified by Berry curvature and quantum metric. While this framework has profoundly advanced the understanding of various electronic phenomena, its potential for illuminating magnetic phenomena has remained less explored. In this Perspective, we highlight how quantum geometry paves a new way for understanding magnetization within a single-particle framework. We first elucidate the geometric origin of equilibrium magnetization in the modern theory of magnetization, then discuss the role of quantum geometry in kinetic magnetization, and finally outline promising future directions at the frontier of quantum geometric magnetization.
Paper Structure (6 sections, 10 equations, 2 figures)

This paper contains 6 sections, 10 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Modern theory of magnetization
  3. Kinetic Magnetization
  4. Spin contribution
  5. Orbital contribution
  6. Challenges and outlook

Figures (2)

  • Figure 1: Wave packet self-rotation as the microscopic origin of the orbital magnetic moment. The black and blue arrows indicate the self-rotation and the resulting magnetization, respectively.
  • Figure 2: Microscopic mechanisms of kinetic orbital magnetization. (a) Extrinsic kinetic orbital magnetization $\delta\mathbf{M}^{\text{O},ex}$ arising from a population imbalance. (b) Intrinsic kinetic orbital magnetization $\delta\mathbf{M}^{\text{O},in}$ arising from the deformation of the wave packet.