Quantum Christoffel Nonlinear Magnetization

TL;DR

This paper introduces a novel nonlinear magnetization induced by electric fields in quantum materials, described by a quantum Christoffel symbol, which can be experimentally probed without relying on spin-orbit coupling or inversion symmetry breaking.

Contribution

It defines a quantum Christoffel symbol in the Hilbert space and demonstrates its role in nonlinear magnetization, expanding the understanding of geometric effects in quantum materials.

Findings

Identified point groups and 2D materials hosting quantum Christoffel nonlinear magnetization.

Proposed optical and transport methods to probe the quantum Christoffel symbol.

Showed that nonlinear magnetization arises without spin-orbit coupling or inversion symmetry breaking.

Abstract

The Christoffel symbol is an essential quantity in Einstein's general theory of relativity. We discover that an electric field can induce a nonlinear magnetization in quantum materials, described by a Christoffel symbol defined in the Hilbert space of quantum states (quantum Christoffel symbol). Quite different from the previous scenarios, this orbital magnetization does not need spin-orbit coupling and inversion symmetry breaking. Through symmetry analysis and first-principles calculations, we identify a number of point groups and 2D material candidates (e.g., BiF$_3$, ZnI$_2$, and Ru$_4$Se$_5$) that host this quantum Christoffel nonlinear magnetization. More importantly, this nonlinear magnetization allows the quantum Christoffel symbol to be probed by optical techniques such as magneto-optical Kerr spectroscopy or transport measurements such as tunneling magneto-resistance. This quantum Christoffel nonlinear magnetization gives a paradigm of how geometry dictates physics.